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Full text of "Works. Translated into English under the editorship of W.D. Ross"




W. D. ROSS, M.A., Hon. LL.D. (Edin.) 



By R. pThARDIE and R. K. GAYE 
















Printed in Great Britain 

special thanks are due to the Trustees of the 

Jowett Copyright Fund for their assistance 

towards the publication of this Volume 

P H Y S I C A 





R. K. GAYE. M.A. 





Printed in Great Britain 


The translation of the first two books of the Physics for 
this series was originally entrusted to Mr. C. D. Robertson, 
Fellow of Trinity College, Cambridge, and he had, before 
his untimely death, prepared a draft translation of these 
books, which was placed at the disposal of Mr. Hardie and 
freely used by him. The present translation of the first 
four books is, however, in the main by Mr. Hardie himself. 
He has received valuable help from Professors Joachim and 
J. A. Smith, and from Dr. J. C. Smith and Mr. Henry 
Barker. The last four books were translated by Mr. Gaye, 
who also died before his time, regretted by all students of 
Greek philosophy. Where the word ' I ' occurs in notes 
on these books, the writer is Mr. Gaye. To me has fallen 
the task of securing comparative uniformity — I have not 
tried to produce complete uniformity — between the two 
halves of the translation. In this I have been much 
helped by Mr. George Brown, M.A., Lecturer in Logic 
in the University of Glasgow, who has kindly read the 
proofs throughout. At the same time I have on the basis 
of a study of the reported manuscript readings and of 
the Greek commentators adopted a good many changes 
of reading in the Greek text and altered the translation to 
suit them. All divergences from Bekker's text are men- 
tioned in the notes. 

Many of the technical terms in the Physics present 
considerable difficulties to the translator. The most diffi- 
cult, perhaps, is klptjo-l?. Kivqa-LS would often be most 
aptly rendered by ' change ' ; but often again it is distin- 
guished from /jL€TapoXrj, and therefore narrower than 
* change '. As the lesser of two evils, I have adopted the 
translation ' motion ' or * movement ', and have very rarely 


departed from this ; this rendering should be recognized as 
being to some extent conventional. The frequent com- 
bination of ^opd with (pipecrdai suggested to Mr. Hardie 
the translation of (popd by ' carry ', but the associations of 
the noun 'carry' are rather too special for this purpose, 
and I have, with his forgiveness, adopted the more common- 
place * locomotion '. 

W. D. ROSS. 

\o January 1930. 



♦ I. The scope and method of this book. 

• 2. The proj^em : the number and character of the first principles 

of nature. 

185* 20. Reality is not one in the way that Parmenides and 
Melissus supposed. 

3. Refutation of their arguments. 

4. Statement and examination of the opinions of the natural philo- 

5. The principles are contraries. 

6. The principles are two, or three, in number. 

7. The number and nature of the principles. 

8. The true opinion removes the difficulty felt by the early philo- 

9. Further reflections on the first principles of nature. 



I. Nature and the natural. 

^ 2. Distinction of the natural philosopher from the mathematician and 
the metaphysician. 

C. The conditions of change. 

3. The essential conditions. 

4. The opinions of others about chance and spontaneity. 

5. Do chance and spontaneity exist ? What is chance and what are its 
characteristics ? 

6. Distinction between chance and spontaneity, and between both and 
the essential conditions of change. 

D. Proof in natural philosophy. 

7. The physicist demonstrates by means of the four conditions of 

8. Does nature act for an end ? 

9. The sense in which necessity is present in natural things. 



^ Motion. 

I, 2. The nature of motion. 
3. The mover and the moved. 


B. The infinite, 

4. Opinions of the early philosophers. 

203^ 15. Main arguments for belief in the infinite. 

5. Criticism of the Pythagorean and Platonic belief in a separately 
existing infinite. 

204^ 34. There is no infinite sensible body. 

6. That the infinite exists and how it exists. 
206^ 33. What the infinite is. 

7. The various kinds of infinite. 

207^34. Which of the four conditions of change the infinite is to be 
referred to. 

8. Refutation of the arguments for an actual infinite. 


Aj Place. 

1. Does place exist? 

209* 2. Doubts about the nature of place. 

2. Is place matter or form ? 

3. Can a thing be in itself or a place be in a place ? 

4. What place is. 

5. Corollaries. 

B., The void. 

6. The views of others about the void. 

7. What * void ' means. 

214* 16. Refutation of the arguments for belief in the void. 

8. There is no void separate from bodies. 

216* 26. There is no void occupied by any body. 

9. There is no void in bodies. 

C. Time. 

10. Doubts about the existence of time. 

218* 31. Various opinions about the nature of time. 

11. What time is. 
219^9. The 'now'. 

12. Various attributes of time. 

220^ 32. The things that are in time. 

13. Definitions of temporal terms. 

14. Further reflections about time. 



1. Classification of movements and changes. ' 

224^ 35. Classification of changes per se. , ^ 

2. Classification of movements per se. 

226^ 10. The unmovable. 

3. The meaning of 'together*, 'apart', 'touch', 'intermediate'. 
* successive ', ' contiguous ', ' continuous '. 

4. The unity and diversity of movements. 

5. Contrariety of movement. ' — 

6. Contrariety of movement and rest. 

230* 18. Contrariety of natural and unnatural movement or rest. 


I, 2. Every continuum consists of continuous and divisible parts. 

3. A moment is indivisible and nothing is moved, or rests, in a 


4. Whatever is moved is divisible. 
234^21. Classification of movement. 

235* 13. The time, the movement, the being-in-motion, the moving 
body, and the sphere of movement, are all similarly divided. 
5; Whatever has changed is, as soon as it has changed, in that 
to which it has changed. 
235^32. That in which (directly) it has changed is indivisible. 
236* 7. In change there is a last but no first element. 

6. In whatever time a thing changes (directly), it changes in any part 
of that time. 

236^ 32. Whatever changes has changed before, and whatever has 
changed, before was changing. 

7. The finitude or infinity of movement, of extension, and of the 

8. Of coming to rest, and of rest. 

239^ 23. A thing that is moved in any time directly is in no part of 
that time in a part of the space through which it moves. 

9. Refutation of the arguments against the possibility of movement. 

10. That which has not parts cannot move. 
241* 26. Can change be infinite ? 


1. Whatever is moved is moved by something. — T" 

242* 19. There is a first movent which is not moved by anything 

2. The movent and the moved are together. 

3. All alteration pertains to sensible qualities. 

4. Comparison of movements. 

5. Proportion of movements. 



1. There always has been and always will be movement. 

2. Refutation of objections to the eternity of movement. 

3. There are things that are sometimes in movement, sometimes 
at rest. 

4. Whatever is in movement is moved by something else. 

5. The first movent is not moved by anything outside itself. 
257* 31. The first movent is immovable. 

6. The immovable first movent is eternal and one. 

259* 20. The first movent is not moved even incidentally. 
259^ 32. Th% primum mobile is eternal. 

7. Locomotion is the primary kind of movement. 

261* 28. No movement or change is continuous except locomotion. 

8. Only circular movement can be continuous and infinite. 

9. Circular movement is the primary kind of locomotion. 
265* 27. Confirmation of the above doctrines. 

10. The first movent has no parts nor magnitude, and is at the circum- 
ference of the world. 


I When the objects of an inquiry, in any department, have 184* 
p rincjo les, conditions, or el emen ts.^ it is through acquaintance ^° ^ 
with these that knowledge, that is to say scientific know- 
ledge, is attained. For we do not think that we know a 
thing until we are acquainted with its pr imary condi tions 
niL^rst principles , and have carried our analysis as far as 
its simplest elements.^ Plainly therefore in the science of 
Nature, as in other branches of study, our first task will be 15 
to try to determine what relates to its principles.* 

The natural way of doing this is to start from the things 
whic h are more knowable and obvious to us a nd proceed, 
towards those which are clearer and more knowable by 
nature ^ ; for the same things are not 'knowable relatively to^ 

* The present treatise, usually called the Physics, deals with 
natural body in general : the special kinds are discussed in Aristotle's 
other physical works, the De Caelo, &c. The first book is concerned 
with the elements of a natural body (matter and form) : the second 
mainly with the different types of cause studied by the physicist. 
Books III-VII deal with movement, and the notions implied in it. The 
subject of VIII is the prime mover, which, though not itself a natural 
body, is the cause of movement in natural bodies. 

The title (pvaiKq aKpoaais (= Lectures on Physics) is as old at least 
as Simplicius (a.D. 530). When Aristotle uses the phrase eV mis 
cf)v(TiKnls he is usually referring to the first two books of the Physics, 
but sometimes to the later books, and sometimes even to the other 
physical treatises. He repeatedly refers to the later books of the 
Physics as rh. nepi Kivrjaeas. 

^ It seems best to take (with Zabarella) the words mv claiv apxat ri 
aiTia rj aroix^la as limitative. Throughout Book I Aristotle uses the 
words apx^i aiTioir, and o-roix^'iov indiscriminately to mean the internal 
principles or factors of a natural body. 

* Pacius takes to. alna to. Trpwrn /cai ras apx(is ras Trpcoraff to be 
proximate causes, as distinct from ra a-roix^ln which are remote. But 
the distinction seems unnecessary : when Aristotle draws the con- 
clusion of his syllogism, he mentions simply apxai 

* It is not clear whether this reference is to the first two books 
as distinct from the rest or to the Physics as a whole {to. KadnXnv nepl 
(puaecos, viii. 257* 34), as distinct from the other physical treatises. 

" Cf. below 189*4 where the phrase yvoipip-^Tipov Kara t6v \6yov 
('more knowable in the order of explanation') is used. Another 


us' and 'knowable' without qualification. So in the present, 
inquiry we must follow this method and advance from what I 

20 is more obscure by nature, but clearer to us, towards what I 
is more clear and more knowable by nature. 

Now what is to us plain and obvious at first is rather 

I confus ed m asses, the elements and principles of which 

become known to us later by analysis. Thus we must 

ad¥anceJi^m-gen£j:alities--to--parti£u]ars ; for it is a wiiole 

25 that is. best known to sense-perception, and a generality is . 

a kind of whole, comprehending many things within it, 
184^ like ^ parts. Much the same thing happens in the relation 

^° of the name to the foonula. A n^ime, e.g. 'round', means 
vaguely a sort of whole : it5_definition analyses this into its 
particular senses. Similarly a child begins by calling all 
men 'father', and all women 'mother', but later on dis- 
tinguishes each of them. 

15 The principles in question must be either (a) one or 2 
(d) more than one. 

If (a) one, it must be either (i) motio^JgsSj^as^Parm^IlLdes 
and Melissys-^sert, or (ii) i n motion , as the physicists hold, 
some declaring air to be the first principle, others water. 

If (l?) more than one, then either ('\) a iir]he. ^r (ii) an 
infinite plurality . If (i) finite (but more than one), then 
20 either two or three or four or some other number. If (ii) 
infinite, then either as Democritus believed one in kin d, 
but differing in shape or form ; or different in kj nd and 
even contrary.^ 

A similar inquiry is made by those who inquire into the 
number of existents : for they inquire whether the ultimate 
constituents*^^\S^sting things^ are one or many, and if many, 

equivalent phrase is Trporepov rrj (f)va€i. The knowledge with which an 
inquiry starts is always the causa cognoscendi of the conclusion : it 
may, or may not, be knowledge of the causa essendi. 

^ Reading in 1. 26 wa-ncp fj-fpn, with E. 

^ 184*' 21. Both Anaxagoras and the Pythagoreans recognized 
contraries as principles, but it is chiefly the former who is referred to 
here. Contraries are ' the most different of the things in the same 
genus' {Met. A. 1018*27). Thus while the atoms of Democritus 
were the same in kind, the principles of Anaxagoras not only differed 
in kind, but were even contrary to each other. 

' Reading in 1. 23 earl npaToiv CrjTovai with Bonitz. 

BOOK I. 2 184* 

whether a finite or an infinite plurality. So they too are | 
inquiring whether the principk-oi^-ekment is one or many.^ H 

Now to investigate whether Being is ope and jaaotionless 25 
is not_a_£ Pntribution to the ^ience QO[atui:e. For just as 185* 
tlTegeometer has nothing more to say to one who denies 
the principles of his science — this being a question for 
a different science ^ or for one common to all — so a man j / / 

investigating prmciples cannot argue with one who denies 
their existence. For if Being is just one, and one in the: 
way nfentioned, there is a principle no longer, since a prin-l 
ciple must be the principle of some thing or things. 

To inquire therefore whether ^ing is one in this sense 5 
would be like arguing against any other position maintained 
for the sake of argument (such as the Heraclitean thesis, or 
such a thesis as that Being is one man) or like refuting a 
merely contentious argument — a description which applies 
to the arguments both of Melissus and of Parmenides : their 
premisses are false and their conclusions do not follow. Or 10 
rather the argument of Melissus is gross and palpable and 
offers no difficulty at all : accept one ridiculous proposition 
and the rest follows — a simple enough proceeding. 

^e physicists, on the other hand, must take for granted!/ ? 
that the things that exist b y nature are, either all or some [ \ ; 
^f them, in mptioj v^which is indeed made plain by in-' '; 
— u4ui|ion.^ Moreover, no man of science is bound .to solve 
every kind of difficulty that may be raised, but only as 15 
many as are drawn falsely from the principles of the science : , y 
it is not our business to refute those that do not arise in 
this way: just as it is the duty of the geometer to refute 
the squaring of the circle by means of segments, but it is 
not his duty to refute Antiphon's proof.* At the same ) 1 j [ 


^ Perhaps Aristotle is thinking of Plato's account in the Sophist 
(242-6) of preceding views about the number and nature of ra ovra 
(a term which includes more objects than those of physics). 

"^ Another special science, if there is one, to which geometry is 
subordinate, as optics (e. g.) is to geometiy. 

^ (irayoiyrj, the process by which a man is led on from the apprehen- 
sion of particular or partial forms of a universal to the apprehension of 
the universal in its complete and purified form. 

* The former method was suggested by Hippocrates of Chios, and 

B 2 


time the holders of the theory of which we are speaking do 
incidentally raise physical questions, though Nature is not 
their subject : so it will perhaps be as well to spend a few 
words on them, especially as the inquiry is not without 
scientific interest. 

20 The most pertinent question with which to begin will be 

\ j this ^ : Xn~what sense is it asserted that alj_ things are one ? 

' ! Eor ' is ' is used in many senses. Do they mean that 'all 

things ' are ' sub^nce or quaniiiies or qualifies ? And, further, 

1 are all things one substance — one man, one horse, or one 

■ 25 soul — or quality and that one and the same — white or hot 

or something of the kind ? These are all very different 

doctrines and all impossible to maintain. 

\ 1 For \iboth substance and quantity and quality are, then, 

f /whether these exist independently of each other or not, 

' Being will be many. 

If on the other hand it is asserted that all things are 
quality or quantity, then, whether substance exists or not, 
30 an absurdity results, if indeed the impossible can properly 
\be called absurd. For nojie of the others can exist in- 
^dependently : substan c ealone is indep endent i for everything 
is predicated- of substance as^ubject,^ Now Melissus says 
that Being is infinite. It is then a quantity. For the 
infinite is in the category of quantity, whereas substance 
or quality or affection cannot be infinite except through 

rested on the rather obvious geometrical fallacy of supposing that 
if a particular kind of lunule can be squared, another kind can be 
squared also. Antiphon's method was that of exhaustion. He drew 
a square in the circle, and then isosceles triangles on its sides, and so 
on, and inferred that ultimately the inscribed polygon was equal in 
area to the circle. This involves a denial of the %&Q>m.^Xx\z?\ principle 
that every geometrical magnitude can be divided ad infinitum, and 
gives only an approximate result. See Heath, Greek Mathematics, 
i. 183-200, 221-3, and Diels, Vorsokratiker^, i. 298 f, ii. 294 f. 

^ omitting Ibnv in 1. 22 with FI Simp. 

^ Aristotle is assuming the doctrine of the Categories which dis- 
tinguishes the different types of predicationji. e. the different senses 
in which * is ' is used. Only things wh4ch (ar^ in the full sense, i. e. 
substances {ovalm), have independent existence : other things are 
attributes {avfx^€^T]KUT(i) of them, and exist only when they are predicated 
of a subject {vTzoKei^icvop) which is a substance. Thus it is self-contra- 
dictory to speak of an attribute which exists unsupported by a 

BOOK I. 2 185* 

a concomitant attribute,^ that is, if at the same time 185* 
they are also quantities. For to define the infinite you 
must use quantity in your formula, but not substance or 
quality.^ If then Being is both substance and quantity, itj 
is two, not one : if only substance, it is not infinite and| 
has no magnitude ; for to have that it will have to be a ' 

Again, 'one' itself, no less than 'being', is used in many 5 . 
senses, so we must consider in what sense the word is used \ 
when it is said that the All is one. ^ 

:Now we say that (a) the continuous is one or that {U) the 
indivisible is one, or {c) things are said to be ' one ', when 
their essence is one and the same, as ' liquor ' and 

If {a) their One is one in the sense of continuous, it is: 
many, for the continuous is divisible ad infinitum. ,0 

There is, indeed, a difficulty about part and whole, per- 
haps not relevant to the present argument, yet deserving 
consideration on its own account — namely, whether the 
part and the whole are one or more than one, and how they 
can be one or many, and, if they are more than one, in what 
sense they are more than one.* (Similarly with the parts 
of wholes which are not continuous.) Further, if each of 15 
the two parts is indivisibly one with the whole, the 
difficulty arises that they will be indivisibly one with each 
other also. 

But to proceed : If {b) their One is one as indivisible, 

^ Kara crvfi^e^rjKos, of which the Latin equivalent was ^er accidefis. 
It is usually opposed to KaO' amo [per se) or j; hvto [quatenus ipstiin). 
Thus a triangle, through its own nature (/ca^' airo), or as such [ri alro)^ 
has its angles equal to two right angles. On the other hand, the 
white (object) is six feet high, not in virtue of its whiteness {Kaff avro)^ 
but through an attribute which is not necessarily involved in whiteness 
{Km a (TVfi^elBrjKos). (In Posterior Analytics^ i. 4, Aristotle draws 
a distinction between Ka& avro and § avro which may here be neglected.) 

^ See below, iii. 207*7. 

^ The point of the paragraph is that Melissus at least is obviously 
committed to a dualism, since he emphasizes the infinity of the one 

* Aristotle seems to have in view a possible objection to the 
statement that the continuous is many. It might be said that the 
continuous is many only potentially, not actually. 


nothing will have quantity or quality,^ and so the one will 
not be infinite, as Melissus says — nor, indeed, limited, as 
Parmenides says, for though the limit is indivisible, the I 
limited is not.^ 

But if (c) all things are one in the sense of having the 
20 same definition, like ' raiment ' and * dress ', then it turns out 
that they are maintaining the Heraclitean doctrine, for it 
will be the same thing ' to be good ' and ' to be bad ', and 
' to be good ' and ' to be not good ', and so the same thing 
will be ' good ' and * not good ', and man and horse ; in fact, 
their view will be, not that all things are one, but that they 
I are nothing ; and that * to be of such-and-such a quality ' is 

the same as * to be of such-and-such a size '. 
25 Even the more recent of the ancient thinkers were in 
a pother lest the same thing should turn out in their hands 
both one and many. So some, like Lycophron,^ were led 
1 to omit ' is ', others to change the mode of expression and 
' say * the man has been whitened ' instead of ' is white ', and 
30 ' walks ' instead of ' is walking ', for fear that if they added 
jthe word ' is ' they should be making the one to de many — 
as if 'one' and 'being' were always used in one and the 
same sense. What 'is' may be many either in defini- 
tion (for example ' to be white ' is one thing, ' to be musi- 
cal' another, yet the same thing* may be both, so the 
one is many) or by division, as the whole and its parts. 
186^ On this point, indeed, they were already getting into diffi- 
culties and admitted that the one was rnany— as if 
there was any difficulty about the same thing being both 
one and many, provided that these are not opposites ; 
for ' one ' naay mean either ' potentially one ' or ' actually 

1 Indivisible unity is inconsistent with any type of predication, 
which always involves a subject and a predicate, and in particular 
with the predication of quantity. 

'^ e. g. a point which terminates a line is indivisible, though the 
line is not. 

^ An orator and a pupil of Gorgias. For what is known of him 
see Zeller i^ 1323, n. 3. 

* Reading in 1. 33 to Se airo, with E. 

^ So that there is no contradiction in supposing that a thing is (say) 
' actually one ', but * potentially many ', at the same time. 

BOOK I. 3 i86^ 

3 If, then, we approach the thesis in this way it seems 
impossible for all things to be one. Further, the arguments 5 
they use to prove their position are not difficult to expose. 
For both of them reason contentiously — I mean both 
Melissus and Parmenides. [Their premisses are false and 
their conclusions do not follow. Or rather the argument 
of Melissus is gross and palpable and offers no difficulty at 
all : admit one ridiculous proposition and the rest follows — 
a simple enough proceeding.] ^ 

The fallacy of Melissus is obvious.^ For he supposes that 10 
the assumption * what has come into being always has 
a beginning' justifies the assumption 'what has not come 
into being has no beginning'. Then this also is absurd, 
that in every case there should be^ a beginning of the 
thifig — not of the time and not only in the case of coming 
to be in the full sense but also in the case of coming to 
have a quality* — as if chang e ^ever took p lace^uddenly. 15 
Again, does it follow that Being, if one, is motionless? 
Why should it not move, the whole of it within itself, as parts 
of it do which are unities, e. g. this water ? Again, why is 
qualitative change impossible ? But, further, Being cannot be 
one in form, though it may be in what it is made of (Even 20 
some of the physicists hold it to be one in the latter way, 
though not in the former.) Man obviously differs from 
horse in form, and contraries from each other. 

The same kind of argument holds good against Parmenides 
also, besides any that may apply specially to his view : the 
answer to him being that *Mw is not true' and * that does not 
follow '. His assumption that one is used in a single sense 
only is false, because it is used in several. His conclusion ^5 
does not follow, because if we take only white things, and if 
' white ' has a single meaning, none the less what is white 
will be many and not one. For what is white will not be 

* The words in brackets are probably wrongly inserted from 
185a 9-12. 

"^ Cf. Diels, Vorsokratikef^ , i. 184. 29-37, 186. 3-10. 
^ Omitting nua-Bm in 1. 13 with F Simp. 

* See Diels, Vorsokratiker^ ^ i. 187-90. Aristotle wishes to say 
that there is always a beginning of the time, but not always of the 
thing. '^ 


one either in the sense that it is continuous or in the sense 
that it must be defined in only one way. ' Whiteness ' will 
be different from ' what has whiteness '. Nor does this 
mean that there is anything that can exist separately, over 
3|> and above what is white. For ' whiteness ' and * that which 
is white ' differ in definition, not in the sense that they are 
things which can exist apart from each other. But Par- 
menides had not come in sight of this distinction. 

It is necessary for him, then, to assume not only that 
J ' being ' has the same meaning, of whatever it is predicated, 
\ but further that it means (i) what just is ^ and (2) what is 
\ just one? 

It must be so,^ for (i) an attribute is predicated of some 
35 subject, so that the subject to which * being ' is attrijjuted 
will not be, as it is something different from * being '. 
186^ Something, therefore, which is not will be. Hence * sub- 
stance ' * will not be a predicate of anything else.^ For the 
subject cannot be a beings unless ' being ' means several 
things, in such a way that each is something. But ex 
hypothesi * being ' means only one thing. 

If, then, 'substance' is not attributed to anything, but 
5 other things are attributed to it, how does ' substance ' 
mean what is rather than what is not ? For suppose that 
* substance ' is also ' white '. Since the definition of the 
latter is different (for being cannot even be attributed to 
white, as nothing is which is not ' substance '), it follows 
that 'white' is not-b«ing — and that .not in the sense 
of a particular not-being, but in the sense that it 
10 is not at all. Hence ' substance ' is not ; for it is true 
to say that it is white ,^ which we found to mean 

* i. e. substance. 

" i.e. indivisible unity. 

' It is necessary to supply some such intermediate step as this : 
' If being is not thus identified with substantial being, it is an attribute, 
and then the following difficulty occurs — '. 

* Or that which y^j-/ is, 

" Consequently to make being = substance does not obviously in- 
volve a plurality (duality) of beings, as identifying it with an attribute 

" Aristotle assumes throughout the possibility of predication. 

BOOK I. 3. 186' 

not-being. If to avoid this^ we say that even 'white' 
means substance, it follows that 'being' has more than 
one meaning. 

In particular, then. Being will not have magnitude, if it is 
substance. For each of the two parts ^ must be in a different 

(2) Substance is plainly divisible into other substances, if 
we consider the mere nature of a definition. For instance, 15 
if ' man ' is a substance, ' animal ' and ' biped ' must also be 
sQbstances. For if not substances, they must be attributes — 
and if attributes, attributes either of (a) man or of {b) some 
other subject. But neither is possible. 

{a) An attribute is either that which may or may not 
belong to the subject or tljat in whose definition the subject 2b ^/^ 
of which it is an attribute is involved.^ Thus ' sitting ' is an 
example of a separable attribute, while ' snubness ' contains 
the definition of 'nose', to which we attribute snubness. 
Further, the definition of the whole is not contained in the 
definitions of the contents or elements of the definitory 
formula ; that of ' man ' for instance in ' biped ', or that of 
' white man ' in ' white '. If then this is so, and if ' biped ' is 25 
supposed to be an attribute of ' man ', it must be either 
separable, so that ' man ' might possibly not be ' biped ', or 
the definition of ' man ' must come into the definition of 
' biped ' — which is impossible, as the converse is the case. 3° 

{b) If, on the other hand, we suppose that ' biped ' and 
' animal ' are attributes not of man but of something else, 
and are not each of them a substance, then ' man ' too will 
be an attribute of something else. But we must assume that 
substance* is not the attribute of anything, and that the 
subject of which both ' biped ' and ' animal ' and each 
separately ^ are predicated is the subject also of the com- 
plex ' biped animal '. 
/Are we then to say that the AH is composed of indivisible 35 

^ Sc. to avoid the self-contradiction involved in saying t6 orrep ov 

OVK ov. 

^ Which are, at the least, involved in its having magnitude. 

^ Omitting ^ eV . . avfx^e^rjKev in 11. 20-2I, with FI Phil. Simp. 

* Omitting n in 1. 34, with E^ I Phil. Simp. 

^ Placing a comma after, not before, ko\ iicdrfpov (11. 34-5). 


186'' PHYSICA 

187^ substances ? * Some thinkers did, in point of fact, give way 
to both arguments. To the argument that all things are 
one if being means one thing, they conceded that not-being 
is ; to that from bisection, they yielded by positing atomic 
magnitudes.^ But obviously it is not true that if being 
means one thing, and cannot at the same time mean the 
5 contradictory of this, there will be nothing which is not, for 
even if what is not cannot de without qualification, there is 
no reason why it should not be a particular not-being. To 
say that all things will be one, if there is nothing besides 
Being itself, is absufd. For who understands 'being itself 
to be anything but a particular substance? But if this 
is so, there is nothing to prevent there being many beings, 
as has been said. 

It is, then, clearly impossible for Being to be one in this 


The physicists on the other hand have two modes of 4 

The first set make the underlying body ^ ong — either one 
of the three* or something else which is denser than fire 

J 5 and rarer than air ^ — then generate everything else from 
this, and obtain multiplicity by c onden sation and rare- 
factign. Now these are contraries, which may be generalized 
into * excess and defect '. (Compare Plato's ' Gre-dt -ind 
Small ' — except that he makes these his matter, the one his 
form, while the others treat the one which underlies as 
matter and the contraries as differentiae, i. e. forms). 

20 The second set assert that the contrarieties are contained 
in the one and emerge from it by segregation, for example 
Anaximander and also all those who assert that * what is ' is 
one and many, like Empedocles and Anaxagoras ; for they 

^ Taking e| ahiaipeTu>v apn to nav in 1. 35 as a question. 

* See Diels, Vorsokratiket^^ i. 170 f, 18 1-3. 

^ 187*^ 13 omitting ov^ of which there is no trace in Simplicius. 

^ Water, air, or fire. Aristotle points out elsewhere [Met. A. 988^ 30) 
that no one made earth the substratum. 

^ Aristotle sometimes mentions a theory that the substratum is 
between water and air, and once a theory that it is between water and 
fire. A substance between air and fire is mentioned by Aristotle in 
four other passages besides the present. See Zeller i'. 283-91, Diels, 
Vors? i. 415. 32-416. 27. 

BOOK I. 4 18/ 

too produce other things from their mixture by segrega- 
tion. These differ, however, from each other in that the 
former imagines a c;^e of such changes, the latter a single 
series. Anaxagoras again made both his ' homoeomerous ' ^ 25' 
substances and his contraries infinite in multitude, whereas 
Empedocles posits only the so-called ^ elements. 

The theory of Anaxagoras that the principles are infinite 
in multitude was probably due to his acceptance of the 
common opinion of the physicists that nothing comes into ^ 
being from not-b eing. For this is the reason why they use 
the phrase '"allthings were together ' and the coming 30 
into being of such and such a kind of thing is reduced to 
change of quality, while some spoke of combination and 
separation.^ Moreover, the fact that the contraries proceed 
from each other led them to the conclusion. The one, they 
reasoned, must have already existed in the other ; for since 
everything tha t comes into being must arise either fr om 
what is or fro m v>jiatjs_not , and it is i mpossible for it to 
arise froni _whatJ s not ion this point all the physicists agree), 
they thought that the truth of the alternative necessarily 35 
followed, n amely that things come into being out of existent 
things, i^ e. out of things already present, but imperceptible 
to our senses because of the smallness of their bulk. So 187^ 
they assert that eve ry thingj ia s been mixed in ever^^ thing, 
because they saw everything arising out of everything. 
But things, as they say, appear different from one another 
and receive different names according to the nature of the 
particles which are numerically predominant among the 
innumerable constituents of the mixture. For nothing, 
they say, is purely and entirely white or black or sweet, 5 
bone or flesh, but the nature of a thing is held to be t hat of 
which it contains the m ost, _ 

Now (i) the infinit e qua infin ite is upkaowable, so thatwhat 

* o^oiofiepTj is Aristotle's temi for substances which are divisible into 
parts like themselves. It means primarily the 'tissues* of plants and 
animals, e.g. flesh, as distinguished from the opyaviKa neprj, such as the 
hand. It includes the metals, but not the four elements. 

'■^ Aristotle himself regards the four * elements * as complex. 

^ Putting only a comma after aWoiovadai in 1. 30. Cf. Diels, ib. 388. 


is infinite in multitude or size is unknowable in quantity, 
and what is infinite in variety of kind is unknowable in 

lo quality. But the principles in question are infinite both 
in multitude and in kind. Therefore it is impossible to 
know things which are composed of them ; for it is when 
we know the nature and quantity of its components that we 
suppose we know a complex. 

Further (2) if the parts of a whole may be of any size in the 

15 direction either of greatness or of smallness (by 'parts' 
I mean components into which a whole can be divided and 
which are actually present in it), it is necessary that the 
whole thing itself may be of any size. Clearly, therefore,^ 
since it is impossible for an animal or plant to be indefinitely 
big or small, neither can its parts be such, or the whole will 
be the same. But flesh, bone, and the like are the parts 

20 of animals, and the fruits are the parts of plants. Hence 
it is obvious that neither flesh, bone, nor any such thing 
can be of indefinite size in the direction either of the greater 
or of the less. 

Again (3) according to the theory all such things are 
already present in one another and do not come into being 
but are cons titu ents which are separat ed ou t, and a thing 
receives its designation from its chieTconstituent. Further, 
anything may come out of anything — water by segregation 

35 from flesh and flesh from water. Hence, since every finite 
body is exhausted by the repeated abstraction of a finite 
body, it seems obviously to follow that everything cannot 
subsist in everything else. For let flesh be extracted from 
water and again more flesh be produced ^ from the remainder 
by repeating the process of separation : then, even though 
the quantity separated out will continually decrease, still it 

30 will not fall below a certain magnitude.^ If, therefore, the 
process comes to an end, everything will not be in every- 
thing else (for there will be no flesh in the remaining water) ; 
if on the other hand it does not, and further extraction is 
always possible, there will be an infinite multitude of finite 

^ Reading in 1. 16 o\ov), el 8ij, with Bonitz. 
^ Reading in 1. 28 yevofxevrjs, with EI. 
' Anaxagoras would deny this. 

BOOK I. 4 iSy** 

equal ^ particles in a finite quantity — which is impossible. 
Another proof may be added : Since every body must 35 
diminish in size when something is taken from it, and flesh 
is quantitatively definite in respect both of greatness and 
smallness, it is clear that from the minimum quantity of 
flesh no body can be separated out ; for the flesh left would 188* 
be less than the minimum of flesh.^ 

Lastly (4) in each of his infinite bodies there would be 
already present infinite flesh and blood and brain — having 
a distinct existence, however, from one another, and no less 
real than the infinite bodies, and each infinite: which is 
contrary to reason. 

The statement that complete separation never will take 5 
place is correct enough, though Anaxagoras is not fully 
aware of jw ^at it -means. For affections are indeed in- 
separable. If then colours and states had entered into 
the mixture, and if separation took place, there would 
be a ' white ' or a ' healthy ' which was nothing hut white 
or healthy, i. e. was not the predicate of a subject. So his 
! ^Mind' is an absu rd perso n aiming 7y\ the impng>;ihlPj if he f 
is supposed to wish to separate them, and it is impossible 10 
to do so, bot h in respect of g nantTty and of quality — of 
quantity, because there is no minimum magnitude,^ and of 

. qual ity, because afl'ect ions_ are inseparable . 

Nor is Anaxagoras right about the coming to be of 
homogeneous bodies.* It is true there is a sense in which 
clay is divided into pieces of clay, but there is another in 

I which it is not. Water ^ and air are, and are generated, 15 
' from ' each other, but not in the way in which bricks come 
* from ' a house and again a house * from * bricks ^ ; and it is 
better to assume a smaller and finite number of principles, 
as Empedocles does."^ 

* Aristotle supposes for simplicity that the finite amounts which are 
extracted are equal. 

^ For Anaxagoras there is no minimum. — It seems best to read 
eXiiTTcot' in 1. I with SimpHcius. 

^ According to Anaxagoras. * Reading in 1. 13 6fxoeL8a>v, with EI. 

^ Omitting Sc in 1. 16, perhaps with Them, and Simp. 

•* i. e. by segregation and aggregation respectively. Water comes 
from air by change of quality. 

' If we accept the possibility of transmutation, it is not necessary to 
assume an infinite multitude of principles. 


r All thinkers then agree in making the coi^'aries 5 
( principles, both those who describe the All as one and 
^o unmoved (for even Parmenides treats hot and cold as prin- 
ciples under the names of fire and earth) ^ and those too 
who use the rare and the dense. The same is true of 
Democritus also, with his plenum ^ and^v^d, both of which) 
exist, he says, the one as being, the other as not-beingj 
Again he speaks of differences in position, shape, and order, 
and these are genera of which the species are contraries, 
namely, of position, above and below, before and behind ; 
25 of shape, angular and angle-less, straight and round.^ 

It is plain then that they all in one way or another 
identify the>con^'aries with the_£rinciples. And with good 
reason. For first pn' pn'plf^g rO']^^ "^^ lT^j^yriY_^^j^[i;2!II/^^ 
another n ^rjrorn^ythjjjg ^else, w^^'l^ ^vpr^rjJTJnCT Viae to be 
derived fom ti i,em. But these conditions are fuTSlled by 
the primary contraries, which are not derived from any- 
thing else because they are primary, nor from each other 
because they are contraries. I 

30 But we must see how this can be arrived at as a reasoned 
result, as well as in the way just indicated. 

Our first presupposition must be that in nature nothing 
acts on, or is acted on by, any nthrr thinr nt randoiPL 
nor may anything come from anything else, unless we 
mean that it does so in virtue of a concomitant attribute. 
35 For how could ' white ' come from * musical ', unless 
' musical ' happened to be an attribute of the not-white * 
or of the black? No, 'white' comes from * not-white' 
— and not from any ' not-white ', but from black or some 
188^ intermediate colour.^ Similarly, ' musical ' comes to be 
from 'not-musical', but not from any thing other than 
musical, but from ' unmu sical_ '_or any intermediate state 
there may be. 

» Cf. fr. 8. 53-9. 

"^ Reading in 1. 22 TrX^pfs- for arcpfov, with E' I Simp. Phil. Them. 

^ Reading in 1. 25 with MS. Par. 1859, Phil., and Simp., ycyioi'no^ievou 
aywviov, €v6v 7Tepi(f)€p(S. 

* Reading in 1. 36 rw fifj XevKa, with E and Simp. 

^ According to Aristotle, the colours form a scale between black 
and white. 

BOOK I. 5 i88' 

Nor again do things pass into the first chance thing ; 
' white ' does not pass into ' musical ' (except, it may- 
be, in virtue of a concomitant attribute), but into 'not- 
white ' — and not into any chance thing which is not white, 
but into black or an intermediate colour ; ' musical ' passes 
into * not-musical' — and not into any chance thing others 
than musical, but into 'unmusical' or any intermediate 
state there may be. 

The same holds of other things also : even things which are 
not simple but complex follow the same principle, but the lo 
opposite state has not received a name, so we fail to notice 
the fact. What is in tune must come from what is not in 
tune, and vice versa ; the tuned passes into untunedness — 
and not into any untunedness, but into the correspond- 
ing opposite. It does not matter^ whether we take attune- 15 
ment, order, or composition for our illustration ; the principle 
is obviously the same in all, and in fact applies equally to 
the production of a house, a statue, or any other complex. 
A house comes from certain things in a certain state of 
separation instead of conjunction, a statue (or any other 
thing that has been shaped) from shapelessness — each of 20 
these objects being partly order and partly composition. 

If then this is true, everything that comes to be or 
passes away comes from, or passes into, its contrar)^ or an 
intermediate state. But the intermediates are derived from 
the contraries — colours, for instance, from black and white. 
Everything, therefore, that comes to be by a natural 1 35 
process is either a contrary or a product of contraries. 

Up to this point we have practically had most of the 
other writers on the subject with us, as I have said already ^: 
for all of them identify their- elements, and what they call 
their principles, with the contraries, giving no reason indeed 
for the theory, but constrained as it were by the truth 
itself They differ, however, from one another in that 30 
some assume contraries which are more primary, others 
contraries which are less so: some those more knowable 

^ Reading in 1. 15 dia(f)€p€i 8' olBiv, with the MSS. 
^ ^19-30. 

i88^ • PHYSICA 

in the order of explanation, others those more familiar to 
sense. For some make hot and cold, or again moist and 
dry, the conditions of becoming; while others make odd 
35 and even, or again Love and Strife ; and these differ from 
each other in the way mentioned. 

Hence their principles are in one sense the same, in 
another different ; different certainly, as indeed most people 
189^ think, but the same ina^nauch-^s they arefanajogous : for 
all are taken from the same table of columns,^ some 01 the 
pairs being wider, others narrower in extent. In this way 
then their theories are both the same and different, some 
better, some worse ; some, as I have said, take as their 
contraries what is more knowable in the order of explanation, 
^others what is more familiar to sense. (The uniyersal is 
more knowable in the order of explanation, the particular in 
the order of sense : for explanation has to do with the 
universal, sense with the particular.) ' The great and the 
small,' for example, belong to the former class, ' t]ie dense 
and the rare ' to the latter. 

It is clear thea-t h a t o mLprin ciples mus t b e f-nn trarjV <;. 

The next question is whether the principles are two or 6 
three or more in number. 

One they cannot be, for there cannot be one contrary. 
Nor can they be innumerable, because, if so, Being will not 
be kn^able : and in any one genus there is only one con- 
trariety, and substance is one genus : also a finite number 
15 is sufficient, and a finite number, such as the principles 
of Empedocles, is better than an infinite multitude ; for 
Empedocles professes to obtain from his principles all that 
Anaxagoras obtains from hisinnumerableprinciples. Lastly, 
some contraries are more primary than others, and some 
arise from others — for example sweet and bitter, white and 
black — whereas the principles must always remain principles. 

^ The following is the table given in Me^. A. 986*23 : — 

Limit . 

. . Unlimited 

Resting . 

. . Moving 

Odd . 

. . Even 

Straight . 

. . Curved 


. , Plurality 


. . Darkness 

Right . 

. . Left 


. . Bad 

Male . 

. Female 

Square . 

. . Oblong 

BOOK I. 6 i89« 

This will suffice to show that the principles are neither 20 
one nor innumerable. 

Granted, then, that they are a limited number, it is 
plausible to suppose them more than twol Forit is difficult 
to see how either density should be of such a nature as to 
act in any way on rarity or rarity on density. The same is 
true of any other pair of contraries ; for Love does not 
gather Strife together and make things out of it, nor does 25 
Strife make anything out of Love, but both act on a third 
thing different from both. Some indeed assume more than 
one such thing from which they construct the world of 

Other objections to the view that it is not necessary 
to assume a third principle as a substratum may be added, 
(i) We do not find that the contraries constitute the j 
substance of any thing. But what is a first principle ought 30 ' 
not to be \kiQ predicate of any subject. If it were, there 
would be a principle of the supposed principle : for the 
subject is a principle, and prior presumably to what is 
predicated of it. Again (2) we hold that a substance is not / 
contrary to another substance. How then can substance ' 
be derived from what are not substances? Or how can 
non-substance be prior to substance ? 

If then we accept both the former argunrient ^ and this 
one,^ we must, to preserve both, assume a t hird s ome\Yhat^7^ 
as the suhatratuinjoLtha-Contrarie^, such as \s spoken of by 189'' 
those who describe the All as one nature — water or fire or 
what is intermediate between them. What is intermediate 
seems preferable ; for fire, earth, air, and water are already^ in- 
volved with pairs of contraries. There is, therefore, much to 5 
be said for those who make the underlying substance different 
from these four ; of the rest, the next best choice is air, as 
presenting sensible differences in a less degree than the 
others ; and after air, water. All, however, agree in this, 
that they differentiate their One by means of the contraries, 
such as density and rarity and more and less, which may 10 

^ That the contraries are principles (ch. 5). 

^ That the contraries need a substratum (11. 21-34). 

^ Reading in 1. 4 nvp yap fj8q, with E Them. Simp. 


of course be generalized, as has already been said,^ into 
excess and defect. Indeed this doctrine too (that the One 
and excess and defect are the principles of things) would 
appear to be of old standing, though in different forms ; 
for the early thinkers made the two the active and the one 
the passive principle, whereas some of the more recent 

15 maintain the reverse. 

To suppose then that the elements are three in number 
would seem, from these and similar considerations, a plausible 
view, as I said before.^ On the other hand, the view that 
they are more than three in number would seem to be 

For the one substratum is sufficient to be acted on ; but if 

20 we have four contraries, there will be two contrarieties, and 
we shall have to suppose an intermediate nature for each 
pair ^ separately.'* If, on the other hand, the contrarieties, 
being two, can generate from each other, the second con- 
trariety will be superfluous. Moreover, it is impossible 
that there should be more than one primary contrariety. 
For substance is a single genus of being, so that the 
principles can differ only as prior and posterior, 7tot in 

25 genus ; in a single genus there is always a single con- 
trariety, all the other contrarieties in it being held to be 
reducible to one. 

It is clear then that the number of elements is neither 
one nor more than two or three; but whether two or three 
is, as I said, a question of considerable difficulty. 

30 We will now give our own account,^ approaching the 7 
question first with reference to becoming in its widest 
sense : for we shall be following the natural order of inquiry 
if we speak first of common characteristic s, and then investi- 
gate the characteristics of special cases. ^ 


\ We say tha^one thing comes to be from another thing, 

land one s,ort^^iliuogi-iri3m another sort of thing, both in 

1 187*16. 2 aji. 

' 189^20 reading cKarepa with Philoponus and Pacius. 

* So that one of these substrata would be superfluous. 

'^ Reading in 1. 30 Xeycofiev, with E. ^ Cf. 184*21-^ 14. 

BOOK I. 7 iSg'^ 

the case of simple and of complex things. I mean the 
following. We can say (i) the ' man becomes musical ', 

(2) what is * not-musical becomes musical V or (3) the * not- 35 
musical man becomes a musical man '. Now what becomes 190^ 
in (i) and (2) — * man ' and * not musical ' — I call simple, and 
what each becomes — ' musical ' — simple also. But when 

(3) we say the * not-musical man becomes a musical man ', 
both what becomes and what it becomes are complex. 

As regards one of these simple 'things that become' we 5 
say not only ' this becomes so-and-so ',^ but also ' from 
being this, comes to be so-and-so ', as ' from being not- 
musical comes to be musical ' ; as regards the other we do 
not say this in all cases, as we do not say (1) * from being 
a man he came to be musical ' but only * the man became 
musical '. 

When a * simple ' thing is said to become something, in 
one case (1) it survive s^ thro yig^ ^^fi p^^^r^'^i in the other (2) 
it does not. For the man remains a man and is such even 10 
when he becomes musical, whereas what is not musical or 
is unmusical does not continue to exist, either simply or 
combined with the subject. 

These distinctions drawn, one can gather from surveying 
the various cases of becoming in the way we are describing 
that, as we say, there must always be an iinddrl j^«"fT gfimf- 
thipg , namely that whi ch l^f-rnmps, anH that t^V'^, t^J^"g^ 15 

qhyn ys one nnm<;-rira1]y^ in form at 1pat;f- \^ nnf- nnp. (By 

that I mean that it can be described in different ways.) For 
* to be man ' is not the same as ' to be unmusical '. One part 
survives, the other does not : what is not an opposite survives 
(for ' man ' survives), but ' not-musical ' ^ or ' unmusical ' does 
not survive, nor does the compound of the two, namely 20 
' unmusical man '. 

We speak of ' becoming that from this ' instead of ' this 
becoming that ' more in the case of what does not survive 
the change — * becoming musical from unmusical ', not ' from 

^ Omitting in 1. 35 rt, with E Them. Phil. Simp. 
" Omitting in 1. 6 n, with E^ Them. Phil. 
' Reading in 1. 19 to \).j] fiovaiKov, with F. 

c a 


man ' — but there are exceptions, as we sometimes use the 
25 latter form of expression even of what survives ; we speak 
of * a statue coming to be from bronze ', not of the ' bronze 
becoming a statue '. The change, however, from an opposite 
which does not survive is described indifferently in both 
ways, * becoming that from this ' or ' this becoming that *. 
30 We say both that * the unmusical becomes musical *, and 
that ' from unmusical he becomes musical'. And so both 
forms are used of the complex, * becoming a musical man 
from an unmusical man ', and * an unmusical man becoming 
a musical man'. 

But there are different senses of Lco ming to ba '. In 
some cases we do not use the expression ' come to be ', but 
* come to be so-and-so '. Only substances are said to ' come 
to be ' in the unqualified sense. 

Now in all cases other than substance it is plain that 
there must be some subject, namely, that which becomes. 
For we know that when a thing comes to be of such 
35 a quantity or quality or in such a relation, time, or place, 
a subject is always presupposed, since substance alone is 
not predicated of another subject, but everything else of 


But that substances too, and anything else that can be 
said 'to be ' without qualification, come to be from some 
substratum, will appear on examination. For we find in 
every case something that u^dgilies from which proceeds 

I that which comes to be ; for instanqe^ animals and |i]ants 

* from seed. 

5 Generally things which come to be, come to be in different 
ways: (1) by change of shape, as a statue^ ; (2) by addi- 
tion, as things which grow ; (3) by taking away, as the 
Hermes from the stone ; (4) by putting together, as a 
house ; (5) by alteration, as things which ' turn ' in respect 
of their material substance.^ 

^ Sc. a bronze statue, e'fc x"^<ov is probably a gloss. 

^ The first four modes of becominj? are cases of artificial production. 
The fifth seems to include both mere change of quality (aWoioxrts) and 
generation in the full sense (arrXf) yevecns), which presumably is always 
accompanied by aXXoiwaty. Milk * turning ' would be merely a case 

BOOK I. 7 190^ 

It is plain that these are all cases of coming to be from 
a substratum. 

Thus, clearly, from what has been said, whatever comes 10 
to be is always comple x. There is, on the one hand, (a) 
something which comes into existence, and again (d) some- 
thing which becomes that — the latter (d) in two senses, 
either the subject or the opposite. By the ' opposite ' I 
mean the 'unmusical', by the 'subject' ' man', and similarly 
I call the absence of shape or form or order the ' opposite ^ 15 
and the bronze or stone or gold the 'subject'. ^^^. ^l*/^ 

Plainly then, if there are conditions and pri ncip les which .>* U 
constitute natural objects and from which they primarily 

1 are or ^ have come to be — have come to be, I mean, what 
each is said to be in its essential nature, not what each is 

i in respect of a concomitant attribute — plainly, I say, every- . 

I thing comes to be from both_ j;i]bj^ and Jbnp. For ao 

^ ' musical man ' is composed (in a way) ^ of ' man ' and 
' musical ' : you can analyse it ^ into the definitions of its 
elements. It is clear then that what comes to be will come 
to be from these elements. 

Now the subject is one n umei ically. though it is two in 
form. (For it is the man, the gold — the ' matter ' * generally . ^ 
— that is counted, for it is more of the nature of a ' this ', and 2J5S - S* 
what comes to be does not come from it in virtue of a con- / / 
comitant attribute ^ ; the privation, on the other hand, and 

of change of quality (dXXotcoo-ts), not of change of substance (ottX^ 
yeveaii) : water turning into wine, or Karanr]via becoming avOpoiiros, 
would be an example of the latter. Since Aristotle is carefully working 
up to the conception of matter (vX??), the words Kara ttjv vXrjv are used 
inadvertently, or are a later addition to explain TpcTrofxeva. 

^ Omitting the comma after dai in 1. 18. 

^ The relation of attribute to subject is only analogous to that 
of form to matter. 

^ Omitting the first tovs \6yovs in 1. 22, with Diels. 

* Aristotle here introduces vXtj as his technical term for * matter '. 
Literally the word means * wood ' or ' timber ', and Aristotle no doubt 
has in view the simplest example of a maker, the tcktcov. 

^ Every transition is of the form XA-^XA', where X is substance. 

A' {orXA') is said to come to be from ^ without quahfication (dTrXois). 

On the other hand. A' comes to be from A, in virtue of an attribute ' 

[Kara avix^f^rjKos), namely A, which X possesses. The contrast is 

r between ' coming to be ' without gualification, and ' coming to be in 

I virtue of an attribute'. If A' is a quality, A is the contrary quality 

igo** PHYSICA 

the contrary are incidental in the process.) And the 
positive formis one^ — the order, the acquired-art of music, 
or any similar predicate. 

There is a sense, therefore, in which we must declare the 
principles to be ^^ and a sense in which they are ^rfee ; 

30 a sense in which the contraries are the principles — say for 
example the musical and the unmusical, the hot and the 
cold, the tuned and the untuned — and a sense in which 
they are not, since it is impossible for the contraries to be 

/ acted on by each other. But this difficulty also is solved by 
the fact that the snhstratiim ig different from the contraries. 

35 for it is itself not a contrary. The principles therefore are, 
in a way, not more in number than the contraries, but as it 
were two, nor yet precisely two, since there is a difference 
191^ of essential nature, but three. For ' to be man ' is different 
from ' to be unmusical V^ and ' to be unformed ' from ' to 
be bronze '. 

We have now stated the number of the principles of 
natural objects which are subject to generation, and how 
the number is reached : and it is clear that there must be 

; La substratu m for the contraries, and that the contraries 

U must be two. (Yet in another way of puttmg it this is not 
necessary, as one of the contraries will serve to effect the 
change by its successive absence and presence.) 
\vA \ The underlying nature is an object of scientific knowledge, 

\ by an ajialogy. For as the bronze is to the statue, the 

10 wood to the bed, or the matter and the formless before 
receiving form to any thing which has form, so is the 
underlying^, natureto^ubstaoc e, i. e. the * this ' or existent. 
^ This th en is one principle (though not one or existent * in 
the same sense as the ' this '), and the definition was one as 
.v;e agreed ^ ; then fuither there is it s contrary, the priva^ 

(or intermediate). But if A' is substance (as well as X)^ A is called 
the privation {a-Tcprjais) of A\ 

^ Incidental = Kara (rv^^f^rjKos. 

' i.e. counts as principle No. 2. 

' Reading in 1. 2 to avBpayrrco KOI TO ayiovaoi elvai, Kn\ to aax^JIJUiTiaT^f 
with E. 

* Reading in 1. 13 tv a>Sf with E. 

^ Altering the reading of the MSS. in 1. 13 (17 6 \6yos) to ^v 6 \6yos, 
\6yos is used by Aristotle as equivalent to (i8os of 190^ 28. 

BOOK I. 7 191* 

tioxL. In what sense these are two, and in what sense 
more, has been stated above. Briefly, we explain f^^d firsts ij; 
that only the contraries were principles, and later ^ that 
a substratum was indispensable, and that the principles were 
three ; our last statement^ has elucidated the difference 
between the contraries, the mutual relation of the principlesJ 
and the nature of the substratum. Whether the form o^ 
the substratum is the essential nature of a physical object 
is not yet clear.* ^But that the principles are three, and in ao 
what sense, and the way in which each is a principle, is 

So much then for the question of the number and the 
nature of the principles. 

8 We will now proceed ^ to show that the difficulty of the 
early thinkers, as well as our own, is solved in this way 

The first of those who studied science were misled in their 
search for truth and the nature of things by thei.r- inex- 25 
perifnce,*^ which as it were thrust them into another path. 
So they say that none of the things that are either comes to 
be or passes out of existence, because what comes to be 
must do so either from what is or from what is aot, both 
of which are impossible. For what is cannot come to be 30 
(because it is already) , and from what vs not nothing could 
have come to be (because something must '^ be present as a 
substratum). So too they exaggerated the consequence of 
this, and went so far as to deny even the existence of a plur- 
ality of things, maintaining that only Being itself is. Such 
then was their opinion, and such the reason for its adoption. 

Our explanation on the other hand is that the phrases 
'something comes to be from what is or from what is not ', 
' what is not or what is does something or has something 35 
done to it or becomes some particular thing ', are to be 
taken (in the first way of putting our explanation) in the 

» Ch. 5. 2 ch_ 6 3 £h. 7. 

* This is discussed below, Bk. II, Ch. i. - 
° Reading in 1. 24 Xeycofxep, with EI. 

* Sc. of logical analysis. So Themistius and Philoponus. 
' Reading in 1. 31 deiv, with Bonitz. 


191^ same sense as * a doctor does something or has something 
done to him ', ' is or becomes something from being a doc- 
tor'. These expressions may be taken in two senses, and 
so too, clearly, may ' from being ', and * being acts or is 
acted on '. A doctor builds a house, not qua doctor, but qua 
5 housebuilder, and turns gray, not qua doctor, but qua dark- 
haired. On the other hand he doctors or fails to doctor qua 
doctor. But we are using words most appropriately when 
we say that a doctor does something or undergoes some- 
thing, or becomes something from being a doctor, if he 
does, undergoes, or becomes qua doctor. Clearly then also 
* to come to be so-and-so from not-being ' means ' qua 
not-being '. 

10 It was through failure to make this distinction that those 
thinkers gave the matter up, and through this error that 
they went so much farther astray as to suppose that not]yng 
^lse-.comes to be or exists apart from Being itself, thus 
doing away with all becoming. 

We ourselves are in agreemen t with them in holding that 
nothing can be said without qualification to come from 
what is not. But nevertheless we maintain tha t a thing 
may ' come to be from what is not ' — that is, in a qiialified 
sense. For_a. thing comes to be from the\privatic)n\ which 
in its own nature is not-being, — this not surviving as a con- 
stituent of the result. Yet this causes surprise, and it is 
thought ^ impossible that something should come to be in 
the way described from what is not. 

^ In the same way we maintain that nothing comes to be 
from being, and that being does not come to be except in 
a qualified sense. In that way, however, it does, just as 
animal might come to be from animal, and an animal of 

20 a certain kind from an animal of a certain kind. Thus, 
suppose a dog to come to be from a horse. The dog 
would then, it is true, come to be frnm animal 2 (as well as 
from an animal of a certain kind) but not as animal^ for 
that is already there. But if anything is to become an 
animal, not in a qualified sense, it will not be from animal ; 

* Omitting in 1. 17 the comma after 5o*:«. 
"^ ^<aoj', i.e. \\it genus. 

BOOK I. 8 igi'^ 

and if being, not from being — nor from not-being either, for 25 
it has been explained ^ that by ' from not-being ' we mean 
from not-being qua not-being. 

/ Note further that we do not subvert the principle that 

) eveiy thing ei ther is or is not.^ 

This then is one way of solving the difficulty. Another 
consists in pointing ^ut that the same things can be 
explained in terms of pote ntiality and g^tuality. But this | 
has been done with greater precision elsewhere.^ 

So, as we said, the difficulties which constrain people 30 
to deny the existence of some of the things we mentioned ^ 
are now solved. For it was this reason which also caused 
some of the earlier thinkers to turn so far aside from the 
road which leads to coming to be and passing away and 
change gene rally. If they had come in sight of this nature,^ 
all their ignorance would have been dispelled. 

9 Others,^ indeed, have apprehended the nature in question, 35 
but not adequately. 

In the first place they allow that a thing may come to be 
without qualification from not-being, accepting on this 
point the statement "^'of Parmenides. Secondly, they think iga^ 
that if the substratum is one numerically, it must have 
also only a single potentiality ^ — which is a very different 

Now we distinguish matter and privation, and hold that 
one of these, namely the matter, is. not-being only in virtue X 
of an attribute which it has, while the privation in its own j 
nature is not-being ; and that the matter is nearly, in 5! a 
a sense(52)suhstance, while the privation in no sen se is. j/ i 
They, on the other hand, identify their Great and Small 

^ 1. 9. ^ Reading in 1. 26 r\ firj dvai, with E and Simp. 

^ Afe^. Bk. e, and A. 1017* 35-^9. 

* e. g. becoming and plurality. 

^ The imoKeiixivT) cfiv(TiSj cf. 191* y. 

^ The Platonists. 

' That if a thing does not come to be from being, it must come to be 
from not-being. 

^ dwafxei = eiSei above (190^24). In Aristotle's theory, the sub- 
stratum plays a double part. 


alike with not-being, and that whether they are taken 
together as one or separately. Their triad is therefore 
of quite a different kind from ours. For they got so far 

10 as to see that there must be some und^ji^dogiiiature, but 
they make it one — for even if one philosopher^ makes 
a dyad of it, which he calls Great and Small, the effect is 
the same, for he overlooked the other na ture.^ For the 
one which persists is a joint cause, with the form, of what 
comes to be — a mother, as it were.^ But th e negative p art 

15 of the contrariety may often seem, if you concentrate your 
attention on it as an evil agent, not to exist at all. 

For admitting with them that there is something divine, 
good, and desirable, we hold that there ar e t\yg othe r princi- 
ples, the one contrary to it, the other such as of its own 
nature to desire and yearn for it. But the consequence of 
their view is that the contrary desires its own extinction. 

20 Yet the form cannot desire itself, for it is not defective ; 
nor can the contrary desire it, for contraries are mutually 
destructive. The truth is tha t what desires thp fo^pii_i<; 
matter, as the female desires the male and the ugly the 
beautiful — only the ugly or the female not per se but per 

25 The matter comes to be and ceases to be in one sense, 
while in another it does not. As that which contains 
-the privation, it ceases to be in its own nature, for what 
jceases to be — the privation — is contained within it. BuIlbs- 
^potentiality it does not cease to be in its own nature, but is 
necessarily outside the sphere of becoming and ceasing 
to be. For if it came to be, something must have existed 
as a primary substratum fr om which it should come and 

30 which should persist in it ; but this is its own special nature,* 
so that it will be before coming to be. (For my definitio n 
of matter is just this^ he^ .primary, substratum - of each 
thing, from which it comes to be without qualification, and 
which persists in the Result.) And if it ceases to -be it will 
pass into that at the last, so it will have ceased to be 
before ceasing to be. 

* Plato. 2 The privation. ' Cf. Tim, 50 D, 51 A. 

* Reading avrr\i in 1. 30 with I and Phil. 

BOOK I. 9 192 

The accurate determination of the first principle in 
respect of form, whether it is one or many and what it is 
or what they are, is the province of the primary type of 35 
science ^ ; so these questions may stand over till then.^ 
But_of_yie_jiatural^^ forpis we shall speak 19a* 

in the expositions which follow.* 

The above, then, may be taken as sufficient to establish 
that there are principles and what they are and how many 
there are. Now let us make a fresh start and proceed. 

^ Metaphysics or ' First philosophy ' {irpmrj (j)i\oao(l)ia) as it is often 
called. 2 j^^^ ^^ y_^^ 

' Omitting in 1. i rcav after /em, with E Them. Phil. 

* i. e. the remaining treatises of * second philosophy ' ((^uo-ikj;), viz. 
the rest of the Physics^ the De Caelo, De Gen. et Corr., &c. (especially 
De Gen. et Corr. II). 




Of things that exist/ some exist by nature, some from i 
other causes. 

'By nature' the animals and their parts exist, and the 

lo plants and the simple bodies (earth, fire, air, water) — for 
we say that these and the like '^ exist ' by nature '. 

All the things mentioned present a , featur^ in which 
they differ from things which are not constituted by nature. 
Each of them has iif ithi^ it^plf a prtnriple ^ of motion and 

J 5 of Lstationariness (in resp^ rt ^^ piar^ or x>f_growt h and 
decrease, nr b y way c^^ 7\\ \er7\\\c)r\\ On the Other hand, 
a bed and a coat and anything else of that sort, qua 
receiving these designations — i.e. in so far as they, are 
products of<^rK-haye no innate impulse to change. \But 
in so far as they happen to be composed of stone , or 

20 of earth or of a mixture of the two, they d.o haye_such 

9 an impulse,* and just to that extent — which seems to . 
indicate that nature is a source or cause of being moved I 
and of being at rest in that to zvhich it belongs primarily^ \ 
in virtue _ of itself and not in virtue of a coijcomitant 

I say * not in virtue of a concomitant attribute ', because^ac 
(for instance) a man who is a doctor might cure himself. 
Nevertheless it is not in so far_as,he is a patient that he 

35 possesses the art of medicine: Jt merely has happened that 
the same man 4s doctor and patient — and that is why these 
attributes are not always found together. So it is with all 
other artificial products. None of them has in itself the 
source of its own production. But while in some cases 
(for instance houses and the other products of manual 

^ ra ovra = substances, which consist of matter and form. Such of 
them as exist by nature {cf)v(ns) are the objects of Physical Science. 

* Inorganic compounds are included (1. 20). 

' Reading in 1. 13 f. tovtuv /xev yap cKaarov ev eaurto dpxrfP ex^'j with 
EAl. Them. Phil. 

* A bed, e. g., tends to fall to the ground or to rest there, not gua 
bed, but gua made of a heavy material. 

BOOK II. I 19a*' 

labour) that principle is in something else external to the 
thing,(Jn others— those "which may cause a change in them- 30 
selves in virtue of a concomitant attribute — it lies in the 
things themselves (but not in virtue of what they are).} 

* Nature ' then is what has been stated. Things * have 
a nature' which have a principle of this kind. Each of/ 
them is a substance ; for it is a subject,^ and nature always 
implies a subject in which it inheres. 

The term 'according to nature' is applied to all these 35 
things and also to the attributes which belong to them in 
virtue of what they are, (for instance the property of fire 
to be carried upwards — which is not a 'nature' nor 'has 
a nature ' but is ' by nature ' or ' accordmgjojiatuj:^ ',) 

IS^_ nature is, then, and the meaning of the terms 193* 
'by nature' and 'according to nature', has been stated. 
That nature exists, it would be absurd to try to prove ; for 
71 is oIdvious tliat there are many things of this kind, and 
to prove what is obvious by what is not is the mark of 5 
a man who is unable to distinguish what is self-evident 
from what is not. (This state of mind is clearly possible. 
A man blind from birth might reason about colours. Pre- 
sumably therefore such persons must be talking about 
words without any thought to correspond.) 
V Some identify the nature or substance of a natural object 
with that immediate cons tituent of it which taken by itself 10 
is without arrangement, e. g. the wood is the ' nature ' of >^" 
the bed, and the bronze the ' nature' of the statue.) 

As an indication of this Antiphon points out that if you 
planted a bed and the rotting wood acquired the power of 
sending up a shoot^ it would not be a bed that would come.^ 
up, but wood'^ — which shows that the arrangement in ' 
accordance'with the rules of the art is merely an incidental 15 
attribute, whereas the real nature is the other, which, 
further, persists continuously through the process of 

But if the <Tfiateria) of each of these objects has itself 


^ Placing a comma after n in 1. 34. 
2 Cf. Antiphon, fr. 15 Diels. 


the same relation to something else, say bronze (or gold) 

3o to water, bones (or wood) to earth and so on, that (they 
say) would be their nature and essence. Consequently 
some assert earth, others fire or air or water or some or alt 
of these, to be the nature of the things that are. For 
whatever any one of them supposed to have this character — 
whether one thing or more than one thing — this or these 

25 he declared to be the whole of substance, all else being its 
affections, states, or dispositions. Every such thing they 
held to be eternal (for it could not pass into anything else), 
but other things to come into being and cease to be times 
without number. 

This then is one account of ' nature ', namely that it is 
the imtTiediatejiiateriaL_substratum_pf things which have 
in themselves a principle of motion or change. 

30 Another account is that 'nature' is^the shape or for rai 
which is specified in the definition of the thing. 

For the word ' nature ' is applied to what is according to 
nature and the natural in the same way as ' art ' is applied to 
what is artistic or a work of art. We should not say in the 
latter case that there is anything artistic about a thing, if it 
is a bed only potentially, not yet having the form of a bed^; 

35 nor should we call it a work of art. The same is true of 
natural compounds. What is potentially flesh or bone has 
not yet its own ' nature ', and does not exist ' by n^ture^ 
193^ until it receives the form specified in the definition, which 
we name in defining what flesh or bone is> Thus in the 
second sense of ' nature ' it would be the shape or form 
(not separable except in statement) of things which have 
5 in themselves a source of m.otion. (The combination 
of the two, e. g. man, is not ' nature ' but ' by nature ' or 
' natural '.) 

The form indeed is ' nature ' rather than the matter ; for 

a tiling is more properly said to be what it is when it has 

"^ attained to fulfilment than when it exists potentially. 

Again man is born from man, but not bed from bed. That 

is why people say that the figure is not the nature of a bedy 

lobut the wood is — if the bed sprouted not a bed but wood 
would come up. But even if the figure fy art, then on the 

BOOK II. I 193^ 

same principle the shape d man is his nature. For man is 
born from manT^ 

We also speak of a thing's nature as being exhibited in 
the j[>rot^pgs. ^f gr owth ^ by which its nature is attained. 
Thjg 'nature' in this sense is not like 'doctoring', which 
leads not to the art of doctoring but toTiealth. Igogoring 15 
must start from the art, not lead to it. But it is not in 
this way that nature (in the one sense) is related to nature 
(in the other). What grows qua growing ^ grows from 
something into something. \^nto what then does it grow ? 
Not mto that from which it arose but into that to which it 
tends.) The shape then is nature. 

1 'Shape' and 'nature', it should be added, arejused in 
two senses. For the pdmlion tTin i'j in a way form BuT 30 
whether in unqualified coming to be there is privation, i. e. 
a contrary to what comes to be, we must consider later.^ 

2 We have distinguished, then, the different ways in which 
the term 'nature' is used. 

The next point to consider is how the rnathem ^t , irian 
differs from the physicist.^ Obviously physical bodies 
contain surfaces and volumes, lines and points, and these 
are the subject-matter of mathematics. 

Further, is astronomy^ different from physics or a depart- 25 
ment of it? It seems absurd that the physicist should be 
supposed to know the nature of sun or moon, but not to 
know any of their essential attributes, particularly as the 
writers on physics obviously do discuss their shape also 
and whether the earth and the world are spherical or not. 30 

Now the mathematician, though he too treats of these 
things,'' nevertheless d oes not treat of them as the j imits 
qf^,,a.-^hy§icalbody ; nor does he consider the attributes 
indicated as the attributes of such bodies. That is why 
he (s6para tes^iem ; for in t^^'^f^ t^^y are sppRiaH^ from — - 
motion , anoit makes no difference, nor does any falsity 

^ Cf. Metaphysics, 1014^ 16. '"The coming to be of growing 
things ", as if the v in <^\j(jii were long ' (as it is in ^uo/xai). 
^ Reading in 1. 17 .^, with E and Them. 

' De Gen. et Corr. i. 3. * Or student of nature {(^vaiKo^). 

* Reading in ]. 25 crt d ^, with Susemihl. ^ Surfaces, &c. 


'35 result, if they are separated. The holders of the theory of 

Forms do the same, though they are not aware of it ; for 

they separate the objects of physics, which are less separable 

194^ than those of mathematics. This becomes plain if one 

tries to state in each of the two cases the definitions of the 

things and of their attributes. ' Odd ' and ' even ', ' straight ' 

-)^ and ' curved ', and likewise ' number ', * line ', and ' figure ', 

5 jo not involve miction; not so 'flesh' and 'bone' and 

'man ' — ^/lese are defined like ' snub nose ', not like ' curved). 

Similar evidence is supplied by the more physical of 

the branches of mathematics, such as optics, harmonics, 

and astronomy. These are in a way the converse of 

geometry. While ^ geometry investigates physical lin es 

10 but not qua physica l, optics investigates mathematical 

Ijnes, bu^ f ^//y phy.sJrill) not qua mathematical. 

Since ' nature ' has two senses, the fomj and the Qi^er, 
' we must investigate its objects as we would the essence of 
snubness. That is, such things are neither independent 
of matter nor can be defined in terms of matter only^ 
15 Here too indeed one might raise a difficulty.^ Since 
there are two natur es, with which is the physic ist_con- 
cerned ? Or should he investigate the combination of 
the two ? ^ But if the combination of the two, then also 
each severally. Does it belong then to the same or to 
different sciences to know each severally ? 

If we look at.the ancients, physics would seem to be 
30 concerned with the iii^Ur. (It was only very slightly 
that Empedocles and Democritus touched on the forms 
r^^ and the essence.) 

But if on the other hand art imitates nature, and it is 
the part of th e_ same dis £ipliae_J:o know the form and the ^ 
matt er up to a point (e. g. the doctor has a knowledge of ^ 
health and also of bile and phlegm, in which health is ^ 
realized, and the builder both of the form of the house and 
2^ of the rnat ter, namely that it is bricks and beams, and so 

^ Reading in 1. 9 77 fxeu yap yea>fjL€Tp(a, with E^ F Simp. 
2 Omitting dix^s in 1. 15, with E^ Them. Phil. Simp. 
^ Putting a full-stop after ^yo-iKoO in 1. 16, and a mark of interroga- 
tion after the first dfi^olv in 1. 17. 

BOOK II. 2 194^ 

forth) : if this is so, it would-be the pa rt of physics also to. 
know nature in both its senses, n 

Again, ' thatTor the sake of which ', or thepnA belongs ' 

to the same department of knowledge as the means! But 

i^ the jjaturfiL-is^-lhe-end or 'that. for the sake of which '. 

For if a thing undergoes a continuous change and there is 

a stage which is last, this stage is the end ^ or ' that for 

the sake of which '. (That is why the poet ^ was carried 3° 

away into making an absurd statement when he said ' he 

has the end ^ for the sake of which he was born '. For notj 

every stage that is last claims to be an end, but only that / 

which is best.) j ^ 3 

j (For * the arts make their material (some simply * make * 

it, others make it serviceable), and we use everything 

as if it was there for our sake. (We also are in a sense 35 

an end. 'That for the sake of which' has two senses: 

the distinction is made in our work Ou Philosophy.^) 

The^arts^ therefore, which govern the matter and have 

knowledge ^ are two, namely the .art which uses the 194'' 

product and the art which directs the production of it^ . 

That is why the using art also is in a sense directive ; but 

it differs in that it knows the form/ whereas the art which 

is directive as being concerned with production knows the « 

matter. For the helmsman knows and prescribes what 5 

sort of form a helm should have, the other from what 

wood it should be made and by means of what operations. 

In the products of art, however, we jnake^the material 

with a view to the function, whereas in the products of 

nature the matter is there all along>, 

Again, matter is a relative terni : to each form there 

corresponds a special matter. How far then must the 

physicist know the form or essence ? Up to a point, 10 

perhaps, as the doctor must know sinew or the smith 

' Reading in 1. 29 f. n eo-;^arov r/js Kij/^o-fco?, rovro reXos (Alexander's 

2 An unidentified comic poet (Kock, Com. Att. Fr. iii, p. 493). 

^ i. e. death. 

* Placing a full stop before eVei in 1. 33. 

^ i. e. in the dialogue De Philosophia, 

^ Reading in 1. i koi yi/copiXouorai, with F and Phil. 

' Omitting 17 apxi-r^KToviKr] in 1. 4, with PrantP. 

64616 D 


bronze (i.e. until he understands the purpose of each): 
and^ the p hysicist is concerned only ^ifh f ^i'^gg -yyVirx^p 
form s are separable jjHf^f^d^ bni- r\n nnt ^vi^i- apa rt from 
jnaJXei^— Man is begotten by man and by the sun as well. 
The mode of existence andjessence of the separable it is j 
15 the business of the primary type of philosophy^ to define. ^ 

Now that we have established these distinctions, we 3 
must proceed Jo consider causeSj^ their character and 
number. Kno wledge is the object of our inquiry, and men 
do not think they know a thing till they ihave grasped ,th £L 
2Q_1^V^ of it (which is to grasp its primary cau se).^ So 
clearly we * too must do this as r ej^ards t^ pth rnmin[^ to bn 
^i^d^P^^'^^'^g awqy pnH f-vf-ry VJnd_^f physical change, in 
order that, knowing their principles, we may try to_ refer 
to these principles each of our problems. 

In ^ one sense, then, (i) that out of which a thing comes 
to be and which persists, is called ^^anse ', e. g. the bronze 
25 of the statue, the silver of the bowl, and the genera of 
which the bronze and the silver are species. 
^ In another sense (2) the form or the archetype, i. e. the 
statement of the essence, and its genera, are called ' causes ' 
(e.g. of the octave the relation of 2 : i, and generally 
number),^ and the parts in the definition. 

Again (3) the primary source of the change or coming 

30 to rest ; e. g. the man who gave advice is a cause, the father 

is cause of the child, and generally what makes of what is 

\ made and what causes change of what is changed. 

Qj}A Again (4) in the sense of end or ' that for the sake of 

which' a thi ng is done , e.g. health Js the cause of walking 

about. ('Why is he walking about?' we say.*^ * To be 

healthy ', and, having said that, we think we have assigned 

^ Reading in 1. 11 f. tov — rivos . . . cKaa-rov — Kai, with Jaeger. 

^ i.e. not of natural philosophy, but of metaphysics. Cf. M^f, Z. 

^ The proximate cause, which is primarily responsible for an 

* i. e. natural philosophers. 

* 194'' 23-195^ 21 is repeated almost verbatim in Met. A. 2. 

* Treating olov . . . opi^/zoy in 11. 27-8 as parenthetical. 
' Placing a full stop after ^a/xei/ in 1. 34. 

BOOK II. 3 194^ 

the cause.) The same is true also of all the intermediate 35 
steps which are brought about through the action of 
something else as means towards the end, e.g. reduction 
of flesh, purging, drugs, or surgical instruments are means 
towards health. AUjhese things are ' for the sake of the 195^ 
end, though they differ from one another in tha^ some are 
activities, others instruments. 

This then perhaps exhausts the number of ways in which 
the term ' cause ' is used. 

As the word has several senses, it follows that there^re 
several _causes of the same th ing, (not merely in virtue of 
a concomitant attribute), e.g. both th e jrt of the sculptor s 
and the bronze are^causes of the statue^ These are causes 
of the statue qua statue, not in virtue of anything else that 
it may be — only not in the same way, the one being the 
material cause, t he other the cause whence the motion 
comes. ^Some things cause each other reciprocally , e.g. 
hard work caiises^ fitness and vtce^versa, but again not_ in 10 
the same way, but the one ascend, the other as the origin 
of change. Further thi same thing is the cause of contrary 
results. For that which by its presence brings about one 
result is sometimes blamed for bringing about the contrary 
by its absence. Thus we ascribe the wreck of a ship to 
the absence of the pilot whose presence was the cause of 
its safety?) 

J All the causes now mentioned fall into four familiar 15 
divisions.^ The letters are the causes of syllables, the 
material o f artificial products, fire, &c., of bodies, the^parts 
of the whole, and the premisses of the conclusion, in the 
sense of ' that from which '. Of these pairs the one set are 15.; - - ( 
causes in the sense of substratum, e ^g. the parts, the other 20 ^^-^^ 
set in the sense of essence-— the^ whole and the coniBmajEioh 
and tEeJorm".' EuTThe seed and^e doctor and the -^-^- x^ , 
adviserpan3~^enerally the maker, are all source s whence 
the_cha nge or statjonariness__ongInates,^ ~while the others 
are causes in the sense of the end or t he good o f the, rest ; 
for ' that for the sake of which ' means what is best and 

^ Reading in 1. 15 rpdrrou?. Bekker's tottovs is a misprint. 
' Omitting in 1. 23 JJ Kivrjo-cas, with E and Mef. 1013^ 25. 

D 2, 


35 the end of the things that lead up to it. (Whether we 
^ay the ' goodMtsel£'^or the ' apparent good ' makes no 

,. dlfferencej ""^^ •- — -^ 

Such then is the number and nature of the kinds of 

Now the modes of causation\ are many, though when 

brought under heads they too can be reduced in number. 

For ' cause ' is used in many senses and even within the 

3D same kind one may be p^rior to another (e.g. the doctor 

and the expert are causes of health, the relation 2 : i and 

. j^ number of the octave), and always what is inclusive to 

^v!> ^^ what is particular. Another mode of causation is tlie 

incidgptal and its genera, e.g. in one way ' Polyclitus ', in 

another * sculptor ' is the cause of a statue, because ' being 

35 Polyclitus ' and ' sculptor ' are incidentally conjoined. Also 

the classes in which the incidental attribute is included ; 

thus ' a man ' could be said to be the cause of a statue or, 

195 generally, ' a living creature '. An incidental attribute too 

may be more or less remote, e. g. suppose that * a pale 

man ' or * a musical man ' were said to be the cause of the 


All causes, both proper and incidental, may be spoken 

^ of either as pojtdntial or as actu al ; e. g. the cause of a house 

\ being built is either ' house-builder ' or ' house-builder 


A Similar distinctions can be made in the things of which 

^ the causes are causes, e.g. of * this statue ' or of ' statue ' or 

of * image ' generally, of ' this bronze ' or of ' bronze ' or of 

* material * generally. So too with the incidental attributes. 

10 Again we may use a complex expression for either and 

say, e.g., neither ' Polyclitus ' nor ' s.culptor ' but ' Polyclitus, 

sculptor '. n 

All these various uses, however, come toiLsi^ in 
number, under each of which again the usage is twofold." 
5a 1> Cause means either what is particular or a genus^ or an 
15 incidental attribute or a genus of that, and these either as 
a complex or each by itself; and all six either as actual or 
as potential. The difference is this much, that causes 
which are actually at work and particular exist and cease 

BOOK II. 3 195** 

to^fi^ist simultaneously with their effect, e.g. this healing 
person with this being-healed person and that housebuilding 
man with that being-built house ; but this is not always 
true of potential causes — the house and the housebuilder 30 
do not pass away simultaneously. 

In investigating the cause of each thing it is always 
necessary to seek what is most precise (as also in other 
things) : thus man builds because he is a builder, and a 
builder builds in virtue of his art of building. This last 
cause then is prior : and so generally. 

Further, generic effects should be assigned to generic 25 
causes, particular effects to particular causes, e.g. statue to 
sculptor, this statue to this sculptor ; and powers are 
relative to possible effects, actually operating causes to 
things which are actually being effected. 

This must suffice for our account of the number of causes 
andjthe modes of causation* 30 

4 But chance., also and spoijjtaneity are reckoned among Ij/ 
causes : many things are said both to be and to come to^ C 
be as a result of chance and spontaneity. We must inquire ^^ 

therefore in what manner chance and spontaneity are C ^^ 

present among the causes enumerated, and whether they 
are the same or different, and generally what chance and 35 
spontaneity are. 

Some people ^ even question whether they are real or 
not. They say that nothing happens by chance, but that 196* 
everything which we ascribe to chance or spontaneity has 
some definite cause, e.g. coming * by chance' into the 
^market aii3nrn3Tng there a man whom one wanted but did 
not expect to meet is due to one's wish to go and buy in 
the market. Similarly in other cases of chance^ it is 5 
always possible, they maintain, to find something which is ^ 
the cause ; but not chance, for if chance were real, it would 
seem strange indeed, and the question might be raised, 
Why on earth none of the wise men of old in speaking of 
the causes of generation and decay took account of chance ;^ T 

^ Apparently Democritus is meant. Cf. Diels, Vors^ ii. 29. 3-1 1. 
'^ Omitting Xeyofiipap in 1. 6 with E^ 



lo whence it would seem that they too did not beh'eve that 
anything is by chance. But there is a further circumstance 
that is surprising. Many things both come tojbe and are 
by chance and spontaneity, and although al l know^t hat 
each of them can be ascribed to some c^ ^se (a s the old 

15 argument^ said which denied chance), nevertheless th ey 
speak of some of these things as happening by chance and 
others not. For this reason also they ought to have at 
least referred to the matter in some way or other. 

Certainly the early physicists found no place for chance 
among the causes which they recognized— love, strife, 
mind, ifire, or the like. This is strange, whether they 
supposed that there is no such thing as chance or whether 

20 they thought there is but omitted to mention it — and that 
too when they sometimes used it, as Empedocles does 
when he says that the air is not always separated into the 
highest region, but 'as it may chance'. At any rate he 
says in his cosmogony that ' it happened to run that way 
at that time, but it often ran otherwise.* ^ He tells us also 
that most of the parts of animals came to be by chance. 

25 There are some ^ too who ascribe this heavenly sphere 
and all the worlds^ io sp ontaneity. They say that the 
vortex arose spontaneously, i. e. thelnotion that separated 
and arranged in its present order all that exists. This 
statement might well cause surprise. For they are asserting 
tha t chance is not responsible forJ :he existence or generation 

30 of animals and plants, na ture or jnind ox something of the 
ki nd being the cause of them ( for it is not any chance 
thing that comes from a given seed but an olive from one 
kind and a man from another) ; and yet at the samejtirne 
they assert that the heavenly sphere ahdThe divinest of 
visible things^arose.S2.ontaneously, having no such cause as 

35 is assigned to animals and plants. Yet if this is so, it is 

a fact which deserves to be dwelt upon, and something 

196^ might well have been said about it. For besides the other 

absurdities of the statement, it is the more absurd that 

•— — — .^ 

1 Cf. 11. 1-7. 2 Pj.. 53. 

' Apparently Democritus is meant. Cf. Simplicius 331. 16. 

* Reading in 1. 25 Koa-ficov, with E Phil. Simp. 

BOOK II. 4 196'' 

people should make it when they see nothing coming to be 
spontaneously in the heavens, but much happening by 
chance among the things which as they say are not due 
to chance ; whereas we should have expected exactly the 

Others ^ there are who, indeed, believe that chance is 5 
a cause, but that it is inscrutable to human intelligence, as 
Jaeing a divine thing and full of mystery. 

Thus we must inquire what chance and spontaneity are, 
whether they are the same or different, and how they fit 
into our division of causes. 

5 First then we observe that some things always come to 10 
pass in the same way, and others for the most part.** It is 
clearly of neither of these that chance is said to be the 
cause,^ nor can [the 'effect of chance' be identified with 
any of the things that come to pass by necessity and 
always, or for the most gart.^ But as there is a third class 
of events besides these two — events which all say are ' by 
chance ' — it is plain that there is such a thing as chance and 
spontaneity ; for we know that things of this kind are due ^5 
to chance and that things due to chance are of this kind. 

But, secondly, some events are for the sake of something, . 

others not. Again, some of the former class are in accor- ^vL^ 
dance with deliberate intention, others not, but both are in ' ^ 
the class of things which are for the sake of something. 
Hence it is clear that even among the things which are 20 
outside the necessary and the normal,^ there are some in 
connexion with which the phrase ' for the sake of some- 
thing ' is applicable. (Events * that are for the sake of some- 
thing include whatever may be done as a result of thought 
or of nature.) Things of this kind, then, when they come to 
pass incidentally are said to be ' by chance '. For just as a 
thing is something either in virtue of itself or incidentally,^ 25 

^ Democritus, cf. Diels, Vors.^ ii. 29. 21-6. 
^ Reading in 11. 11, 13, 20 «? eVi t6 no\v, with I. 
' Putting a comma after Xeyerai, not after tvxv^, in 1. 12. 
* With 11. 21-5 cf. Me/. 1065^26-30. 

^ A may ' be ' B, either because it is A or because A is casually 
conjoined with some other attribute of the subject which is B. 


so may it be a cause. For instance, the housebuilding 

faculty is in virtue of itself the cause of a house, whereas 

the pale or the musical^ is the incidental cause. That 

which \s per se cause^of the effect is determinate, but the 

incidental cause is indeterminable, for the possible attributes 

of an individual are innumerable. To resume then ; when 

30 a thing of this kind comes to pass among events which are 

for the sake of something, it is said to be spontaneous or by 

chance. (The distinction between the two must be made 

later ^ — for the present it is sufficient if it is plain that both 

are in the sphere of things done for the sake of something.) 

Example : A man is engaged in collecting ^ subscriptions 

for a feast. He would have gone to such and such a place 

for the purpose of getting the money, if he had known. He 

35 actually went there for another purpose, and it was only 

incidentally that he got his money by going there * ; and 

this was not due to the fact that he went there as a rule or 

197^ necessarily, nor is the end effected (getting the money) 

a cause present in himself — it belongs to the class of things 

^ that are intentional and the result of intelligent deliberation. 

. It is when these conditions are satisfied that the man is 

said to have gone ' by chance '. If he had gone of deliberate 

purpose and for the sake of this — if he always or normally 

went there when he was collecting payments — he would 

not be said to have gone ' by chance '. 

5 It^ is clear then that chance is an incidental cause 

in the sphere of those actions for the sake of something 

which involve purpose. Intelligent reflection, then, and 

chance are in the same sphere, for purpose implies intelligent 

reflection. . 

It is necessary, no doubt, that the causes of what comes 

to pass by chance be indefinite ; and that is why chance is 

supposed to belong to the class of the indefinite and to be 

10 inscrutable to man, and why it might be thought that, in 

a way, nothing occurs by chance. For all these statements 

^ Incidental attributes of the housebuilder. ^ In ch. 6. 

' Reading in 1. 34 /co/xt^o'/Mfj/o?, with E^. 

'^ Omitting in 1. 35 rov KOfxicraadai evcKa, with Bonitz. 

^ With 11. 5-14 cf. Me^. 1065* 30-5. 

BOOK II. 5 197 

are correct, because they are well grounded. Things do, in 
a way, occur by chance, for they occur incidentally and 
chance is an mcidental cause. But strictly it is not the 
cause — without qualification — of anything ; for instance, a 
housebuilder is the cause of a house ; incidentally, a flute- 
player may be so. 

And the causes of the man's coming and getting the 15 
money (when he did not come for the sake of that) are 
innumerable. He may have wished to see somebody or 
been following somebody or avoiding somebody, or may 
have gone to see a spectacle.^ Thus to say that chance is 
a thing contrary to rule is correct. For ' rule ' applies to 
what is always true or true for the most part, whereas chance 
belongs to a third type of event. Hence, to conclude, since ao 
causes of this kind ^ are indefinite, chance too is indefinite. 
(Yet in some cases one might raise the question whether 
any incidental fact might be the cause of the chance 
occurrence, e. g. of health the fresh air or the sun's heat ^ 
may be the cause, but having had one's hair cut cannot) 
for some incidental causes are more relevant to the effect 
than others.) 

Chance * or fortune is called ' good ' when the result is 25 
good, ' evil ' when it is evil. The terms * good fortune' and 
* ill fortune ' are used when either result is of considerable 
magnitude. Thus one who comes within an ace of some 
great evil or great good is said to be fortunate or unfortu- 
nate.^ The mind affirms the presence of the attribute, 
ignoring the hair's breadth of difference. Further, it is with 30 
reason that good fortune is regarded as unstable ; for chance 
is unstable, as none of the things which result from it can 
be invariable or normal. 

Both are then, as I have said, incidental causes — both 
chance and spontaneity — in the sphere of things which 
are capable of coming to pass not necessarily, nor normally, 

* Reading in 1. 17 (pevyav kqI Ofaa-ofxevos, with Simp. 
^ I. e. incidental causes. 

^ Reading in 1. 23 eiXr/o-ty, with Simp. 

* With 11. 25-7 cf. Met. 1065*35-^1. 

^ Reading in 1. 28 rj evrvxelv ^ drvx^^^v, with E and Simp. 



35 and with reference to such of these as might come to pass 
for the sake of something. 

They differ in that ' spontaneity ' is the wider term. 6 
Every result of chance is from what is spontaneous, but not 
everything that is from what is spontaneous is from chance. 
197^ Chance and what results from chance are appropriate to 
agents that are capable of good fortune and of moral action 
p^yrv't.* J generally. Therefore necessarily chance is in the sphere of 
M moxal actions. This is indicated by the fact that good for- 
tune is thought to be the same, or nearly the same, as 
happiness, and happiness to be a kind of moral action, 
5 since it is well-doing. Hence whatjs not-X^ able of moral 
action_caj}iioLdo_ajniyJ^ Thus an inanimate 

J thing or a lower animal or a child cannot do anything by 
^ } chance, because it is incapable of deliberate in tention ; nor 
** i: can ' good fortune ' or * ill fortune ' be ascribed to them, 
, ^ except metaphorically, as Protarchus,^ for example, said 
iAy^ of that the stones of which altars are made are fortunate 
^* TO because they are held in honour, while their fellows are 
trodden under foot. Even these things, however, can in 
a way be affected by chance, when one who is dealing with 
them does something to them by chance, but not otherwise. 
The spontaneous on the other hand is found both in the 
T5 lower animals and in many inanimate objects. We say, 
for example, that the horse came ' spontaneously ', because, 
though his coming saved him, he did not come for the 
sake of safety. Again, the tripod fell ^ ' of itself, because, 
though when it fell it stood on its feet so as to serve for 
a seat, it did not fall for the sake of that. 

Hence it is clear that events which (i). belong to the 
general class of things that may come to pass for the sake 
of something, (2) do not come to pass for the sake of what 
actually results, and (3) have an external cause, may be 
20 described by the phrase ' from spontaneity '. These ' spon- 
taneous ' events are said to be * from chance ' if they have 
the further characteristics of being the objects of deliberate 

^ Probably the reference is to the Protarchus described as a pupil 
of Gorgias in Plat. PkiL 58 A. Cf. Zeller, FM. d. Gr., i.^ 1323, n. 4. 
^ i. e. on its feet. 

BOOK II. 6 197^ 

intention and due to agents capable of that mode of action. 
This is indicated by the phrase ' in vain', which is used 
when A, which is for the sake of B, does not result in B, 
For instance, taking a walk is for the sake of evacuation of 
the bowels ; if this does not follow after walking, we say- 
that we have walked ' in vain ' and that the walking was 
' imin '. This implies that what is naturally the means to 25 
an end is ' in vain ', when it does not effect the end towards 
which it was the natural means — for it would be absurd for 
a man to say that he had bathed in fain because the sun 
was not eclipsed, since the one was not done with a view 
to the other. Thus the spontaneous is even according to 
its derivation the case in which the thing itself happens 
in vain.^ The stone that struck the man did not fall for 30 
the purpose of striking him ; therefore it fell spontaneously, 
because it might have fallen by the action of an agent and 
for the purpose of striking. /The difference between spon- 
taneity and what results by chance ^ is greatest in things 
that come to be by nature ; for when anything comes to be 
contrary to nature, we do not say that it came to be by 
chance, but by spontaneity. Yet strictly this too is differ- 35 
ent from'the spontaneous proper ; for the cause of the latter 
is external, that of the former internal. 

We have now explained what chance is and what spon- 198* 
taneity is, and in what they differ from each other. Both 
belong to the mode of causation ^ * source of change ', for 
either some natural or some intelligent agent is always the 
cause ; but in this sort of causation the number of possible 
causes is infinite. 

Spontaneity * and chance are causes of effects which, 
though they might result from intelligence or nature, have 
in fact been caused byvsomething incidentally. Now since 
nothing which is incidental is prior to what is per se, it 
is clear that no incidental cause can be prior to a cause 
per se. Spontaneity and chance, therefore, are posterior to 

^ There is no parallel in English for this false derivation. 

^ Reading in 1. 33 rov, with E and Phil. 

^ Reading in 1. 2 t^? 8' aiTlas rcbv TpoTrcov, with E. 

* With 11. 5-13 cf. Met. 1065^ 2^4. 


lo intelligence and nature. Hence, however true it may be 
that the heavens are due to spontaneity, it will still be true 
that intelligence and nature will be prior causes ^ of this 
All 2 and of many things in it besides. 

^^' It is clear then that there are causes, and that the 7 

15 number of them is what we have stated. The number is 
the same as that of the things comprehended under the 
question ' why \ The ' why ' is referred ultimately either 
(i), in things which do not involve motion, e. g. in mathe- 
matics, to the ' what ' (to the definition of ' straight line ' 
or * commensurable,!,; &c.), or (2) to what initiated a motion, 
e.g. 'why did they go to war?— because there had been 

20 a raid ' ; or (3) we are inquiring ' for the sake of what ? ' — 
* that they may rule ' ; or (4), in the case of things that 
come into being, we are looking for the matter. The caus es, 
therefore, are these and so many in number. 

Now, the causes being four , i t is the business of the 
physicist to know about them all, and if he refers his 
problems back to all of them, he will assign the * why ' in 
the way proper to his science — the mattei*, the form, the 

25«.movei-, ' that for the s ake of w hich \ The last three often 
coincide ^ ; for the ' what 'and * that for the sake ofwhich ' 
are one, while the primary source of motion is the same in 
species as these * (for man generates man), and so too, in 
general, are all things which cause movement by being therrr-^ 
selves moved ; and such as are not of this kind are no longer 
Inside the province of physics, for they cause motion not 
-7 t)y possessing motion or a source of motion in themselves, 
but being themselves incapabk of motion. Hence there 

30 are tji ree branche s of study, one^^o£jhings which a re 
incapable ot motion,*" the s'econd of things in motion, but 
indestructible,^ the third of.d.estruc_ti_Ule things.^ 

^ Reading in 1. 12 vovv oltiou koi <j)v(ni/ elvai with FI Simp. 
^ Reading in 1. 13 rod ttuvtos, with Fl Them. Phil. Simp. 

* Reading in 1. 25 eh ev, with Them, and Simp. 

* They are different individuals, 

^ Reading in 1. 30 aKivryrfnv^ with E and Phil. 
^ Reading in 1. 30 f. Kivovfiepcov ixh a^BapTcav, with E^ and Phil. 
■^ (2) and (3) belong to physics, (i) to pliysics only in so far as such 
things are the cause of motion. 



BOOK 11. 7 198* 

r The question ' why \ then, is answered by reference to 
(the matter, to the form, and to the primary moving cause. 
I For in respect of coming to be it is mostly in this last way 
<f that causes are investigated — ^y^^iatcomesjQ be after what ^^ 
\ what was the primary agent or patient ? ' and so at each 
step of the series. 

vNow the principles which cause motion in a physical 35 
way -are two, of which one is not physical, as it has no 
principle of motion ^ in itself. Of this kind is whatever 198^ 
causes movement, not being itself moved, such as (i) that 
which is completely unch ang eable, the primary reality, and 
(2) the essence of that which is coming to be^ i. e. thejonn ; 
for this is the end or ' that for the sake of which '. Hence 
since natuie-is-for the sake of something, we must knov/ this 
cause also. We must explain the \why ' in all the senses of 5 
the term, namely, (i) that from, this that will necessarily 
result r from this ' either without qualification or in most 
cases) ; (2) that * this must be so if that is to be so ' (as the 
conclusion presupposes the premisses) ^ ; (3) that this was 
the essence of the thing ; and (4) because it is better thus 
(not without qualification, but with reference to the essential 
nature in each case). 

8 We must explain then (i) that Nat ure, belongs to the 10 
^class^of^caoisas^which^act Jorthe^ (2) 

about the nec^ssa xY ^nd its place in physica l jH'oblgmg, for 
all writers ascribe things to this cause, arguing that since 
the hot and the cold, &c., are of such and such a kind, 
therefore certain things necessarily are and come to be — 
and if they mention any other cause (one ^ his ' friendship 15 
and strife ', another* his * mind '), it is only to touch on it, 
and then good-bye to it. 

A difficulty presents itself: why should not nature wor k, 
not for the sake of something, nor because it is better so, 
but just as the sky rains, not in order to make the corn 
grow, bjut^f necessity ? What is drawn up must cool, and 

^ i. e^no capacity of being itself moved. 

"^ i.e. the material cause or the condicio sine qua non\ cf. 195* 
^ Empedocles. * Anaxagoras. 



20 what has been cooled must become water and descend, the 
result of this being that the corn grows. Similarly if a 
man's crop is spoiled on the threshing-floor, the rain did 
not fall for the sake of this— in order that the crop might 
be spoiled — but that result just followed. Whj^^en should 
it not be the same wi th the parts in nature, e. g. tliat our 
teeth should come up of necessity— Xh^ front teeth sharp, 

35 fitted for tearing, the molars broad and useful for grinding 
down the food — since they did not arise for this end, but it 
was merely a coincident result ; and so with all other 
parts in which we suppose that there is purpose ? Wherever 
then all the parts came about just what they would have 

30 been if they had come to be for an end, such things sur- 
vived, being organized spontaneously in a fitting way ; 
whereas those which grew otherwise perished and con- 
tinue to perish, as Empedocles says his ' man-faced ox- 
progeny' did.^ 

Such are the ^argumants ( and others of the kind) which 
may cause difficulty on this point. Yet it is Jmpos slide 
th at this sho uld be th e true view. v For teeth and all other 

35 natural things either invariably or normally come about in 
a given way ; but of not one of the results of chance or 
spontaneity is this true. We do not ascribe to chance or 
199* mere coincidence the frequency of rain in winter, but fre- 
quent rain in summer we do; nor heat in the dog-days, 
but only if we have it in winter. If then,. it is agreed that 
things are either the result of coincidence or for an end , 
and these cannot be the result of coincidence or spontaneity, 
5 it follows that they must be for an end ; and that such 
things are all due to nature even the champions of the 
theory which is before us would agree. Therefore a ction 
for an end is _present in thi ngs which comeJLo_Jb£_and are_ 
b y nature . 

Further, where a series has a co mple tion, all the pre- 
ceding steps are for the sake of that. Now surely as in 
- ri4 . 10 intelligent action, so in nature ; and as in nature, so it is in 
' each action, if nothing interferes.^ Now intelligent action 

^^^ ^ Fr. 61. 2. 

CUa^o^ ^ Reading in 11. 9-1 1 ovkow . . . (unodiCrj ; with Susemihl. 

BOOK II. 8 199* 

is for the sake of an end ; therefore the nature of things 
'also is so.^ Thus if a house, e.g., had been a thing made 
Iby nature, it would have been made in the same way as it 
is now by art ; and if things made by nature were made 
^ also by art, they would come to be in the same way as by 
nature. Each s tep then in the series is for the gake of the 1 5 
ftext_; and genprally prt part ly CQ^ £letes what nature 
cannot Jbring. to _a finish, and partly imitatgs her. If, 
therefore, artificial product^are for the sake of an end, so 
clearly also are natural products. The relation of the later 
to the eariier terrns of the series is the same in both. 

This is most obvious in th e animals other than man : 30 
they make things neither by art nor after inquiry or delibe- 
ration. Wherefore people discuss whether it is by intelli- 
gence or by some other faculty that these creatures work, 
— spiders, ants, and the like. By gradual advance in this 
direction we come to see clearly that in plants too that is_ 
pro duced which is conducive to the end — leaves, e. g. grow 25 
to provide shade for the fruit. If then it is both by nature 
a nd for an en d that the swallow makes its nest and the 
spider its web, and plants grow leaves for the sake of the 
Jruit and send their roots down (not up) for the sake of 
nourishment, it is plain that this kind of cause i.«s operative 
in things wh i ch come to be a nd are by nature . And since 30 
' nature ' means twQ.. things, the matter and the form, of 
which the latter is the end, and since all the rest is for the 
sake of the end, t he form must be the r^ qse in the sense 
o f * that for the sake of which ' . 

Now mistakes come to pass even in the operations of art : 
the^rammarian makes a mistake in writing and the doctor 
pours out the wrong dose. Hence clear ly mista kes are 35 
possible in th e operad onsof nature also. If then'm art 199^ 
there are cases in which what is rightly produced serves a 
purpose, and if where mistakes occur there was a purpose 
jn what was attempted, only it was not attain"ed,"so"must it 
.be also in natural products, and monstrosities will be 
jaHures jn the purposive effort. Thus in the original com- 5 
binations ^ the ' ox-progeny ' if they failed to reach a deter- 

* Reading in 1. 11 apa euem rov, with Phil. Simp. ^ ^f. 198^32. 


minate end must have arisen through the corruption of 
some principle corresponding to what is now the seed. 

Further, seed must have come into being first, and not 
straightway the animals: the words * whole-natured first . . .'^ 
must have meant seed. 

Again, in plants too we find the relation of means to end, 

lo though the degree of organization is less. Were there then 
in plants also * olive-headed vine-progeny ', like the ' man- 
headed ox-progeny ', or not? An absurd suggestion ; yet 
there must have been, if there were such things among 

Moreover, among the seeds anything must have corne to 
be at random. But the person who asserts this entirely 

] 5 does away with * nature ' and what- exists ' by nature '. For 
ihoss ^ings are natural whirh^ hy ^ rontinuous movement 
orig inated from a p intprn al principle, arrive at some com- 
^letion : the same completion is not reached from every 
principle ; nor any chance completion, but always the 
tendency in each is towards the same end, if there is no 

The end and the means towards it may come about by 

20 chance. We say, for instance, that a stranger has come by 
chance, paid the ransom,^ and gone away, when he does so 
as if he had come for that purpose, though it was not for 
that that he came. This is incidental, for chance is an 
incidental cause, as I remarked before.^ But when an event 
takes place always or for the most part, it is not incidental 

35 or by chance. In natural pr oducts the sequence is in yarir- 
able^if there is no impediment. 

It is absurd to suppose that purpose is not present 
because we do not observe the agent deliberating. Art 
does not deliberate. If the ship-building art were in the 
wood, it would produce the same results by nature. If, 
therefore, purpose is pr esent in art,_i tJs_p.resent_alsQ,in_ 

^ Empedocles, Fr. 62. 4. 

2 Reading in 1. 20 \v(Ta\iivoi {yp. I, yp. Phil.). There is probably 
a reference to Plato's imprisonment in Aegina and to his being 
ransomed by Anniceris, who had accidentally arrived there {D. L. iii. 
20 ; Lucian, Dem, Enc. 23 ; Aelian, F<:zr. Hist. ii. 27). 

3 196^23-7. 

BOOK II. 8 199^ 

nature. The best illustration is a doctor doctoring him- 30 
self: nature is like that. 

It is plain then that nature is a cause, a cause that 
operates for a purpos e. 

As regards whiat is ^ of necessity ', we must ask whether 
the necessity is ' hypoth etical ', or ' simple ' as well. The 25 
current view places what is of necessity i.n_lhe. process of 
production, just as if one were to suppose that the wall of 200* 
a house necessarily comes to be because what is heavy is 
naturally carried downwards and what is light to the top, 
wherefore the stones and foundations take the lowest place, 
with earth ^ above because it is lighter, and wood at the 
top of all as being the lightest. Whereas, though the wall 5 
does not come to be without these, it is not _^^i^to_ these, 
except as its material cause : it comes. to be for the sake of 
sheltering and guarding certain things. Similarly in alj 
other things which Lnyolve .production for an end ; the 
product cannot come to be without things which have a 
necessary nature, but it is not due to these (except as its "-^ 

material) ; it comes to be for an end, For instance, why 10 d^I^j^^^* 
is a saw such as it is? To effect so-and-so and for the ^ ^:' , \\ 
sake of so-and-so. This^endj however, cannot be realized - v^ . ^ . ! 
unless the saw is made of iron. It is, therefore, necessary 
for it to be of iron,^ we are to have a saw and perform the Ip • '^ ' ■ 
operation of sawing. What is necessary then, is necessary u-^^oof-^cu^ 
on a hypothesis ; it is not a result necessarily determined 'vT ■ < < -, ^^ 
JDy antecedents. Necessity is in the matter^ while * that for 
the sake of which ' is in the definition. . ..,c,r . . - 

Necessity in mathematics is in a way similarjp^n^cessity 15 -, ^^ -,4^ 
ia^.things which come to be through the operation of ijj 

nature. Since a straight line is what it is,^ it is necessary 
that the angles of a triangle should equal two right angles. 
But not conversely ; though if the angles are not equal to 
two right angles, then the straight line is not what it is 
either. But in things which come to be for an end, the 

^ i. e. baked earth, bricks. 

^ i. e. since it is such that one line standing on another makes with 
it angles = 2 right angles. 

646.16 E 


reverse is true. If the end is, to exist or does exist, that 

ao 9,lso which precedes it will exist or does exist ; otherwise 

just as there, if the conclusion is not irue, the p/emiss will_ 

not be^true^so here the end or ' that for the sake of which * 

wiiljnpJLexi&t- For this too is itself a starting-point, but of 

the reasoning, not of the action ; while in mathematics the 

starting-point isjt he startin gf^Qlat_Qf thp.jeasonillg onlv,_as 

there is no action. I f theji there J ^ t o b^ ^ v>r>^iPAj r»^v .- 

25 and-such things must be made or be there already or exist, 

or generally the matter relative to the end, bricks and stones 

: if it is a house. But the en d is not due_ t Q tl^^ se except as 

\ the ma4:ter, Jior will it come to exist because, of, them. Yet 

if they do not exist at all, neither will the house, or the 

saw— the former in the absence of stones, the latter in the 

absence of iron — just as in the other case the premisses will 

not be true, if the angles of the triangle are not equal to 

two right angles. 

o The.necessary in nature, then, is plainly what we call by 

the Q^me of- matter, and^^thg^fiiangesuflkiii Both causes 

must be stated by the physicist, but especially the end ; ^ for 

that is the cause of the matter, not vice- versa ; and the end is 


/r^\\ ' that for the sake of which ', and the beginning starts from the 

35 definition or essence ; as in artificial products, since a house 

200^ is of such-and-such a kind, certain things' must necessarily 

j^X- ' come to be or b^ there already, or since health is this, 

these things must necessarily come to be or be there 

^ already. Similarly if man is this, then these ; if these, then 

those.^ Perhaps the necessary is present also in the defini- 

5 tion. For if one defines the operation of sawing as being 

a certain kind of dividing, then this cannot come about 

unless the saw has teeth of a certain kind ; and these cannot 

be unless it is of jron. For in the definition too there are 

some parts that are, as it were, its matter. 

^ Reading in 1. 33 nVoy, with Them. Phil. Simp. 
^ i. e. what ' these ' presuppose. 


I Nature h as been defined as a^' principleojl motion and 
change', and it is the subject of our inquiry. We must 
therefore see that we under stand the meaning of ' motion ' ; 
for if it were unknown, the meaning of * nature ' too would 
be unknown. 

When we have deterq:iined the nature of motion, our 15 
next task will be to attack in the same way the terms 
which are involved in it. Now .motion is supposed to 
belong to the class of things which are continuous ; and the 
infiniie presents itself first in the continuous — that is how 
it comes about that 'infinite' is often used in definitions 
of the continuous ('what is infinitely divisible i s continuous '|. 
EesideF tnese, pLQ£e. voidj and ^^ are thought to be 20 
necessary conditions of motion. 

Clearly, then, for these reasons and also because the 
attributes mentioned are common tp, and coextensive with, 
all the objects of our .science, we must first take each of 
them in hand and discuss it. For the investigation of 
speQial attributes comes after that of the common attri- 

To.begijaJthen, as we said, wjth motion^ 25 

We^ may start by distinguishing^ (i) what exists in 
a state of fulfilment only, (2) what exists as potential, 
(3) what exists as potential* and also in fulfilment — one 
being a 'this', another *so much', a third 'such', and 
similarly in each of the other modes of the predication of 

Further, the word ' relative ' is used with reference to 
(i) excess and defect, (a) agent and patient and generally 3° 

^ The subject of Physics {cfyvaiKr]) is natural bodies and their 
properties. Their common properties are the subject of the preserkt 

2 With 11. 26-8 cf. Met. 1065^ 5-7. 

^ Omiting n in 1. 26, with Phil, and Met. 

* Reading in 1. 26 t6 8e dvvdfxei, to de dvvaixei, with Met. 1065^ 5 
(EJ). , 

E 2 

20o*» PHYSICA 


^hat can move and what can be moved^ For ' what can 
cause movement ' is relative to ' what can be moved ', and 
vice versa, 

Again,^ there is no such thing as motion over and above .- 
the things. It is always with respect t o suto^nce or to I 
qu antity or to'^ quality or to place that what changes 
" cfianges^ But it is impossible, as we assert, to find any^ 
35 thing common to these which is neither * this ' nor quantum 
201* nor quale nor any of the other predicates. Hence neither 
will motion and change have reference to something over 
and above the things mentioned, for there is nothing over 
and above them. 

Now each of the se belongs to all its subjects in either of 
two ways : namely (i) substance — the one is positive form, 
5 the other privation ; {i) in quality, white and black ; (3) in 
quantity, complete and incomplete ; (4) in respect of loco- 
motion,^ upwards and downwards or light and heavy. 
Hence there are as many types of motion or change as 
there are meanings of the word ' js^'.* 

We have now before us the distinctions in the various 

classes of being between what is fully real and what is 


10 Def. The fulfilment of what exists potentially^ in so far 

I as it exists potentially , is motion — namely, of what is alter- 

I able qua alterable, alteration : of what can be increased 

I and its opposite what can be decreased (there is no common 

j name), increase and decrease : of what can come to be and 

I can pass away, coming to be and passing away : of what 

' can be carried along, locomotion. 

15 Examples will elucidate this definition of motion. When 
the buildable, in so far as it is just that, is fully real, it 
is being built, and this is build 2;/^. Similarly, learning, 
doctoring, rolling, leaping, ripening, ageing. 

' The former pair denote a special kind of the latter, namely 
change of qtiality (' such-ness') or alteration. 

^ With 1. 32-201* 19 cf. Met. 1065-^ 7-20. 

3 = <^opa, * being carried ', translatio. In the Categories (c. 14) this 
kind of ' motion ' is simply called fxeTa^okr) Kara tottov. 

* While the wider term nera^oX^ (change) is used in all the cate- 
gories, Kivrja-is (motion) holds only in Quality, Quantity, and Place. 

BOOK III. I 201* 

The same thing, if it is of a certain kind, can be both 
potential and fully real, not indeed at the same time or not 20 
in the same respect, but e. g. potentially hot and actually 
cold. Hence at once such things will act and be acted on 
by one another in many ways : each of them will be capable 
at the same time of causing alteration and of being altered. 
Hence, too, what effects motion as a physical agent can be 
moved : when a thing of this kind causes motion, it is 
itself also moved. This, indeed, has led some people to 35 
suppose that every mover is moved. But this question 
depends on another set of arguments, and the truth will be 
made clear later.^ It is possible for a thing to cause motion, 
though it is itself incapable of being moved. 

It^ is the fulfilm ent of what is potential whe n it is 
already fully real and operates not as itself but as moj^iad/e,^ 
that is motion. What I mean by ' as ' is this : Bronze is 
potentially a statue. But it is not the fulfilment of bronze 30 
as bronze which is motion. For 'to be bronze' and * to be 
a certain potentiality'* are not the same. If they were 
identical without qualification, i. e. in definition^ the ful- 
filment of bronze as bronze would have been motion. But 
they are not the same, as has been said. (This is obvious 
in contraries. ' To be capable of health 'Nfti^d ' to^be capable 35 
of illness ' are not the same, for if they were there wbuld 201 
be no difference between being ill and being well. Yet the 
subject both of health and of sickness — whether it is humour 
or blood — is one and the same.) 

We can distinguish, then, between the two — ^just as, to 
give another example, ' colour ' and * visible ' are different — 
and ^clearlyit is the fulfilmen t of what is pote ntial as ^ 
_potential that is motion. S o this, precisely, is motion. 5 

Further^ it is evident that motion is an attribute of 

^ viii. 5. 2 With 1. 27-202*3 cf. Met, 1065^ 21-1066*26. 

^ Reading in 1. 28 ivepyfj ov^ § avro dXX' § kivtjtov, with yp. I Asp. 

* Omitting Kivrjrw in 1. 32, with Simp, and Met. 1065^26. 

^ When A and B are identical in definition (or intension), it 
is also true that whatever is A is also £. But even when they are 
different in definition, we can still say that '^ is ^', if a subject 
which has the attribute A has also the attribute B. 

^ With 11. 6-7 cf. Met. 1065^ 20-1. 


a thing just when it is fully real in this way, and neither 
before nor after. For each thing of this kind ^ is capable 
of being at one time actual, at another not. Take for 
instance the buildable as buildable.^ The actuality of the 

lo buildable as buildable is the process of building. For the 
actuality of the buildable must be either this or the house. 
But when there is a house, the buildable is no longer 
buildable. On the other hand, it is the buildable which 
is being built. The process then of being built must be 
the kind of actuality required. But building is a kind of 
motion, and the same account will apply to the other 

15 kinds also. 

The soundness of this definition is evident both when we 2 
consider the accounts of motion that the others have given, 
and also from the difficulty of defining it otherwise. 

One could not easily put motion and change in another 
genus — this is plain if we consider where some people put 

20 it ; they identify motion with ' difference ' or * inequality ' ^ 
or ' not being ' ; but such things are not necessarily moved, 
whether they are * different ' or ' unequal ' or ' non-existent ' ; 
Nor is change either to or from these rather than to or 
from their opposites. 

The reason why they put motion into these genera is 

25 that it is thought to be something indefinite,'* and the 
principles in the second column are indefinite because they 
are privative : none of them is either * this ' or ' such ' or ^ 
comes under any of the other modes of predication. The 
reason in turn why motion is thought to be indefinite is 
that it cannot be classed simply as a potentiality or as an 
actuality — a thing that is merely capable of having a certain 

30 size is not undergoing change, nor yet a thing that is 

^ i. e. all things which are (jivaiKa crafiara. 

^ Reading in 1. 8 to oiKodoiJLrjTop jj olKodofxr^Tov with Met. 1066* 2, 
Simp., Them., and inserting a comma thereafter. 

2 Plato in the Timaeus (52 E, 57 E, 58 a) makes motion depend on 

* In the Pythagorean columns of opposites (e. g. Arist. Met. 986^ 25), 
Tjpeixovv and Kivovfxepov are placed under nepas and aneipop respec- 

^ Omitting on in 1. 27, with Met. 1066* 16, Them., and Bonitz. 

BOOK III. 2 201^ 

actually of a certain size, and motion is thought to be 
a sort of actuality^ but incomplete, the reason for this 
view being that the potential whose actuality it is is in- 
complete. This is why it is hard to grasp what motion is. 
It is necessary to class it with privation or with potentiality 
or with sheer actuality, yet none of these seems possible. 
There remains then the suggested mode of definition, 35 
namely that it is a sort of actuality, or actuality of the 202^ 
kind described, hard_to grasp, but not incapable of existing. 

The mover too is moved, as has been said — every mover, 
that is, which is capable of motion, and whose immobility 
is rest — when a thing is subject to motion its immobility is 
rest.^ For to act on the movable as such is just to move 5 
it. But this it does by contact^ so that at the same time 
it is also acted on. Hence we can define motion as the 
fulfilment of the movable qua movable^ the cause of the attri- 
bute being contact ivith what can move^ so that the mover 
is also acted on. The mover or agent will always be the 
vehicle of a form, either a ' this ' or a ' such ',^ which, when 10 
it acts, will be the source and cause of the change, e. g. the 
full-formed man begets man from what is potentially man. 

3 The * solution of the difficulty that is raised about the 
motion — whether it is in the movable — is plain. It is the 
ful filment of this potentiality ^ ^ and by the action of that 
which has the power of causing motion ; and the actuality 
of that which has the power of causing motion is not other 
than the actuality of the movable, for it must be the fulfil- 15 
ment of both, A thing is capable of causing motion because 
it can do this, it is a mover because it actually does it. But 

^ Tjpefiia is the privatio^ not the contradictory {aKiprja-ia), of Kivrjai^j 
i. e. it can be predicated only of a thing which is capable of motion. 

^ ' move' in the sense of cat^se motion. This seems to be intended 
to be the complete or real definition of the attribute * motion ', i. e. the 
definition which embodies the cause of the attribute. Cf. Post. An. 

93^ 39- 

^ All the manuscripts except E add in 1. 10 17 ToaovSe. It seems better 
to omit these words, as Aristotle is thinking mainly of the generation of 
substance, and of alteration of quality — the cases in which form is 
most obviously transferred. 

^ With 11. 13-21 cf. Met. 1066^ 26-34. 


it is on the movable that it is capable of acting. Hence 
there is a single actuality of both alike, just as one to two 
and two to one are the same interval, and the steep ascent 

30 and the steep descent are one — for these are one and the 
same, although they can be described in different ways. 
So it is with the mover and the moved. 

This view has a dialectical difficulty. Perhaps it is 
necessary that the actuality of the agent and that of the 
patient should not be the same. The one is * agency ' and 
the other ' patiency ' ; and the outcome and completion 
of the one is an * action ', that of the other a ' passion '} 

25 Since then they are both motions, we may ask : in what 
are they, if they are different? Either (a) both are in 
what is acted on and moved, or (d) the agency is in the 
agent and the patiency in the patient.^ (If we ought to 
call the latter also * agency ', the word would be used in 
two senses.) 

Now, in alternative (3)^ the motion will be in the mover, 
for the same statement will hold of ' mover ' and^ moved '.^ 

30 Hence either everj/ mover will be moved, or, though having 
motion, it will not be moved. 

If on the other hand (a) both are in what is moved and 
acted on — both the agency and the patiency (e.g. both 
teaching and learning, though they are iwOf in the learner)^ 
then, first, the actuality of each will not be present in each, 
and, a second absurdity, a thing will have two motions at 

35 the same time. How will there be two alterations of 
quality * in 07ie subject towards one definite quality ? The 
thing is impossible : the actualization will be one. 
2Q2b But (some one will say) it is contrary to reason to 
suppose that there should be one identical actualization 
of two things which are different in kind. Yet there will 
be, if teaching and learning are the same, and agency and 

* iraBos = affection, modification, change caused in a thing ab extra. 
^ Aristotle omits the two other possibilities as they obviously lead 

to absurdity. 

^ i.e. we can substitute 'mover* and 'moved' for 'agent' and 
' patient ' in the formulation of the hypothesis. 

* Alterations of quality = aWoidoaas. Aristotle sometimes tends to 
think of Kivrja-is as primarily change of quality, rather than as change 
of position. 

BOOK III. 3 20 

patiency. To teach will be the same as to learn, and to 
act the same as to be acted on — the teacher will necessarily 
be learning everything that he teaches, and the agent will 
be acted on. 

One may reply : 5 

(i) It is not absurd that the actualization of one thing 

should be in another. Teaching is the activity of a person 

who can teach, yet the operation is performed on some 

patient — it is not cut adrift from a subject, but is of A on B. 

(2) There is nothing to prevent two things having one 
and the same actualization,^ provided the actualizations 
are not described in the same way, but are related as what 
can act to what is acting.^ 

(3) Nor is it necessary that the teacher should learn, 10 
even if to act and to be acted on are one and the same, 
provided they are not the same in definition (as * raiment ' 
and * dress '), but are the same merely in the sense in 
which the road from Thebes to Athens and the road from 
Athens to Thebes are the same, as has been explained 
above.^ For it is not things which are in a way the same 
that have all their attributes the same, but only such as 15 
have the same definition. But indeed it by no means 
follows from the fact that teaching is the same as learning, 
that to learn is the same as to teach, any more than it 
follows from the fact that there is one distance between 
two things which are at a distance from each other, that 
the two vectors AB and BA are one and the same. To 
generalize, teaching is not the same as learning, or agency 
as patiency, in the full sense, though they belong to the 20 
same subject, the motion ; for the ' actualization of X in F' 
and the ' actualization of Y through the action of X ' differ 

in definition. 

What then Motion is, has been stated both generally 
and particularly. It is not difficult to see how each of 

^ Reading in 1. 8 with FI and Simp. KcoXi^et ovBkv rrjv avrrjp ehai for 

avTrjv eipai KcoXvei. 

^ What can act and what is acting are idem subjecto, but not idem 
dejinitione. Read hvva\xivov in 1. 10, with E. 

^ Cf. ^18-20. 


35 its types will be defined — alteration is the fulfilment of the 
alterable qua alterable (or, more scientifically, the fulfilment 
of what can act and what can be acted on, as such) — 
generally and again in each particular case, building, 
healing, &c. A similar definition will apply to each of 
the other kinds of motion. 

730 The science of nature is concerned with sp^al magni- 4 
tudes and motion and time, and each of these at least is 
necessarily infinite or finite, even if some things dealt with 
by the science are not, e. g. a quality ox 3. point — it is not 
necessary^m^feps that such things should be put under 
either head. Hence it is incumbent on the person who 
35 specializes in physics to discuss the infinite and to inquire 
whether there is such a thing or not, and, if there is, 
w/ta^ it is. 

The appropriateness to the science of this problem is 

203* clearly indicated. All who have touched on this kind of 

science in a way worth considering have formulated views 

about the infinite, and indeed, to a man, make it a principle 

of things. 

(i) Some, as the Pythagoreans and Plato, make the 
5 infinite a principle in the sense of a self-subsistent sub- - 
s tance , and not as a mere attribute of some other thin^ . 
Only the Pythagoreans place the infinite among the 
objects of sense (they do not regard number as separable 
from these), and assert that what is outside the heaven is 
infinite. Plato, on the other hand, holds that there is no 
body outside (the Forms are not outside, because they are 
nowhere), y et that the infinite is presep t pot nply in the 
obje cts of sense but in the Form s also. 
10 Further, the Pythagoreans identify the infinite with the 
e^en. For this, they say, when it is cut off and shut in by 
the odd, provides things with the element of infinity. An 
indication of this is what happens with numbers. If the 
gnomons are placed round the one, and without the one,^ 

^ 7repLTi6(fj.€vaiv yap tcov yvayiovuiv 7T(p\ to ev /cai p^copiy. No thoroughly 
satisfactory explanation of Ka\ x^P^^ has been given. But Aristotle's 
general meaning is fairly plain. He is describing i-zvo constructions : 
in the one oa(i gnomons are placed round the one, in the other ev£n 

BOOK III. 4 203 

in the one construction the figure that results is always 
different, in the other it is always the same. But Plato 15 
has two infinites, the Gre^t and the Sii^all. 

The physicists, on the other hand, all of them, always 
regard the infi nite as aniattributeiof a # lbstance which is 
different from it a> d belongs to the class of the so-called 
elements ^ — water or air or what is intermediate between 
them. Those who make them limited in number never make 
them infinite in amount. But those who make the elements 
infinite in number, as Anaxagoras and Democritus do, say 20 
that the infinite is continuous by contact — compounded of 
the homogeneous parts according to the one, of the seed- 
mass of the atomic shapes according to the other. 

Further, Anaxagoras held that any part is a mixture in 
the same way as the All, on the ground of the observed 
fact that anything comes out of anything. For it is pro- 
bably for this reason that he maintains that once upon a 
time all things were together. {This flesh and this bone 25 
were together, and so of any thing : therefore all things : 
and at the same time too.) For there is a beginning of 
separation, not only for each thing, but for all. Each thing 
that comes to be comes to_^be f^'onya .^irpi^^^' body, and 
there is a coming to be of all things, though not, it is true, 
at the same time. Hence there must also be an origin of 30 
coming to be. One such source there is which he calls 
]\^jnd, and Mind begins its work of thinking from some 
starting-point. So necessarily all things must have been 
together at a certain time, and must have begun to be 
moved at a certain time. 

Democritus, for his part, asserts the contrary, namely 
that no element arises from another element. Nevertheless 
for him ^ the rr^-nrnrw] ^r^dy is a source of qll thi il^^^iffp^- 203^ 
ing from part to part in size and in shape. 

It is clear then from these considerations that the inquiry 
concerns the physicist. Nor is it without reason that they 

gnomons are placed round the two. The translation follows Milhaud 
{Philosophes-geotnetres, p. 115). See also Burnet, Early Greek 
Philosophy^ ^ p. 103, n. 2. 

^ Aristotle does not regard them as elements. 

"^ Reading in 1. 34 atro), with Phil, and Bonitz. 


all make it a principle or source. We cannot say that the 
5 infinite has no effect, and the only effectiveness which we 
can ascribe to it is that of a principle. ^E^verything is either 
n^.«;r>nrrp or Ht^ri ved fro m a sourc e. But there cannot be 
a source of>-the^iimite or limitless, for that would be a limit 
of it. Further, as it is a beginning, it is both uncreatable 
and indestructible. For there must be a point at which 
what has come to be reaches completion, and also a termi- 

10 nation of all passing away. That is why, as we say, there 
is no principle of this, but it is this which is held to be the 
principle of other things, and to encompass all and to steer 
all, as those assert who do not recognize, alongside the 
infinite, other causes, such as Mind or Friendship. Further 
they identify it with the Divine, for it is ' deathless and 
imperishable * as Anaximander says, with the majority of 
the physicists. 

15 Belief in the existence of the infinite comes mainly from 
five considerations : 
(i) From the nature _of time — for it is infinite. 

(2) Frofn the divisjjDn of magnitudes — for the mathe- 

maticians also use the notion of the infinite. 

(3) If coming to be and passing away do not give out, it 

is only because that from which things come to 
be is infinite. 
20 (4) Because the limited always finds its limit in some- 
thing, so that there must be no limit, if everything is 
always limited by something different from itself. 
(5) Most of all, a reason which is peculiarly appropriate 
and presents the difficulty that is felt by every- 
body — not only number but also mathematical 
magnitudes and what is outside the heaven are 
supposed to be infinite because they never give out 
in our thojight, 
25 The last fact (that what is outside is infinite) leads people 
to suppose that body also is infinite, and that there is an 
infinite number of worlds. Why should there be body in 
one part of the void rather than in another ? Grant only 
that mass is anywhere and it follows that it must be every- 
where. Also, if void and place are infinite, there must be 

BOOK III. 4 203*' 

infinite body too, for in the case of eternal things what 
may be must be. 

But the problem of the infinite is difficult : many contra- 30 
dictions j-esult whether we suppose it to exist or not to 
exist. If it exists, we have still to ask how it exists ; as 
a substance or as the essential attribute of some entity ? 
Or in neither way, yet none the less is there something 
which is infinite or some things which are infinitely many ? 

The problem, however, which specially belongs to the 204^ 
physicist is \cs ipvestigate whetjier there is a sensib le ^^ 
mao^nitufje which is infinite . 
^ We must begin by distinguishing the various senses in 
which the term ' infinite ' is used. 

! (i) ^ What is incapable of being gone through, because it 
is not its nature to be gone through (the sense in 
which the voice is ' invisible '). 
(2) What admits of being gone through, the process 
however having no termination, or (3) what scarcely 
admits of being gone through. 5 

(4) What naturally admits of being gone through, but is 
not actually gone through or does not actually reach 
an end. 
Further, everything that is infinite may be so in respect ^^ 
of addition or division or both. 
5 Now it is impossible that the infinite should be a thing 
which is itself infinite, separable from sensible objects. If 
the infinite is neither a magnitude nor an aggregate, but is 10 
itself a slibstaiiGe and not an attribute, it will be indivisible ; 
for the divisible must be either a magnitude or an ap - gre- 
g;ate. But if indivisible, then not infinite, except in the 
sense (1) in which the voice is ' invisible '. But this is not the 
sense in which it is used by those who say that the infinite 
exists, nor that in which we_are investigating jt^, namely as 
(2), ' that which cannot be gone through '. But ^ if the 
infinite exists as an attribute, it would not be, qua infinite, 15 
an element in substances, any more than the invisible would 
be an element of speech, though the voice is invisible. 

1 With 11. 3-14 cf. Met. 1066* 35-^7. 

2 With 11. 14-17 cf. Met. 1066^8-11. 



Further/ how can the infinite be itself any thing, unless 
both number and magnitude, of which it is an essential 
attribute, exist in that way ? If they are not substances, 
a fortiori the infinite is not. 

20 It 2 is plain, too, that the infinite cannot be an actual 
thing and a substance_and^ principle. For any part of it 
that is taken will be infinite, if it has parts : for * to be 
infinite ' and * the infinite * are the same, if it is a substance 
and not predicated of a subject. Hence it will be either 

25 indivisible or divisible into infinites. But the same thing 
cannot be many infinites. (Yet just as part of air is air, 
so a part of the infinite would be infinite, if it is supposed 
to be a substance and principle.) Therefore the infinite / 
must be without pa£ts and indi\asible. But this cannot be J 
true of what is infinite in full completion : for it must be 
a definite quantity. 

Suppose then that infinity belongs jto substance as an 

30 attribute. But, if so, it cannot, as we have said, be de- 
scribed as a principle, but rather that of which it is an 
attribute — the air or the even number. 

Thus the view of those who speak after the manner of 
the Pythagoreans is absurd. With the same breath they 
treat the infinite as substance, and divide it into parts. 
This ^ discussion, however, involves the more general 

35 question whether the infinite can be present in mathe- 
matical objects and things which are intelligible and do not 
204^ have extension, as well as among sensible objects. Our 
inquiry (as physicists) is limited to its special subject-matter, 
the objects of sense, and we have to ask whether there is j 
or is not among them a body which is infinite in the direc-J 
tion of* increase. 

We may begin with a dialectical argument and show as 
follows that there is no such thing. 
5 If * bounded by a surface ' is the definition of body there ^ 
cannot be an infinite body either intelligible or sensible. 

1 With 11. 17-19 cf. Met. 1066^ 7-8. 

2 With 11. 20-32 cf. Met. 1066^ 11-21. 
5 With 11. 34-^8 cf. Met. 1066^ 21-6. 

* Reading in 1. 4 knL Bekker's vrepi is a misprint. 

BOOK III. 5 204»» 

Nor can number taken in abstraction be infinite, for number 
or that which has number is numerable. If then the 
numerable can be numbered, it would also be possible to 
go through the infinite. 

If,^ on the other hand, we investigate the question more lo 
in accordance with principles appropriate to physics, we are 
led as follows to the same result. 

The infinite body must be either (i) compound, or {2) 
simple ; yet neither alternative is possible. 

(i) Compound the infinite body will not be, if the 
elements are finite in number. For they must be more 
than one, and the contraries must always balance, and no 
o^ie of them can be infinite. If one of the bodies falls in 
any degree short of the other in potency — suppose fire is 15 
finite in amount while air is infinite and a given quantity of 
fire exceeds in power the same amount of air in any ratio 
provided it is numerically definite — the infinite body will 
obviously prevail over and annihilate the finite body. On 
the other hand, it is impossible that eack should be infinite. 
* Body ' is what has extension in all directions and the 20 
infinite is what is boundlessly extended, so that the infinite 
body would be extended in all directions ad infinitum? 

Nor (2) can the infinite body be one and simple, whether it 
is, as some ^ hold, a thing over and above the elements (from 
which they generate the elements) or is not thus qualified. 

{a) We must consider the former alternative ; for there 
are some people who make this the infinite, and not air or 
water, in order that * the other elements may not be annihi- 25 
lated by the element which is infinite. They have con- 
trariety with each other — air is cold, water moist, fire hot ; 
if one were infinite, the others by now would have ceased 
to be. As it is, they say, the infinite is dift*erent from them 
and is their source. 

It is impossible, however, that there should be such 
a body ; not because it is infinite — on that point a general 30 

^ With 11. 10-24 cf. Met. 1066^ 26-36. 

^ There could not be two such bodies. 

^ The reference is probably to Anaximander. 

* Reading in 1. 25 ottw?, with 1 Phil. 

204** PHYSICA 

proof can be given which applies equally to all, air, water, 
or anything else — but ^ simply because there is, as a matter 
of fact, no such sensible body, alongside the so-called 
elements. Everything can be resolved into the elements 
of which it is composed. Hence the body in question 
would have been present in our world here, alongside air 
and fire and earth and water : but nothing of the kind is 
35 (b) Nor can fire or any other of the elements be infinite. 
205* For generally, and apart from the question how any of 
them could be infinite, the All, even if it were limited, can- 
not either be or become one of them, as Heraclitus says 
that at some time all things become fire. (The same argu- 
5 ment applies also to the one which the physicists suppose 
to exist alongside the elements : for everything changes 
from contrary to contrary, e.g. from hot to cold). 

The preceding consideration of the various cases serves 
to show us whether it is or is not possible that there should 
be an infinite sensible body. The following arguments 
give a general demonstration that it is not possible. 

10 It ^ is the nature of every kind of sensible body to be/ 
somev^ere, and there is a place appropriate to eachJ 
the same for the part and for the whole, e.g. for the^ 
whole earth and for a single clod, and for fire and forj 
a spark. 

Suppose {a) that the infinite sensible body 
geneous. Then each part will be either 
always being carried along. Yet neither is 
why downwards rather than upwards or in knB 
tion? I mean, e.g., if you take a clod, where will it be 

15 moved or where will it be at rest ? For ex hypothesi the 
place of the body akin to it is infinite. Will it occupy the 
whole place, then ? And how ? What then will be the 
nature of its rest and of its movement, or where will they 
be ? It will either be at home everywhere — then it will not 

1 With 1. 32-205'^ 7 cf. Met, 1066^ 36-1067* 7. 

2 With 11. 10-25 cf. Met. 1067*7-20. 

BOOK III. 5 205* 

be moved ; or it will be moved everywhere — then it will 
not come to rest.^ 

But if (d) the All has dissimilar parts, the proper places 
of the parts will be dissimilar also, and the body of the All 20 
will have no unity except that of contact. Then, further, 
the parts will be either finite or infinite in variety of kind, 
(i) Fijtite they cannot be, for if the All is to be infinite, 
some of them would have to be infinite, while the others 
were not, e. g. fire or water will be infinite. But, as we 
have seen before, such an element would destroy what is 
contrary to it. (This indeed is the reason why none of thei25 
physicists made fire or earth the one infinite body, but' 
either water or air or what is intermediate between them, 
because the abode of each of the two was plainly deter- 
minate, while the others have an ambiguous place between 
up and down.)^ 

But ^ (ii) if the parts are infinite in number and simple, 
their proper places too will be infinite in number, and the 
same will be true of the elements themselves. If that is 30 
impossible, and the places are finite, the whole too must 
be finite ; for the place and the body cannot but fit each 
other. Neither is the whole place larger than what can be 
filled by the body * (and then the body would no longer ^ 
be infinite), nor is the body larger than the place ; for 35 
either there would be an empty space or a body whose 
nature it is to be nowhere. 

Anaxagoras gives an absurd account of why the infinite 205^ 
is at rest. He says that the infinite itself is the cause of — ' 
its being fixed. This because it is in itself, since nothing 
else contains it — on the assumption that wherever anything 
is, it is there by its own nature. But this is not true: 5 
a thing could be somewhere by compulsion, and not where 
it is its nature to be. 

Reading in 11. 18-19 h T^^vTayov fxevfl — oit KivrjOrjo-eTai apa' j; 
navTaxov KivrjOrjaerai — ovK apa crTr](T€Tai. 

^ This sentence should probably come, as Pacius suggests, after cimt 
in ^i. 
^ With 11. 29-32 cf. Met. 1067*20-3. 
* Omitting the first apa in 1. 34, with E Them. Phil. 
" Reading in 1. 35 acopa en* ovre, with E and Phil. 


Even if it is true as true can be that the whole is not 
moved (for what is fixed by itself and is in itself must be 
immovable), yet we must explain why it is not its nature* 
to be moved. It is not enough just to make this state- 
ment and then decamp. Anything else might be in a 

10 state of rest, but there is no reason why it should not be 
its nature to be moved. The earth is not carried along, 
and would not be carried along if it were infinite, provided 
it is held together by ^ the centre. But it would not be 
because there was no other region in which it could be carried 
along that it would remain at the centre, but because this is 
its nature.^ Yet in this case also we may say that it fixes 
itself. If then in the case of the earth, supposed to be 

15 infinite, it is at rest, not because it is infinite, but because 
it has weight and what is heavy rests at the centre and 
the earth is at the centre, similarly the infinite also would 
rest in itself, not because it is infinite and fixes itself, but 
owing to some other cause. 

Another difficulty emerges at the same time. Any part 
of the infinite body ought to remain at rest. Just as the 
infinite remains at rest in itself because it fixes itself, so 

20 too any part of it you may take will remain in itself. The 
appropriate places of the whole and of the part are alike, 
e. g. of the whole earth and of a clod the appropriate place 
is the lower region ; of fire as a whole and of a spark, the 
upper region. If, therefore, to be in itself is the place of the 
infinite, that also will be appropriate to the part. Therefore 
it will remain in itself. 

In ^ general, the view that there is an infinite body is 

35 plainly incompatible with the doctrine that there is neces- 
sarily a proper place for each kind of body, if every 
sensible body has either weight or lightness, and if a body 
has a natural locomotion towards the centre if it is heavy, 
and upwards if it is light. This would need to be true of 
the infinite also. But neither character can belong to it : it 
cannot be either as a whole, nor can it be half the one and 

^ Reading in 1. 11 utto, with Simp. Phil, and Bonitz. 
^ Omitting oh in 1. 13 with E and Them. 
^ With 1. 24-206* 7 cf. Met, 1067* 23-33. 

BOOK III. 5 205^ 

half the other. For how should you divide it ? or how can 30 
the infinite have the one part up and the other down, or an 
extremity and ^ a centre ? 

Further, every sensible body is in place, and the kinds or 
differences of place are up-down, before-behind, right-left ; 
and these distinctions hold not only in relation to us and by 
arbitrary agreement, but also in the whole itself. But in 35 
the infinite body they cannot exist. In general, if it is 
impossible that there should be an infinite place, and if 
every body is in place, there cannot be an infinite body. 206* 

Surely what is in a special place is in place, and what is 
in place is in a special place. Just, then, as the infinite 
cannot be quantity — that would imply that it has a par- 
ticular quantity,^ e. g. two or three cubits ; quantity just 
means these — so a thing's being in place means that it is 5 
somewhere, and that is either up or down or in some other 
of the six differences of position : but each of these is a limit. 

It is plain from these arguments that there is no body 
which is actually infinite. 

5 But on the other hand to suppose that the infinite does 
not exist in any way leads obviously to many impossible^ 
consequences: there will be a beginning and an epd oj 
time, a magnitude will not be divisible into magnitudes 
number will not be infinite. If, then, in view of the above^ 
considerations, neither alternative seems possible, an arbiter 
must be called in ; and clearly there is a sense in which the 
IilQjiit' <i»;'N i >il'i iTTTrrnTni nv i i n ^v ll il _llJM^Jl(^^__m)l 

We must keep in mind that the word * is ' means either 
w\\?X potentially is or v^h^it fully is. 

Further, a thing is infinite either by addition or by 15 

Now, as we have seen, magnitude is not actually infinite. 
But by division it is infinite. (There is no difficulty in 
refuting the theory of indivisible lines.*) The alternative 
then remains that the infinite has a potential existence. 

^ Reading in 1. 31 Za-xnrov Koi fieaov, with Simp, and Met. 1067* 28. 

^ Reading in 1. 3 n-oa-ou yap ti, with Bonitz. 

^ Reading in 1. 15 8iaipeaei, with F Them. Phil. Simp. 

* Cf. Bk. vi and £>e Lineis Insecabilibus, 

F 1 


But the phrase * potential existence ' is ambiguous. When 
we speak of the potential existence of a statue we mean that 

20 there will be an actual statue. It is not so with the infinite. 
There will not be an actual infinite. The word ' is ' has 
many senses, and we say that the infinite ' is ' in the sense 
in which we say ' it is day ' or Mt is the games ', because 
one thing after another is always coming into existence. 
For of these things too the distinction between potential 
and actual existence holds. We say that there are Olympic 
games, both in the sense that they may occur and that they 
are actually occurring. 

25 The infinite exhibits itself in different ways — in time, in 
the generations of man, and in the division of magnitudes. 
For generally the infinite has this mode of existence : one 
thing is always being taken after another, and each thing 
that is taken is always finite, but always different. Again, 

30* being' has more than one sense,^ so that we must not 
regard the infinite as a ' this ',2 such as a man or a horse, 
but must suppose it to exist in the sense in which we speak 
of the day or the games as existing — things whose being 
has not come to them like that of a substance, but consists 
in a process of coming to be or passing away ; definite if 
you like at each stage, yet always different. 
206^ But when this takes place in spatial magnitudes, what is 
taken persists, while in the succession of time and of men 
it takes place by the passing away of these in such a way 

~ that the source of supply never gives out. 

In a way the infinite by addition is the same thing as the 
infinite by division. In a finite magnitude, the infinite by 
addition comes about in a way inverse to that of the other. 
5 For in proportion as we see division going on, in the same 
proportion we see addition being made to what is already 
marked off. For if we take a determinate part of a finite 
magnitude and add another part determined by the same 
ratio (not taking in the same amount of the original whole) ,^ 

^ Inserting in 1. 29 en (on E) t6 uvai rrXiouaxoos XeytTai, with E Phil. 

^ A fully existent individual. 

^ Reading in 1. 8 n rov okov ixeyeBo?, with F and Simp. 

BOOK III. 6 ao6^ 

and so on, we shall not traverse the given magnitude. But lo 
if we increase the ratio of the part, so as always to take in the 
same amount, we shall traverse the magnitude, for every ^ 
finite magnitude is exhausted by means of any determinate 
quantity however small. 

The infinite, then, exists in no other way, but in this way 
it does exist, potentially and by reduction. It exists fully 
in the sense in which we say ' it is day ' or * it is the games ' ; 
and potentially as matter exists, not independently as what 15 
is finite does. 

By addition then, also, there is potentially an infinite, 
namely, what we have described as being in a sense the 
same as the infinite in respect of division. For it will always 
be possible to take something ab extra. Yet the sum of the 
parts taken will not exceed every determinate magnitude,] ust 
as in the direction of division every determinate magnitude 
is surpassed in smallness and there will be a smaller part. 

But in respect of addition there cannot be an infinite 20 
which even potentially exceeds every assignable magnitude, 
unless it has the attribute of being actually infinite, as the 
physicists hold to be true of the body which is outside 
the world, whose essential nature is air or something of 
the kind. But if there cannot be in this way a sensible 
body which is infinite in the full sense, evidently there 25 
can no more be a body which is potentially infinite in 
respect of addition, except as the inverse of the infinite by 
division, as we have said. It is for this reason that Plato . 
also made the infinites two in number, because it is supposed 
to be possible to exceed all limits and to proceed ad infini- 
tum in the direction both of increase and of reduction. Yet 
though he makes the infinites two, he does not use them. 
For in the numbers the infinite in the direction of reduction 30 
is not present, as the_monad_Js th^jj^^ ; nor is the 
infinite in the direction of increase, for the parts number 
only up to the decad. 

The infinite turns out to be the contrary of what it is said 
to be. It is not what has nothing outside it that is infinite, 207^ 
but what always has something outside it. This is indicated 
^ Omitting the second to in 1. 11, with E F. 

207*^ PHYSICA 

b)'' the fact that rings also that have no bezel are described 
as * endless V because it is always possible to take a part 
which is outside a given part. The description depends on 
a certain similarity, but it is not true in the full sense of the 

5 word. This condition alone is not sufficient : it is necessary 
also that the next part which is taken should never be the 
same. In the circle, the latter condition is not satisfied : 
it is only the adjacent part from which the new part is 

Our definition then is as follows : 

A quantity is iftfiuite if it is such that we can always 
take a part outside what has been already taken. On the 
other hand, what has nothing outside it is complete and 
whole. For thus we define the whole — that from which 

lo nothing is wanting, as a whole man or a whole box. What 
is true of each particular is true of the whole as such — the 
whole is that of which nothing is outside. On the other 
hand that from which something is absent and outside, 
however small that may be, is not ' all '. ' Whole ' and 
^ complete ' are either quite identical or closely akin. 
Nothing is complete (riKeiov) which has no end (rcAos) ; 
and the end is a limit. 

15 Hence Parmenides must be thought to have spoken 
better than Melissus. The latter says that the whole is 
infinite,^ but the former describes it as limited, ' equally 
balanced from the middle'.^ For to connect the infinite 
with the all and the whole is not like joining two pieces of 
string ; * for it is from this they get the dignity they ascribe 

20 to the infinite — its containing ^ all things and holding ^ the all 
in itself — from its having a certain similarity to the whole. 
It is in fact the matter of the completeness which belongs to 
size, and what is potentially a whole, though not in the full 
sense. It is divisible both in the direction of reduction and 
of the inverse addition. It is a whole and limited ; not. 

^ Reading in 1. 16 airnpov to 6\op, with Bonitz. 

3 Fr. 8. 44. 

* A proverbial exampleof combining things which are homogeneous. 

^ Reading in 1. 19 mpux^iv, with E and Them. 

^ Reading in 1. 20 ex^f-v, with Them, and Bonitz. 

BOOK III. 6 207» 

however, in virtue of its own nature, but in virtue of what is 
other than it. It does not contain, but, in so far as it is 
infinite, is contained. Consequently, also, it is unknowable, 25 
qua infinite ; for the matter has no form. (Hence it is plain 
that the infinite stands in the relation of part rather than 
of whole. For the matter is part of the whole, as the 
bronze is of the bronze statue.) If it contains in the case 
of sensible things,^ in the case of intelligible things the great 
and the small ought to contain them. But it is absurd 30 
and impossible to suppose that the unknowable and inde- 
terminate should contain and determine. 

7 It is reasonable that there should not be held to be 
an infinite in respect of addition such as to surpass every 
magnitude, but that there should be thought to be such an 
infinite in the direction of division. For the matter ^ and 35 
the infinite are contained inside what contains them, while it 
is the form which contains. It is natural too to suppose that 207^ 
in number there is a limit in the direction of the minimum, 
and that in the other direction every assigned number is 
surpassed. In magnitude, on the contrary, every assigned 
magnitude is surpassed in the direction of smallness, while 
in the other direction there is no infinite magnitude. The 5 
reason is that what is one is indivisible whatever it may be, 
e. g. a man is one man, not many. Number on the other 
hand is a plurality of * ones ' and a certain quantity of them. 
Hence number must stop at the indivisible : for * two ' and 
' three ' are merely derivative terms, and so with each of 
the other numbers. But in the direction of largeness it is 10 
always possible to think of a larger number : for the number 
of times a magnitude can be bisected is infinite. Hence 
this infinite is potential, never actual : the number of parts 
that can be taken always surpasses any assigned number. 
But this number is not separable from the process of 
bisection, and its infinity is not a permanent actuality 
but consists in a process of coming to be, like time and the 
number of time. 

^ Putting the comma before /cat in 1. 29, not before eSei in 1. 30. 
"^ Omitting w? in 1. 35, with E and Simp. 


15 With magnitudes the contrary holds. What is continuous 
is divided ad infinitum ^hnt there is no infinite in the direc- 
tion of increase. For the size which it can potentially be, 1 
it can also actually be.^ Hence since no seasihle_rnagnitude J 
is infinite, it is impossible to exceed every assigned magni- 

20 tude ; for if it were possible there would be something 
bigger than the heavens. 

The infinite ^ is not the same in magnitude and movement 
and time, in the sense of a single nature, but its secondary 
sense depends on its primary sense, i. e. movement is called 
infinite in virtue of the magnitude covered by the move- 
ment (or alteration or growth), and time because of the 

25 movement. (I use these terms for the moment. Later 
I shall explain what each of them means, and also why 
every magnitude is divisible into magnitudes.) 

Our account does not rob the mathematicians of their 
science, by disproving the actual existence of the infinite in 
the direction of increase, in the sense of the untraversable. 
In point of fact they do not need the infinite and do not 

30 use it. They postulate only that the finite straight line 
may be produced as far as they wi^h. It is possible to have 
divided in the same ratio as the largest quantity another 
magnitude of any size you like. Hence, for the purposes 
of proof, it will make no difference to them to have such an 
infinite instead, while its existence will be in the sphere of 
real magnitudes. 

.^5 In the four-fold scheme of causes, it is plain that the 
infinite is a cause in the sense of matter, and that its essence 
208* is privation, the subject as such being what is continuous 
and sensible. All the other thinkers, too, evidently treat 
the infinite as matter — that is why it is inconsistent in 
them to make it what contains, and not what is con- 

5 It remains to dispose of the arguments ^ which are sup- 8 
posed to support the view that the infinite exists not only 

^ Otherwise the potentiality would be unintelligible. 
2 YVith 11. 21-5 cf. Met. 1067^ 33-7. 

^ Cf. 203^ 15-30. 

BOOK III. 8 ao8» 

potentially but as a separate thing. Some have no cogency ; 
others can be met by fresh objections that are valid. 

(i) In order that coming to be should not fail, it is not 
necessary that there should be a sensible body which is 
actually infinite. The passing away of one thing may be 
the coming to be of another, the All being limited. lo 

(a) There is a difference between touching and being 
limited. The former is relative to something and is the 
touching of something (for everything that touches touches 
something), and further is an attribute of some one of the 
things which are limited. On the other hand, what is 
limited is not limited in relation to anything. Again, 
contact is not necessarily possible between any two things 
taken at random. 

(3) To rely on mere thinking is absurd, for then the excess 1 5 
or defect is not in the thing but in the thought. One might 
think that one of us is bigger than he is and magnify him 
adi7ifinitum. But it does not follow that he is bigger ^ than 
the size we are, just because ^some one thinks he is, but 
only because he is the size he is. The thought is an 
(a) Time indeed and movement are infinite, and also 20 
thinking, in the sense that each part that is taken 
passes in succession out of existence. 
{b) Magnitude is not infinite either in the way of reduc- 
tion or of magnification in thought. 

This concludes my account of the way in which the 
infinite exists, and of the way in which it does not exist, 
and of what it is. 

^ Omitting rov aa-reos and *; in 1. 18, with yp. Phil, and D^els. 



The physicist must have a knowledge of Place, too, as i 
well as of the infinite — namely, whether there is such a 
thing or not, and the manner of its existence and what it 

30 is — both because all suppose that things which exist are 
somewhere (the non-existent is nowhere — where is the 
goat-stag or the sphinx ?), and because * motion ' in its 
most general and primary sense is change of place, which 
we call * locomotion '. 

The question, what is place? presents many difficul- 
ties. An examination of all the relevant facts seems to lead 

35 to divergent conclusions. Moreover, we have inherited 
nothing from previous thinkers, whether in the way of 
a statement of difficulties or of a solution. 
208^ The existence of place is held to be obvious from the fact 

^of mutual replacement. Where water now is, there in turn, 
when the water has gone out as from a vessel, air is present. 
When therefore another body occupies this same place, 

5 the place is thought to be different from all the bodies 
which come to be in it and replace one another. What 
now contains air formerly contained water, so that clearly 
the place or space into which and out of which they passed 
was something different from both. 

Further, the typical locomotions of the elementary natural 
bodies — namely, fire, earth, and the like — show not only that 

10 place is something, but also that it exerts a certain influence. 

J Each is carried to its own place, if it is not hindered, the 
one up^ the other down. Now these are regions or kinds 
of place— up and down and the rest of the six directions. 
Nor do such distinctions (up and down and right and left, 

15 &c.) hold only in relation to us. To us they are not always 
the same but change with the direction in which we are . 
turned : that is why the same thing may be both right 

\ and left, up and down, before and behind. But in nature 
each is distinct, taken apart by itself. It is not every 

BOOK IV. I 2o8*» 

chance direction which is ' up ', but where fire and what is 
light are carried ; similarly, too, ' down ' is not any chance 30 
direction but where what has weight and what is made of 
earth are carried— the implication being that these places 
do not differ merely in relative position, but also as 
possessing distinct potencies. This is made plain also by 
the objects studied by mathematics. Though they have 
no real place, they nevertheless, in respect of their position 
relatively to us, have a right and left as attributes ascribed 
to them only in consequence of their relative position, not 
having by nature these various characteristics ^ Again, 
the theory that the void exists involves the existence 25 
of place: for one would define void as place bereft of 

These considerations then would lead us to suppose that -"^ 
place is s omething distin^ L-from-b^Ldies, and that every ' 
sensible body is in place. Hesiod too might be held to 
have given a correct account of it when he made chaos 
first. At least he says : 30 

First of all things came chaos to being, then broad- 
breasted earth,^ 

implying that things need to have space first, because he 
thought, with most people, that everything is somewhere 
and in place. If this is its nature, the potency of plac^ 
must be a marvellous thing, and take precedence of all 
other things. For that without which nothing else can 35 
existj_ while it can exi st without the others , must needs be 
~^rst; for place does not pass out of existence when the 209^ 
things in it are annihilated. 

True, but even if we suppose its existence settled, the . 
question of its naiure presents difficulty — whether it is* 
some sort of * bulk ' of body or some entity other than that, 
for we must first determine its genus. 

(1) Now it has three dimensions, length, breadth, depth, 5 
the dimensions by which all body also is bounded. But 

^ Reading in 1. 24 ^^ \x6vov Xeyofieua 8ia de'criv^ ovk exovra (pvaei, 

with Laas (w? rh fxovov kt\. Simp.). The readings of the MSS. are due 
to a conjecture by Alexander. 
^ Theog. ii6f. 


the place cannot be bo dy; for if it were t here would be 
two bo dies in the same placeT ~~ " 

(2) Further, if body has a place and space, clearly so 
too have surface and the other limits of body; for the 
same statement will apply to them : where the bounding 

10 planes of the water were, there in turn will be those of the 
air. But when we come to a point we cannot make a 
distinction between it and its place. Hence if the place 
of a point is not different from the point, no more will that 
of any of the others be different, and place will not be some- 
thing different from each of them. 

(3) What in the world then are we to suppose place to be ? 
If it has the sort of nature described, it cannot be an element 

15 or composed of elements, whether these be corporeal or 
incorporeal : for while it has size, it has not body. But the 
elements of sensible bodies are bodies, while nothing that 
has size results from a combination of intelligible elements. 

(4) Also we may ask : of what in things is space the 
cause ? None of the four modes of causation can be 

20 ascribed to itT it is neither cause in the sense of the 
matter of existents (for nothing is composed of it), nor as 
the form and definition of things, nor as end, nor does it 
move existents. 

(.5) Further, too, if it is itself an existent, where will it 
be ? Zeno's difficulty ^ demands an exj)lanation : for if 

25 everything that exists h^s a place, place too will have a 
place, and so on ad infinitum. 

(6) Again, just as every body is in place, so, too, every 
place has a body in it. What then shall we say about 
growing things ? It follows from these premisses that their 
place must grow with them, if their place is neither less nor 
greater than they are. 

By asking these questions, then, we must raise the whole 
30 problem about place — not only as to what it is, but even 
whether there is such a thing. 

We may distinguish generally between predicating B of 2 
A because it (A) is itself, and because it is something else ; 
1 Cf. Diels, Vors? i. 171. 15-26. 

BOOK IV. 2 209* 

and particularly between place which is common and in 
which all bodies are, and the special place occupied pri-' 
marilj^y^each. I mean, for instance, that you are now in 
the heavens because you are in the air and it is in the 
heavens ; and you are in the air because you are on the 
earth ; and similarly on the earth because you are in this 35 
place which contains no more than you. 

Now ^ if place is what primarily contains each body, it 209^ 
would be a limit, so that the place would be the form or 
shape of each body by which the magnitude or the matter 
of the magnitude is defined : for this is the limit of each 

If, then, we look at the question in this way the place of 5 
a thing i s its form . But, if we regard the place as the 
extension of the magnitude, it is th^jjiatter. For this is 
different from the m.agnitude : it is what is contained and 
defined by the form, as by a bounding plane. Matter or 
the indeterminate is of this nature ; when the boundary and 
attributes of a sphere are taken away, nothing but the 10 
matter is left. 

This is why Plato in the Timaeiis ^ says that matter and 
space are the same ; for the * participant ' and space are 
identical. (It is true, indeed, that the account he gives there 
of the * participant ' is different from what he says in his 
so-called 'unwritten teaching'.^ Nevertheless, he did 15 
identify place and space.) I mention Plato because, while 
all hold place to be something, he alone tried to say what 
it is. 

In view of these facts we should naturally expect to find 
difficulty in determining wha]^_place is, if indeed it is one 
of these two things, matter or form. They demand a very 20 
close scrutiny, especially as it is not easy to recognize them 

But it is at any rate not difficult to see that place cannot | 
be either of them. The form and the matter are not 

^ Xe'yo) ... (re ^33-^ I is parenthetical, and there should be a comma 
before d in ^i (so Bonitz). 

' 52. 

' Where he apparently identified * the participant * with * the great 
and the small'; cf. 1. 35. 

209** PHYSICA 

separate from the thing, whereas the place can be separated. 
As we pointed out/ where air was, water in turn comes to 
35 be, the one replacing the other ; and similarly with other 
-^ bodies. Hence the place of a thing is neither a part nor 
^ a state of it, but is separa ble from L t. For place is sup- 
posed to be something like a vessel — the vessel being 
a transportable place. But the vessel is no part of the 
30 In so far then as it is separable from the thing, it is not 
^ the form : qua containing, it is different from the matter. 
Also it is held that what is anywhere is both itsel f some- 
thing and that the re is a different thing outsi de it.^ (Plato 
ot course, if we may digress, ought to tell us why the form 
35 and the numbers are not in place, if ' what participates ' is 
place — whether what participates is the Great and the Small 
210^ or the matter, as he called it in writing in the Timaeus.) ^ 
Further, how could a body be carried to its own place, 
if place was the matter or the form ? It is impossible that 
what has no reference to motion or the distincti on of up 
and down can be place. S o place must be looked for 
among things which have these characteristic s. 
5 If the place is in the thing ^ (it must be if it is either shape 
or matter) place will have a place : for both the form and 
the indeterminate undergo change and motion along with 
the thing, and are not always in the same place, but are 
where the thing is. Hence the place will have a place. 
Further, when water is produced from air, the place has 
\o been destroyed, for the resulting body is not in the same 
place.^ What sort of destruction then is that ? 

This concludes my statement of the reasons why s£ace 
must be somethi ng, and a gain o fjhe^diffir"^^^<"«^ ^^af may 
be raised about its essential nature. 

The next step we must take is to see in how many^ 
senses one thing is said to b e * in ' another . 

1 208^2. 

2 Cf. 212'' 14-16. 3 52. 
* Reading avra in 1. 5, with the MSS. 

^ The place of the air is part of the substance air. 

BOOK IV. 3 210^ 

(i) As the finger is 'in' the hand and generally the part 15 
* in ' the whole. 

(2) As the whole is ' in ' the parts : for there is no whole 

over and above the parts. 

(3) As man is ' in ' animal and generally species ' in ' 


(4) As the genus is ' in ' the species and generally the 

part of the specific form * in * the definition of the 
specific form. 

(5) As health is ' in ' the hot and the cold and generally 20 

the form ' in ' the matter. 

(6) As the affairs of Greece centre ' in ' the king, and gene- 

rally events centre ' in ' their primary motive agent. 

(7) As the existence of a thing centres ' in ' its good and 

generally *in' its end, i.e. in *that for the sake of 
which * it exists. 

(8) In the strictest sense of all, as a thing is ' in ' a vessel, ^ 

and generally ' in ' place. 

One might raise the question w hether a thing can be in 2 a 
itself, or whether nothing can be in itself — everything being ' 
either ;/<?where or in something else. 

The question is ambiguous ; we may mean the thing qua 
itself or qua something else. 

When there are parts of a whole— the one that in which 
a thing is, the other the thing which is in it— the whole 
will be described as being in itself For a thing is described 
in terms of its parts, as well as in terms of the thing as a 
whole, e. g. a man is said to be white because the visible 
surface of him is white, or to be scientific because his 
thinking faculty has been trained. The jar then will not 30 
be in itself and the wine will not be in itself But the ja r 
oTwine wHl : for the contents and the container are both 
parts of the same whole. 

In^thi^jensejhen, but not primarily, a thing can be in 
itself, naniely, as ' white ' is in body (for the visible surface 
isTn body), and science is in the mind.^ 

^ Because the faculty of reasoning is in the mind. 77 i7n4)dveia . . . 
acanaTi (*34-^i) is parenthetical. 


It is from these, which are * parts * (in the sense at least 
of being 'in' the man), that the man is called white, &c. 
But the^ ar^ and the OTieJn^s e pa ra ti o n are - nnt p arfg r>f 
a whole, though together they are. So when there are 
parts, a thing will be ilTTtself, as ' white * is in man because 
it is in body, and in body because it resides in the visible 
5 surface. We cannot go further and say that it is in surface 
in virtue of something other than itself. (Yet it is not in 
itself: though these are in a way the same thing,) they 
differ in essence, each having a special nature and capacity, 
' surface ' and * white '. 

Thus if we look at the matter in ducli vely w e do not find 
a nything to h^ ' in * itself in a n y of the senses that {lav e 
been distinguished ; and it can be seen by argument that it 

lo is impossible. For each of two thing s will have to be both, 
e. g. the jar will have to be bjQi±L-,y£S 5el and win e, and the 

wine both wine and jar, if it is possible for a thing to be in 

itsfill ; so that, however true it might be that they were in 
each other, the jar will receive the wine in virtue not of its 

15 being w'ine but of the wine's being wine, and the wine 
will be in the jar in virtue not of its being a jar but of 
the jar's being a jar. Now that they are different in 
respect of their essence is evident ; for ' that in which 
something is ' and ' that which is in it ' would be differently 

Nor is it possible for a thing to be in itself eV -fia^inci- 
dentalJX' for two things would be at the same time in the 

20 same thing. The jar would be in itself — if a thing whose 
nature it is to receive can be in itself ; ^ and that which it 
receives, namely (if wine) wine, will be in it. 

Obviously then a thing cannot bejn itself /z^i^izri^. — 

Zen o's problem ^ — that if Place is something it must be 

in something ^ — is not difficult to solve. There is nothing 

to prevent the first place from being ' in ' something else — 

25 not indeed in that as ' in ' place, but as health is ' in ' the 

^ Reading a comma after (hai in 1. 20. 

2 Cf. Diels, Vors.^ i. 171. 15-26. 

^ Reading ev rm in 1. 23, with Them. Phil. Simp. 

BOOK IV. 3 210 

hot as a positive determination of it or as the hot is ' in ' 
body as an affection. So we escape the infinite regress. 

Another thing is plain: since the vessel is no part of 
what is in it ^ (what contains in the strict se nse is different 
fro m what is contained), place could not be either the \ 
matter or the form of the thing contained, l^!it^J]|]^ust_be 
different — for the latter, both the matter and the shape, 30 
are parts of what is contained. 

This then may serve as a critical statement of the diffi- 
culties involved. 
4 What then after all is place? The answer to this 
question may be elucidated as follows. 

Let us take for granted about it the various character- 
Jstics- which are supposed correctly to belong to it essen- 
tially.^ We assume then — 

(1) Place is what contains that of which it is the place. 

(2) Place is no part of the thing. 211 

(3) The immediate place of a thing is neither less nor 

greater than the thing. 

(4) Place can be left behind by the thing and is separable. 
In addition: 

(5) All place admits of the distinction of up and down, 

and each of the bodies is naturally carried to its 
appropriate place and rests there, and this makes 5 
the place either up or down. 
Having laid these foundations, we must complete the 
theory. We ought to try to make our investigation such 
as will render an account of place, and will not only solye^ 

th e diffi culties connected with it, but w ^l also ^ show that ^ 

the a ttributes supp osedLta-belong. t Q_it do really belong to 

it, and further will make clear the cause of the trouble andjo 
of the difiiculties ab out i t. Such is the most satisfactory 
kind ofexposition. 

First then we must understand that place would not » 

^ Reading avr<Z in 1. 28, with Simp, and Bonitz, 
"^ Reading aviov in 1. 33, with G. 


have been thought of, if there had not been a special kind 
of mo^on, namely that with respect to place. It is 
chiefly for this reason that we suppose the heaven also to 
be in place, because it is in constant movement. Of this 
kind of change there are two species — locomotion on the 

15 one hand and, on the other, increase and diminution. For 
these too involve variation of place : what was then in this 
place has now in turn changed to what is larger or smaller. 
Again, when we say a thing is ' moved ', the predicate 

t either (i) belongs to it actually, in virtue of its own nature, 
or (2) in virtue of something conjoined with it. In the 
latter case it may be either (a) something which by its own 

30 nature is capable of being moved, c. g. the parts of the 
body or the nail in the ship, or (3) something which is not 
in itself capable of being moved, but is always moved 
through its conjunction with something else, as ' whiteness * 
or ' science '. These have changed th eir place only becaus e 
the subjects to which they belong do so. 

We say that a thing is in the world, in the sense of in 

35 place, because it is in the air, and the air is in the world ; 
and when we say it is in the air, we do not mean it is in 
every part of the air, but that it is in the air because^oflhfL 
o uter surface o f the air which surrounds it ; for if all the 
air were its place, the place of a thing would not be equal 
to the thing — which it is supposed to be, and which the 
primary place in which a thing is actually is.^ 

When what surroun ds, then, is n^t^ separale„£ix)m the 

30 thing, but is in continuity with it, the thing is said to be in 
what surrounds it, not in the sense of in place, but as a part 
in a whole. But whe n the th ing is separate a nd in con tact, 

I it i s immediately ' in ' the inner surlace of the surrounding 
body, and this surface is neither a part of what is in it nor 
v et greater than its extension, but equal to it ; for the 
extremities of things which touch are coincident. 

Further, if one body is in continuity with another, it is 

35 not moved in that but with that. On the o ther hand it is 

^ As Bonitz pointed out, «' . . . eVnV (11. 27-9) is parenthetical, and 
there should be a comma after dvai (1. 28), and a colon after the 

BOOK IV. 4 211* 

moved in that if k Js^aeparate. It makes no_difijeren€e 
vvhslli ei^what conta ins Jsjrio\i£ii or not. 

Again, when it is not separate it is described as a part in 211^ 
a whole, as the pupil in the eye or the hand in the body : 
wh en it is separa te, as the water in the cask or the wine in 
the jar. For the hand is moved with ^ the body and the 
water in the cask. 

It will now be plain from these considerations what place 5 
is. There are ju sj four things of which p lace must be one 
— the shape, or the matter, 01* some sort of extension between 
the bounding surfaces of the containing body, ^r this 
boundary itself if it contains no extension over and above 
the bulk of the body which comes to be in it. 

Three of these it obviously cannot be : 

(i) The shape is supposed to be place because it sur- ib 
rounds, for the extremities of what contains and of what 
is contained are coincident. Both the shape and the place, 
it is true, are boundaries. But not of the same thing : the 
form is the boundary of the thing, the place is the boundary 
of the body which contains it_ 

(2) The extension between the extremities is thought to 1 
be something, because what is contained and separate^ may 
often be changed while the container remains the same (as i 
water may be poured from a vessel) — thg_assumption being 
that th e extension is something over and above^tHe body 
dis place d. But there is no such ex tension . One of the ^' 
bodies which change places and are naturally capable of 
being in contact with the container falls in — whichever it 
may chance to be. 

If there were an extension which were such as to exist 
independently and be permanent, there would be an infinity 20 
of places in the same thing.^ For when the water and 
the air change places, all the portions of the two together 
will play the same part in the whole which was previously 
played by all the water in the vessel ; at the same time 

^ Reading [ma in 1. 4 ; Bekker's Kara is a misprint. 

^ Reading in 1. 19 ti didcTTrjiia (Phil. Simp.) (/ca^') avro 7rf(f)VKns (fii/oi) 
(Laas) Ka\ fievov, €v TO) nvTcp aneipoi kt\. (F Phil. Simp., except that Simp, 
has the comma after avrco). 

G 2 


the place too will be undergoing change ; so that ther 
will be another place which is the place of the place, an( 

25 many places will be coincident. There is not a differen 
place of the part, in which it is moved, when the whol 
vessel changes its place : it is always the same : for it i 
in the (proximate) place where they are that the air an( 
the water (or the parts of the water) succeed each other, no 
in that place in which they come to be, which is part c 
the place which is the place of the whole world. 
I30 (3) The matte;', too, might seem to be place, at least i 
we consider it in what is at rest and is thus separate but ii 
continuity. For just as in change of quality there is some 
thing which was formerly black and is now white, 
formerly soft and now hard — this is just why we say tha 
the matter exists — so place, because it presents a simila 

35 phenomenon, is thought to exist — only in the one case w 

say so because tvhat was air is now water, in the othe 

because where air formerly was there is now water. Bu 

212^* the matt er, as we said before,^ is n either separable from th 

i thing nor contains^it, whereas place has bo t h character 

Well, then, if place is none of the three— neither th 

Jbrm nor the m atte r nor an extension which is alw avs_ther( 

different from, and over and above, the extension of th 

5 thing which is displaced — ;^lac£jT ecessarilv is the oneofth 

four which is left, namely, the boundary of the co nta inin ; 

I body at w hir h if tc; in contact with the contained body. 
(By the contained body is meant what can be moved b; 
way of locomotion.) 

Place is thought to be something important and hard t( 
grasp, both because the matter and the shape present them 
selves along with it, and because the displacement of thi 
body that is moved takes place in a stationary container 

10 for it seems possible that there should be an interval whici 
is other than the bodies which are moved. The air, toe 
which is thought to be incorporeal, contributes something t< 

^ 209^22-32. 

^ Reading in 1. 6 (Toi}[iaTos Kad' 6 crvj/aTrrei t<o ir^piixpfx^vcd^ with Them 
Phil. Simp. 

BOOK IV. 4 212* 

the belief: it is not only the boundaries of the vessel which 
seem to be place, but also what is between them, regarded \ 
as empty. Just, in fact, as the vessel is transportable place, 
so place is a non-portable vessel. So when what is within 15 
a thing which is moved, is moved ^ and changes its place, as 
a boat on a river, what contains plays the part of a vessel 

rather than that of place. Place on the other h^nH is 

rather what is motionless : so it is rather th^ whplf^ nv^** 
tEat is place, becaus e as a whole it is motionless. 

Hence wc conclude that the innermost motionless boun- 2o_| » 
dary of ivhat con tains isjlace. 

This explains why the middle of the heaven and the 
surface which faces us of the rotating system are held to be 
' up ' and ' down ' in the strict and fullest sense for all men : 
for the one is always at rest, while the inner side of the 
rotating body ^ remains always coincident with itself. 
Hence since the light is what is naturally carried up, and 25 
the heavy what is carried down, the boundary which con- 
tains in the direction of the middle of the universe, and the 
middle itself, are down, and that which contains in the 
direction of the outermost part of the universe, and the 
outermost part itself, are up. 

For this reason, too, place is thought to be a kind of sur- 
face, and as it were a vessel, i. e. a container of the 

Furthe r^ place is coincident with thp jf^ii^gj for honnd-j^ 
aries^re coincident with the bound57_ 

) If then a b o dy h as another body outside it and contain- 
ing it, it is in place, an d if not, not. T hat is why, even if 
IHere~were to Be^ water which had not a container, the parts 
of it, on the one hand, will be moved (for one part is con- 
tai4ied in another), while, on the other hand, the whole will 
be moved in one sense, but not in another. For as a whole 35 
it does not simultaneously change its place, though it will 
be moved in a circle : for this place is the place of its 212^ 
parts. (Some things are moved, not up and down, but in 

^ Omitting n in 1. 16 with EFG. 
^ Reading in 1. 24 kvkXco, with FGI. 


a circle ; others up and down, such things namely as admit 
of condensation and rarefaction.) 

i As was explained/ some things are potentially in place, 

others actually. So, when you have a homogeneous sub- 

5 stance which is continuous, the parts are potentially in place : 

when the parts are separated, but in contact, like a heap, 

they are actually in place. 

Again, (i) some things are per se in place, namely every 
body which is movable either by way of locomotion or by 

I way of increase is J^er se somewhere, but the heaven, as has 
been said,^ is not anywhere as a whole, nor in any place, if 

10 at least, as we must suppose, no body contains it. On the 
line on which it is moved, its parts have place ^ : for each 
is contiguous to the next. 

But (2) other things are in place indirectly, through some- 
thing conjoined with them, as the soul and the heaven. The 
latter is, in a way, in place, for all its parts are : for on the 
orb one part contains another. That is why the upper 
part is moved in a circle, while the All is not anywhere. 

15 F or wha t is somewhere is itself something, and there 
must be alongside it some^ other th ing wherein it is and 
which contains it. But alongside the All or the Whole 
there is nothing outside the All, and for this reason all 
things are in the heaven ; for the heaven, we may say, is 
the All. Yet their place is not the same as the heaven. 
It is part of it, the innermost part of it, which is in contact 

20 with the movable body ; * and for this reason the earth is 
in water, and this in the air, and the air in the aether, and 
the aether in heaven, but we cannot go on and say that 
the heaven is in anything else. 

It is clear, too, from these considerations that all the 
problems which were raised^ about place will be solved 
when it is explained in this way : 
(i) There is no necessity that the place should grow with 
the body in it, 

1 21 1^ 17-^5. 2 332. 

^ It is only in reference to its parts that it can be said to be moved. 

* Omitting nepas rjpefiovp in 1. 1 9, with E Them. Simp. 

6 209^2-30. 

BOOK IV. 5 aia* 

(2) Nor that a point should have a place, 

(3) Nor that two bodies should be in the same place, 35 

(4) Nor that place should be a corporeal interval: for >> 

what is between the boundaries of the place is any- 
body which may chance to be there, not an interval 
in body. 

Further, (5) place is also somewhere, not in the sense o(\j 
being in a place, but as the limit is in the limited ; for not 
everything that is is in place, but only movable body. 

Also (6) it is reasonable that each kind of body should 
be carried to its own place. For a body which is next in 3° 
the series and in contact (not by compulsion) is akin, and 
bodies which are united do not affect each other, while 
those which are in contact interact on each other.^ 

Nor (7) is it without reason that each ^ should remain 
naturally in its proper place. For this part has the same 
relation to its place,^ as a separable part to its whole, as 35 
when one moves a part of water or air : so, too, air is 213* 
related to water, for the one is like matter, the other form — 
water is the matter of air, air as it were the actuality of 
water, for water is potentially air, while air is potentially 
water, though in another way. 

These distinctions will be drawn mor ^ carefully later. * 
On the present occasion it was necessary to refer to them : 5 
what has now been stated obscurely will then be made 
more clear. If the matter and the fulfilment are the same 
thing (for water is both, the one potentially, the other 
completely), water will be related to air in a way as part 

* The scheme suggested is 


Hot / 

Water ! Wet ^ 

Earth SCold^ 
I Dry 

^ Omitting in 1. 33 cKaarov, with FG. 
^ Omitting in 1. 34 oXw, with E and Phil. 
* De Gen, et Corr. i. 3. 


to whole. That is why these have contact-, it is organic 
union when both become actually one. 
10 Thi s concludes my account of place — both o Mts exis - 
tence a nd of it s n ature. 

The investigation of similar questions about th e void ^ 6 
also, must be held to belong to the physicist — namely 
whether it exists or not, and how it exists or what it is — 
just as about place. The views taken of it involve argu- 
ments both for and against, in much the same sort of way. 

15 For those who hold that the void exists regard it as a sort 
of place or vessel which is supposed to be ' full ' when it 
holds the bulk which it is capable of containing, ' void ' 
when it is deprived of that — as if ' void ' and * full ' and 
* place ' denoted the same thing, though the essence of the 
three is different. 

3o We must begin the inquiry by putting down the account 
given by tjiose wlia-say-4hatut,_£xists*Jthen the account of 
those who say that it does not exist , and third the current 
view on these questions. 


Those who try to show that the void does not exist do 
not disprove what people really mean by it, but only their 
erroneous way of speaking ;^ this is true of Anaxagoras and 
of those who refute the existence of the void in this way. 

25 They merely give an ingenious demonstration that air is 
something — by straining wine-skins and showing the resis- 
tance of the air, and by cutting it off in clepsyd/as. But 

. people r eally mean that there is an empty interval in which 
there is m sensible body. They hold that everything 

30 which is is body and say that w hat has nothing in it at all 
is void (so what js full of air is v oid). It is not then the 
exis tence o f air that needs to be proved, but the non^exi s- 

I tence of an interval, different from the bodies, either separ- 
able or actual — an interval which divides the whole body 
so as to break its continuity, as Democritus and Leucippus 
213^ hold, and many other physicists — or even perhaps as some- 

^ Reading in 1. 24 aXX* o d/uaprdj^oi^Tey, with Them. Phil. Simp, and 

BOOK IV. 6 213^ 

thing which is outside the whole body, which remains con- 

These people, then, have not reached even the threshold 
of the problem, but rather those Avho say that the void 

(if They argue, for one thing, that change in place (i. e. 
locomotion and increase) would not be. For it is main- 5 
tained that motion would seem not to exist, if there were 
no void, since what is full cannot contain_anylhJng more. 
If it could, and there were two bodies in the same place, it 
would also be true that any number of bodies could be 
together ; for it is impossible to draw a line of division 
beyond which the statement would become untrue. If 
this were possible, it would follow also that the smallest 
body would contain the greatest ; for * many a little makes 10 
a mickle ' : thus if many equal bodies can be together, so 
also can many unequal bodies. 

Melissus,^ indeed, infers from these considerations that 
the All is immova ble ; for if it were moved there must, he 
says, be void, but void is not among the things that exist. 

This argument, then, is one way in which they show that 
there is a void. 

(2) They reason from the fact that some things are 15 
observed to contract and be compressed, as people say that 
a cask will hold the wine which formerly filled it, along with 
the skins into which the wine has been decanted,^ which 
implies that the compressed body contracts into the voids 
present in it. 

Again (3) increase, too, is thought to take place always 
by means of void, for nutriment is body, and it is impos- 20 
sible for two bodies to be together. A proof of this they 
find also in what happens to ashes, which absorb as much 
water as the empty vessel. 

The Pythagoreans,^ too, (4) held that void exists and 
that it enters the heaven itself,^ which as it were inhales it, 
from the infinite air. Further it is the void which distin- 1 

^ Cf. De Gen. et Corr. 32 5^ 2-16. ^ Cf. Probl. xxv. 8. 

' Cf. Diels, Vors? i. 354. 20-28. 
* Reading in 1. 23 avri^^ with G. 


25 guishes the natures of things, as if it were like what separ- 
ates and distinguishes ^ the terms of a series. This holds 
primarily in the numbers, for the void distinguishes their 

These, then, and so many, are the main grounds on 
which people have argued for and against the existence of 
the void. 

30 As a st ep towards settling which view is true, we must j 

det ermine the meaning of the name . 
I The void is though t to be place with nothing in it. The 
reason for this is that people take what exists to be body, 
and hold that while ever y body is in place, void is place in 
which there is no bocj y^^o th at where there is no body, 
t here must be void. 
214^ Every body, again, they suppose to be tangible ; and of 
this nature is whatever has weight or lightness. 

Hence, by a syllogism, what has nothing heavy or lig ht 
in it, is voidi.-^ 

This result, then, as I have said, is reached by syllogism. 
5 It would be absurd to suppose that the point is void ; for 
the void must h^ place which has in it an interval in tangible 

But at all events we observe then that in one way the 
void is described as what is not full of body perceptible to 
touch ; and what has heaviness and lightness is perceptible 
to touch. So we would raise the question : what would 
they say of an interval that has colour or sound — is it void 
10 or not ? Clearly they would reply that if it could receive 
what is tangible it was void, and if not, not. 

In another way void is that in which there is no ' this ' 

* or corporeal substance. So some say that the void is the 

matter of the body (they identify the place, too, with this), 

and in this ^ they speak incorrectly ; for the matter is not 

15 separable from the things, but they are inquiring about the 

void as about something separable. 

I Since we have determined the nature of place.^ and voi d, 

^ Omitting Tr\s in 1. 26, with Bonitz. 

^ Placing the comma after rh avTo in 1. 14. ' ch. 4. 

BOOK IV. 7 ai4» 

must, if it exists,^ be place deprty eH of body, and we have 
stated both in what sense place exists and in what sense it 
does not, it is plain that on this showin g void_does not 
exist, either unseparated or separated ; torthe void is 

meant to be, not body but rather an interv al in body. 29 
This is why the void is thought to be something-, viz. 
because place is, and for the same reasons. For the fact 
of motio n in respect of place comes to the aid both of 
those who maintainth at place is som ething^oyer_and__above 
thc^^ bodies^ that come to occupy it, and of those who main- 

tain that the void is something. They state that the yoij^ » 
is the condition of movement in the sense of that in which 
movement takes place ; and this would be the kind of thing 25 
that some say place is. 

But there is no necessity for there being a void if there 
is movement. It is not in the least needed as a condition 
of movement in general, for a reason which,^ incidentally, 
escaped Melissus ; viz. that the full can suffer qualitative \ 

But not even movement in respect of plac ^ invnlvpg a vr>iH ; 
for bodies may simultaneously make room for one another, 
though there is no interval separate and apart from the 30 
bodies that are in movement. And this is plain even in 
the rotation of continuous things, as in that of liquids. 

And things ca n also b e j^o m pres sed not into a void but 
because they squeeze out what is contained in them (as, for 
instance, when water is compressed the air within it is 
squeezed out) ; and things can inc rease_ jn..sjzg not only by 214^ 
the entrance of something but also by qualitative change ; 
e. g. if water were to be transformed into air. 

In general, both the argument about increase of size ^ and 
that about the water poured on to the ashes ^ get in their 
own way. For either not any and every part of the body 5 
is increased, or bodies may be increased otherwise than by 
the addition of body, or there may be two bodies in the 
same place (in which case they are claiming to solve a quite 

^ Reading commas before and after et earii/ in 1. 17. 

"^ Reading hC in 1. 27. 

^ 213^18-20 * ib. 21 f. 


general difficulty, but are not proving the existence of 
void), or the whole body must be void, if it is increased in 
every part and is increased by means of void. The same 
argument applies to the ashes, 
lo It is evident, then, tha t it is easy to refute the arguments 
by which they prove the existence of the vo id. 

Let us explain again that there is no void existing 8 
separatel}^ as some maintain. It each ot the simple bodies 
has a natural locomotion, e. g. fire upward and earth down- 

15 ward and towards the middle of the universe, it is clear 
that it c annot be t he void that is the condition of locomo- 
tion. What, then, will the void be the condition of ? It is 
y thought to be the condition of movement in respect of 
place, and it is not thecondition of this. 

Again, if void is a sort of place deprived of body, when 
there is a void where will a body placed in it move to ? 
It certainly cannot move into the whole of the void. The 

20 same argument applies as against those who think that 
place is something separate, into which things are carried ; 
viz. how will what is placed in it move, or rest ? Much the 
same argument will apply to the void as to the * up ' and 
* down ' in place, as is natural enough since those who 
maintain the existence of the void make it a place. 

And in what way will things be present either in place ^ 

25 or in the void ? For the expected ^ result does not take 
place when a body ^ is placed as a whole in a place con- 
ceived of as separate and permanent ; for a part of it, 
unless it be placed apart, will not be in a place but in the 
whole. Further, if separate place does not exist, neither 
will void. 

If peopl e say that the void must exist, as being neces- 
sary if there is^be rnovement, what rather turns out to be 

30 the case, if one studies the matter, is the opposite, that not __ 
a single thing can be moved if there is a void ; for as with 
those who for a like reason say the earth is at rest, so, too, 

^ Expected by those who believe in a separately existing place 
or void. 

"^ Reading in 1. 26 aco/xa ti^ with Phil's and Simp.'s paraphrase. 

BOOK IV. 8 314** 

in the void things must be at rest.; for there is no place to 
which things can move more or less than to another ; since 
the void in so far as it is void admits no difference. ^ ' 

The second reason is this ^ : all movement is either com- 215* 
pulsory or according to nature, and if there is compulsory 
movement there must also be natural (for compulsory 
movement is contrary to nature, and movement contrary to 
nature is posterior to that according to nature, so that if 
each of the natural bodies has not a natural movement, 
none of the other movements can exist) ; but how can there 5 
be natural movement if there is no difference throughout a 
the void or the infinite ? For in so far as it is infinite, there 
will be no up or down or middle, and in so far as it is 
a void, up differs no whit from down; for as there is no 
difference in what is nothing, there is none in the void (for 10 
the void^ seems to be a non-existent and a privation of 
being), but natural locomotion seems to be differentiated, so 
that the things that exist by nature must be differentiated. 
Either, then, nothing has a natural locomotion, or else there 
is no void. 

Further, in goiat ofjact things that are thrown rnove 
though that which gave them their impulse is not touching 
them, either by reason of mutual replacement, as some 15 
maintain, or because the air that has been pushed pushes 
them with a movement quicker than the natural locomotion 
of the projectile wherewith it moves to its proper place.^ 
But in a void none of these things can take place, nor can 
anything be moved save as that which is carried is moyed. 

Further, i^o one couldsay why a thing ojace^etjnjnotjon^ 
should stop anywhere ; for why should it stop here rather 20 
than here ? So that a thing will either be at rest or must 
be moved ad infinitum^ unless something more powerful get 
in its way. 

Further, things are now thought to move into the void 
because it yields ; but in a void this quality is present equally 
everywhere, so that things should move in all directions. 

^ Reading in 1. i eVet^' ort, with I Them. Simp. 

^ Reading in 1. 10 /cat rov ksuov' to yap Kfuouy with H Them. Simp. 

^ i. e. downwards. 


Further, the truth of what we assert is plain from the 

35 following considerations. We see the same weight or body- 
moving faster than another for two reasons, either because 
there is a difference in what it moves through, as between 
water, air, and earth, or because, other things being equal, 
the moving body differs from the other owing to excess of 
weight or of lightness. 

Now the medium causes a difference because it impedes 
the moving thing, most of all if it is moving in the opposite 

30 direction, but in a secondary degree even if it is at rest ; and 
especially a medium that is not easily divided, i. e. a medium 
that is somewhat dense. 
215^ A, then, will move through B in time F, and through A, 
which is thinner,^ in time E (if the length of B is equal to A), 
in proportion to the density of the hindering body. For 
let B be water and A air ; then by so much as air is thinner 
5 and more incorporeal than water, A will move through A 
faster than through B. Let the speed have the same ratio 
to the speed, then, that air has to water. Then if air is 
twice as thin, the body will traverse B in twice the time 
that it does A, and the time T will be twice the time E. 

10 And always, by so much as the medium is more incorporeal 
and less resistant and more easily divided, the faster will be 
the movement. 

Now there is no ratio in which the void is exceeded by 
body, as there is no ratio of o to a number. For if 4 
exceeds 3 by 1, and 2 by more than i, and i by still more 

15 than it exceeds 2, still there is no ratio by which it exceeds 
o ; for that which exceeds must be divisible into the 
excess + that which is exceeded, so that 4 will be what it 
exceeds o by + o. For this reason, too, a line does not 
exceed a point — unless it is composed of points ! Similarly 

20 the void can bear no ratio to the full, and therefore neither 
can movement through the one to movement through the 
other, but if a thing moves through the thickest medium 
such and such a distance in such and such a time, it moves 
through the void with a speed beyond any ratio.^ For let 

^ Reading in 1. 2 XfwTOTepov, with E G Them. Simp. 
* Placing the comma in 1. 22 before 8ia tov Ktvov. 

BOOK IV. 8 215^ 

Z be void, equal in magnitude to B and to A. Then if A 
is to traverse and move through it in a certain time, H, 
a time less than E, however, the void will bear this ratio 25 
to the full. But in a time equal to H, A will traverse the 
part of A. And it will surely also traverse in that time 
any substance Z which exceeds air in thickness in the ratio 
which the time E bears to the time H. For if the body Z 30 
be as much thinner than A as E exceeds H, A, if it moves 
through Z, will traverse it in a time inverse to the speed of 
the movement, i. e. in a time equal to H. If, then, there is 216* 
no body in Z, A will traverse Z still more quickly. But 
we supposed that its traverse of Z when Z was void 
occupied the time H. So that it will traverse Z in an 
equal time whether Z be full or void. But this is impos- 
sible. It is plain, then, that if there is a time in which it 
will move through any part of the void, this impossible I 
result will follow : it will be found to traverse a certain 5 
distance, whether this be full or void, in an equal time ; for 
there will be some body which is in the same ratio to the 
other body as the time is to the time. 

To sum the matter up, the cause of this result is obvious, 
viz. that betw een any two movements there is a ratio (f or they 
occupy time, and there is a ratio between any two times , so 10 
long as both are finite), but there is no ratio of void to full. 

These are the consequences that result from a difference 
in the media ; the following depend upon an excess of one 
moving body over another. We see that bodies which ^ 
have a greater impulse either of weight or of lightness, 
if they are alike in other respects,^ move faster over an 15 
equal space, and in the ratio which their magnitudes bear 
to each other. Therefore they will also move through the 
void with this ratio of speed. But that is impossible ; for 
why should one move faster ? (In moving through plena it 
must be so ; for the greater divides them faster by its force. 
For a moving thing cleaves the medium either by its shape, 
or by the impulse which the body that is carried along or 
is projected possesses.) Therefore all will possess equal 20 
velocity. But this is impossible. 

^ Omitting rols (rxwatn in 1. 14, as Simplicius may have done. 


It is evident from what has been said, then, that, if there 
is a void, a result follows which is the very opposite of the 
reason for which those who believe in a void set it up. 
They think that if movement in respect of place is to exist, 
the void cannot exist, separated alP by itself; but this is 

25 the same as to say that place is a separate cavity ; and this 
has already been stated to be impossible.^ 

But even if we consider it on its own merits the so-called 
vacuum will be found to be really vacuous. For as, if one 
puts a cube in water, an amount of water equal to the cube 
will be displaced ; so too in air ; but the effect is imper- 
ceptible to sense. And indeed always, in the case of any 

30 body that can be displaced, it must, if it is not compressed, 
be displaced in the direction in which it is its nature to be 
displaced — always either down, if its locomotion is down- 
wards as in the case of earth, or up, if it is fire, or in both 
directions — whatever^ be the nature of the inserted body. 
Now in the void this is impossible ; for it is not body ; the 
void must have penetrated * the cube to a distance equal to 

35 that which this portion of void formerly occupied in the 
216^ void, just as if the water or air had not been displaced by 
the wooden cube, but had penetrated right ^ through it. 

But the cube also has a magnitude equal to that occupied 
by the void ; a magnitude which, if it is also hot or cold, 
5 or heavy or light, is none the less different in essence from 
all its attributes, even if it is not separable from them ; 
I mean the volume of the wooden cube. So that even if it 
were separated from everything else and were neither heavy 
nor light, it will occupy an equal amount of void, and fill 
the same place, as the part of place or of the void equal to 
itself. How then will the body of the cube differ from the 

10 void or place that is equal to it ? And if there can be two 
such things, why cannot there be any number coinciding ? 
This, then, is one absurd and impossible implication of the 

* Reading in 1. 24 a-rroKCKpifieuov. dn-oKpivnuevov is a misprint. 
^ 2ilbi9sqq., 213*31. 

^ Omitting the second 7 in 1. 33, with Prantl, and apparently with 

* Omitting 86^€iev in 1. 35, with E. 

•* Reading navTr] in 1. 2, with EH I Them. 

BOOK IV. 8 216^ 

theory. It is also evident that the cube will have this same 
volume even if it is displaced, which is an attribute possessed 
by all other bodies also. Therefore if this differs in no 
respect from its place/ why need we assume a place for 
bodies over and above the volume of each, if their volume be 
conceived of as free from attributes? It contributes nothing 15 
to the situation if there is an equal interval attached to it as 
well. [Further, it ought to be clear by the study of moving 
things what sort of thing void is. But in fact it is found 
nowhere in the world. For air is something, though it does 
not seem to be so — nor, for that matter, would water, if 
fishes were made of iron ; for the discrimination of the 
tangible is by touch.^] 

It is clegTiJ hen, from these considerations that the re isjio_2o_ 

? There are some who think that the existence of rarity 
and density shows that there is a void. If rarity and 
density do not exist, they say, neither can things contract 
and be compressed. But if this were not to take place, 
either there would be no movement at all, or the universe ^5 
would bulge, as Xuthus ^ said, or air and water must* always 
change into equal amounts (e. g. if air has been made out of 
a cupful of water, at the same time out of an equal amount 
of air a cupful of water must have been made), or void must 
necessarily exist ; for compression and expansion ^ cannot 
take place otherwise. 

Now, if they mean by the rare that which has many 30 
voids existing separately, it is plain that if void cannot 
exist separate any more than a place can exist with an 
extension all to itself, neither can the rare exist in this 
sense. But if they mean that there is void, not separately 
existent, but still present in the rare, this is less impossible, 
yet, first, the void turns out not to be a condition of all 

^ Reading toO ronov in 1. 14 ; Bekker's roCrd irov is a misprint. 
^ The words in brackets are unknown to the Greek commentators 
and probably spurious. 

^ A Pythagorean of Croton ; cf. Diels, Vors.^ i. 284. 22-5. 

* Inserting bd after ad in 1. 26, with Bonitz. 

• Reading in 1. 29 imKTflv^aOaiy with E and apparently Simp. 

646.19 H 

2i6^ • PHYSICA 

35 movement, but only of movement upwards (for the rare is 
217^ light, which is the reason why they say fire is rare) ; second, 
the void turns out to be a condition of movement not as that 
in which it takes place, but in that the void carries things 
up as skins by being carried up themselves carry up what 
is continuous with them. Yet how can void have a local 
movement or a place ? For thus that into which void moves 
is till then void of a void. 

5 Again, how will they explain, in the case of what is 
heavy, its movement downwards ? And it is plain that if 
the rarer and more void a thing is the quicker it will move 
upwards, if it were completely void it would move with 
a maximum speed ! But perhaps even this is impossible, 
that it should move at all ^ ; the same reason which showed 
that in the void all things are incapable of moving shows 
that the void cannot move, viz., the fact that the speeds 
are incomparable. 

10 Since we deny that a void exists, but for the rest the 
problem has been truly stated,^ that either there will be 
no movement, if there is not to be condensation and rare- 
faction, or the universe will bulge, or a transformation of 
water into air will always be balanced by an equal trans- 
formation of air into water (for it is clear that the air pro- 

15 duced from water is bulkier than the water) ^ : it is 
necessary therefore, if compression does not exist, either 
I that the next portion will be pushed outwards and make the 
outermost part bulge, or that somewhere else there must be 
an equal amount of water produced out of air, so that the 
entire bulk of the whole may be equal, or that nothing moves. 
For when anything is displaced this will always happen, 
unless it comes round in a circle ; but locomotion is not 
always circular, but sometimes in a straight line. 

20 These then are the reasons for which they might say 
that there is a void ; our statement is based on the assump- 
tion that there is a single matter for contraries, hot and 
cold and the other natural contrarieties, and that what 
exists actually is produced from a potential existent, and 

^ Reading a comma after ahvvaTov in 1. 8. ^ 216^24-6. 

' Putting a colon before avayKr\ in 1, 15, with Bonitz. 

BOOK IV. 9 2i7« 

that matter is not separable from the contraries but its 
being ^ is different, and that a single matter may serve for 35 
colour and heat and cold. 

The same matter also serves for both a large and a small 
body. This is evident ; for when air is produced from 
water, the same matter has become something different, 
not by acquiring an addition to it, but has become actually 
what it was potentially, and, again, water is produced from 
air in the same way, the change being sometimes from 30 
smallness to greatness, and sometimes from greatness to 
smallness. Similarly, therefore, if air which is large in 
extent comes to have a smaller volume, or becomes greater 
from being smaller, it is the matter which is potentially 
both that comes to be ^ each of the two. 

For as the same matter becomes hot from being cold, 
and cold from being hot, because it was potentially both, so 
too from hot it can become more hot, though nothing in 217^ 
the matter has become hot that was not hot when the 
thing was less hot ; just as, if the arc or curve of a greater 
circle becomes that of a smaller, whether it remains the 
same or becomes a different curve, convexity has not come 
to exist in anything that was not convex but straight (for 5 
differences of degree do not depend on an intermission of 
the quality) ; nor can we get any portion of a flame, in 
which both heat and whiteness are not present. So too, 
then, is the earlier heat related to the later.^ So that the 
greatness and smallness, also, of the sensible volume are 
extended, not by the matter's acquiring anything new, but 
because the matter is potentially matter* for both states ; 
so that the same thing is dense and rare, and the two 10 
qualities have one matter. 

The dense is heavy, and the rare is light. [Again, as the 

arc of a circle when contracted into a smaller space does 

not acquire a new part which is convex, but what was there 

has been contracted ; and as any part of fire that one takes 

will be hot ; so, too, it is all a question of contraction and 15 

^ Reading in I. 24 ro d* elvat, with EFG Them. 

^ Reading in 11. 32-3 vXrj yivirai, with E. 

^ Reading in 1. 8 Trpoy ttjv varepov (so perhaps Simp.). 

* Omitting 77 in 1. 10, with E. 

11 2 


expansion ^ of the same matter.^] There are two types in 
each case, both in the dense and in the rare ; for both the 
heavy and the hard are thought to be dense, and con- 
trariwise both the h'ght and the soft are rare ; and weight 
and hardness fail to coincide in the case of lead and iron. 

20 From what has been said it is evident, then, that void 
does not exist either separate (either absolutely separate or 

' as a separate element in the rare) or potentially, unless one 
is willing to call the condition of movement void, whatever 
it may be. At that rate the matter of the heavy and the 
light, qua matter of them, would be the void ; for the 
dense and the rare are productive of locomotion in virtue of 

25 this contrariety, and in virtue of their hardness and softness 
productive of passivity and impassivity, i. e. not of loco- 
motion but rather of qualitative change. 

So much, then, for the discussion of the void, and of the 
sense in which it exists and the sense in which it does not 

^*^****^ Next for discussion after the subjec ts mentioned is T ime. 
j« The best plan will be to begin by working out the diffi- 
jT culties connected with it, making use of the current argu- 
ments. First, does it belong to the class of things that 
cxisi : or to that of things that do not exist ? Then seqmidly, 
what is its nature ? To start, then : the following con- 
siderations would make one suspect that it either does not 
exists at all or barely, and i n _an obsc ure wa^. One part 
of it has been and is notjjvhile the other is go i ng to be^and 
218^ is not yet. Yet Jiine — both infinite time and any time you 
iTke to ta"ke — is madejup of ^hjese^ One would naturally 
suppose that what is made up of things which do not exist 
could have no share in reality. 

Further, if a divisible thing is to exist, it is necessary 
that, when it exists, all or some of its parts must, exi st. 
5 But of time some ^arts^haye_beenijA^hik^he^ 
and no partjif it ;>, though it is divisible. For what is 

^ Reading nwayaiyr] Kai diaaroXt] in 1. 1 5, with Simp, and Diels. 
^ The words in brackets appear to be an alternative version of 
11. 2-1 1 ; they are not in place here. 

BOOK IV. lo 218* 

*noiiL' is not a£art : a part is a measure of the whole, ^>^ 

which must be made up of parts. Time, on the other ' ^ 
hand, is not held to be made up of ' nows '. sj k-^^" 

Again, the *now' which seems to b ound the past and ^ ^--/ 

the future— does it^lw ays remain one and the same or is it_ . • 

always other ^nd other? it is hard to say. 10 

(i) If It is always different and different, and if none of 
the parU in time which are other and other are simul- 
tane^jis (unless the one contains and the other is contained, 
as the shorter time is by the longer), and if the 'now' 
which is not, but formerly was, must have ceased-to-be at 
some time, the ' noivs ' t oo cannot be^nmltaneous with 15 
one another, but the prior ' now ' must always have ceased- 
to-be. But the prior ' now ' cannot have ceased-to-be in -^ 
itself (since it then existed) ; yet it cannot have ceased-to- 
be in another ' now '. For we may lay it down that one 
* now ' cannot be next to another, anv more t ^lan point to 
point.^ If then it did not cease-to-be in the next ' now ' 
but in another, it would e'xisT simultaneously with the 20 
innumerable *nows 'between the two^ — which is impos- 

Yes, but (a) neither is it possible for the * now ' to remain 
always the same. No determinate divisible thing has a 
single termination, whether it is continuously extended in 
one or in more than one dimension : but the * now' is ^^^ 
a termin ation, and it is possible to cut off a determinate 
time. Further, if coincidence in time (i. e. being neither 25 
prior nor posterior) means to be ' in one and the same 
" now " ',* then, if both what is be fore and what is^fter are 
in this same * now ', things which happened ten thousand 
years ago would be simultaneous with what has happened 
to-day, and nothing would be before or after anything else. 

This may serve as a statement of the difficulties about 30 
the attributes of time. 

^ The argument would be clearer if we could say * during ' itself. 
If the existent perished ' in * itself, it would never exist without 

^ Reading (TTiyfxi)v o-Tiy^TJs in 1. 19, with E Phil. Simp. 

^ Omitting toIs vvv in 1. 21, as Phil, apparently does. 

* Reading in 1. 26 f. Ka\ h\ vvvy with Diels. 


As to wha t time is or what is its nature, the traditional 
accounts give us as littleHght as the preliminary problems 
which we have worked through. 

Some assert that it is (i) the movement of the whole, 
218 others that it is (2) the sphere itself.^ 

(i) Yet part, too, of the revolution is a time, but it 
certainly is not a revolution : for what is taken is part of 
a revolution, not a revolution. Besides, if there were more 
heavens than one, the movement of any of them equally 
would be time, so that there would be many times at the 
same time. 
5 {2) Those who said that time is the sphere of the whole 
thought so, no doubt, on the ground that all things are in 
time and all things are in the sphere of the whole. The 
view is too naive for it to be worth while to consider the 
impossibilities implied in it. 

But as time is most usually supposed to be (^) motion and 

a kind of chang e, we must consider this view. 

10 Now (a) the change or j iQvpmeixt of each thing 4s only 

Jn the thing w hich changes or w/tere the thing itself which 

..^ moves or changes may chance to be. But time is present 

equally everywhere and with a ll thir|gg. ^ 

Again, (d) change is always faster or slower, whereas 

15 time is not: for 'fast' and 'slow' are defined by time^ — 

' fast ' is what moves much in a short time, * slow ' what 

moves little in a long time ; but time is not defined by time, 

by being either a certain amount or a certain kind of it. 

Clearly then it is n^ t_i3lQ3^eBi^J^t^ (We need not dis- 

20 tinguish at present between ' movement ' and * change '.) 

jut neither does time exist without^ change; for when I 

'{_the state of ouFown minds does not change at all, or we 

have not noticed its changing, we dojiot realize thattime 

has elapsed, any more than those who are fabled to sleep 

^5 among the heroes in Sardinia ^ do when they are awakened ; 

for they connect the earlier *now^ with the later and make 

^ Aristotle is probably referring to Plato and the Pythagoreans 
respectively. Cf. Diels, Vors.^ i. 355. 6. 
2 For the fable cf. Rohde, Mem. Mus, xxxv. 1 57 ff. 

BOOK IV. n ^'""'■'^ '^^ '""'1i,^6' " '"^ 

them one, cutting out the interval because of t heir failure 
to notice it. So, just as, if the * now ' were not different 
but one and the same, there would not have been time, so 
too when its difference escapes our ^ . y^ic e the interva l does- <*-^/<*^-^ • 

n ot seem to_ be_time^ If, then, the non-realization of the ^- 

existence of time happens to us when we do not distinguish 30 
any change, but the soul seems to stay in one indivisible 
state, and when we perceive and dist inguish we say time 
ha s elap sed, evidently time is not independenFof move- ~ 
ment and change. It is evident, then, that timejsjidther 219^ "^ 
movement nor ind ep endent of movement . 

We must take this as our ^tarting-point and try to 
discover — since we \Vish to know what time is — ^what 
exactly it has t o do with moveme nt. 

Now we pero dye movement and time together : f or q 
even when it is dark and we are not being affected 
through the body, if any movement takes place in the 5 
mind we at once suppose that some time also has elapsed ; 
and not only that but also, when some time is thought to 
have passed, some movement aiso along with it seems 
to have taken place. Hence time is either movement or -^ 
something that belo ngs to movement . Since then it is not 
movement, it must be the other. 

But what k mnvpH 1 \^ pioved from something to som e- 10 / 

thing, and all magnitude is continuous. Therefore the move- 
ment goes with the magnitude. Becaus e th e ma^enitude^is 
continu ous, the movement too mu st bel:ontinuo us, and if 
the m oveinenf, then tM time ; for the time that haTpassed 
is always thought to be in proportion to the movement. 

The distinction of 'before* and ' after ' holds primarily , 
then,2 in place ; and there in virtue of relative position. 
Since then 'before' and 'after' hold in magnitude, they 15 
must hold also in mo vement, these corresponding to those. 
But also in time the distinction of ' before ' and ' after ' must 
hold, fo r time an d, rnoyem ent always correspond with each 
other. The * before' and * after '^ in motion identical in 

^ KivTjo-is here must be restricted to that Kara t6v tSttov. 

2 Omitting 8e in 1. 14, with EH Them. Al. 

^ Omitting avTa>v in 1. 20, with H Them. Phil. Simp. 


20 substratum with motion yet differs from it in definition, and 
is not identical with motion. 

But we appre hend time o nly ^^1^^" w*^ ^r^.Y^.^nn^^^'^ 

motion, marking it by ^ * before 'and * after ' ; and it is only 

«^ Tvvhen we have perceived * before ' and * after ' in motion that 

y^ 25|we^ say that tim e has elapsed. Now we mark them by 

. ^^'^ ^ judging that A and B are different, and that some third thing 

'^ ^^rf^ is intermediate to them. When we think of the extremes 

as different from the middle and the mind pronounces that 

the 'nows' are two, oneTBefpre and_one^aiier, it is then 

that we say that there is tijnCj^and this that we say is time. 

F or what is bounded by the * now ' is thought to be time — 

we may assume this. 

V^ 30 When, therefore, we perceive th^^^oaLLssone, and 

neither as b '^f'^^'^^ ^ pd after in a motion nor as an identity 

but in relation to a ' before ' and an * after ', no time is 

thought to have elapsed, because there has been no motion 

either! (Jn t he other Tiand, when we do perceive a ^ befo re/ 

219^ and an ' after ', then we s ay that JthereusJtime. For time — 

is just this — n umber of motion in res pect of 'before' and 


Hence time is not movemen t, but onl y movemen t in, so 

far ^s it adm i ts of enum erati"" - A proof of this: we 

discriminate the more or the less by number, but more or, 

less movement by tijrie. Ti me then is n kind Q ^TnumS er. 

t (Number, we must note, is used in two senses — both of 

Iwhat is counted or the countable and ajso_of that witlL 

^ which we count. Time obviously'^ is what is counted, 

not that with which we count : these are different kinds of 


Just as motion is a perpetual succession, so also is time. 

10 But every simultaneous time is self-identical ; for the ' now ' 

as a subject is an identity, but it accepts different attributes.^ 

^ Reading rw in 1. 23, with EFG. 

^ Reading 8r} in 1. 7, with FG. 

' E. g. if you come in when I go out, the time of your coming in is 
in fact the time of my going out, though for it to be the one and to be 
the other are different things. 

BOOK IV. II aig** 

The ' now ' measures time, in so far as time involves the 

* before and after '. 

The * now ' in one sense is the same, in another it is not 
the same. In so far as it is i n successio n, it is different 
(which is just what its being now^ was supposed to mean), 
but its sub stratu m ^ is an jdentjt y : formation, as was said,^ 15 
^oes with magnitud e,^ and ^time , as we maintain, ^ith 
motion . Similarly, then, there corresponds to the point ^ 
the body which is carried along, and by which we are 
aware of the motion and of the ' before and after ' involved 
in it. This is an identical stibstratzim (whether a point or 
a stone or something else of the kind), but it has different 
attributes — as the sophists assume that Coriscus' bemgTn 20 
fReLyceum is a different thing from Coriscus' being in the 
market-place.^ And the body ^which is carried alon ^ is 
different , in so far as it is at one time here and at another 
there. But the ' now ' corresponds to the body that is 
carried along, as time corresponds to the motion^ For it 
is by means of the body th at is carried along that we 
become aware of the ' before and after ' in the motion, and 25 
if we regard these as countable we get the ' now '. Hence 
in these also the ' now ' as substratum '^ remains th e sam e (for 
it is what is before ^ and after in movement)jj3Ut what_j,s 
predicated of it isiiifferent ; for it is in so far as the ' before 
and after ' is numerable that we get the ' now '. This is 
what is most knowable : for, similarly, motion is known 
because of that which is moved, locomotion because of 
that which is carried. For what is carried is a real thing, 30 
the movement is not. Thus what is called ^now* in one 
sense is always t he sam e ; in another it is not the same : for 
this is true also of what is carried. " 

Clearly, too, if the re were no time, the re would, -be-no. 

* now^^nd vice versa. Just as the moving body and its loco- 220* 

^ Reading in 1. 14 to vvv elmi, with Phil, and Bonitz. 
^ Reading 6 fie nore, with H and Simp. ^ *II. 

* i. e. witii the path traversed. ' 'i.e. in the path. 

* sc. to prove that Coriscus is different from himself. I.e., they 
assume that a difference in the attribute means a difference in the 

' Reading in 1. 26 vvv eVn, to (cf. 11. 14 f.). 
^ Reading to np6T€pov in 1. 26, with EH I Phil, 


motion involve each other mutually, so too d o the number 
of the moving body and th^ number of its locomotion. For 
the number of the lo(;:omntif >n i*^ tip ppj y jhWp. the * now ' corre- 
sponds to the moving body, and is like the unit of number. 
.Tmie, then, alsoj s bot h made continu^"'^ b y the ' now ' . 
and divided at it. For here too there is a correspondence 
with the locomotion and the moving body. For the motion 
or locomotion is made one by the thing which is moved, 
because it is one — not because it is one in its own nature (for 

there might be pauses in the movement of such a thing) — 
but because it is one in definition ^ : for this determines the 
movement as ^before' pind ^afterL Here, too, there is a corre- 
spondence with- the point ; for the poinf also both connects 
and terminates the length — it is the be ejnning of one and the 
end of another. But when yo u take it i" this way, using the 
one point as two , a (paus^ is necessary, if the same point is to 
be the beginning and the end. The ' now ' on the other hand, 
since the body carried is moving, is always different. 

Hence time is not number in the sense in which there is 
' number ' of the same point because it is beginning and end, 
but rather as the extremities of a line^ form a number, and 
not as the parts of the line do so, both for the reason given 
(for we can use the middle point as two, so. that on that 
analogy time mi ght stand still ), and further because obvi- 
ously the j-now' is no^ part of time n or the sec tion any 
^rt of the mnyem pnt, any more than the points_ a re parts 
of the li ne — for it is two lines that arQ parts of one line. 

In so far then as the ' now ' is a boundar y, it is not time, 
but an attribute of it ; in so far as it numbers, it is 
number; for~ buuiidaiig s belong only to that which they 
bound, but number (e. g. ten) is the number of these * horses, 
and belongs also elsewhere. 

It is clear, then, that time is ' number of move ment in 
2.^ jespect of the before and after,, and is contmuous si nce jt 
is an attribute ofwhaLiajCQIitinuous. 

' i. e. as moved. 

^ Reading in 1. i6 ttjs ypafj.firjs ixaWov, with Phil. Simp. 

^ Reading ouSeV in 1. 19, with EG Al. Asp. Simp. 

* Reading dpidfios Tcovde in 1. 23, with E Phil. Simp. 


BOOK IV. 12 220^ 

12 The smallest number, in the strict sense of the word 
' number ', is two.^ But of number as concrete, sometimes 
there is a minimum, sometimes not : e. g. of a ' line ', the 
smallest in respect oi multiplicity is two (or, if you like, one), 
but in respect of j/'-s'^there is no minimum ; fo r every line ^ 
is divided ad infinitu m-^ Hence it is so w ith X}vne.. In 
respect of number the minimum is one (or two) ; in point 
of extent there is no minimum. 

It is clear, too, that time is not described as fast or slow, 
but as many or few ^ and as long or short. F or as continuous 220^ 
j tjs lon , g or .^ hni -l ; and as a n umber many or fe w, but it is not 
fast or slow — any more than any number with which we 
number is fast or slow. 

Further, there is the same time everywhere at once, but 5 
not the same time before and after, for while the present 
change is one, the change which has happened and that 
which will happen are different. Ti gie is not numb^r^ 
with which w e count, but the number of things which are_ * 
counte d, and this according as it occurs betore or after is 
always different, for the * nows ' are different. And the to 
number of a hundred horses and a hundred men is the 
same, but the things numbered are different — the horses 
from the men. Further, as a movement can be one and 
the same again and again, so too can time, e. g. a year or 
a spring or an autumn. 

Not only do we measure the movemen t by the time, but 15 
also the time by the movement^ because they define each 
other. The time marks the movement, since it is_Jts_ 
numb er, and tlTe movement the timeT"" We descj-ihe the 
^p as miirh r>r little, !r>p;^.spnn p- it by the movemen t, just 
as we know the number by what is numbered, e.g. the 
number of the horses by one horse as the unit. For we 20 
know how many horses there are by the use of the number ; 
and again by using the one horse as unit we know the 
number of the horses itself. So it is with the time and 
the movement ; for we measure the movement by the 
time and vice vexsa. It is natural that this should happen ; 

^ Reading in 1. 27 iarriv 17 bvas. 
'^ e. g. * many years '. 

aao** PHYSIC A 

25 for the movement goes with the distance, and the tim^ 
wit h the movement , because they are quanta and con- 
tinuous and divisible. The movement has these attributes 
because the distance is of this nature, and the _time has 
them because of the movement.^' And we measure both 
the distance by the movement and the movement by the 
distance ; for we say that the road is longT^Flhe journey 

30 is long, and that this is long, if the road is long — the time, 
to o, if the movement, and the movement, if the time. 

221* Tmi<^ i<^ a pipagnrp pf mntinn i^p^ of beill^ f- moved^ and 

it measures the motion by determining a motion which 
will measure exactly the whole motion, as the cubit does 
the length by determining ^ an amount which will measure 
out the whole. Further * to be in time ' means, for move- 
ment, that both it and its essence are measured by time 
5 (for simultaneously it measures both the movement and its 
essence, and this is what being in time means for it, that 
its essence should be measured). 

Clearly then ^ ' to be in time ' has the same meaning for 
other things also, namely, that their being should be 
measured by time. ' To be in time ' is one of two things : 
JO (i) to exist when time exists, (2) as we say of some things 
that they are * in number '. The latter means either what 
is a part or mode of number — in general, something which 
belongs to number — or that things have a number. 

Now, since time is number, the ' now ' and the ' before ' 
15 and the like are in time, just as ' unit ' and ' odd ' and ' even ' 
are in number, i. e. in the sense that the one set belongs to 
number, the other to time. But things are in time as they 
are in number. If this is so, they are contained by time 
as things in place are contained by place. 

Plainly, too, to be in time does not mean to coexist with . 
20 time, any more than to be in motion or in place means to 
coexist with motion or place. For if ' to be in something ' 
is to mean this, then all things will be in anything, and the 
heaven will be in a grain ; for when the grain is, then also 
is the heaven. But this is a merely incidental conjunction, 

^ Reading Spiaai in 1. 3, with EG Them. Simp. 

^ Reading in 11. 5-7 {dfxa . . . etfoi), 8rj\ov oTt, with Al. Simp. 

BOOK IV. 12 221* 

whereas the other is necessarily involved : that which is in 
time necessarily involves that there is time when it is, and 25 
that which is in motion that there is motion when it is. 

Since what is ' in time ' is so in the same sense as what 
is in number is so, a time greater than everything in time 
can be .found. So it is necessary that all the things in time 
should be contained by time, just like other things also which 
are ' in anything ', e. g. the things * in place ' by place. 

A thingj then, will be affected by time,^just as we ares© 
accustomed to say that time wastes things away, and that 
all things grow old through time, and that there is oblivion 
owing to the lapse of time, but we do not say the same of 
getting to know or of becoming young or fair. For time 221^ 
is by its nature the cause r ather of decay, since it is the 
number of change , and change rejUQyes what is. 

Hence, plainly, things which are always are not, as such, 
in time, for they are not contained by time, nor is their 
being measured by time. A proof of this is that none of 5 
them is affected by time, which indicates that they are not 
in time. 

Since time is the measure of motion^ it will _be^jth£ 
measure of rest too — indirectly. For all rest isJ L tim e. 
For it does n ot follow that what is in time is moved, thou gh 
what is in motion is necessarily moved. For ^ime is noL^Q 
motjoiij^butjjiumber of motion': and wFat is at rest, also, 
can be in the number of motion. Not everything that is 
not in motion can be said to be * at rest * — but on l y that . 
which can be irioved^_though it actually is not moved, as 
was said above.^ 

' To be in number ' means that there is a number of the 
thing, and that its being is measured by the number in 15 
which it is. Hence if a thing is 'in time' it will be 
measured by time. B ut time will m easure what is moved 
and what is at _r£st, the one qua moved, the other qua at 
rest; for it will measure their motion and rest respec- 

Hence w hat is moved will not be measurable by the 
time simply vcTso far as it has qualititv. but in so far as 

^ 202*4. 


2 its motion has quantity. Thus none of the things which are 
neither moved nor at rest are in time : for ' to be in time ' is 
* to be measured by time', while time is the measure of 
motion and rest. 

Plainly, then, neither will everything that does not exist 
be in time, i. e. those non-existent things that cannot exist, 
as the diagonal cannot be commensurate with the side. 
25 Generally, if time is directly the measure of motion and 
indirectly of other things, it is clear that a thing whose 
existence is measured by it will have its existence in rest or 
motion. Those tnings therefore which are subject to perish- 
ing and becoming— generally, those which at one time exist, 
30 at another do not — are necessarily in time : for there is a 
greater time which will extend both beyond their existence 
and beyond the time which measures their existence. 
Of things which do not exist but are contained by time 
222^ some were, e. g. Homer once was, some will be, e. g. 
a future event ; this depends on the direction in which 
time contains them ; if on both, they have both modes of 
existence.^ As to such things as it does not contain in any 
way, they neither were nor are nor will be. These are 
those non-existents whose opposites always are, as the 
5 incommensurability of the diagonal always is — and this 
will not be in time. Nor will the commensurability, 
therefore ; hence this eternally is not, because it is contrary 
to what eternally is. A thing whose contraiy is not eternal 
can be and not be, and it is of such things that there is 
coming to be and passing away. 

10 The ^ now' isjhe link of tirne, a s has _b.ecn said '^ (for jtj 
co nnects past_ ^nd_ jiUure_lim.Qk and jt_J s_a limit ^ of tim e 
( for it is the beginning of the one and the end of the other}^ 
But this is not obvious as it is with the point, which is 
fixed. It divides potentially, and in so far as it is divid JQg, 

15 t he * now ' is alway s differ ent, but in so far a s it connec 
iti s always the samg^ as it is with mathematicaTlines. 

^ Putting a comma after dficpdrepa in 1. 2. 

2 220^5. 

' Omitting o\a>s in 1. 11, with E and Simp. 

BOOK IV. 13 222^ 

For the intellect it is not always one and the same point, 
since it is other and other ^ when one divides the line ; but in 
so far as it is one, it is the same in every respect. 

So the ' now ' also is in one way a potential dividing of time, 
in another the termination of both parts, and their unity. 
And the dividing and the uniting are the same thing and in 
the same reference, but in essence they are not the same. 

So 2 one kind -of ' now ' is described in this way : another 20 
is when |he time is near this kind of ' now '. ' He will 
come now ' because he will come to-day ; ' he has come 
now ' because he came to-day. But the things in the Iliad 
have not happened * now '/nor is^ the flood 'now' — not 
that the time * from now to them is not continuous, but 
because they are not near. 

' At some time ' means a time determined in relation to 
the first of the two types of *now',^ e.g. * at some time' 25 
Troy was taken, and * at some time ' there will be a flood ; 
for it must be determined with reference to the ' now '. 
There will thus be a determinate time from this * now ' to 
that,^ and there zvas such in reference to the past event. 
But if there be no time which is not ' sometime ', every 
time will be determined. 

Will time then fail ? Surely not, i fmotion always exists . 
Is time then always different or does me same time recur? 30 
Clearly time is, in the same way as motion is. For if one 
and the same motion sometimes recurs, it will be one and 
the same time, and if not, not. 

Since th e ' now ' is an end and a beginning of time, not 2 22 
of the same time however , but th^_end of that which is 

past and the beginning of that which is to come, it follows 
that, as the circle nas its convexity and its coilcavity, in 
a sense, in the same thing, so time is always at a beg inning ^ 
and at an end. And for this reason it seems to be always 
differen t ; for the * now ' is not the beginning and the end 5 
of the same thingj if it were, it would be at the same time 

^ Reading in 1. 17 ahXr] koI oXX?;, with F Them. Phil. 
^ Reading in 1. 20 \iiv ovv oiJro), with GHI Them. Simp. 
' Omitting yeyoi/e in 1. 23, with Them. 

* Reading in 1. 24 ow^x^^ o XP°''Of with E Them. Phil. Simp. 

* Cf. 11. 20 f. « Omitting Km before etV in 1. 28, with GH Phil. 

222** PHYSICA 

and in the same respect two opposites.^ And time will not 
fail ; for it is always at a beginning. 

* Presen tly ' or ^just ' refers to the part o f future time 
lo which is near the indivisible present ' now' (' When do you 
walk ? ' * Presently', because the time in which he is 
going to do so is near), and to the part of past time 
which is not far from the ' now ' (' When do you walk ? ' 
'I have just been walking'). But to say that Troy has 
just been taken — we do not say that, because it is too far 
from the ' now '. ' Lately ', too, refers to the part of past 
time which is near ^ the present ' now '. ' When did you 
go ? ' ' Lately ', if the time is near the existing now. 

* Long ago ' refers to the distant past. 

15 ' Suddenly' refers to what has departed from its former 
condition in a time imperteptible because of its smallness ; 
but it is the nature of al/ change to alter things from their 
former condition. In time all things corne into being and 
pass away ; for which reason some called it the wisest of 
all things, but the Pythagorean Paron ^ called it the most 
stupid, because in it we also forget ; and his was the truer 
view. It is clear then that it must be in itself, as we said 

30 before,* the condition of destruction rather than of coming 
into being (for change, in itself, makes things depart from 
their former condition), and only incidentally of coming 
into being, and of being. A sufficient evidence of this is 
that nothing comes into being without itself moving some- 
how and acting, but a thing can be destroyed even if it does 
not move at all. And this is what, as a rule, we chiefly 

35 mean by a thing 's being destroyed by time. Still, time 
does not work even this change ; even this sort of change 
takes place mcidentally in time. 

W e have stated, then, that time ex ists and what i t is. 
an d jn how man y senses we sp eak of the * now ', a nd what 

* at some time '/ la-teiy '/^presently ' or *just ', ' long ago ', 
and * suddenly ' mean. 

^ Putting a full stop after ei?; in 1. 6, with Bonitz. 

^ Reading in 1. 13 vvv \to\ fiopiov, with Them. Simp. Bonitz. 

^ Nothing further is known of Paron. * 221'' 

BOOK IV. 14 222^ 

These distinctions having been drawn,^ it is evident that 30 
every change and everything- that moves is in time : for 
the distinction of faster and slower ex is ts in reference to 
all chang e, since it is found in every instance. In the 
phrase ' moving faster ' I refer to that which changes before 
another into the condition in question, when it moves over 223* 
the same interval and with a regular movement ; e. g. in 
the case of locomotion, if both things move along the 
circumference of a circle, or both along a straight line ; 
and similarly in all other cases. But what is before is in 
time ; for we say ' before ' and ' after ' with reference to the 5 
distance from the ' now', and the 'now' is the boundar y pf 
tl ie past and the future ; so that since ' nows ' are in time, 
the before and the after will be in time too; for in that 
in which the 'now' is, the distance from the 'now' will 
a^so be. But 'before' is used contrariwise with reference 
to past and to future time ; for in the past we call ' before ' 10 
what is farther from the ' now ', and ' after ' what is nearer, 
but in the future we call the nearer ' before ' and the farther 
'after'. So that since the 'before' is in time, and every 
movement involves a ' before', evid ently every change and 15 
every movement is in time. 

It is also worth considering how time can be rel ated to 
the soul ; ^nd why time is thought to be in everything, 
botlTin earth and in sea and in heaven. Is it because it is 
an attribute, or state, of movement (since it is the number 
of movement) 2 and all t hese things ar e movable^(for they 
are all in place), and time and movement are together, both ao 
in respect of potentiality and in respect of actuality ? 

Whether if soul did not exist time would f ^xis t f>r not, i.q ^Q^^ |^--*^* 
a^ question that may fair l y he asked ; for if there cannot 
be some one to count there cannot be anything that can be 
Cdunted, s6 that evidently there cannot be number; for 
number is either what has been, or what can be, counted. 
But if nothing but soul, or in _soul re ason, is q ualified to 25 
:ount, there would no ^be time unless there were soul, but 

^ Reading in 1. 30 8i(opi(Tix€V(ov, with H Them. Phil. 
^ Treating eV . . . navra in 1. igf. as parenthetical. 


only that of which time is an att ribute, i. e . if mo vement. 
can exist vvitnout soul, and the betore and after are attri- 
butes of movement, and time is these qua numerable. 

One might also raise the question what sort of movement, 

30 time is t he number of. Must we not say ' of" any kind ' ? 
For things both come into being in time and pass away, 
and grow, and are altered in time, and are moved locally ; 
thus it is of each movement qua movement that time is 
the number. And so it is si mply the number of continuo us 
movement, not of ^ny p articularjkmd of it. 
223^ But other things as well may have been moved now, 
and there would be a number of each of the two move- 
ments. Is there another time, then, and will there be two 
equal times at once ? Surely not. For a time th at is -both 
equal and s-imultaneous 7s"^one and the same t ime.^ and 
even those that are not simultaneous are one in kind ; for 
5 if t here were dogs, and hors es^ajid _sev^ of each, i t would 
be th e same number . So, too, mo vements that have simul - 
tane ous limits have the same time Tvet the one mav in fact 
be fast and the other not, and one may be locomotion 
and the other alteration ; still the time of the two changes, 
is the same if their number alsols equal and simultaneous ; 

10 and for this reason, while the movements are different and 
separate, tjie time is eve rywhere the sam e^ ^because the 
number of equal and simultaneous movements is every- 
where one and the same. 

Now there is such a thing as locomotion, and in 
locomotion there is included circula r movement^ and 
everything is measured by some one thing homogeneous 
with it, units by a unit, horses by a horse, and similarly 

15 times by some definite time, and, as we said,^ time is 
measured by motion as well as mot ion by time (this "Being 
so because by a motion definite in time "tFe quantity both 
of the motion and of the time is measured) : ^ if, then, what 

^ Reading in 1. 3 6 aiVor yap X9^^'^^ ^'^*- ^'^ ° ''^^^ '^"* ^V^"- ^| 

2 220^28. V 

' Placing a comma after cbpta/xeVa) in 1. 15 and a semicolon befor( 

et in 1. 18, and treating tovto . . . x9^^^^ i" li* 16-18 as parenthet ical 1 

with Bonitz. JH 

BOOK IV. 14 223^^ 

is first is the measure of everything homogeneous with it, 
regular circular motion is above all else the measure, 
because the number of this is the best known. Now neither 20 
alteration nor increase nor coming into being can be 
regular, but locomotion can be. This also is why time is 
thought to be the movement of the sphere, viz. because 
the other movements are measured by this, and time by 
this movement. 

This also explains the common saying that human affairs 
form a circle, and that there is a circle in all other things 25 
that have a natural movement and coming into being and ¥- 
passing away. This is because all other things are dis- 
criminated by time, and end and begin as though conform- 
ing to a cycle ; for eve n time itself is thought to be a circle. ♦ 
And this opinion again is hel d because time Jg th^ mpat;nre.:;n 
of this kind of locomotion and is itself measured by 
such. So that to say that the things that come into 
"Being form a ^circle is to say th at there is a circ le of 
time ; and this is to say that it is measured by the circular 
movement ; for apart from the measure nothing else to be 
measured is observed; the whole is just a plurality of 224^ 

It is said rightly, too, that the number of the sheep and of 
the dogs is the same fiumber if the two numbers are equal, 
but not the same decad or the same ten ; just as the equi- 
lateral and the scalene are not the same trimigle^ yet they 5 
are the sdiVae figure, because they are both triangles. For 
things are called the same so-and-so if they do not differ 
by a differentia of that thing, but not if they do ; e. g. 
triangle differs from tr iangle by a differentia of triang le,^ 
therefore they are different triangles ; but they do not 
differ b y a differentia of figure, b ut are in one and the 
same division of it. For a figure of one kind is a ^ircle 
and a figure of another kind a triangle, and a triangle of 10 
one kind is equilateral and a triangle of another kind 
scalene. They are the same figure^ then, and that, t W^"gl^j — 

^ Reading in 1. 7 rpiyavov Tpiyd>vov rpiyavovy with Torstrik and 
perhaps with SimpHcius. 

I 2 


but not the same triangle.^ Therefore the number of two 
groups also is the same number^ (for their number does 
not dififer by a differentia of number), but it is not the 
same decad ; for the things of which it is asserted differ ; 
one group are dogs, and the other horses. 
T5 We have now discussed^^time— ^bpth time itse lf and the 
matters appropriate to the consideration of it. 

^ Reading in 1. 12 tovto rpiyavov, rplyoivov 6* ov. 
^ Omitting 6 in 1. 13, with F and Phil. 


Everything ^ which changes does so in one of three 224 
senses. It may change (i) acc iden tally ^ as for instance when 
we say that something musical walks, that which walks 
being something in which aptitude for music is an accident. 
Again (2) a thing is said without qualification to change 
because somethmg^belonging to it changes, i. e. in statements 
which refer to part of the thing in question : thus the body 25 
is restored to health because the eye or the chest, that is 
to say a part of the whole body, is restored to health. 
And above all there is (3) the case of a thing which is in 
motion neither accidentally nor in respect of something 
else belonging to it, but in virtue of being it^lf directly in 
motion. Here we have a thing which is essentially movable : 
and that which is so is a different thing according to the 
particular variety of motion : for instance it may be a thing 
capable of alteration : and within the sphere of alteration 
it is again a different thing according as it is capable of 
being restored to health or capable of being heated. And 30 
there are the same distinctions in the case of the mover ; 
(i) one thing causes motion accidentally, (2) another parti- 
ally (because something belonging to it causes motion), 
(3) another of itself directly, as, for instance, the physician 
heals, the hand strikes. We have, then,^ the following \ 
factors : (a) on the one hand that which directly causes [ 
motion, and {b) on the other hand that which is in motion : 
further, we have {c) that in which motion takes place, 35 
namely time, and (distinct from these three) {d) that from 
which and {e) that to which it proceeds : for every motion 21^ 
proceeds from something and to something, that which is ( 
directly in motion being distinct from that to which it is in 
motion and that from which it is in motion : for instance, 

^ With 1. 21-^1 cf. Met. 1067^^ 1-9. 

^ The apodosis to eVei 6' eVn ktK. begins at h dq Kivrjais ktX. (224^ 4). 


we may take the three things * wood ', ' hot ', and ' cold ', of 
which the first is that which is in motion, the second is that to 
which the motion proceeds, and the third is that from which 
it proceeds. This being so, it is clear that the motion is in 
5 the wood, not in its form : for the motion is neither caused 
nor experienced by the form or the place or the quantity. 
So we are left with a mover, a moved, and a goal of motion. 
I do not include the starting-point of motion : for it is the 
goal rather than the starting-point of motion that gives its 
name to a particular process of change. Thus ' perishing ' 
is change ^o 7tot-being^ though it is also true that that 
which perishes changes from being : and ' becoming ' is 
change /o being, though it is also change from not-being, 

lo Now a definition of motion has been given above,^ from ^ 
which it will be seen that every goal of motion, whether it 
^ be a form, an affection, or a place, is immovable, as, for 
instance, knowledge and heat. Here, however, a difficulty 
may be raised. Affections, it may be said, are motions, 
and whiteness is an affection : thus there may be change to 

15 a motion.^ To this we may reply that it is not whiteness 
but w liitening t hat is a motion. Here also the same dis- 
tinctions are to be observed : a goal of motion may be so 
accidentally, or partially and with reference to something 
other than itself, or directly and with no reference to any- 
thing else : * for instance, a thing which is becoming white 
changes accidentally to an object of thought, the colour 

20 being only accidentally the object of thought ; it changes 
to colour,^ because white is a part of colour, or to Europe, 
because Athens is a part of Europe ; but it changes 
essentially to white colour. It is now clear in what sense 
a thing is in motion essentially, accidentally, or in respect 
of something other than itself, and in what sense the phrase 

^ 201^ 10. ^m 

2 With 11. 1 1-16 cf. i^^/. 1067^9-12. ^ ^ ■■ 

^ i.e. there may be motion not only in ro Kivovfievov but alsoTn 

TO els o Kivurai. 
* Omitting in 1. 17 to before both kcit aWo and nrj Kar aWn, which are 

intended merely to amplify ^nra n^pos and Trpcbrajs- respectively : there 

are only f/iree distinct senses, as may be seen from the opening words 

of the book. 
^ Here kotu fxepos must be supplied in sense, if not in the text. 


BOOK V. I 224'' 

' itself directly ' is used ^ in the case both of the mojier and 
of the moved : and it is also clear that the motion is not in 25 
the form but in that which is in motion, that is to say ' the 
movable in activity'. Now accidental change we may 
leave out of account : for it is to be found in everything, at 
any time, and in any respect. Change ^ which is not acci- 
dental on the other hand is not to be found in everything, 
but only in contraries, in things intermediate between con- 
traries, and in contradictories, as may be proved by indue- 30 
tion. An intermediate may be a starting-point of change, 
since for the purposes of the change it serves as contrary 
to either of two contraries : for the intermediate is in a 
sense the extremes. Hence we speak of the intermediate 
as in a sense a contrary relatively to the extremes and of 
either extreme as a contrary relatively to the intermediate : 
for instance, the central note is low relatively to the highest 
and high relatively to the lowest, and grey is light rela- 
tively to black and dark relatively to white.^ 

And since every c hange is from so mething to some thing 35 
— as the word^TtSell' {\k^ra^o\r\) indicates, implying some- 225^ 
thing * after ' {{i^ra) something else, that is to say some- 
thing earlier and something later — that which changes 
must change in one of foi^r y^avs^ fro m ^ subject to subject, 
from subject to non-subject, from non-subject to subject, 5 
or from non-subject to non-subject, where by * subject ' 
I mean what is affirmatively expressed. So it follows 
necessarily from what has been said above ^ that there are 

^ It seems possible to keep (with Bekker) the words koi nm to avro 
irpoiTovy regarding avro npcoTov as a phrase quoted from above. 
Argyropylus, however, renders ' et quomodo idem primum sit ', which 
seems pointless. Others regard the words as a mere repetition of the 
preceding ttms Kad* avro Kivelrai — though in order to do so they have to 
emend to to roi — and therefore bracket them as an interpolation. 

' With 11. 28-30, cf. AfeL 1067^ 12-14. 

' It seems necessary to use four terms in English, though two are 
sufficient in Greek, since both neXav and XevKop are more elastic 
in meaning than the English ' black ' and * white ', which, however, 
must be used here to translate to peXav and to XevKov, the two extremes. 

* With 1. 3-226" 16 cf. MeL 1067^ 14-1068^ 15. 

^ 224^^ 28, 29. Or €K Ta>p dp}}fi€vou might mean * of the four con- 
ceivable kinds of change just mentioned ' : but Aristotelian usage 
seems in favour of the rendering adopted in the text, which gives just 
as good sense. 


only th ree kinds of change, that from subject to subject, that 
from subject to non-subject, and that from non-subject to 

lo subject : for the fourth conceivable kind, that from non- 
subject to non-subject, is not change, as in that case there 
is no opposition either of contraries or of contradictories. 

Now change from non-subject to subject, the relation 
being that of contradiction, is ^ coming to be * — ' unqualified 
coming to be ' when the change takes place in an unqualified 
way, * particular coming to be ' when the change is change in 
a particular character : for instance, a change from not- 
white to white is a coming to be of the particular thing, white, 

15 while change from unqualified not-being to being is 
coming to be in an unqualified way, in respect of which we 
say that a thing ' comes to be ' without qualification, not that 
it ' comes to be ' some particular thing. Chang|^e from subject 
to non-subject is 'perishingr ^ — * unqualified perishing ' when 
the change is from being to not-being, ' particular perishing ' 
when the change is to the opposite negation, the distinction 
being the sam.e as that made in the case of coming to be. 

20 Now ^ the expression ^not-being' is used in several senses : 
and there can be motion neither of that which ' is not ' in re- 
spect of the affirmation or negation of a predicate,^ nor of that 
which ' is not' in the sense that it only potentially *\^ ', that isto 
say the opposite of that which actually ' is ' in an unqualified 
sense : for although that which is * not-white ' or * not-good ' 
may nevertheless be in motion cwcidentaMy (for example 
that which is ' not-white ' might be a man), yet that which 
is without qualification ' not-so-and-so ' cannot in any sense 

25 _be in motion : therefore it is impo^ffi hl^" ^"^^ ^^^^ wJnYh Vcj;^ 
to be in motion. This being so, it follows that ' bec om:;, 
ing ' cannot be~a motion : for it is that which * is not ' that 
* becomes '. For however true it may be that it accidei 

^ The following sentences are very loosely joined together, but the 
sequence of thought is fairly clear. The apodosis to the €t-clause 
must be found in the words ahvvajov t6 \x^ ov Kiveiadm, 1. 25, where yap 
must be omitted, with Themistius and with some MSS. in Met 1067^30. 

^ Lit. * in respect of conjunction or separation ' : i. e. in /a/j<? judge- 
ments, which 'join together' things which ought not to be joined 
together, e. g. ' man has wings *, or * separate ' things which ought not 
to be separated, e. g. * man has not arms '. 


BOOK V. I 225^ 

' becomes V it is nevertheless correct to say that it is that 
which * is not ' that in an unqualified sense * becomes '. And 
similarly it is impossible for that which ' is not ' to be at rest. 

There are these difficulties, then, in the way of the 30 
assumption that that which * is not ' can be in motion : and 
it may be further objected that, whereas everything which 
is in motion is in space, that which ' is not ' is not in space : 
for then it would be somewhere. 

So, too, ' perishing ' is not a motion : for a motion has 
for its contrary either another motion or rest, whereas 
* perishing ' is the contrary of * becoming '. 

Since, then, every mnti<^" J*^ a kip*^ nf rlianorp^ and there 
are only the three kinds of change mentioned above ; ^ and 35 
since of these three those which take the form of ' becom- 
ing ' and ' perishing ', that is to say those which imply a 225^ 
relation of contradiction, aji^ not motions : it necessarily 
fol lows that only ch ange from subj ect to subject is motJQn . 
And every such subject is either a contrary or an inter- 
mediate (for**^ a privation may be allowed to rank as a con- 
trary) and can be affirmatively expressed, as naked, tooth- 
less,* or black. If, then, the categories are severally 5 
distinguished as Being, Quality, Place, Time, Relation, 
Quantity, and Activity or Passivity, it necessarily follows 
that there are three kinds of motion — qualj^a tivPj gnantifa- 

tive, and local. , 

a In_respgct oLSubstan ce there is no motion, bec ause Sub - 10 

stanrg_ha«; no fonffary atnnng things that are. Nor is 
there motion in respect of Relation : ^ for it may happen 
that when one correlative changes, the other, although this 
does not itself change, is no longer*' applicable, so that in 
these cases the motion is accidental. Nor is there motion 

^ i. e. * that it is something in which ro /x^ ov is an accident that 
becomes, and not to fiq ov itself. ^ 1. 7. 

^ The connexion of thought is : * the fact that there are motions 
(K aTeprjaecDs or els aT€pr](Tiv does not affect the validity of the assertion 
that the vnoKei^evn of motion are ^ euavTia J) fxira^v : for a areprjais 
which is a vTroKtljievov of motion (sc. oi kivtjois as distinct from yhecm) 
is after all in a sense ivavrlov and (like other ivavrla) dijXovTai KaTa(f>da6i.* 

* 1. 5, read voodou for X^vkov, with Me^. 1068^7. 

^ Reading in 1. 11 tov npos n, with the MS. A^ in Mef. ic68* il. 

° Reading in 1. 12 {firj) dXrjdeveadai, with Schwegler. 


225*^ PHYSICA 

in respect of Agent and Patient — in fact there can never be 
i motion of mover and moved, because there cannot be 

15 motion of motion or becoming of becoming or in general 
change of change. 

For in the first place there are two senses in which 
motion of motion is conceivable, (i) The motion of which 
there is motion might be conceived as subject ; e. g. a man 
is in motion because he changes from fair to dark. Can it 
be that in this sense motion grows hot or cold, or changes 

20 place, or increases or decreases ? Impossible : for change 
is not a subject. Or {2,) can there be motion of motion in 
the sense that some other subject changes from a change to 
another mode of being, as e. g. a man changes from falling 
ill to getting well ? Even this is possible only in an acci- 
dental sense. For, whatever the subject may be,^ movement 
is change from one form to another. (And the same holds 

25 good of becoming and perishing, except that in these pro- 
cesses we have a change to a particular ^ kind of opposite, 
while the other, motion, is a change to a different ^ kind.)^ 
So, if there is to be motion of motion, that which is chang- 
ing from health to sickness must simultaneously be chang- 
ing from this very change to another. It is clear, then,^ 
that by the time that it has become sick, it must also have 
changed to whatever may be the other change concerned 
(for that it should be at rest, though logically possible, is 
excluded by the theory). Moreover this other can never 
be any casual change, but must be a change from some- 

30 thing definite to some other definite thing. So in this case 
it must be the opposite change, viz. convalescence. It is 
only accidentally that there can be change of change, e. g. 
there is a change from remembering to forgetting only 
because the subject of this change changes at one time to 
knowledge, at another to ignorance.^ 

^ Reading in 1. 23 aTraa-i for avri], with MS. A^ in Mef. 1068*23. 

^ sc. a contradictory. ^ sc. a contrary. 

* 225^25-6 reading ds avTiKfifieva w5i, t) 5' wdl, tj KiuTjais, wi 
Simplicius and with the MS. A^ in Afef. 1068^25. 

^ Reading in 1. 28 dfj, with E H I. 

^ Reading in 1. 33 ciyvoiav, with (apparently) Philoponus and 




BOOK V. 2 225»> 

In the second place, if there is to be change of change 
and becoming of becoming, we shall have an infinite re- 
gress. Thus if one of a series of changes is to be a change 35 
of change, the preceding change must also be so : e. g. if 226* 
simple becoming was ever in process of becoming, then that 
which was becoming simple becoming was also in process of 
becoming, so that we should not yet have arrived at what 
was in process of simple becoming but only at what was 
already in process of becoming in process of becoming.^ 
And this again was sometime in process of becoming, so 
that even then we should not have arrived at what was in 
process of simple becoming. And since in an infinite 
series there is no first term, here there will be no first stage 
and therefore no following stage either. On this hypo- 5 
thesis, then, nothing can become or be moved or change. 

Thirdly, if a thing is capable of any particular motion, it 
is also capable of the corresponding contrary motion or the 
corresponding coming to rest, and a thing that is capable of 
becoming is also capable of perishing: consequently, if 
there be becoming of becoming, that which is in process of 
becoming is in process of perishing at the very moment 
when it has ^ reached the stage of becoming : since it can- 
not be in process of perishing when it is just beginning to 
become or after it has ceased to become : for that which is 
in process of perishing must be in existence. 

Fourthly, there must be a substrate underlying all pro-_ io 
cess^ s^ f beco ming anH rhanging. What can this be in the 
present case ? It is either the body or the soul that under- 
goes alteration : what ^ is it that correspondingly becomes 
' motion or becoming ? And again what * is the goal of their 
motion ? It must be the motion or becoming of something 
from something to something else.^ But in what sense 
can this be so ? For the becoming of learning cannot be 15 
learning : so neither can the becoming of becoming be 

^ Reading in 1. 2 dWa yivoiitvov yivofievov ^§7, with Bonitz. 
^ Reading in 1. 8 yevrjTai, with EF. 

' Reading in 1. 12 ovt<o tl to yivo^ievov, with FSimp. and some 
MSS. in MeL 1068^ 12. 
* Reading in 1. 13 n, with Me/. 1068*^ 12. 
Reading in 1. 13 fivai rrjv . . . els rode Kivrjatv ^ ye'veaiv, with Simp. 



becoming, nor can the becoming of any process be that 

Finally, since there are three kinds of motion , the sub- 
stratum and the goal of motion must be one or other of 
these, e. g. locomotion will have to be altered or to be 
• locally moved. 

To sum J J2, then, since everything that is moved is 
moved in one o f three ways, either accidentally, o r partially, 

20 o r essentially , change can change onlyaccidentally, as e.g. 
when a man who is being restored to health runs or learns : 
and accidental change we have long ago ^ decided to leave 
out of account. 

Since,^ then, motion can b elong neithe r to Being nor to 

Rela tion nor to Agent and Patient,j t remains tha t ther e 

can be motion only in respect of Quality , (Quantity , an^ 

25 Place : for with each of these we have a pair of contraries. 
Motion in respect of Qu ality l et us call alifiiatioil, a general 
designation that is used to include both contraries : and by 
Quality I do not here mean a property of substance (in 
that sense that which constitutes a specific distinction is 
a quality) but a passive quality in virtue of which a thing 
is said to be acted on or to be incapable of being acted on. 

30 Motion in respect of Quant ity has no name that includes 
both contraries, but it is called increase or decrease accord- 
ing as one or the other is designated : that is to say motion 
in the direction of complete magnitude is increase, motion 
in the contrary direction is decrease. Motion in respect_of 
Place h as no name either general or particular : but we may 
designate it by the general name of locomotion, though 
strictly the term ' locomotion ' is applicable to things that 
change their place only when they have not the power to 

35 come to a stand, and to things that do not move themselves 
226^ Change within the same kind from a lesser to a greater 
or from a greater to a lesser degree is alteration : for it is 
motion either from a contrary or to a contrary,^ whether in 
an unqualified or in a qualified sense : for change to a lesser 

' 224^ 26. , , , f ^V^t^ P- 23-9 cf. Met 1068^ 15-20. 

^ Reading in 1. 2 ^ -yap e^ evavriov j) (MS. E) eis evavriov. 


BOOK V. 2 226^ 

degree of a quality will be called change to the contrary of 
that quality, and change to a greater degree of a quality 5 
will be regarded as change from the contrary of that quality 
to the quality itself.^ It makes no difference whether the 
change be qualified or unqualified, except that in the 
former case the contraries will have to be contrary to one 
another only in a qualified sense : and a thing's possessing 
a quality in a greater or in a lesser degree means the 
presence ^ or absence in it of more or less of the opposite 
quality. It is now clear, then, that ther e are only these^ 
three kinds of motion. 

The^ term ' immovable ' we apply in the first place to that 10 
which is absolutely incapable of being moved (just as we 
correspondingly apply the term invisible to sound) ; in the 
second place to that which is moved with difficulty after 
a long time or whose movement is slow at the start — in 
fact, what we describe as hard to move ; and in the third 
place to that which is naturally designed for and capable 
of motion, but is not in motion when, where, and as it 
naturally would be so. This last is the only kind of 
immovable thing of which I use the term * being at rest ' : 
for rest is contrary to motion, so that rest will be negation 15 
of motion in that which is capable of admitting motion. 

The foregoing remarks are sufficient to explain the 
essential nature of motion and rest, the number of kinds of 
change, and the different varieties of motion. 

3 Let us now proceed to define the terms ' together ' and 
' apart ', * in contact ', ' between ', ' in succession ', ' contigu- 
ous ', and ' continuous ', and to show in what circumstances 20 
each of these terms is naturally applicable. 

Things * are said to be together in place when they are 
in one place (in the strictest sense of the word ' place *) and to 
be apart when they are in different places. 

Things are said to be in contact when their extremities 
are together. 

^ Reading in 1. 5 eh airof with F. 
^ Reading in 1. 8 to trXeov, with E. 
'^ With 11. 10-16 cf. Afe^. 1068^ 20-5. 
* With 11. 21-5 cf. Met. 1068^26-30. 

226^ PHYSICA , 

That which a changing thing, if it changes continuously 
35 in a natural manner, naturally reaches^ before it reaches 
that to which it changes last, is between. Thus * between ' 
implies the presence of at least three things : for in a pro- 
cess of change it is the contrary that is ' last ' : and a thing is 
moved continuously if it leaves no gap or only the smallest 
possible ^ gap in the material — not in the time (for a gap in 
the time does not prevent things having a ' between ', while, 
on the other hand, there is nothing to prevent the highest 
30 note sounding immediately after the lowest) but in the 
material in which the motion takes place. This is mani- 
festly true not only in local changes but in every other kind 
227* 7 as well. (Now ^ every change implies a pair of opposites, 
and opposites may be either contraries or contradictories ; 
since then contradiction admits of no mean term, it is 
obvious that ' between ' must imply a pair of contraries.) 
226^ 32 That * is locally contrary which is most distant in a straight 
line : for the shortest line is definitely limited, and that 
which is definitely limited constitutes a measure.^ 

A thing is * in succession ' when it is after the beginning ^ 
35 in position or in form "^ or in some other respect in which it 
227^ is definitely so regarded, and w^hen further there is nothing 
of the same kind as itself between it and that to which it is 
in succession, e. g. a line or lines if it is a line, a unit or 
units if it is a unit, a house if it is a house (there is nothing 
to prevent something of a different kind being between). 
For that which is in succession is in succession to a parti- 
cular thing, and is something posterior : for one is not * in 
5 succession ' to two, nor is the first day of the month to the 
second : in each case the latter is ' in succession ' to the 

A thing that is in succession and touches is ' contiguous '. 
10 The 'continuous' is a subdivision of the contiguous: 

^ Reading in 1. 24 nporepovj with MeL 1068^^ 28. 
^ Reading in 1. 28 rj on oXiyia-Tou, with E. 

' Sense seems to require this transposition : v. Prantl, ad loc, and 
cf. Themistius. 

^ With 1. 32-227*31 cf. Met. 1068^30-1069* 14. 

^ sc. for TO n\ii(TTov. ^ Omitting in 1. 35 p.6vov^ with E. 

"* Reading in 1. 35 «5ct for ^uo-ft, with EH. 

BOOK V. 3 227* 

things are called continuous when the touching limits of 
each become one and the same and are, as the word implies, 
contained in each other : continuity is impossible if these 
extremities are two. This definition makes it plain that 
continuity belongs to things that naturally in virtue of their 
mutual contact form a unity. And in whatever way that 15 
which holds them together is one, so too will the whole be 
one, e. g. by a rivet or glue or contact or organic union. 

It is obvious that of these terms ' in succession ' is first 
in order of analysis : for that which touches is necessarily 
in succession, but not everything that is in succession 
touches : and so succession is a property of things prior in 
definition, e. g. numbers, while contact is not. And if there 20 
is continuity there is necessarily contact, but if there is 
contact, that alone does not imply continuity : for the 
extremities of things may be * together ' without necessarily 
being one : but they cannot be one without being necessarily 
together. So natural junction is last in coming to be : for 
the extremities must necessarily come into contact if they 
are to be naturally joined : but things that are in contact 25 
are not all naturally joined, while where there is no con- 
tact clearly there is no natural junction either. Hence, if 
as some say ' point ' and ' unit ' have an independent 
existence of their own, it is impossible for the two to be 
identical : for points can touch while units can only be in 
succession. Moreover, there can always be something 30 
between points (for all lines are intermediate between 
points 1), whereas it is not necessary that there should 
possibly be anything between units : for there can be 
nothing between the numbers one and two. 

We have now defined what is meant by ' together ' and 
* apart ', ' contact ', ' between ' and * in succession ', * con- 227^ 
tiguous ' and ' continuous ' : and we have shown in what 
circumstances each of these terms is applicable. 

There are many senses in which motion is said to be 
' one ' : for we use the term * one' in many senses. 

Motion is one generically according to the different cate- 

^ Cf. 231^9. 


5 gories to which it may be assigned : thus any locomotion 
is one generically with any other locomotion, whereas 
alteration is different generically from locomotion. 

Motion is one specifically when besides being one gene- 
rically it also takes place in a species incapable of sub- 
division : e. g. colour has specific differences : therefore 
blackening and whitening differ specifically ; but at all 
events ^ every whitening will be specifically the same with 
every other whitening and every blackening with every 

lo other blackening. But whiteness is not further subdivided 
by specific differences : hence any whitening is specifically 
one with any other whitening. Where it happens that the 
genus is at the same time a species, it is clear that the 
motion will then in a sense ^ be one specifically though not 
in an unqualified sense: learning is an example of this, 
knowledge being on the one hand a species of apprehension 
and on the other hand a genus including the various know- 
ledges. A difficulty, however, may be raised as to whether 

15 a motion is specifically one when the same thing changes 
from the same to the same, e. g. when one point changes 
again and again from a particular place to a particular 
place : if this motion is specifically one, circular motion 
will be the same as rectilinear motion, and rolling the 
same as walking. But is not this difficulty removed by 
the principle already laid down that if that in which the 
motion takes place is specifically different (as in the present 
instance the circular path is specifically different from the 

30 straight) the motion itself is also different ? We have ex- 
plained, then, what is meant by saying that motion is one 
generically or one specifically. 

Motion is one in an unqualified sense when it is one 
essentially or numerically : and the following distinctions 
will make clear what this kind of motion is. There are 
three classes of things in connexion with which we speak 
of motion, the * that which ', the ' that in which ', and the 
' that during which '. I mean that ^ there must be some- 

^ Reading in 1. 9 S' oZv, with EH. 

* Reading in 1. 12 hr]Kov o)? t(TTiv coy, with E^ 

^ Omitting in 1. 24 o, with EF. 


BOOK V. 4 227* 

thing that is in motion, e. g. a man or gold, and it must be 25 
in motion in something, e. g. a place or an affection, and 
during something, for all motion takes place during a time. 
Of these three it is the thing in which the motion takes 
place that makes it one generically or specifically,^ it is the 
thing moved that makes the motion one in subject, and it 
is the time that makes it consecutive : but it is the three 
together that make it one without qualification : to effect 
this, that in which the motion takes place (the species) must 30 
be one and incapable of subdivision, that during which it 
takes place (the time) must be one and unintermittent, and 
that which is in motion must be one — not in an accidental 
sense (i. e. it must be one as the white that blackens is 
one or Coriscus who walks is one, not in the accidental 
sense in which Coriscus and white may be one), nor 228^ 
merely in virtue of community of nature (for there might 
be a case of two men being restored to health at the 
same time in the same way, e.g. from inflammation of 
the eye, yet this motion is not really one, but only speci- 
fically one). 

Suppose, however, that Socrates undergoes an alteration 
specifically the same but at one time and again at another : 
in this case if it is possible for that which ceased to be 
again to come into being and remain numerically the same, 
then this motion too will be one : otherwise it will be the 5 
same but not one. And akin to this difficulty there is 
another ; viz. is health one ? and generally are the states and 
affections in bodies severally one in essence although (as is 
clear) the things that contain them are obviously in motion 
and in flux ? Thus if a person's health at daybreak and at 
the present moment is one and the same, why should not 10 
this health be numerically one with that which he recovers 
after an interval ? The same argument applies in each case.^ 
There is, however, we may answer, this difference : that if 

' The text seems faulty, though Simplicius read the same. The 
translation follows the suggestion of Bonitz in inserting, after KivtiTai 
in 1. 28, TO 5e rep vnoKei^evco jxlav ev t(5 TrpdyfiuTi 6 Kive'iTai, But the next 

clause is, in view of 228* 26-31, best emended by reading to 6* 

eXOfievr}v iv tw ^povco. 

' sc. the case of e^ets and the case of Kivrjaeis. 

«45.1« K 


the states are two then it follows simply from this fact^ 
that the activities must also in point of number be two 
(for only that which is numerically one can give rise to an 

15 activity that is numerically one), but if the state is one, this 
is not in itself enough to make us regard the activity also 
as one : for when a man ceases walking, the walking no 
longer is, but it will again be if he begins to walk again. 
But, be this as it may, if in the above instance the health 
is one and the same, then it must be possible for that 
which is one and the same to come to be and to cease to 
be many times. However,^ these difficulties lie outside our 
present inquiry. 

20 Since every motion is continuous, a motion that is one in 
an unqualified sense must (since every motion is divisible) 
be continuous, and a continuous motion^ must be one. 
There will not be continuity between any motion and any 
other indiscriminately any more than there is between any 
two things chosen at random in any other sphere : there 
can be continuity only when the extremities of the two 
things are one. Now some * things have no extremities at 
all : and the extremities of others differ specifically although 

35 we give them the same name of ' end ' : how should e. g. 
the ' end ' of a line and the * end ' of walking touch or come 
to be one ? Motions that are not the same cither speci- 
fically or generically may, it is true, be consecutive (e. g. a 
man may run and then at once fall ill of a fever), and again, 
in the torch-race we have consecutive but not continuous 
locomotion : for according to our definition there can be 
continuity only when the ends of the two things are one 

30 Hence motions may be consecutive ^ or successive in virtue 
of the time being continuous, but there can be continuity 
only in virtue of the motions themselves being continuous 
that is when the end of each is one with the end of th( 
228^ other. Motion, therefore, that is in an unqualified sense 
continuous and one must be specifically the same, of ont 

^ Reading in 1. 13 St avrb tovto u>s tS dpidfia Koi ras evepyeia 

^ Reading in 1. 19 fiev odv, with FHI. 

^ Reading in 1. 22 ixiav, with Them, and Bonitz. * sc. indivisibles 

• Reading in 1. 30 exofxeuai, with^EH. 

BOOK V. 4 228^ 

thing, and in one time. Unity is required in respect of 
time in order that there may be no interval of immobility, 
for where there is intermission of motion there must be rest, 
and a motion that includes intervals of rest will be not one 
but many, so that a motion that is interrupted by stationari- 5 
ness is not one or continuous, and it is so interrupted 
if there is an interval of time. And though of a motion that 
is not specifically one (even if the time is unintermittent) 
the time ^ is one, the motion is specifically different, and so 
cannot really be one, for motion that is one must be speci- 
fically one, though motion that is specifically one is not 10 
necessarily one in an unqualified sense. We have now 
explained what we mean when we call a motion one with- 
out qualification. 

Further, a motion is also said to be one generically, 
specifically, or essentially when it is complete, just as in 
other cases completeness and wholeness are characteristics 
of what is one : and sometimes a motion even if incom- 
plete is said to be one, provided only that it is continuous. 

And besides the cases already mentioned there is another 15 

in which a motion is said to be one, viz. when it is regular : 

"or in a sense a motion that is irregular is not regarded as 

Dne, that title belonging rather to that which is regular, as a 

straight line is regular,^ the irregular being as such ^ divisible. 

But the difference would seem to be one of degree.* In 

i very kind of motion we may have regularity or irregularity: 

hus there may be regular alteration, and locomotion 20 

n a regular path, e. g. in a circle or on a straight line, 

ind it is the same with regard to increase and decrease. 

The difference that makes a motion irregular ^ is some- 

imes to be found in its path : thus a motion cannot be 

egular if its path is an irregular magnitude, e. g. a broken 

^ Omitting in 1. 8 ov, with E, and reading 6 xpovos, 6 fxev xp^^vos, with 

^ o/xaXjjs (= SfioioixepTjs of mathematical writers), regular in the 
ense that any part applied to any other part can coincide with it. 

^ e.g. a line partly straight and partly curved (and the motion 
long it) may be divided accordingly. 

* i. e. regularity and irregularity do not constitute distinct species of 
lotion : they occur in every kind of motion, making it more or less 
hat it is. ^ Reading in 1. 21 avcufxaXia, with E Them. 

K a 


line/ a spiral,^ or any other magnitude that is not such 
that any part of it taken at random fits on to any other 
25 that may be chosen. Sometimes it is found neither in the 
place nor in the time nor in the goal but in the manner 
of the motion: for in some cases the motion is differen- 
tiated by quickness and slowness: thus if its velocity 
is uniform a motion is regular, if not it is irregular. So 
quickness and slowness are not species of motion nor do 
they constitute specific differences of motion, because this 
distinction occurs in connexion with all the distinct species 
30 of motion. The same is true of heaviness and lightness ^ 
when they refer to the same thing : e. g. they do not 
specifically distinguish earth from itself or fire from itself. 
229^ Irregular motion, therefore, while in virtue of being con- 
tinuous it is one, is so in a lesser degree, as is the case with 
locomotion in a broken line : and a lesser degree of some- 
thing always means an admixture of its contrary. And 
since every motion that is one can be both regular and 
irregular, motions that are consecutive but not specifically 
5 the same cannot be one "* and continuous : for how should 
a motion composed of alteration and locomotion be regular ? 
If a motion is to be regular its parts ought to fit one another. 

We have further to determine what motions are contrary 
to each other, and to determine similarly how it is with 
rest. And we have first to decide whether contrary motions 
are motions respectively from and to the same thing, e.g. 
10 a motion from health and a motion to health (where the 
opposition, it would seem, is of the same kind as that 
between coming to be and ceasing to be) ; or motions 
respectively from contraries, e. g. a motion from health 
and a motion from disease ; or motions respectively to 
contraries, e. g. a motion to health and a motion to disease; 
or motions respectively from a contrary and to the opposite 
contrary, e. g. a motion from health and a motion to disease ; 

* i. e. as we should say, two lines meeting in an angular point. 

^ One spiral — the cylindrical helix — is regular : but this property 
was first proved for it by Apollonius. 
^ Which cause quick and slow motion. 

* Reading in 1. 4 eiSo? aX avrai exofifvai fiia. 

BOOK V. 5 229^ 

or motions respectively from a contrary to the opposite 
contrary and from the latter to the former, e. g. a motion 
from health to disease and a motion from disease to health : 
for motions must be contrary to one another in one or 15 
more of these ways, as there is no other way in which they 
can be opposed. 

Now motions respectively from a contrary and to the 
opposite contrary, e. g. a motion from health and a motion 
to disease, are not contrary motions ; for they are one and 
the same. (Yet their essence is not the same, just as 
changing from health is different from changing to disease.) 
Nor are motions respectively from a contrary and from the 20 
opposite contrary contrary motions, for a motion from a 
contrary is at the same time a motion to a contrary or to 
an intermediate (of this, however, we shall speak later),^ 
but changing to a contrary rather than changing from 
a contrary would seem to be the cause of the contrariety 
of motions, the latter being the loss, the former the gain, 
of contrariness. Moreover, each several motion takes its 25 
name rather from the goal than from the starting-point of 
change, e. g. motion to health we call convalescence, motion 
to disease sickening. Thus we are left with motions re- 
spectively to contraries, and motions respectively to con- 
traries from the opposite contraries. Now it would seem 
that motions to contraries are at the same time motions 
lom contraries (though their essence may not be the same ; 
to health' is distinct, I mean, from 'from disease', and 
from health ' from 'to disease '). 

Since then change differs from motion (motion being 30 
:hange from a particular subject to a particular subject), 
t follows that contrary motions are motions respectively 
Tom a contrary to the opposite contrary and from the 
atter to the former, e. g. a motion from health to disease 229^ 
ind a motion from disease to health. Moreover, the con- 
ideration of particular examples will also show what kinds 
)f processes are generally recognized as contrary : thus 
ailing ill is regarded as contrary to recovering one's health, 
hese processes having contrary goals, and being taught as 5 

^ 1. 28 sqq. 


contrary to being led into error by another, it being possible 
to acquire error, like knowledge, either by one's own agency 
or by that of another. Similarly we have upward loco- 
motion and downward locomotion, which are contrary 
lengthwise,^ locomotion to the right and locomotion to the 
left, which are contrary breadthwise, and forward locomo- 
tion and backward locomotion, which too are contraries. 

10 On the other hand, a process simply to a contrary, e. g. 
that denoted by the expression * becoming white ', where 
no starting-point is specified, is a change but not a motion. 
And in all cases of a thing that has no contrary we have as 
contraries change from and change to the same thing. 
Thus coming to be is contrary to ceasing to be, and losing 
to gaining. But these are changes and not motions. And 

15 wherever a pair of contraries admit of an intermediate, 
motions to that intermediate must be held to be in a sense 
motions to one or other of the contraries : for the inter- 
mediate serves as a contrary for the purposes of the motion, 
in whichever direction the change may be, e. g. grey in 
a motion from grey to white takes the place of black as 
starting-point, in a motion from white to grey it takes the 
place of black as goal, and in a motion from black to grey it 
takes the place of white as goal : for the middle is opposed 

20 in a sense to either of the extremes, as has been said above.^ 
Thus we see that two motions are contrary to each other 
only when one is a motion from a contrary to the opposite 
contrary and the other is a motion from the latter to the 

But since a motion appears to have contrary to it not 
only another motion but also a state of rest, we must deter- 
mine how this is so. A motion has for its contrary in the 
strict sense of the term another motion, but it also has for 
an opposite a statfi__Qfj;est_(for rest is the privation oi 
25 motion and the privation of anything may be called its 

^ Cf. de Caelo 284^ 24 eart be TO fieu ava tov htjkovs apxr), to 6e df^iop 
Toi) irXdrovs, to de Trp6(r6ev tov ^ciBovs. 

^ 224^ 32 sqq. There is no need to insert ivavriov (with Prantl) 
after yLtaov in 1. 1 9. 


BOOK V. 6 229* 

contrary), and motion of one kind ^ has for its opposite rest 
of that kind, e. g. local motion has local rest. This state- 
ment, however, needs further qualification : there remains 
the question, is the opposite of remaining at a particular 
place motion from or motion to that place ? It is surely 
clear that since there are two subjects between which motion 
takes place, motion from one of these (A) to its contrary 30 
(B) has for its opposite remaining in A, while the reverse 
motion has for its opposite remaining in B. At the same 
time these two are also contrary to each other : for it would 
be absurd to suppose that there are contrary motions and not 
opposite states of rest. States of rest in contraries are 230' 
opposed. To take an example, a state of rest in health is (i) 
contrary to a state of rest in disease, and (2) the motion to 
which it is contrary is that from health to disease. For (2) 
it would be absurd that its contrary motion should be that 
from disease to health, since motion to that in which a thing 
is at rest is rather a coming to rest, the coming to rest 5 
being found to come into being simultaneously with the 
motion ; and one of these two motions it must be. And 
(i) rest in whiteness is of course not contrary to rest in 

Of all things that have no contraries there are opposite 
changes (viz. change from the thing and change to the thing, 
e. g. change from being and change to being), but no motion. 
So, too, of such things there is no remaining though there is 
absence of change. Should there be a particular subject, 10 
absence of change in its being will be contrary to absence 
of change in its not-being. And here a difficulty may be 
raised : if not-being is not a particular something, what is 
it, it may be asked, that is contrary to absence of change 
in a thing's being ? and is this absence of change a state of 
rest } If it is, then either it is not true that every state of 
rest is contrary to a motion or else coming to be and 
ceasing to be are motion. It is clear then that, since we 15 
exclude these from among motions, we must not say that 
this absence of change is a state of rest : we must say that 
it is similar to a state of rest and call it absence of change. 
^ Reading in 1. 26 Troia hi Troia, with Phil. 



And it will have for its contrary ^ either nothing or absence 
of change in the thing's not-being, or the ceasing to be of 
the thing : for such ceasing to be is change from it and the 
thing's coming to be is change to it. 

Again, a further difficulty may be raised. How is it, it 
may be asked, that whereas in local change both remaining 

20 and moving may be natural or unnatural, in the other changes 
this is not so ? e. g. alteration is not now natural and now 
unnatural, for convalescence is no more natural or unnatural 
than falling ill, whitening no more natural or unnatural 
than blackening ; so, too, with increase and decrease : these 
are not contrary to each other in the sense that either of 

25 them is natural while the other is unnatural, nor is one 
increase contrary to another in this sense ; and the same 
account may be given of becoming and perishing : it is not 
true that becoming is natural and perishing unnatural (for 
growing old^ is natural), nor do we observe one becoming 
to be natural and another unnatural. We answer that if 

30 what happens under violence is unnatural, then violent 
perishing is unnatural and as such contrary to natural 
perishing. Are there then also some becomings that are 
violent and not the result of natural necessity, and are 
therefore contrary to natural becomings, and violent in- 
230^ creases and decreases, e. g. the rapid growth to maturity of 
profligates and the rapid ripening of seeds even when not 
packed close in the earth ? And how is it with alterations ? 
Surely just the same : we may say that some alterations are 
violent while others are natural, e.g. patients alter naturally 
5 or unnaturally according as they throw off fevers on the 
critical days or not. But, it may be objected, then we shall 
have perishings contrary to one another, not to becoming.^ 
Certainly : and why should not this in a sense be so ? * Thus 
it is so if one perishing is pleasant and another painful : 
and so one perishing will be contrary to another not in an 

* If there is no firj 6v to be contrary to the of, then afxeTa^Xrjo-la in the 
6v will have no contrary : if there is, it will have for contraries (a) the 
a/LierajSXiyata in the fi/7 ov and (d) the (f)6opd which = /i€ra/3oXj) f^ dfiera- 
^Xrjcrias tov outos {fls dfxfra^Xrjcriav tov fxf) optos). 

^ Reading in 1. 28 17 yap yrjpavais, with EH. 

^ Reading in 1. 7 yeveaei (Bekker's yevea-cis is a misprint). 

^ Reading in 1. 7 KwXvd earip cos ; with E Phil. Simp. 

BOOK V. 6 230^ 

unqualified sense, but in so far as one has this quality and 
the other that. 

Now motions and states of rest universally^ exhibit 10 
contrariety in the manner described above,^ e.g. upward 
motion and rest above are respectively contrary to down- 
ward motion and rest below, these being instances of local 
contrariety ; and upward locomotion belongs naturally to 
fire and downward to earth, i.e. the locomotions of the two 
are contrary to each other. And again, fire moves up 
naturally and down unnaturally : and its natural motion is 
certainly contrary to its unnatural motion. Similarly with 15 
remaining : remaining above is contrary to motion from 
above downwards, and to earth this remaining comes un- 
naturally, this motion naturally. So the unnatural remaining 
of a thing is contrary to its natural motion, just as we find 
a similar contrariety in the motion of the same thing : one 20 
of its motions, the upward or the downward, will be natural, 
the other unnatural. 

Here, however, the question arises, has every state of rest 
that is not permanent a becoming, and is this becoming 
a coming to a standstill ? If so, there must be a becoming 
of that which is at rest unnaturally, e. g. of earth at rest 
above : and therefore this earth during the time that it was 
being carried violently upward was coming to a standstill. 
But whereas the velocity of that which comes to a stand- 
still seems always to increase, the velocity of that which is 
carried violently seems always to decrease : so it will be in 25 
a state of rest without having become so. Moreover ' coming 
to a standstill ' is generally recognized to be identical or at 
least concomitant with the locomotion of a thing to its 
proper place.^ 

There is also another difficulty involved in the view that 
remaining in a particular place is contrary to motion from 
that place. For when a thing is moving from or discarding 
something, it still appears to have that which is being dis- 
carded, so that if a state of rest is itself contrary to the 30 

^ i.e. the contrariety of natural )( violent is no exception. 
"^ In chapter 5. 

^ .'.we must not use the term IcrTaadai to describe the process that 
ends in unnatural rest. 



motion from the state of rest to its contrary, the contraries 
rest and motion will be simultaneously predicable of the 
same thing. May we not say, however, that in so far as 
the thing is still stationary it is in a state of rest in a quali- 
fied sense ? For,^ in fact, whenever a thing is in motion, 
part of it is at the starting-point while part is at the goal 
231^ to which it is changing : and consequently a motion finds 
its true contrary rather in another motion than in a state ^ 
of rest. 

With regard to motion and rest, then, we have now 
explained in what sense each of them is one and under 
what conditions they exhibit contrariety. 
5 ^ [With regard to coming to a standstill the question may 
be raised whether there is an opposite state of rest to un- 
natural as well as to natural motions. It would be absurd 
if this were not the case : for a thing may remain still 
merely under violence : thus we shall have a thing being in 
a non-permanent state of rest without having become so. 
But it is clear that it must be the case : for just as there is 
unnatural motion, so, too, a thing may be in an unnatural 
10 state of rest. Further, some things have a natural and an 
unnatural motion, e. g. fire has a natural upward motion 
and an unnatural downward motion : is it, then, this un- 
natural downward motion or is it the natural downward 
motion of earth that is contrary to the natural upward 
motion? Surely it is clear that both are contrary to it 
though not in the same sense : the natural motion of earth 
is contrary inasmuch as the motion of fire is also natural, 
15 whereas the upward * motion of fire as being natural 
is contrary to the downward motion of fire as being un- 
natural. The same is true of the corresponding cases of 
remaining. But there would seem to be a sense in which 
a state of rest and a motion are opposites.] 

' Cf. vi. 5. 

2 r]p€^T](ns seems to be used for rjpefjLia. Cf. 251^ 26. 

^ This contused paragraph following what should be the final 
sentence of the book is omitted by six MSS., ignored by Themistius, 
and considered superfluous by Simplicius. 

* Reading in 1. 14 r^y alrov' rj 6' avco. 



I Now if the terms ' continuous ', ' in contact ', and * in 
succession ' are understood as defined above ^ — things being 
* continuous ' if their extremities are one, ' in contact ' if 
their extremities are together, and ' in succession ' if there 
is nothing of their own kind intermediate between them — 
nothing t hat is continuous can be composed of indivisibles: 
e.g. a hne cannot be composed of points, the line being 25 
continuous and the point indivisible. F or the extremities 
of two points can neither be one (since of an indivisible 
there can be no extremity as distinct from some other part) 
nor together (since that which has no parts can have no 
extremity, the extremity and the thing of which it is the 
extremity being distinct). 

Moreover, if that which is continuous is composed of 
points, these points must be either continuous or in contact 30 
with one another : and the same reasoning applies in the 
case of all indivisibles. Now for the reason given above 231^ 
they cannot be continuous : and^ne thingjcan be in con- 
tact with another only if whole is in contact with whole or 
part with part or pal't with whole.^'But since indivisibles have 
no parts, they must be in contact with one another as whole 
with whole. And if they are in contact with one another as 
whole with whole, they will not be continuous : for that which 
is continuous has distinct parts : and these parts into which 5 
it is divisible are different in this way, i.e. spatially separate. 

Nor, again , c an a point be in success ion to a point or | 
a moment to a moment in such a way thaFTength can 
be composed of points o r time of moments : for things are 
in succession if there is nothing of their own kind inter- 
mediate between them, whereas that which is intermediate 
between points is always a ^ line and that which is inter- 
mediate between moments is always a period of time. 

Again, if length and time could thus be composed of 

> . 

'^ i. e. if we take any two points (moments) A and B, since they 
cannot touch there is a line (time) between them : and on this line (in 

^ V. 3. 



indivisibles, they could be divided into indivisibles, since 
each is divisible into the parts of which it is composed. 
But, as we saw, no continuo us thing is divisible into things 
without parts. Nor can there be anything of any other 
kind intermediate between the parts or between the 
moments : for if there could be any such thing it is clear that 
it must be either indivisible or divisible, and if it is divisible, 
it must be divisible either into indivisibles or into divisibles 
that ar e infinitely divisible. in.w kLch case it is continuous^ 

15 Moreover, it is pla in that ever ything continuous is divis-, 
ible into divisibles tha t are mfinitely divisibl e : for if it 
were divisible into indivisibles, we should have an indi- 
visible in contact with an indivisible, since the extremities 
of things that are continuous with one another are one and ^ 
are in contact. 

The same reasonin g ap plies equally to magnitude, to 
time, and to motion : either all of these are composed of 
indivisibles and are divisible into indivisibles, or none. 
• 30 This may be made clear as follows. If a magnitu de is^ 
composed o f indivisibles ^the motion over that magnitude 
m ust be composed of correspondmp^ indivisible motions : 
e. g. if the magnitude ABF is composed of the indivisibles 
A, B, r, each corresponding part of the motion AEZ of 12 

25 over ABr is indivisible. Therefore,^ since where there is 
motion there must be something that is in motion, and 
where there is something in motion there must be motion, 
therefore the being-moved will also be composed of indi- 
visibles. So i2 traversed A when its motion was A, B when 
its motion was E, and T similarly when its motion was Z. 
Now ^ a thing that is in motion from one place to another 
cannot at the moment when it was in motion both be in 
motion and at the same time have completed its motion at 
the place to which it was in motion : e. g. if a man is 
walking to Thebes, he cannot be walking to Thebes and at 

this time) we can always take another point (moment) r. .'. A and B 
have between them another thing of the same kind, and so are not 

^ Omitting the comma in 1. 18. "^ 1. 25 reading B-q, with EHIK. 
^ There is a slight anacoluthon, the virtual apodosis being intro- 
duced by coo-r (232* 2). 

^ BOOK VI. I 231^ 

^^ the same time have completed his walk to Thebes : and, as 30 
we saw, i2 traverses the partless section A in virtue of the 232* 
presence of the motion A. Consequently, if X2 actually- 
passed through A afUr being in process of passing through, 
the motion must be divisible : for at the time when 12 was 
passing through, it neither was at rest nor had completed 
its passage but was in an intermediate state : while if it is 
passing through and has completed its passage at the same 
moment, then _that w hich is walking ^ wi ll at the moment 5 

when it is walking have completed its walk and willj)e^ in 

the place to which it is walking^ ; that is to say, it will have 
completed its motion at the place to which it Js in motion.^ 
And if a thingJs in motion over the whole ABr and its 
motion is the three A, E, and Z, and if it is not in motion 
at all over the partless section A but has completed its 
motion over it, then the motion will consist not of motions 
but of starts^ and will take place by ^ a thing's having 
completed a motion without being in motion : for on this 
assumption it has comp leted its passage t hrough A without 
passing through it. ^o it will be possible for a thing to 10 
have completed a walk without ever walking : for on this 
assumption it has completed a walk over a particular 
distance without walking over that distance. Since, then, 
everything must be either at rest or in motion, and il is 
therefore at rest in each of the sections A, B, and r, i tfoUo ws 
that a thin^ can be continuously at rest and at the same 
time in motion : for, as we saw, 12 is in motion over the 
whole ABr and at rest in any part (and consequently in 
the whole) of it. Moreover, if the indivisibles composing 15 
AEZ are motions, it w ould be possible for a thing in smto.^ 
of Jhe prese nce in it of motion to be not in motion but at 
rest, while if thev are not motions, it would be possible for 

motion to be composed of something other than motions. 

And i Hength and m otion arethusjndbiisiJile, it is neither 
more nor less necessary that time also be simijarly ujdii- 
visible, that is to say be composed ot mdiv jsiSI^m^'^^"tg : 

^ Reading commas before and after to 0a8i^ou in 1. 4. 
' Which is ex hypothesi impossible (231^ 28-30). 
^ Reading in 1. 9 kcli r«w. 


20 for i f the whole distance is di visible and an equal velocit y 
wtlTcause a thingJLo pass throug h 1^^^ "f it in less time^ t he 
time must also be divisible, and conversely, if the time in 
which a thing is carried over the section A is divisible, this 
section A must also be divisible. 

y And since every magnitude is divisible into magnitudes — 3^ 

for we have shown that it is impossible for anyth ingjcon^^ 
tinuous to be composed of indivisible parts, and every 

35 magnit ude is continuous:— it necessarily follows that the 
quicker of two things traverses a greater magnitude in an 
equal time, an equal magnitude in less time, and a greater 
magnitude in less time, in conformity with the definition 
sometimes given of * the quicker '. Suppose that A is 
quicker than B. Now since of two things that which 
changes sooner is quicker, in the time ZH, in which A has 

30 changed from T to A, B will not yet have arrived at A but 
will be short of it : so that in an equal time the quicker 
will pass over a greater magnitude. More than this, it will 
pass over a greater magnitude in less time : for in the time 
in which A has arrived at A, B being the slower has arrived, 
let us say, at E. Then since A has occupied the whole 
232^ time ZH in arriving at A, it will have arrived at in less 
time than this, say ZK. Now the magnitude T© ^ that A 
has passed over is greater than the magnitude FE, and the 
time ZK is less than the whole time ZH : so that the 
quicker will pass over a greater magnitude in less time. 
5 And from this it is also clear that the quicker will pass 
over an equal magnitude in less time than the slower. 
For since it passes over the greater magnitude in less time 
than the slower, and (regarded by itself) passes over AM 
the greater in more time than AH the lesser, the time HP 
in which it passes over AM will be more than the time 112 

10 in which it passes over AH : so that, the time OP being 
less than the time HX in which the slower passes over AH, 
the time 02 will also be less than the time HX : for it is 
less than the time HP, and that which is less than some- 

E e A. Bekker's TA in 1. 3 is a misprint. 

BOOK VI. 2 232^ 

thing else that is less than a thing is also itself less than 
that thing. Hence it follows that the quicker will traverse 
an equal magnitude in less time than the slower. Again, 
since the motion of anything must always occupy either 15 
an equal time or less or more time in comparison with that 
of another thing, and since, whereas a thing is slower if its 
motion occupies more time and of equal velocity if its 
motion occupies an equal time, the quicker is neither of 
equal velocity nor slower, it follows that the motion of the 
quicker can occupy neither an equal time nor more time. 
It can only be, then, that it occupies less time, and thus 
we get the necessary consequence that the quicker will pass 
over an equal magnitude (as well as a greater) in less time 
than the slower. 20 

And since every motion is in time and a motion may 
occupy any time, and the motion of everything that is in 
motion may be either quicker or slower, both quicker 
motion and slower motion may occupy any time : and this 
being so, it necessarily follows that time also is continuous. 
By continuous I mean th a t which is divisible into divisibles 
that are infinitely divisible : and if we take this as the defi- 35 
nition of continuous, it follo ws necessarily tha t time is con- 
tinuous. For since it has been shown that the quicker will 
pass over an equal magnitude in less time than the slower, 
suppose that A is quicker and B slower, and that the slower 
has traversed the magnitude FA in the time ZH. Now it is 30 
clear that the quicker will traverse the same magnitude in 
less time than this : let us say in the time Z0. Again, 
since the quicker has passed over the whole FA in the time 
Z0, the slower will in the same time pass over FK, say,^ 
which is less than FA. And since B, the slower, has passed 233* 
over FK in the time Z0, the quicker will pass over it in less 
time : so that the time Z0 will again be divided. And if 
this is divided the magnitude FK will also be divided just 
as FA was : and again, if the magnitude is divided, the time 
will also be divided. And we can carry on this process for 5 
ever, taking the slower after the quicker and the quicker 
after the slower alternately, and using what has been 
^ 1. 33 reading co-rco, with E Them. Simp. 


demonstrated at each stage as a new point of departure ; 
for the quicker will divide the time and the slower will 
divide the length. If, then, this alternation always holds 
good, and at every turn involves a division, it is evident 

lo that a ll time must be continuous. And at the same time 
it is clear that all magnitude is also continuous ; for the 
divisions of which time and magnitude respectively are 
susceptible are the same and equal. 

Moreover, the current popular arguments make it plain 
that, if time is continuous, magnitude is continuous also, 
inasmuch as a thing passes over half a given magnitude in 

15 half the time taken to cover the whole : in fact without 
qualification it passes over a less magnitude in less time ; 
for the divisions of time and of magnitude will be the same. 
And if either is infinite, so i s the othe r, and the one is so Tn 
the same way as the other ; i. e. if time is infinite in respect 
of its extremities,^ length is also infinite in respect of its 
extremities : if time is infinite in respect of d ivisibility, 

20 length is also infinite in respect of divisibilit y : and if time 
is infinite in both respects, magnitude is also infinite in both 

Henc^^..^£Do's,,^rgumgxitl. makes a false assumption in 
asserting that it is impossible for a thing to pass over or 
severally to come in contact with infinite things in a finite 
time. For there are two senses in which length and time 
and generally anything continuous are called ' infinite ' : 

25 they are called so either in respect of divisibility or in 
respect of their extremities. So while a thing in a finite 
time cannot come in contact with things quantitatively 
infinite, it _can come in contact with things infinite in respect 
of divisibility : for in this sense the time itself is also infinite : 
and so we find tha jtjhe time occupied by the passage over, 

30 the infin ite is not a finite but an infi nit e time, a nd the con- 
tact with the infinites is ma de by means of moments not 
finite but infinite in numher^_ 

JLJ.€. extends infinitely in both directions. 
I^^^'x.^. one of his arguments for the impossibility of motion, which 
ran as follows : if motion is possible, a thing can in a finite time pass 
over infinite things touching each of them ; but this is impossible : 
therefore motion is impossible. Cf. 239^9-14, Top. 160^7. 


BOOK VI. 2 233* 

The passage over the infinite,^ then, cannot occupy 
a finite time, and the passage over the finite cannot occupy 
an infinite time : if the time is infinite the magnitude must 
be infini te also, a nd if J;^.^_!IL?i^^^'^"^<' ''^ infinitf^, «^o f^|<yr> i«^__ 
the time. This may be shown as follows. Let AB be 
a finite magnitude, and let us suppose that it is traversed 
in infinite time F, and let a finite period FA of the time be 35 
taken. Now in this period the thing in motion will pass 233^ 
over a certain segment of the magnitude : let BE be the 
segment that it has thus passed over. (This will be either 
an exact measure of AB or less ^ or greater than an exact 
measure : it makes no difference which it is.) Then, since 
a magnitude equal to BE will always be passed over in an 
equal time, and BE measures the whole magnitude, the 5 
whole time occupied in passing over AB will be finite : for 
it will be divisible into periods equal in number to the 
segments into which ^ the magnitude is divisible. More- 
over, if it is the case that infinite time is not occupied in 
passing over every magnitude, but it is possible to pass 
over some magnitude, say BE, in a finite time, and if this 
BE measures the whole of which it is a part, and if an equal 10 
magnitude is passed over in an equal time, then it follows 
that the time like the magnitude is finite. That infinite 
time will not be occupied in passing over BE is evident if 
the time be taken as limited in one direction * : for as the 
part will be passed over in less time than the whole, the 
time occupied in traversing this part must be finite, the limit 
in one direction being given. The same rea soning w ill also 
show the falsity of the assumption that infinite length can 
be traversed in a finite time. It is evident, then, from what 15 

^ i. e. in the strict sense, viz. extending infinitely in both directions. 

' i. e. the nearest multiple of BE to AB will be less or greater than 
AB : e. g. 4 feet Kara fx^r pel 1 6 feet (i6 being an exact multiple of 4), 
3 feet eWeiirei (the nearest multiple being 15, i.e. less than 16), 6 feet 
vwep^dWei (the nearest multiple being 18, i.e. greater than 16). 
Obviously, since the amount by which BE fAXetVei or vTrepdaWei is 
always less than BE, it makes no difference to the argument whether 
BE is an exact measure or not. 

' 1. 7 omit <»$•, with E, and the comma. 

* i. e. the point B at which the motion begins is fixed, and the 
moment at which the motion begins must similarly be regarded 
as fixed. 


has beer gairj that npith er a line nor a surface nor in fact 
^nything continu ous can be indivisible. 

This conclusion follows not only from the present argu- 
ment but from the consideration that the opposite assump- 
tion implies the divisibility of the indivisible. For since 
the distinction of quicker and slower may apply to motions 

20 occupying any period of time and in an equal time the 
quicker passes over a greater length, it may happen that 
it will pass over a length twice, or one and a half times, as 
great as that passed over by the slower : for their respective 
velocities may stand to one another in this proportion. 
Suppose, then, that the quicker has in the same time been 
carried over a length one and a half times as great as that 
traversed by the slower, and that the respective magnitudes 
are divided, that ^ of the quicker, the magnitude ABrA,^ 
into three indivisibles, and that ^ of the slower into the two 

35 indivisibles EZ, ZH. Then the time may also be divided 
into three indivisibles, for an equal magnitude will be passed 
over in an equal time. Suppose then that it is thus divided 
into KA, AM, MN. Again, since in the same time the slower 
has been carried over EZ, ZH, the time may also be simi- 
larly divided into two. Thus the indivisible will be divisi- 

30 ble, and that which has no parts will be passed over not in 
an indivisible but in a greater time.^ It is evident, there- 
fore, thatnotjung^contin^ 

Th e present also is ne cessarily tndivisihlp — the present, 
that is, not in the sense in which the word is applied to one 
thing in virtue of another,^ but in its proper and primary 
35 sense ; in which sense it is inherent in all time. For the 
234^ present is something that is an extremity of the past (no part 
of the future being on this side of it) an d also of th e future 
(no part of the past being on the other side of it) : it is, as 
we have said,® a limit of both. And if it is once showr 

^ Reading in 11. 23-4 to fxev, with Simp. ^11 

2 Reading in 1. 24 ABFA, with EIK. ^■1 

^ Reading in 1. 25 to Se, with E Simp. 

* The slower will traverse EZ in a greater time than the indivisibl* 
time in which the quicker traverses KA. 

^ i. e. in which it means a period of time including the present proper 
^ 222^ 12. .^Mi 

BOOK VI. 3 a34' 

that it is essentially of this character and one and the 
same, it will at once be evident also th at it is indivisible. • 

Now the present that is the extremity of both times i 
must be one and the same : for if each extremity were 
different, the one could not be in succession to the other, 
because nothing continuous can be composed of things 

h aving no parts : and if the one is apart from the other, 
there will be time intermediate between them, because 
everything continuous is such that that there is something 
intermediate between its limits and described by the same 
name as itself. But if the intermediate thing is time, it 
will be divisible : for all time has been shown ^ to be divisible. 

Thus on this assumption the present is divisible. But if 
the present is divisible, there will be part of the past in the 
future and part of the future in the past : for past time will 
be marked off from future time at the actual point of 
division. Also the present will be a present not in the 
proper sense but in virtue of something else : for the division 
which yields it will not be a division proper.^ Furthermore, 
there will be a part of the present that is past and a part 
that is future, and it will not always be the same part that 
is past or future : in fact one and the same present will not 
be simultaneous ^ : for the time may be divided at many 
points.* If, therefore, the present cannot possibly have these 
characteristics, it follows that it must be the same present 
that belongs to each of the two times.^ But if this is so it \o 
is evident that the present is also indivisible : for if it is 
divisible it will be involved in the same implications as before. 
It is cle a£^then, from what has been said that time contai ns 
som ething indivisible, and this is what we call a presen t. 

We will now show that nothing can be in motion in 
a present.^ For if this is possible,^ there can be both quicker 25 
and slower motion in the present. Suppose then that in 

^ Chapter 2. 

^ i. e. it will cot be a poini of division but merely something 
intermediate between past and future. 

' 234* 18 reading t6 avro cifxa, with E. 

* i. e. the present, being a period of time, can itself be divided Into 
a number of presents. 

** i. e. that ends one period of time and begins the next. 

® Omitting ifrrw after yap in 1. 25, with E. 

L 2 

23t^^ PHYSICA 

the present N the quicker has traversed the distance AB. 
That being so, the slower will in the same present traverse 
a distance less than AB, say AF. But since the slower will 
have occupied the whole present in traversing AF, the 

30 quicker will occupy less than this in traversing it. Thus 
we shall have a division of the present, whereas we found 
it to be indivisible. l\ i<; impnssil^le^ t hprpf^r^, {nr any- 
thing to be in motion in r pr^*f^"t 

Nor can anything be at rest in a p resent : for, as we 
were saying,^ that only can be at rest which is naturally 
designed to be in motion but is not in motion when, where, 
or as it would naturally be so : since, therefore, nothing is 
naturally designed to be in motion in a present, it is clear 
that nothing can be at rest in a present either. 

Moreover, inasmuch as it is the same present that belongs 

35 to both the times,^ and it is possible for a thing to be in 
motion throughout one time and to be at rest throughout 
234^ the other, and that which is in motion or at rest for the 
whole of a time will be in motion or at rest as the case 
may be in any part of it in which it is naturally designed 
to be in motion or at rest : this being so, the assumption 
that there can be motion or rest in a present will carry 
with it the implication that the same thing can at the same 
time be at rest and in motion : for both the times have the 
same extremity, viz. the present. 

5 Again, when we say that a thing is at rest, we imply that 
its condition in whole and in part is at the time of speaking 
uniform with what it was previously : but the present con- 
tains no 'previously' : consequently, there can be no rest in it. 
It follows then that the motion of that which is in motion 
and the rest of that which is at rest must occupy time. 

JO Further, everything that chang^es must be divisi ble. For 4 
smce every change is from something to something, and 
when a thing is at the goal of its change it is no longer 
changing, and when both it itself and all its parts are at the 
starting-point of its change^ it is not changing (for that 

^ 226^ 12 sqq. "^ viz. past and future. 

* Reading in 1. 12 f. els o /iCTe/SaXXev . . . c'^ ov fiere^aWcp (so EK), 
Koi avTo . . . ndvTa, ov fMera^aXXei. 


BOOK VI. 4 234^ 

which is in whole and in part in an unvarying condition is 
not in a state of change) ; it follows, therefore,^ that part of 15 
that which is changing must be at the starting-point and 
part at the goal : for as a whole it cannot be in both or in 
neither. (Here by 'goal of change' I mean that which 
comes first in the process of change : e. g. in a process of 
change from white the goal in question will be grey, not 
black : for it is not necessary that that which is changing 
should be at either of the extremes.) It is evident, there- 20 
fore , that everything that change_s mnc^t bp Hivisihle. 

Now motiori is divisible in two senses. In the first place 
it is divisible in virtue of the time that it occupies. In the 
second place it is divisible according to the motions of the 
several part s of t hat which is in motjon ^: e. g. if the whole 
Ar is in motion, there will be a motion of AB and a motion of 
Br. That being so, let AE be the motion of the part AB and 
EZ the motion of the part Br. Then the whole AZ ^ must 25 
be the motion of Ar : for AZ must constitute the motion of 
Ar inasmuch as AE and EZ severally constitute the motions 
of each of its parts. But the motion of a thing can never be 
constituted by the motion of something else : consequently 
the whole motion is the motion of the whole magnitude. 

Again, since every motion is a motion of something, and 
the whole motion AZ is not the motion of either of the 
parts (for each of the parts AE, EZ is the motion of one of 
the parts AB, Br) or of anything else (for, the whole motion 30 
being the motion of a. whole, the parts of the motion are 
the motions of the parts of that whole : and the parts of 
AZ are the motions of AB, BF ^ and of nothing else : for, 
as we saw,* a motion that is one cannot be the motion of 
more things than one) : since this is so, the whole motion 
will be the motion of the magnitude ABr. 

Again, if there is a motion of the whole other than AZ, 
say 01, the motion of each of the parts may be subtracted 
from it : and these motions will be equal to AE, EZ 35 
respectively : for the motion of that which is one must be 235^ 

* Placing a colon before dvdyKr] in 1. 15. 

* Omitting 17 in 1. 25, with E. 

^ Reading in 1. 32 AB Br with Them, Simp. , ■* 223^ i sqq. 


one. So if the whole motion 01 may be divided into the 
motions of the parts, 01 will be equal to AZ : if on the 
other hand there is any remainder, say Kl, this will be a 
5 motion of nothing : for it can be the motion neither of the 
whole nor of the parts (as the motion of that which is one 
must be one) nor of anything else : for a motion that is 
continuous must be the motion of things that are con- 
tinuous. And the same result follows if the division of 
01 reveals a surplus on the side of the motions of the 
parts.^ Consequently, if this is impossible, the whole 
motion must be the same as and equal to AZ. 

This then is what is meant by the division of motion 
ac cording to t he motions of the parts : and it must be 
applicable to everything that is divisible into parts. 

lo Motion is also susceptible of another kind of division, 
that according to time. For since all motion is in time 
and all time is divisible, and in less time the motion is less, 
it follows that every motion must be divisible according to 
time. And since everything that is in motion is in motion 
in a certain sphere and for a certain time and has a motion 

15 belonging to it, it follows that the time, the motion, the 
being-in-motion, the thing that is in motion, and the sphere 
of the motion must all be susceptible' of the same divisions 
(though spheres of motion are not all divisible in a like 
manner: thus quantity is essentially ,'quality accidentally 
divisible). For suppose that A is the time occupied by the 

20 motion B. Then if all the time has been occupied by 
the whole motion, it will take less of the motion to occupy 
half the time, less again to occupy a further subdivision of 
the time, and so on to infinity. Again, the time will^be 
divisible similarly to the motion : for if the whole motion 
occupies all the time half the motion will occupy half the 
time,^ and less of the motion again will occupy less of 
the time. 

25 In the same way the being-in-motion will also be divisible. 
For let r be the whole being-in-motion. Then thebeing-in- 

^ i. e. of what can this surplus motion be the motion ? 
^ i. e. if the motion is regular. 

BOOK VI. 4 235* 

motion that corresponds to half the motion^ will be less 
than the whole being-in-motion, that which corresponds to 
a quarter of the motion will be less again, and so on to 
infinity. Moreover by setting out successively the being- 
in-motion corresponding to each of the two motions AF 
(say) and FE, we may argue that the whole being-in-motion 
will correspond to the whole motion (for if it were some 30 
other being-in-motion that corresponded to the whole 
motion, there would be more than one being-in-motion 
corresponding to the same motion), the argument being 
the same as that whereby we showed ^ that the motion of 
a thing is divisible into the motions of the parts of the 
thing : for if we take separately the being-in-motion corre- 
sponding to each of the two motions, we shall see that the 
whole being-in-motion is continuous.^ 

The same reasoning will show the divisibility of the 
length, and in fact of everything that forms a sphere of 
change (though * some of these are only accidentally 35 
divisible because that which changes is so) : for the division 
of one term will involve the division of all. So, too, in the 
matter of their being finite or infinite, they will all alike be 
either the one or the other. And we now see that in most 235'' 
cases ^ the fact th at all the terms are divis ible pi- infinite is 
a direct conseq uence of the fact that the t hi ng that changes 
^s divisible or infinite: f or the attributes 'd ivisible' and 
* infinite' belong i n the first instance to the thing that 
changes. T hat divisibility does so we have already ^ shown ; 5 
that infinity does so will be made clear in what follows. ''' 

5 Since eve rything that changes changes from something 
to something, that which has changed must at th^ rp^"^f^"^ 

^ i. e. in which half the motion is realized, to KiveiaBai being the 
state of the Kivov^evov in so far as it actually exhibits Kivrjais. 
^ 234^ 24 sqq., especially 234^ 34 sqq. 
^ Cf. 235* 6 : Kivqaii being continuous, KLveladm is so also. 

* The accepted punctuation seems wrong : the sentence fi/oyyap . . . 
8iaipfdrj(reTni serves to justify not the reservation introduced by nXrjv 
but the general conclusion as to the divisibility of the terms involved in 

■ An exception would be xp^v"s, the divisibility of which would 
follow from that of Kivrjais rather than from that of klvovucvov. 

* 234^ 10-20. "^ Chapter 7. 


when it has first changed be in that to which it has changed. 
For fFar^whrcfrndTahges^ret ires from or leaves that from 
which it changes : and leaving, if not identical with changing, 

lo is at any rate a consequence of it. And if leaving is a con- 
sequence of changing, having left is a consequence of having 
changed : for there is a like relation between the two in 
each case. 

One kind of change, then, being change in a relation of 
contradiction, where a thing has changed from not-being 

^5 to being it has left not-be jn£^_^ Therefore it will be in 
being: for everything must either be or not be. It is 
evident, then, that in contradictory change that which has 
changed must be in that to which it has changed. And 
if this is true in this kind of change, it will be true in all 
other kinds as well : for in this matter what holds good in the 
case of one will hold good likewise in the case of the rest. 

Moreover, if we take each kind of change separately, the 
truth of our conclusion will be equally evident, on the 
ground that th at which has chf i ^ged must he. somewhere 

20 or in som ethin g. F or, sin ce it has left that from which 
i t hasj ^hangpd ap d must h^ so mewhere, it m ust be either 
in t hat to which it has changed or in something el se. If, 
then, that which has changed to B is in something other 
than B, say F, it must again be changing from r to B : for 
it cannot be assumed that there is no interval ^ between F 

25 and B, since change is continuous. Thus we have the 
result that t he thing that hjs changed , at the moment 
when it has changed, is changing to that to which it has 
changed, w lych is impossible : th at which has c han gpf^T 
therefore, musFbe in iharro'^which it has changed. So it 
is evident likewise that that which has come to be, at the 
moment when it has come to be, will de^ and that which 

^ Cf. the definition of €x6fi€vov as 6 av ecf^f^^s ov aTtrrrrai (227*6). 
The exact connexion of thought is a little obscure : but the argument 
seems to be this : since the change is continuous, the changing thing, 
if it has not yet reached the state B, must be m process of reaching it, 
for there must be a gap between B and any intermediate state r which 
is different from B, and this gap can be bridged only by a process of 
change : .*. the change being continuous, the changing thing when it 
reaches r must be in process of change towards B. Read to B in 1. 24, 
with Hayduck. 

BOOK VI. 5 235 

has ceased to be will not-be : for what w e have said a^ ^lks 
u niversally to ev ery kind of change, a nd its truth is most 
obvious in the case of contradictoFy change. It is clear, 30 
then, that that which has changed, at the moment when 
it has tirst changed, is in that to whic h it has changed. 

We will now show that the 'primary when' in which 
that which has changed effected the completion of its 
change must be indivisible, where by 'primary' I mean 
possessing the characteristics in question of itself and not 
in virtue of the possession of them by something else 
belonging to it. For let Ar be divisible, and let it be 
divided at B. If then the completion of change has been 35 
effected in AB or again in BF, Ar cannot be the primary 
thing in which the completion of change has been effected. 
If, on the other hand, it has been changing in both AB and 
Br (for it must either have changed or be changing in each 
of them), it must have been changing in the whole AF: 236^ 
but our assumption was that Ar contains only the completion 
of the change. It is equally impossible to suppose that 
one part of AF contains the process and the other the 
completion of the change : for then we shall have some- 
thing prior to what is primary.^ S^ L^tha t in which the_ 
completion o f change has been effected must be indivisibl e. 
It is also evident, therefore, that that in which that which 5 
has ceased to be has ceased to be and that in which that 
which has come to be has come to be are indivisib le. 

But there are two senses of the expression ' the primary 
when in which something has changed '. On the one hand 
it may mean the primary when containing the completion 
of the process of change — the moment when it is correct \ 
to say * it has changed ' : on the other hand it may mean 
the primary when containing the beginning of the process 
of change. Now the primary when that has reference to 10 
the end of the change is something really existent : for 
a change may really be completed, and there is such 
a thing as an end of change, which we have in fact shown 
to be indivisible because it is a limit. But that which has 

^ sc. Br will have more right than Ar to be regarded as that in 
which the change has been completed. 


reference to the beginning is not existent at all : for there 
is no such thing as a beginning of a process of change,^ 
and the time occupied by the change does not contain 

15 any primary when in which the change began. For 
suppose that AA is such a primary when. Then it cannot 
be indivisible: for, if it were, the moment immediately 
preceding the change and the moment in which the change 
begins would be consecutive (and moments cannot be con- 
secutive). Again, if the changing thing is at rest in the 
whole preceding time TA ^ (for we may suppose that it is 
at rest), it is at rest in A also ^ : so if AA is without parts, it 
will simultaneously be at rest and have changed : for it is 

20 at rest in A and has changed in A.^ Since then AA is not 
without parts, it must be divisible, and the changing thing 
must have changed in every part of it (for if it has changed 
in neither of the two parts into which A A is divided, it has 
not changed in the whole either : if, on the other hand, it is 
in process of change in both parts, it is likewise in process 
of change in the whole : and if, again, it has changed in one 
of the two parts, the whole is not the primary when in 

25 which it has changed : it must therefore have changed in 
every part). It is evident, then, that with reference to the 
beginning of change there is no primary when in which 
change has been effected : for the divisions are infinite. 

So, too, of that which has changed ther e is no primary 

part that has changed. For suppose that of AE the 

^pnmsry~p2Lft~l!Kat has changed is AZ (everything that 

30 changes having been shown ^ to be divisible) : and let 01 

^ i. e. no parf of the process can be called absolutely first, because 
that part may be divided again, thus reaching a prior * first ', and so 
on to infinity. Similarly of course no par^ of the process can strictly 
be called the end : but the /zw// (nepas) exists as such, because it is 
«^/ a part of the process but an indivisible something marking the 
fact that the process is concluded. In the same sense there is an dpxnj 
but it is not strictly speaking an dpxr) /ierajSoXJjs, because as yet the 
process has not begun ; so it remains true that there is no such thing 
as TO ep <a npdoTO) fjp^aTO /iera/3aXXeij/. 

M e. if the tWo moments mentioned above are assumed to be really 
only one (A). 

^ It would be more correct to say ' is not in motion in A ', for in a 
moment nothing can be either at rest or in motion (234^24sqq.). 

* sc. because AA being indivisible is the same as A. 

•^ 234^ 10 sqq. 

BOOK VI. 5 236* 

be the time in which AZ has changed. If, then, in the 
whole time AZ has changed, in half the time there will be 
a part ^ that has changed, less than and therefore prior to 
AZ : and again there will be another part prior to this, and 
yet another, and so on to infinity. Thus of that which 
changes there cannot be any primary part that has changed. 
It is evident, then, from what has been said, that neither 35 
of that which changes nor of the time in which it changes 
i nhere any primary p art. 

With regard, however, to the actual s ubject of change^ — ^3^ 
that is to say that in respect of which a thing changes — 
there is a difference to be observed. For in a process 
of change we may distinguish t hree terms — that which 
changes, that in which it changes, and the actual subject 
of change,^ e. g. the man, the time, and the fair complexion. 
Of these the man and the time are divisible : but with the 5 
fair complexion it is otherwise (though they are all divisible 
accidentally, for that in which the fair complexion or any 
other quality is an accident is divisible). For* of actual 
subjects of change it will be seen that those which are 
classed a s essen tially, not accidentally, divisible have no 
primary part. Take the case of magnitudes : let AB be 1° 
a magnitude, and suppose that it has moved from B to 
a primary ' where ' F. Then if Br is taken to be indivisible, 
two things without parts will have to be contiguous (which 
is impossible) : if on the other hand it is taken to be 
divisible, there will be something prior to F to which the 
magnitude has changed, and something else again prior to 
that, and so on to infinity, because the process of division 
may be continued without end. Thus there can be no 15 

* 1. 32 reading tarai n, with Simp. 

^ Keeping in 1. i the reading of all the MSS. — nvro be 6 /xera.SaXXei 
(* the actual thing that changes ' in the particular utradaXXov, e. g. its 
place, its quantity, its quality), explained immediately as Ka6' 6 


* Reading in 1. 3 with four MSS. Km 6 /^era^aXXft, to be explained as 

* The generally accepted punctuation can hardly be right, as the 
eVet clause contains no sort of justification of the immediately pre- 
ceding statement : it connects rather with the sentence ending ovKed' 
ofjioiois e$€i (236^ i), the intervening sentence being of a parenthetical 


primary ' where ' to which a thing has changed. And if 
we take the case of quantitative change, we shall get a like 
result, for here too the change is in something continuous. 
It is evident, then, that only in qualitative motion can there 
be anything essentially indivisible. 

20 Now everything that changes changes in time, a nd that ( 
in two senses : for the time in which a thing is said to 
change may be the primary time, or on the other hand it 
may have an extended reference, as e. g. when we say that 
a thing changes in a particular year because it changes in 
a particular day. That being so, that which changes must 
be changing in any part of the primary time in which 
it changes. This is clear from our definition of * primary V 
in which the word is said to express just this : it may also, 
however, be made evident by the following argument. 

35 Let XP be the primary time in which that which is in 
motion is in motion : and (as all time is divisible) let it be 
divided at K. Now in the time XK it either is in motion 
or is not in motion, and the same is likewise true of the 
time KP. Then if it is in motion in neither of the two 
parts, it will be at rest in the whole : for it is impossible 
that it should be in motion in a time in no part of which 

30 it is in motion. If on the other hand it is in motion in 
only one of the two parts of the time, XP cannot be the 
primary time in which it is in motion : for its motion will 
have reference to a time other than XP. It must, then, 
have been in motion in any part of XP. 

And now that this has been proved, it is evident that 
everything that is in motion must have been in motion 
before. For if that which is in motion has traversed the 

35 distance KA in the primary time XP, in half the time 
a thing that is in motion with equal velocity and began 

. its motion at the same time will have traversed half the 

distance. But if this second thing whose velocity is equal 

237^ has traversed a certain distance in a certain time, the 

^ 235^ 33. The * primary time ' is the irreducible minimum : thus the 
very terms of the definition make it dear that a thing must be chang- 
ing in the whole of the ' primary time ' in which it changes. 

BOOK VI. 6 237* 

original thing that is in motion must have traversed the 
same distance in the same time. Hence that which is in 
motion must have been in motion before. 

Again, if by taking the extreme moment of the time — 
for it is the moment that defines the time, and time is that 5 
which is intermediate between moments — we are enabled 
to say that motion has taken place in the whole time XP 
or in fact in any period ^ of it, motion may likewise be said 
to have taken place in every other such period. But half 
the time finds an extreme in the point of division. There- 
fore motion will have taken place in half the time and in 
fact in any part of it : for as soon as any division is made 
there is always a time defined by moments. If, then, all 
time is divisible , and that which is intermediate between 10 
moments is time, everything that is changing must have 
completed an infinite number of changes. 

Again, since a thing that rVi^ncrpg^rnntip^^Q^igly anH has 
not perished or ceased from its change must either be 
changing or have changed in any part of the time of its 
change, and since it cannot be changing in a moment, it 
follows that it must have changed, at every moment in 
the time : consequently, since the moments are infinite in 15 
number,~everything that is changing must have r ompl^^d 
an infinite number of changes. 

And not only must that which is changing have changed, 
but that which has changed must also previously have been 
changing, since everything that has changed from some- 
thing to something has changed in a period of time. For 20 
suppose that a thing has changed from A to B in a moment. 
Now the moment in which it has changed cannot be the 
same as that in which it is at A (since in that case it would 
be in A and B at once) : for we have shown above ^ that 
that which has change d, when it has changed^ is not in 

^ Reading in 1. 4 ^ o\<os iv orcdovv xpov(?' The insertion of a second ^ 
after oX(os seems to make oXcos pointless, h tw iravTi xpoJ'w having pre- 
ceded : and cf. below oXcos ev otcoovv t5)v fxepmv (237* 8). If the text is 
otherwise right, xpo^? here must mean ' period of the whole time * : 
otherwise no sense can be given to rots (iWois : but one would like to 
read something like ev otcdovv xpova> (jcov rourou), rco Xa^e'iv ktX. 

2 235b6sqq. 


that from which it has changed. J lf^ on the other hand, it 
is a different moment, there will be a period of time inter- 
mediate between the two: for, as we saw,^ moments are 

25 not consecutive. Since, then, it has changed in a period 
of time, and all time is divisible, in half the time it will 
have completed another ^ change, in a quarter another, and 
so on to infinity: co nsequently when it has chan ^ red, it 
must h ave previously been changing . 

Moreover, the truth of what has been said is more 
evident in the case of magnitude, because the magnitude 

30 over which what is changing changes is continuous. For 
suppose that a thing ^ has changed from r to A. Then if 
TA is indivisible, two things without parts will be consecu- 
tive. But since this is impossible, that which is inter- 
mediate between them must be a magnitud^^md divisib le 
^nto an infinite number of s egmeats : consequently, before 
the change is completed, the thing changes to those segments. 
Everything that has changed, therefore, must previously 

35 have been changing : for the same proof also holds good 
237^ of change with respect to what is not continuous, changes, 
that is to say, between contraries and between contradic- 
tories. In such cases we have only to take the time in 
which a thing has changed and again apply the same 
reasoning. S o that which has changed must ha ve been 
^hanging and that which is changing must have changed, 
and rj;mt^ss of rh^nge is prer/^H ed hy_ a comple tion of 
5 chan ge and a co m pletion b y a prrtress • an d we can never 
take any stage and sa y that it is absolutely the first. The 
reason of this is that no two things without parts can be 
contiguous, and therefore in change the process of division 
is infinite,* just as lines may be infinitely divided so that 
one part is continually increasing and the other continually 

* 231^6 sqq. : where it is shown that moments cannot be ((fx^n^, of 
which exofxfvop is a subdivision (V. 3. 227* 6). 

^ i. e. different from the whole change. 
^ 1. 30 reading yup n, with F. 

* \. 8 reading aneipos, with E. 

° i. e. you may begin by cutting oflf half the line, then half of what 
remains, and so on, the part cut off thus continuously increasing and 
the part remaining continually decreasing. 

BOOK VI. 6 237^ 

So it is evident also that that whi ch has become must 10 
p reviously have b een in proce ss o f becomings and that 
which is in process of becoming must previously have 
become, everything (that is) that is divisible and continuous : 
though it is not always the actual thing that is in process 
of becoming of which this is true : sometimes it is some- 
thing else, that is to say, some part of the thing in question, 
e. g. the foundation-stone of a house.^ So, too, in the case 
of that which is perishing and that which has perished : 
for that which becomes and that which perishes must 
contain an element of infiniteness as an immediate con- 
sequence of the fact that they are continuous things^: and 15 
so a thing c annot be in process of becn minpr without having 
become or have become without having been in process of 
becoming. So, too, in the case of perishing and having 
perished : perishing must be preceded by having perished, 
and having perished must be preceded by perishing. It is 
evident, then, that that which has become must previously 
have been in process of becoming, and that which is in 
process of becoming must previously have become : for all 20 
magnitudes and all perio ds of time are infinitel y divisible. 

Consequently no absolutely first stage of change can be 
represented by any particular part of space or time which 
the changing thing may occupy. • 

7 Now since the motion of everything that is in motion 
occupies a period of time, and a greater magnitude is 
traversed in a longer time, it is im.possible that a thing 
should undergo a finite motion in an infinite time, if this is 35 
understood to mean not that the same motion or a part of 
it is continually repeated,^ but that the whole infinite time 
is occupied by the whole finite motion. In all cases where 
a thing is in motion with uniform velocity it is clear tha_L 
the finite magnitude is traversed in a finite time. Fo r if 

^ i. e. the ' having become ' (completion) of a house must be pre- 
ceded by its ' becoming ' : for when a foundation-stone is being laid, 
the process is to be regarded not merely as the laying of the founda- 
tion-stone but also as the building of the house, of which it is a part. 

^ i. e. they are o-Q)/x«ra, which being awtxri are therefore els dneipov 

' as e. g. in the case of rotation or the swing of a pendulum. 


we take a part of the motion which shall be a measure of 
the whole, the whole motion is completed in as many equal ^ 

30 periods of the time as there are parts of the motion. Con- 
sequently, since these parts are finite, both in size individu- 
ally and in number collectively, the whole time must also 
be finite: for it will be a multiple of the portion, equal to 
the time occupied in completing the aforesaid part multi- 
plied by the number of the parts. 

But it makes no difference even if the velocity is not 
uniform. For let us suppose that the line AB^ repre- 

35 sents a finite stretch over which a thing has been 
moved in the given time, and let TA be the infinite time. 
238^ Now if one part of the stretch must have been traversed 
before another part (this is clear, that in the earlier and in 
the later part of the time a different part of the stretch has 
been traversed : for as the time lengthens a different part 
of the motion will always be completed in it, whether the 

5 thing in motion changes with uniform velocity or not : and 
whether the rate of motion increases or diminishes or 
remains stationary this is none the less so),^ let us then 
take AE a part of the whole stretch of motion AB which 
shall be a measure of AB. Now this part of the motion 
occupies a certain period of the infinite time : it cannot 
itself occupy an infinite time, for we are assuming that that 
is occupied by the whole AB. And if again I take another 

10 part equal to AE, that also must occupy a finite time in 
consequence of the same assumption. And if I go on 
taking parts in this way, on the one hand there is no part 
which will be a measure of the infinite time (for the infinite 
cannot be composed of finite parts whether equal or unequal, 
because there must be some unity which will be a measure 

15 of things finite in multitude or in magnitude, which, whether 
they are equal or unequal, are none the less limited in 
magnitude) ; while on the other hand the finite stretch of 
motion AB is a certain multiple of AE : consequently the 
motion AB must be accomplished in a finite time. More- 

1. 29 omitting to7s, with E. 

Reading in 1. 35 to AB, with Simp, and Bonitz. 

Reading a comma after tjttop in 1. 6, with Bonitz. 


BOOK VI. 7 238* 

over it is the same with coming to rest as with motion.^ 
And so it is impossible for one and the same thing to be 
infinitely in process of becoming or of perishing.^ 

The same reasoning will prove that i n a finite time there 20 ^ 
cannot be an infinite extent of moti on or of com ing to rest, 
whether the motion is regular or irregular. For if we take 
a part which shall be a measure of the whole time, in this 
part a certain fraction, not the whole, of the magnitude 
will be traversed, because we assume that the traversing of 
the whole occupies all the time. Again, in another equal 
part of the time another part of the magnitude will be 
traversed : and similarly in each part of the time that we 25 
take, whether equal or unequal to the part originally taken. 
It makes no difference whether the parts are equal or not, 
if only each is finite : for it is clear that while the time is 
exhausted by the subtraction of its parts, the infinite 
magnitude will not be thus exhausted, since the process of 
subtraction is finite both in respect of the quantity subtracted 
and of the number of times a subtraction is made. Con- 
sequently the iii finite magnitude will not be trave rsed in 
a^^finjt^^jhirrip; and it makes no difference whether the 30 
magnitude is infinite in only one direction or in both : for 
the same reasoning will hold good. 

This having been proved, it is evident that neither can 
a finite magnitude traverse an infinite magnitude in a finite 
:ime, the reason being the same as that given above : in 
Dart of the time it will traverse a finite magnitude and in 35 
^ach several part likewise, so that in the whole time it will 
raverse a finite magnitude. 

And since a finite magnitude will not traverse an infinite 
n a finite time, it is clear that neither will an infinite 238^ 
raverse a finite in a finite time. For if the infinite could 
raverse the finite, the finite could traverse the infinite ; for 
t makes no difference which of the two is the thing in 
|;notion : either case involves the traversing of the infinite 

* viz. a finite process of coming to rest (completion of motion) cannot 
ccupy an infinite time. 

' A thing that is to avro koi €V is 7r€iTepuaiJ.evov : its yeveais or (pdopd is 
lerefore also nencpaayLevrj and cannot be iu direipw XP^*'^ (to which 
Ft is here equivalent). 

645-16 M 


5 by the finite. For when the infinite magnitude A is in 
motion a part of it, say TA, will occupy the finite B,^ and 
then another, and then another, and so on to infinity. 
Thus the two results will coincide: the infinite will have 
completed a motion over the finite and the finite will have 
traversed the infinite : for it would seem to be impossible 

lo for the motion of the infinite over the finite to occur in 
any way other than by the finite traversing the infinite 
either by locomotion over it or by measuring it.^ There- 
fore, since this is impossible, the infinite cannot traverse the 

Nor again will the infinite traverse the infinite in a finite 

15 time. Otherwise it would also traverse the finite, for the 
infinite includes the finite. We can further prove this in 
the same way by taking the time as our starting-point.^ 

Since, then, it is established that in a finite time neither 
will the finite traverse the infinite, nor the infinite the 
finite, nor the infinite the infinite/ it is evident also that in 

20 a finite time there cannot be infinite motion : for what 
difference does it make whether we take the motion or the 
magnitude to be infinite? If either of the two is infinite, 
the other must be so likewise : for all locomotion is in 

Since everything to which motion or rest is natural is in 
motion or at rest in the natural time, place, and manner, 
that which is coming to a stand, when it is coming to 
35 a stand, must be in motion : for if it is not in motion it 
must be at rest : but that which is at rest cannot be coming 
to rest.^ From this it evidently follows that coming to 
a stand must occupy a period of time : for the motion of 
that which is in motion occupies a period of time, and that 

^ Reading in 1. 6 t6 B to 7r(7repaafX€iov, with E. 

"^ i. e. the finite must either travel from end to end of the infinite 
(if the infinite could have ends) or be itself traversed by the infinite 
thus ' measuring up ' the infinite with itself as the measure. 

^ viz. by dividing up the TreTrepnafievos xpoi'oy in the way desc ribe 
above (238* 22 sqq.) instead of the Trenfpacrpkvov p-eyedos. ^ 

* Reading in 1. 18 to aTrnpov to amipov, with FHPK. 
^ And therefore infinity in any of the terms must imply s\ 

infinity of some sort. 

• In this connexion rjpeiiiCfadai is identical in meaning with torac 



BOOK VI. 8 238" 

which is coming to a stand has been shown to be in motion : 
consequently coming to a stand must occupy a period of 

Again, since the terms ' quicker ' and ' slower ' are used 
only of that which occupies a period of time, and the process 30 
of coming to a stand may be quicker or slower, the same 
conclusion follows. 

And ^ that which is coming to a stand must be coming to 
a stand in any part of the primary time in which it is coming 
to a stand. For if it is coming to a stand in neither of 
two parts into which the time may be divided, it cannot be 
coming to a stand in the whole time, with the result that 
that which is coming to a stand will not be coming to a 
stand. If on the other hand it is coming to a stand in 
only one of the two parts of the time, the whole cannot be 
the primary time in which it is coming to a stand : for it 35 
is coming to a stand in the whole time not primarily but in 
virtue of something distinct from itself,^ the argument 
being the same as that which we used above about things 
in motion.^ 

And just as there is no primary time in which that which 
is in motion is in motion, so too there is no primary time 239^ 
in which that which is coming to a stand is coming to a 
stand, there being no primary stage either of being in 
motion or of coming to a stand. For let AB be the primary 
time in which a thing is coming to a stand. Now AB 
cannot be without parts : for there cannot be motion in 
that which is without parts, because the moving thing 
would necessarily have been already moved for part of the 
time of its movement:* and that which is coming to 5 
a stand has been shown to be in motion. But since AB is 
therefore divisible, the thing is coming to a stand in every 
one of the parts of AB : for we have shown above ^ that it 

^ A new point is here introduced. It is not the apodosis to the 
previous sentence en 6' fl kt\., which serves only to substantiate the 
conclusion already reached : the apodosis is not expressed, but is 
easily supplied. 

"^ Reading in 1. 35 xa^' hepovj with EF. 

' Ch. 6. 

* Reading in 1. 5 n au avrov, with E. ^ 238^^31 sqq. 

M 2 

239^ PHYSIC A 

is coming to a stand in every one of the parts in which it is 
primarily coming to a stand. Since, then, that in which 
primarily a thing is coming to a stand must be a period of 
time and not something indivisible, and since all time is 
infinitely divisible, there cannot be anything in which 
primarily it is coming to a stand. 

lo Nor again can there be a primary time at which the 
being at rest of that which is at rest occurred : for it cannot 
have occurred in that which has no parts, because there 
cannot be motion in that which is indivisible, and that in 
which rest takes place is the same as that in which motion 
takes place : for we defined ^ a state of rest to be the state 
of a thing to which motion is natural but which is not in 
motion when (that is to say in that ^ in which) motion would 
be natural to it. Again, our use of the phrase 'being at 

15 rest' also implies that the previous state of a thing is still 
unaltered, not one point only but two at least being thus 
needed to determine its presence : consequently that in 
which a thing is at rest cannot be without parts. Since, 
then, it is divisible, it must be a period of time, and the 
thing must be at rest in every one of its parts, as may be 
shown by the same method as that used above in similar 

20 So there can be no primary part of the time : and the 
reason is that rest and motion are always in a period of 
time, and a period of time has no primary part any more 
than a magnitude or in fact anything continuous : for every- 
thing continuous is divisible into an infinite number of 

And since everything that is in motion is in motion in 
a period of time and changes from something to something, 
when its motion is comprised within a particular period of 
time essentially — that is to say when it fills the whole and 

25 not merely a part of the time in question ^ — it is impossible 

^ 226^ 12 sqq. 

^ sc. time. Km iv a (which is here equivalent to ore) is added 
simply for the sake of mlroducing the exact expression used immedi- 
ately before. 

^ 1. 24. It is hard to get any sense out of Bekker's reading — t5>v (v 
iKelvov TivL The reading of EH I Simp, tw iv cKeivov nvi will give the 


BOOK VI. 8 239^ 

that in that time that which is in motion should be over 
against some particular thing primarily.^ For if a thing — 
itself and each of its parts — occupies the same space for 
a definite period of time, it is at rest : for it is in just these 
circumstances that we use the term * being at rest ' — when 
at one moment after another it can be said with truth that 
a thing, itself and its parts, occupies the same space. So 
if this is being at rest it is impossible for that which is 30 
changing to be as a whole, at the time when it is primarily 
changing, over against any particular thing (for the whole 
period of time is divisible), so that in one part of it after 
another it will be true to say that the thing, itself and its 
parts, occupies the same space. If this^is not so and the 
aforesaid proposition is true only at a single moment, then 
the thing will be over against a particular thing not for any 
period of time but only at a moment that limits the time. 
It is true that at any moment it is always over against 35 
something stationary : but it is not at rest : for at a moment 239^ 
it is not possible for anything to be either in motion or at 
rest. So while it is true to say that that which is in motion 
is at a moment not in motion and is opposite some particular 
thing, it cannot in a period of time be over against that 
which is at rest : for that would involve the conclusion that 
that which is in locomotion is at rest. 

Zeno^s reasoning, h owever, is fallacious, when he says that 5 
if everything when it occupies an equal space is at rest, 
and if that which is in locomotion is always occupying such 
a space at any moment, the flying arrow is therefore 
motionless.^ This is false, for time is not composed of 

required sense, as also would rw iu roov ckhvov tivI, which I would 
suggest as best accounting for the variants. 

^ i.e. a space only just large enough to contain it, not a larger space 
of which only part is occupied. 

* Zeno's argument apparently does not prove that the arrow is 
.at rest because it is not in motion, del rjpefxfiTrav r) Ktvehm is therefore 
not used as a premise, and the best way of emending the passage is 
(with Zeller) to treat 17 Kivelrai as a gloss introduced through the 
influence of such passages as 238^ 23. eort 1. 6 can in the context 
stand for eo-rt Kara to tcrov, but possibly we should insert Kara t6 'iaov 
ifter vvv 1. 7, with Zeller and some MS. support. 


indivisible moments any more than any other magnitude 
is composed of indivisibles. 

lo Zeno's arguments ^ about motion, which cause so much 
disquietude to those who try to solve the problems that 
they present, are four in number. The first asserts the 
non-existence of motion on the ground that that which is 
in locomotion must arrive at the half-way stage before it 
arrives at the goal.^ This we have discussed above.^ 
The second is the so-called 'Achilles*, and it amounts 

15 to this, that in a race the quickest runner can never over- 
take the slowest*, since the pursuer must first reach the 
point whence the pursued started, so that the slower must 
always hold a lead. This argument is the same in principle 
as that which depends on bisection,^ though it differs from 
it in that the spaces with which we successively have to 

20 deal are not divided into halves. The result of the 
argument is that the slower is not overtaken : but it 
proceeds along the same lines as the bisection-argument 
(for in both a division of the space in a certain way leads 
to the result that the goal is not reached, though the 
'Achilles' goes further in that it affirms that even the 
quickest runner ® in legendary tradition must fail in his 

25 pursuit of the slowest '^), so that the solution must be the 
same. And the axiom that that which holds a lead is 
never overtaken is false : it is not overtaken, it is true, 
while it holds a lead : but it is overtaken nevertheless if it 
is granted that it traverses the finite distance prescribed. 
These then are two of his arguments. 

30 The third is that already given above, to the effect that 

* On the arguments generally see Noel in the Revue de Metci' 
physique et de Morale^ vol. i, pp. 107 sqq., and Russell, Principles of 
Mathematics^ vol i, chs. 42, 43. Further references to the literature 
of the subject are given in Zeller, i.^ 755 n., and in Heath, Gk. Mathe- 
matics^ i. 279, 280 n. I, 283 n. 2. The first two arguments are addressed 
to those who assert, the second two to those who deny the infinite 
divisibility of space and time. 

^ The remaining half being again divisible into two, and so on to 

s 233a 13 sqq^ 

* Reading in 1. 15 jSpaSuraroi/, with E, Themistius, and Simplicius. 
° viz. the first argument given above, 11. 11-14. 

^ sc. Achilles as described by Homer — ttoSo? oxci/j 'A;(iXXevff. 

' sc. the tortoise, proverbial for slowness : cf. Plut. Mor. 1082 E. 



the flvinp - arrow J s at rest, which result follows from the 
assumption that time is c omposed of moments : if this 
assumption is not granted, the conclusion will not follow. 
The fourth argument ^ is that concerning the two rows of 

^ Zeno's fourth argument may be represented thus : — 
'Apx>} Tov (TTablov Mfo-ov tov arradiov TeXos tov oraStoi; 


ea-^fiT-oj/ Tols r). (= fieaov tcov A). (= icrxnTOV Toi^ 



^ 1 









Fig. I 


B8 B7 




B3 JB-3 


< — 

















Fig. 3 
(240* 9). 









— > 


















Fig. 3 
(240* 13). 



















Let O have reached B^ at the moment Af in the time T, 

Then at the same moment M — 

(i) Since B^ and C^ are travelling with equal velocity, B^ must 
have reached C^ (= A^) arid must have occupied the same time as C^. 
Therefore ^^*s time = T. 

(2) C^ must have travelled a distance equal to A^-A^, since (a) it 

has passed all the B's, (iS) each B = each A , {y) spaces of equal size 

must be traversed in equal times if the speed be equal. B^^ however, 

has only travelled the distance A^-A^. Therefore B^^ having travelled 

only half the distance, can have occupied only half the time that has 

been occupied by O. Therefore -5^'s time = — . 

(3) C^ must have completed the course, since having started at the 
middle point of the course it has travelled a distance equal to A^-A^ 
(= half the course). Therefore B^ must also have completed the 
course. But for this to have happened (that is to say, for all the -5's 
to have passed all the C's) twice as much time must have elapsed as 


bodies, each row being composed of an equal number of 

bodies of equal size, passing each other on a race-course as 

they proceed with equal velocity in opposite directions, the 

one row originally occupying the space between the goal 

and the middle point of the course and the other that 

35 between the middle point and the starting-pos t. This, he 

thinks, involves the conclusion that half a given ti'pipl is 

240 ^ equal to double that time. Th^ falla cy of the reasogj i ng 

lies in the assumption that a body occupies an equal time 

in passing with equal velocity a body that is in motion and 

a body of equal size that is at rest ; which is false. For 

instance (so runs the argument), let A, A . . . be the 

5 stationary bodies of equal size, B, B . . . the bodies, equal 

in number and in size to A, A . . ., originally occupying the 

half of the course from the starting-post to the middle of the 

A's, and F, T . . . those originally occupying the other half 

from the goal to the middle of the A's, equal in number, size, 

and velocity to B, B . . . . Then three consequences follow : 

First, as the B's and the T's pass one another, the first B 

reaches the last T at the same moment as the first T 

10 reaches the last B. Secondly,^ at this moment the first T 

has passed all the A's,^ whereas the first B^ has passed 

was necessary to enable C^ to reach B^. But the time occupied by 
C^ in reaching £^ = T. Therefore B^'s time = 2T. 
Thus at the same moment M the time occupied since the start by 


B^ is both — and 2 T. Consequently, if motion is possible, half a given 

time is equal to double that time, which is absurd. Therefore motion 
is impossible. Q.E.D. 

As the argument is intended for those who attempt to evade the 
first two by denying the infinite divisibility of space and time, and to 
refute scientific theories as to the structure of matter that involve the 
view that matter is divisible ultimately into units {oyKoi) occupying 
a certain amount of space and yet not themselves divisible, the 
assumption that Aristotle stigmatizes as false is not an arbitrary 
assumption of Zeno's own but a deduction from the view criticized. 

For a further discussion of the passage and justification of the 
rendering given above, see an article by R. K. Gaye in i^t Journal 
of Philology, xxxi. 95 sqq. 

^ Reading (rv/i|3at j/a 6e, with E^FHK, Alex. 

' Reading iravra to. A, with FKE^ and Simplicius. 

^ Reading to M B, with E and Simplicius. 

BOOK VI. 9 240^ 

only half the A's, and has consequently occupied only half 
the time occupied by the first T, since each of the two 
occupies an equal time in passing each A. Thirdly, at the 
same moment all the B's have passed all the F's : for the 
first r and the first B will simultaneously reach the opposite 
ends of the course, since (so says Zeno) the time occupied 15 
by the first F in passing each of the B's is equal to that 
occupied by it in passing each of the A's, because an equal 
time is occupied by both the first B and the first F in passing 
all the A's. This is the argument, but it presupposed the 
aforesaid fallacious assumption. 

Nor in reference to contradictory change shall we find 
anything unanswerable in the argument that if a thing is 20 
changing from not-white, say, to white, and is in neither 
condition, then it will be neither white nor not-white : for 
the fact that it is not ivholly in either condition will not 
preclude us from calling it white or not-white. We call a 
thing white or not- white not necessarily because it is wholly 
either one or the other, but becaus ejpost of its parts or the 
most essential parts ^ of it are so: not being in a certain 25 
.condition is different from not being wholly'in that condition. 
So, too, in the case of being and not-b eing a nd all other 
conditions which stand in a contradictory relation : while 
the changing thingmust of necessity b e in one of the two 
opposites, it is neverwhp l ly in either ! 

Again, in the case of circles and spheres and everything 
whose motion is confined within the space that it occupies, 
it is not true to say that the motion ca n be nothing b ut 30 
rest, on tne ground that such thmgs in motion, themselves and 
their parts, will occupy the same position for a period of time, 
and that therefore they will be at once at rest and in motion. 
For in the jirst place the parts do not occupy the same 
position for any period of time : and in the second pl ace, 
the whole also is always changing to a different position : 
for if we take the orbit as described from a point A on a 240^ 

^ i. e. the parts (not necessarily a majority of the whole) the white- 
ness of which more especially justifies us in calling the whole thing 
white : e. g. we may speak of the sea being white if the crests of the 
waves are white. 

240*' PHYSICA 

circumference, it will not be the same as the orbit as 
described from B or T or any other point on the same 
circumference except in an accidental sense, the sense that 
is to say in which a musical man is the same as a man.^ 
5 Thus one orbit is always c hanging into another, and the 
thing will never be at r est. And it is the same with the 
sphere a nd everything else whose motion is confined within 
the space that it occupies. 

Our next point is that that which is without parts cannot ic 
be in motion except accidentally : i. e. it can be in motion 
only in so far as the body or the magnitude is in motion 

lo and the partless is in motion by inclusion therein,^ just as 
that which is in a boat may be in motion in consequence of 
the locomotion of the boat, or a part may be in motion in 
virtue of the motion of the whole. (It must be remembered, 
however, that by ' that which is without parts ' I mean that 
which is quantitatively indivisible (and that the case of the 
motion of a part is not exactly parallel Y : for parts have 
motions belonging essentially and severally to themselves 

15 distinct from the motion of the whole. The distinction 
may be seen most clearly in the case of a revolving sphere, 
in which the velocities of the parts near the centre and of 
those on the surface are* different from one another and 
from that of the whole ; this implies that there is not one 
motion but many.) As we have said, then, tha^jvhirh is 
without parts can be in motion in the sense in which a man 
sitting in a boat is m motion when the boat is travelling, 

20 but it cannot be in motion ojjtsfiLL For suppose that it is 

* i. e. the one orbit is the same as the other only in the sense that 
they both belong to or are ' accidents ' of (avfx(3e^i]Kf) the same portion 
of space, just as the attributes ixovo-ikos and dv^pcoTroy may belong to the 
same individual. 

^ Reading in 1. 10 tc3 ewnapx^iv, with Simplicius (tcov evvniipx^ 


' The point is that t6 cififpes can have no motion of its own jui 
because it is apepes, whereas pfprj, not being apepri, may have motior 
of their own as well as accidental motions. It is only in so far as the 
pepos is in motion merely in virtue of the motion of the oXov that iti 
motion is comparable with that of the dpepes. 

* Reading in 1. 16 earl, with E. 



BOOK VI. lo 240^ 

changing from AB to BE — either from one magnitude to 
another,^ or from one form to another,^ or from some state 
to its contradictory — and let A be the primary time in which 
it undergoes the change. Then in the time in which it is 
changing it must be either in AB or in Br or partly in one 
and partly in the other : for this, as we saw,^ is true of 25 
everything that is changing. Now it cannot be partly in 
each of the two : for then it would be divisible into 

parts. Nor again can it be in BT: for then it will have 
completed the change, whereas the assumption is that the 
change is i n process . It remains, then, that in the time in 
which it is changing, it is in AB. That being so, it will be 
at rest : for, as we saw,* to be in the same condition for 
a period of time is to be at rest. So it is not possible for 30 
that which has no parts to be in motion or to change in any 
way : for only one j:ondition could have made it possible 
for it to have motjo n, viz. t hat time should be composed o f 
moments, in which case at any moment it would have 
completed a motion or a change, so that it would never be 241* 
in motion, but would always have been in motion. But 
this we have alread y shown above ^ to be impossible : time 
is not composed of m oments, jus t as a l ine is not composed 
of points^ and motion is not composed o^ start s: for this 
theory simply make s motion consist of indivisibles in exact ly 5 
the same way as time is made to co n.^if ?t of mnmpnfg nr 
aje ngth ^ of points. 

Again, it may be shown in the following way th^tlherg,.^ 
can be no motion of a point or of a ny other indivisibl e. 
That which is in motion can never traverse a space greater 
than itself without first traversing a space equal to or less 
than itself. That being so, it is evident that the point also 
must first traverse a space equal to or less than itself. But 10 
since it is indivi sible, th ere can be no space less than ii-^^plf 

SC. either Kara tottov or Kara ito(t6v. 


^ 234^l(ysqq., where, however, it is pointed out that only the third 
alternative here mentioned is really possible (234^ 15) : the other two 
are included here only for the sake of completeness. 

* 239*27. 

° 231^ 18 sqq. « Reading in 1. 6 h?jko9, with E and Simp. 


for it to traverse first : so it will have to traverse a distance 
equal to itself. Thus the line will be composed of points, 
for the point, as it continually traverses a distance equal to 
itself, will be a measure of the whole line. But since this 
is impossible, it is likewise impossible for the indivisible to 
be in motion. 

15 Again, since motion is always in a period of time and 
never in a moment, and all time is divisible, for every- 
thing that is in motion there must be a time less than that ^ 
in which it traverses a distance as great as itself For that 
in which it is in motion will be a time, because all motion 
is in a period of time ; and all time has been shown above ^ 
to be divisible. Therefore,^ if a point is in motion, there 
'must be a time less than that ^ in which it has itself traversed 

20 any distance.^ But this is impossible, for in less time it 
must traverse less distance, and thus the indivisible will be 
divisible into something less than itself, just as the time is 
so divisible : the fact being that the only condition under 
which that which is without parts and indivisible could be 
in motion would have been the possibility of the infinitely 

25 small being in motion in a moment : for in the two 
questions — that of motion in a moment and that of 
motion of something indivisible — the same principle is 

Our next point is that no process of change is infinite : 
for every change, whether between contradictories or 
between contraries, i s a chang efrom something to., SDme- 
thing.^ Thus in contradictory changes the positive or the 
negative, as the case may be, is the limit, e. g. being is the 
limit of coming to be and not-being is the limit of ceasing 
to be: and in contrary changes the particular contraries 

30 are the limits, since these are the extreme points of any 
such process of change, and consequently of every process 

^ Reading in 1. 17 (with E and apparently Simplicius) ^ eV «. 

2 232^ 23 sqq. 

^ Omitting fi' in 1. 19, with FHK. 

* Reading (with E Them. Phil.) rj iv <u. 

° sc. a distance equal to itself, which is the least it can travel (241* 
11). It would be easier if we could read ocrov avrr] or tarov avrfj for avTT] 
with(apparently) Philoponus and Themistius. 

BOOK VI. lo 241* 

of alteration : for alteration is always dependent upon ^ 
some contraries. Similarly contraries are the extreme 
points of processes of increase and decrease : the limit of 
increase is to be found in the complete magnitude proper 
to the peculiar nature of the thing that is increasing, while 241^ 
the limit of decrease is the complete loss of such magnitude. 
Locomotion, it is true, we cannot show to be finite in this 
way, since it is not always between contraries. But since 
that which cannot be cut (in the sense that it is incon- 
ceivable that it should be cut, the term 'cannot* being 
used in several senses ^) — since it is inconceivable that that 5 
which in this sense cannot be cut should be in process of 
being cut, and generally that that which cannot come to 
be should be in process of coming to be, it follows that it 
is inconceivable that that w^hich cannot complete a change ^ 
should be in process of changing to that to which it cannot 
complete a change.^ If, then, it is to be assumed that that 
which is in locomotion is in process of changing, it must 
be capable of completing the change.^ Consequently its 
motion is not infinite, and it will not be in locomotion 
over an infinite distance, for it cannot traverse such a 10 

It is evident, then, that a process of change cannot be 
infinite in the sense that it is not defined by limits. But 
it remains to be considered whether it is possible in the 
sense that one and the same process of change may be 
infinite in respect of the time which it occupies. If it is 
not one process, it would seem that there is nothing to 
prevent its being infinite in this sense ; e. g. if a process 15 
of locomotion be succeeded by a process of alteration and 
that by a process of increase and that again by a process 

* Tfiat this is the meaning of e^ here seems clear. It is unlikely 
that the starting-point of the change should be insisted upon rather 
than the final limit ; cf. 241^ 29, 30 above. Aristotle means that 
the existence of dWoiaxris always implies the existence of a pair of 

^ For the different senses of abvvarov see Metaph, A. 1019^ 19 sqq. 

' Reading in 11. 7 (after ro)^ 8, and 9 (with one MS.) /xera/SaXetv, 
the aorist being necessary to denote the act as opposed to the 
process of change : cf. TfirjOr^vai )( Tfuveadai above. Simplicius appa- 
rently had /Mera/SaXcij/. 

241*^ PHYSICA 

of coming to be : in this way there may be motion for ever 
so far as the time is concerned, but it will not be one 
motion, because all these motions do not compose one. 
If it is to be one process, no motion can be infinite in 
respect of the time that it occupies, with the single excep- 
20 tion of rotatory locomotion. 




Everything that is in motion must be moved by some- 
thing. For if it has not the source of its motion in itself 35 
it is evident that it is moved by something other than itself, 
for there must be something else that moves it. If on the 
other hand it has the source of its motion in itself, let AB 
be taken to represent that which is in motion essentially of 
itself and not in virtue of the fact that something belonging 
to it is in motion. Now in the first place to assume that 
AB, because it is in motion as a whole and is not moved 30 
by anything external to itself, is therefore moved by itself — 
this is just as if, supposing that KA is moving AM and is 
also itself in motion, we were to deny ^ that KM is moved 
by anything on the ground that it is not evident which is 
the part that is moving it and which the part that is moved. 
In the second place that which is in motion without being 
moved by anything does not necessarily cease from its 
motion because something else is at rest, but a thing must 242^ 
be moved by something if the fact of something else having 
ceased from its motion causes it to be at rest. Thus,^ if 
this is accepted, everything that is in motion must be 
moved by something. For AB, which has been taken to 5 
represent that which is in motion, must be divisible, since 
everything that is in motion is divisible. Let it be divided, 
then, at F. Now if TB is not in motion, then AB will not 
be in motion : for if it is, it is clear that AF would be in 
motion while BF is at rest, and thus AB cannot be in 10 

' On the text of this book, see Shute, Anecdota Oxoniettsia^ 
Classical Series, vol. i, part 3. For the purposes of this translation 
the Teubner text of Prantl has been taken as the standard for chapters 
I to 3. 

^ It will make no difference to the translation whether et is repeated 
before \xr] ^Actkoi or not. In view of the intervening clause the repe- 
tition does not seem impossible. 

^ The use of ydp implies a slight ellipse : ' (I make this point) for . . .* 


motion essentially and primarily. But ex hypothesi AB 
is in motion essentially and primarily. Therefore if FB 
is not in motion AB will be at rest. But we have agreed 
that that which is at rest if something else is not in motion 
must be moved by something. Consequently, everything 
that is in motion must be moved by something : for that 

15 which is in motion will always be divisible, and if a part of 
it is not in motion the whole must be at rest. 

Since everything that is in motion must be moved by 
something, let us take the case in which a thing is in 
locomotion and is moved by something that is itself in 
motion, and that again is moved ^ by something else that 
is in motion, and that by something else, and so on con- 

20 tinually : then the series cannot go on to infinity, but 
there must be some first movent. For let us suppose that 
this is not so and take the series to be infinite. Let A 
then be moved by B, B by T, T by A, and so on, each 
member of the series being moved by that which comes 
next to it. Then since ex hypothesi the movent while 
causing motion is also itself in motion, and the motion of 
the moved and the motion of the movent must proceed 
simultaneously (for the movent is causing motion ^ and 

25 the moved is being moved simultaneously) it is evident 
that the respective motions of A, B, T, and each of the 
other moved movents are simultaneous. Let us take the 
motion of each separately land let E be the motion of 
A, Z of B, and H and respectively the motions of T and A: 
for though they are all moved severally one by another, 
yet we may still take the motion of each as numerically 

30 one, since every motion is from something to something 
and is not infinite in respect of its extreme points. By 
a motion that is numerically one I mean a motion that 
proceeds from something numerically one and the same to 
something numerically one and the same in a period of 
time numerically one and the same : for a motion may be 

25 the same generically, specifically, or numerically : it is 

*^ ^ Reading in 1. 19 KivPirm, with Par. 1859. 

*^ 2 Reading in 1. 24 (with the MSS.) yap Kive'i. 




BOOK VII. I 242«* 

generically the same if it belongs to the same category, 
e. g. substance or quality : it is specifically the same if it 
proceeds from something specifically the same to something 
specifically the same, e. g. from white to black or from 
good to bad, which is not of a kind specifically distinct : ^ 
it is numerically the same if it proceeds from something 242^ 
numerically one to something numerically one in the same 
period of time, e. g. from a particular white to a particular 
black, or from a particular place to a particular place, in 
a particular period of time : for if the period of time were 
not one and the same, the motion would no longer be 
numerically one though it would still be specifically one. 
We have dealt with this question above.^ I Now let us ^ 
further take the time in which A has completed its motion, 
and let it be represented by K. Then since the motion of 
A^ is finite the time will also be finite. But since the 
movents and the things moved are infinite, the motion 
EZH0, i. e. the motion that is composed of all the in- 
dividual motions, must be infinite. For the motions of 15 
A, B, and the others may be equal, or the motions of the 
others may be greater : but assuming what is conceivable,* 
we find that whether they are equal ^ or some are greater, in 
both cases the whole motion is infinite. And since the 
motion of A and that of each of the others are simultaneous, 
the whole motion must occupy the same time as the motion 
of A : but the time occupied by the motion of A is finite : 
consequently the motion will be infinite in a finite time, 
which is impossible.^ 

It might be thought that what we set out to prove ^ has 

^ i. e. aya$d and KUKo. themselves admit of further differences kut 
ei8os. Read in 1. 37 els kqkov a8id(f)opovy with the MSS. 
^ V. 4. 227^ 3 sqq. 
^ Reading in 1. 10 r^s tov A, with the MSS. 

* i. e. certain conceivable cases : it will not do to assume the other 
possible case, viz. that in which, as we proceed backwards along the 
series of motions, they become less : for if Z were less than E, H than 
Z, and so on to infinity, 17 oXi] Kivrja-is would not be anfipos. 

* Reading in 1. 17 ei re lo-ai, with Simp. 

® i. e. it is impossible in such cases as we are considering, though 
the present case has not as yet been shown to be one of such cases : 
cf. the immediate sequel. 

^ sc. that there is a npatTov kivovv. 

•45-16 N 

242'' PHYSICA 

20 thus been shown, but our argument so far does not prove 
it, because it does not yet prove that anything impossible 
results from the contrary supposition : for in a finite time 
there may be an infinite motion, though not of one thing, 
but of many : and in the case that we are considering this 
is so: for each thing accomplishes its own motion, and 
there is no impossibility in many things being in motion 
simultaneously. But if (as we see to be universally the 
case) that which primarily is moved locally and cor- 

25 poreally ^ must be either in contact with or continuous 
with that which moves it, the things moved and the mov- jj 
ents must be continuous or in contact with one another, 
so that together they all form a single unity : whether this 
unity is finite or infinite makes no difference to our present 
argument ; for in any case since the things in motion are 
infinite in number the whole motion will be infinite, if. as is 
theoretically possible, each motion is either equal to or 
greater than that which follows it in the series : for we 
shall take as actual that which is theoretically possible. 

30 If, then. A, B, T, A form an infinite magnitude^ that 
passes through the motion EZH0 in the finite time K, 
this involves the conclusion that an infinite motion is 
passed through in a finite time : and whether the magnitude 
in question is finite or infinite this is in either case im- 
possible. Therefore the series must come to an end, and 
there must be a first movent and a first moved : ^ for the 
243* fact that this impossibility results only from the assumption 
of a particular case^ is immaterial, since the case assumed 
is theoretically possible, and the assumption of a theore- 
tically possible case ought not to give rise to any impossible 

^ Locomotion caused by something acting on the body is here 
opposed to locomotion caused by something acting on the mind, e. g. 
TO €pncn6v. 

^ Reading in 1. 31 (with the MSS.) arrfipop ti. There is no need to 
alter (with Prantl) imetpov to Ta>v andpaiv, as it is easy to take the words 
r) TO Trfnepacrp-fvov ^ to airnpov at the end of the sentence as an after- 
thought added for the sake of completeness. 

' P'or Koi Kivovpfvov we should rather expect/*)) Kivovpevov (not moved 
by anything else), and this is what Simplicius seems to have read. 

* sc. the case in which each motion is either equal to or greater 
than the motion that follows it in the series. 

BOOK VII. 2 243* 

2 That which is the first movent of a thing— in the sense 
that it supplies not * that for the sake of which ' but the 
source of the motion — is always together with that which is 
moved by it (by 'together' I mean that there is nothing 
intermediate between them). This is universally true 5 
wherever one thing is moved by another. And since there 
are three kinds of motion, local, qualitative, and quanti- 
tative, there must also be three kinds of movent, that 10 
which causes locomotion, that which causes alteration, and 
that which causes increase or d^rease. 

Let us begin with locomotion, for this is the primary 
motion. Everything that is in locomotion is moved either 
by itself or by something else. In the case of things that 
are moved by themselves it is evident that the moved and 
the movent are together: for they contain within them- 
selves their first movent, so that there is nothing in 
between. The motion of things that are moved by some- 15 
thing else must proceed in one of four ways : for there are 
four kinds of locomotion caused by something other than 
that which is in motion, viz. pulling, pushing, carrying, and 
twirling. All forms of locomotion are reducible to these. 
Thus pushing on is a form of pushing in which that which 
is causing motion away from itself^ follows up that which 
it pushes and continues to push it : pushing off occurs 
when the movent does not follow up the thing that it 
has moved : throwing when the movent causes a motion 20 
away from itself' more violent than the natural locomotion 243^' 
of the thing moved, which continues its course so long as 
it is controlled by the motion imparted to it. Again, 
pushing apart and pushing together are forms respectively 
of pushing off and pulling : pushing apart is pushing off, 
which may be a motion either away from the pusher or 
away from something else, while pushing together is pulling, 5 
which may be a motion towards something else as well as 
towards the puller. We may similarly classify all the 
varieties of these last two, e. g. packing and combing : 
the former is a form of pushing together, the latter a form 
of pushing apart. The same is true of the other processes 
^ Reading in * 19, ^ I, d^' uvtov. 
N 2 


of combination and separation (they will all be found to 
be forms of pushing apart or of pushing together),^ except 
such as are involved in the processes of becoming and 

lo perishing. (At the same time it is evident that there is no 
other kind of motion but ^ combination and separation : for 
they may all be apportioned to one or other of those already 
mentioned.) Again, inhaling is a form of pulling, exhaling 
a form of pushing : and the same is true of spitting and of 
all other motions that proceed through the body, whether 
secretive or assimilative, the assimilative being forms of 

15 pulling, the secretive of pushing off. All other kinds 
of locomotion must be similarly reduced, for they all fall 
under one or other of our four heads. And again, of these 
four, carrying and twirling are reducible to pulling and 
pushing. For carrying always follows one of the other 
three methods, for that which is carried is in motion 
accidentally, because it is in or upon something that is in 

20 motion, and that which carries it is in doing so being either 
244* pulled or pushed or twirled ; ^ thus carrying belongs to all 
the other three kinds of motion in common. And twirling 
is a compound of pulling and pushing, for that which is 
twirling a thing must be pulling one part of the thing and 
pushing another part, since it impels one part away from 
itself and another part towards itself. If, therefore, it can 
be shown that that which is pushing and that which is 
pulling are adjacent respectively to that which is being 
5 pushed and that which is being pulled, it will be evident 
that in all locomotion there is nothing intermediate between 

^ 11. 8-9 arrauai . . . (Twaxms is parenthetical. 

^ Reading in 1. 11 (with the MSS.and Bekker) rj avyKpia-is. Prantl 
alters ^ to ^7 : the meaning would then be ' combination and separation 
do not constitute a kind of motion distinct from those enumerated '. 
But this would be in part a repetition, and in part (so far as yevean and 
cpSopd are concerned) a contradiction, of the preceding sentence. The 
reading of the MSS. is defensible if we regard afxn di . . . tiprjiievau as 
a parenthesis, the sense being that from another point of view we may 
reduce all kinds of motion to o-uy/cpio-ts and 5taK/ji<nf, which are coexten- 
sive with oxTLs and eX|t?. 

' i. e. unless to oxovp happens to be a living being, but that case 
need not be considered, as Aristotle's object is to prove that t6 npcorov 
KLvovv apa tw Kivovfievcp €(ttI, which has already been proved in the case 
of things that avra i;0' aurcoi/ Kiveiraiy among which €fi\lrvxa are of course 
included. Cf. 243* 13 above. 



BOOK VII. 2 244» 

moved and movent. But the former fact is clear even 
from the definitions of pushing and pulling, for pushing is 
motion to something else from oneself or from something 
else, and pulling is motion from something else to oneself 
or to something else, when the motion of that which is 
pulling is quicker ^ than the motion that would separate ^ lo 
from one another the two things that are continuous : " 
for it is this that causes one thing to be pulled on along 
with the other. (It might indeed be thought that there is 
a form of pulling that arises in another way : that wood, 
e.g. pulls fire in a manner different from that described 
above. But it makes no difference whether that which 
pulls is in motion or is stationary when it is pulling : in the 
latter case it pulls to the place where it is, while in the 
former it pulls to the place where it was.) Now it is impos- 
sible to move anything either from oneself to something else 15 
or from something else to oneself without being in contact 
with it : it is evident, therefore, that in all locomotion there 244^ 
is nothing intermediate between moved and movent. 

Nor again is there anything intermediate between that 
which undergoes arid that which causes alteration : this can 
be proved by induction : for in every case we find that the 
respective extremities of that which causes and that which 
undergoes alteration are adjacent. For^ our assumption 
is that things that are undergoing alteration are altered in 
virtue of their being affected in respect of their so-called 

* Reading in 1. 9 Outtoov, with Simp. 

^ Reading in 1. 10 cXkovtos t/)? x^P^Cf^'^^^^t ^^^h Par. 1859 and 

^ i. e. the thing pulling and the thing pulled. The second motion 
is the natural resistance of the thing pulled, which seeks to disconnect 
itself from that which is pulling it. 

* Reading in 1. 4 to Trpoorov aWoiovfievov, viroKeirai yap rjfuv to to. 
dWoiovfxeua KaTci tus naOqTiKcti Xeyopevas TTOiorfjraf Traa-xovra aXKoiovcrOaL' 
TO yap noiov dWoiovTai ro) aladqTov clvai' alcrdrjTO. 8' eaTLv^ oh 8t.a(f)(povai to. 
(TOip.aTa aWrjXcov' anav yap aw/xa (TO)fiaTOS 8ia(f)(pei to7s aladqToTs rj 
■rrXeioaiv rj eXaTTOaiv ^ to) paXXop kqI tjttov toIs avrols' dXXa p.r)v Ka\ 
uXXoLOhTai TO dXXoLovp.€vov vTTo Toiv elprjpivoiv. It seems clear that in the 
text as given by Bekker something ;must have dropped out between 
dXXoLoi'pevov and vivo tcov €lpi]fi€v<i>v: and Prantl would restore it 
as above, partly from Simplicius and partly from the second text as 
given in six MSS. Even so the connexion of thought is not quite 
clear. For the term 7ra6r)Ti<a\ Troiorrjres cf. Ca^. viii. 9^ 28 sqq. 


affective qualities, since that which is of a certain quality is 
altered in so far as it is sensible, and the characteristics in 
which bodies differ from one another are sensible charac- 
teristics : for every body differs from another in possessing 
a greater or lesser number of sensible characteristics or in 
possessing the same sensible characteristics in a greater or 
lesser degree. But the alteration of that which undergoes 
alteration is also caused by the above-mentioned charac- 
5 teristics, which are affections of some particular underlying 
quality.^ Thus we say that a thing is altered by becoming 
hot or sweet or thick or dry or white ; and we make these 
assertions alike of what is inanimate and of what is animate, 
and further, where animate things are in question, we make 
them both of the parts that have no power of sense- 
lo perception and of the senses themselves. For in a way 
even the senses undergo alteration, since the active sense 
is a motion through the body in the course of which the 
sense ^ is affected in a certain way. We see, then, that 
the animate is capable of every kind of alteration of which 
the inanimate is capable : but the inanimate is not capable 
of every kind of alteration of which the animate is capable, 
since it is not capable of alteration in respect of the senses : 
15 moreover the inanimate is unconscious of being affected by 
245^ alteration, whereas the animate is conscious of it, though 
there is nothing to prevent the animate also being un- 
conscious of it when the process of the alteration does not 
concern the senses. Since, then, the alteration of that 
which undergoes alteration is caused by sensible things, 
in every case of such alteration it is evident that the 
respective extremities of that which causes and that which 
5 undergoes alteration are adjacent. Thus the air is con- 
tinuous with that which causes the alteration,^ and the 
body that undergoes alteration is continuous with the air. 
Again, the colour is continuous with the light and the light 

^ Reading in I. 6 (with the MSS. and Bekker) ttjs vnoKeifievrji 

^ al(rdr}(rii in this passage is used in such a way as to inckide the 
meanings of ' sense-perception ' and of ' sense-organ '. 

' i. e. in cases of dcpfj such as depfxarais. 

BOOK VII. 2 245^ 

with the sight.^ And the same is true of hearing and 
smelling : for the primary movent in respect to the moved is 
the air. Similarly, in the case of tasting, the flavour is 
adjacent to the sense of taste. And it is just the same in the 10 
case of things that are inanimate and incapable of sense-per- 
ception. Thus there can be nothing intermediate between 
that which undergoes and that which causes alteration. 

Nor, again, can there be anything intermediate between 
that which suffers and that which causes increase : for the 
part of the latter that starts the increase does so by 
becoming attached in such a way to the former that the 
whole becomes one. Again, the decrease of that which 
suffers decrease is caused by a part of the thing becoming 
detached. So that which causes increase and that which 15 
causes decrease must be continuous with that which suffers 
increase and that which suffers decrease respectively : and 
if two things are continuous with one another there can be 
nothing intermediate between them. 

It is evident, therefore, that between the extremities of 
the moved and the movent that are respectively first and last 245^ 
in reference to the moved there is nothing intermediate. 

3 Everything, we say, that undergoes alteration is altered 
by sensible causes, and there is alteration only in things 
that are said to be essentially affected by sensible things. 
The truth of this is to be seen from the following con- 5 
siderations. Of all other things it would be most natural 
to suppose that there is alteration in figures and shapes, 
and in acquired states and in the processes of acquiring and 
losing these : but as a matter of fact in neither of these 
two classes ^ of things is there alteration. 

In the first place, when a particular formation^ of a 
thing is completed, we do not call it by the name of its 10 
material : e. g. we do not call the statue ' bronze ' or the 

^ Terms are used somewhat loosely all through this passage, cf. 
aia-Brjats above. Here xpoi/ia is the coloured surface, cfiSys the illumi- 
nated air, and 6'^is the organ of sight. 

^ (Txr]tiaTa and ^opcpai make up one class as against e^eis : hence 


' Omitting koi pv$fjLiC6fi€vov in 1. 9, with Par. 1859 and Simp. 

245*^ PHYSICA 


pyramid ^ ' wax ' or the bed * wood ', but we use a derived 
expression and call them ' of bronze \ ' waxen,' and 
* wooden ' respectively. But when a thing has been affected 
and altered in any way we still call it by the original 
name : thus we speak of the bronze or the wax being dry 
or fluid or hard or hot.^ 

15 And not only so : we also speak of the particular fluid 
or hot substance as being bronze, giving the material the 
same name as that which we use to describe the affection.^ 
246^ Since, therefore, having regard to the figure or shape of 
a thing we no longer call that which has become of a certain 
figure by the name of the material that exhibits the figure, 
whereas having regard to a thing's affections or alterations 
we still call it by the name of its material, it is evident that 
becomings of the former kind cannot be alterations. 

Moreover it would seem absurd even to speak in i/iis way, 
5 to speak, that is to say, of a man or house or anything else 
that has come into existence as having been altered. Though 
it may be true that every such becoming is necessarily the 
result of something's being altered, the result, e. g. of the 
material's being condensed or rarefied or heated or cooled, 
nevertheless it is not the things that are coming into exist- 
ence that are altered, and their becoming is not an alteration. 

10 Again, acquired states, whether of the body or of the soul, 
are not alterations. For some are excellences and others 
are defects, and neither excellence nor defect is an alteration: 
excellence is a perfection (for when anything acquires its 
proper excellence we call it perfect, since it is then if ever 

15 that we have a thing in its natural state : e. g. we have 
a perfect circle when we have one as good as possible),^ 
while defect is a perishing of or departure from this condi- 
tion. So just as when speaking of a house we do not call 
its arrival at perfection an alteration (for it would be absurd 
to suppose that the coping or the tiling is an alteration or 

* sc. candle. 

^ Reading in 1. 13 (with four MSS.) ^j/pov yap koI vypov koi (tkKijpop 
Koi QeppLOv. 

^ i. e. that which is vypov or Bepfiov (has the nddos of vyporrjs or 
6 ppoTTjs) we may denote by the expression to Oeppov or to vypov. 

* Omitting in 1. 16 koI otuv, with Par. 1859. 

BOOK VII. 3 246* 

that in receiving its coping or its tiling a house is altered 20 
and not perfected), the same also holds good in the case of 
excellences and defects and of the persons or things that 
possess or acquire them : for excellences are perfections 246^ 
of a thing's nature and defects are departures from it : 
consequently they are not alterations. 
^ Further, we say that all excellences depend upon par- 
ticular relations. Thus bodily excellences such as health 
and a good state of body we regard as consisting in a 5 
blending of hot and cold elements within the body in due 
proportion, in relation either to one another or to the sur- 
rounding atmosphere: and in like manner we regard beauty, 
strength, and all the other bodily excellences and defects. 
Each of them exists in virtue of a particular relation and 
puts that which possesses it in a good or bad condition 
with regard to its proper affections, where by * proper ' 
affections I mean those influences that from the natural 
constitution of a thing tend to promote or destroy its 
existence. Since, then, relatives are neither themselves 10 
alterations nor the subjects of alteration or of becoming 
or in fact of any change whatever, it is evident that neither 
states nor the processes of losing and acquiring states are 
alterations, though it may be true that their becoming or 
perishing is necessarily, like the becoming or perishing of 15 
a specific character or form, the result of the alteration 
of certain other things, e. g. hot and cold or dry and wet 
elements or the elements, whatever they may be, on which 
the states primarily depend. For each several bodily defect 
or excellence involves a relation with those things from 
which the possessor of the defect or excellence is naturally 
subject to alteration: thus excellence disposes its possessor 
to be unaffected by these influences or to be affected by 
those of them that ought to be admitted,^ while defect 
disposes its possessor to be affected by them or to be 
unaffected by those of them that ought to be admitted. 

And the case is similar in regard to the states of the 20 
soul, all of which (like those of body) exist in virtue of 247* 

* The alternative is added because, while some would use nddq only 
in a bad sense, others would recognize both good and bad miBr}. 


particular relations, the excellences being perfections of 
nature and the defects departures from it : moreover, 
excellence puts its possessor in good condition, while defect 
puts its possessor in a bad condition, to meet his proper 
affections. Consequently these cannot any more than the 
^ 5 bodily states be alterations, nor can the processes of losing 
and acquiring them be so, though their becoming is neces- 
sarily the result of an alteration of the sensitive part of the 
soul, and this is altered by sensible objects : for all moral 
excellence is concerned with bodily pleasures and pains, 
which again depend either upon acting or upon remember- 
ing or upon anticipating. Now those that depend upon 

10 action are determined by sense-perception, i. e. they are 
stimulated by something sensible: and those that depend 
upon memory or anticipation are likewise to be traced to 
sense-perception, for in these cases pleasure is felt either 
in remembering what one has experienced or in anticipating 
what one is going to experience. Thus all pleasure of this 
kind ^ must be produced by sensible things : and since the 
presence ^ in any one of moral defect or excellence involves 

15 the presence ^ in him of pleasure or pain (with which moral 
excellence and defect are always concerned), and these 
pleasures and pains are alterations of the sensitive part,^ 
it is evident that the loss and acquisition of these states no 
less than the loss and acquisition of the states of the body 
must be the result of the alteration of something else. 
Consequently, though their becoming is accompanied by 
an alteration, they are not themselves alterations. 
247^ Again, the states of the intellectual part of the soul are 
not alterations, nor is there any becoming of them. In 
the first place it is much more * true of the possession of 
knowledge that it depends upon a particular relation. And 
further, it is evident that there is no becoming of these 
states. For that which is potentially possessed of know- 

^ sc. of the sensitive part of the soul. 

' It is hardly possible without awkwardness to give the full force of 
eyyiveaOai here in English. It means strictly ' to come to be present 

^ Aristotle really means ' arise from the alteration of tjie sensitive 
part ' : but his mode of expression is as often somewhat loose. 

* Reading in 1. 2 fxaXXov, with (apparently) Simp. 

BOOK VII. 3 247^ 

ledge becomes actually possessed of it not by being set in 
motion at all itself but by reason of the presence ^ of some- 5 
thing else : i. e. it is when it meets with the particular 
object that it knows in a manner ^ the particular through 
its knowledge of the universal. (Again, there is no be- 
coming of the actual use and activity of these states, unless 
it is thought that there is a becoming of vision and touching 
and that the activity in question is similar to these.) And 
the original acquisition of knowledge is not a becoming or 
an alteration ^ : for the terms ' knowing ' and * understand- 10 
ing' imply that the intellect has reached a state of rest and 
come to a standstill,* and there is no becoming that leads 
to a state of rest, since, as we have said above,^ no change 
at all can have a becoming. Moreover, just as to say, 
when any one has passed from a state of intoxication or 
sleep or disease to the contrary state, that he has become 
possessed of knowledge again is incorrect in spite of the 15 
fact that he was previously incapable of using his know- 
ledge, so, too, when any one originally acquires the state, 
it is incorrect to say that he becomes possessed of know- 
ledge : for the possession of understanding and knowledge 
is produced by the soul's settling down ^ out of the restless- 
ness natural to it. Hence, too, in learning and in forming 
judgements on matters relating to their sense-perceptions 
children are inferior to adults owing to the great amount 248* 
of restlessness and motion in their souls. Nature itself 
causes the soul to settle down and come to a state of rest 
for the performance of some of its functions, while for the 

^ No one English word will quite give the force of vrrdp^at. here : 
it implies that something objective 'appears on the scene', * comes 
into existence in relation to t6 ema-Trjfxop \ 

^ The qualification is added because knowledge (emaTtjur)) in the 
strict sense is concerned not with the particular but with the universal. 
The point here is that knowledge of the universal includes a sort of 
knowledge of the particular, out of which it was originally built up. 

^ Reading in 1. 10 ea-nv ov6' aXAoicotrir, with Par. 1859 and Simp. 

* The etymological connexion between (iriaTTjixr] and arrival can 
hardly be adequately given in translation. Read Xeyofxeda in 1. II, 
with Par. 1859. 

^ V. 2. 225^^15 sqq. 

' The same etymological connexion is here present to Aristotle's 
mind as that noted above. 


performance of others other things ^ do so : but in either 
case the resuh is brought about through the alteration of 
something in the body, as we see in the case of the use^ 
5 and activity of the intellect arising from a man's becoming 
sober or being awakened. It is evident, then, from the 
preceding argument that alteration and being altered occur 
in sensible things and in the sensitive part of the soul and, 
except accidentally, in nothing else. 

lo A difficulty may be raised as to whether every motion 4 
is commensurable with every other or not. Now if they 
are all commensurable and if two things to have the same 
velocity must accomplish an equal motion in an equal 
time, then we may have a circumference equal to a straight 
line, or, of course, the one may be greater or less than the 
other. Further, if one thing alters and another accom- 
plishes a locomotion in an equal time, we may have an 

J 5 alteration and a locomotion equal to one another: thus 
an affection will be equal to a length, which is impossible. 
But is it not ^ only when an equal motion is accomplished 
by two things in an equal time that the velocities of the 
two are equal ? Now an affection cannot be equal to 
a length. Therefore there cannot be an alteration equal 
to or less than a locomotion : and consequently it is not the 
case that every motion is commensurable with every other. 
But how will our conclusion work out in the case of the 
circle and the straight line ? It would be absurd to suppose 

20 that the motion of one thing in a circle and of another in 
a straight line cannot be similar, but that the one must 
inevitably move more quickly or more slowly than the 
other, just as if the course of one were downhill and of the 
other uphill. Moreover it does not as a matter of fact 
make any difference to the argument to say that the one 
motion must inevitably be quicker or slower than the other : 

^ e. g. education, experience, etc. 

^ Reading in 1. 5 XPW^<^^ with several MSS. This gives a much 
better balance to the sentence than iy^paecas which Bekker and Prantl 
adopt : becoming sober and bei?ig awakened lead to the recovery of 
the use and the activity of the intellect. 

^ Reading in 1. 16 apa . . . laorax^s ; with Bonitz. 

BOOK VII. 4 248* 

for then the circumference can be greater or less than the 
straight line ; and if so it is possible for the two to be 
equal. For if in the time A the quicker (B) passes over 35 
the distance B' and the slower (F) passes over the distance 
r', B' will be greater than F': for this is what we^ took 248^ 
' quicker ' to mean : and so quicker motion also implies 
that one thing traverses an equal distance in less time than 
another: consequently there will be a part of A in which B 
will pass over a part of the circle equal to F', while F will 
occupy the whole of A in passing over r\ None the less, 
if the two motions^ are commensurable, we are confronted 5 
with the consequence stated above, viz. that there may be 
a straight line equal to a circle. But these are not com- 
mensurable: and so the corresponding motions are not 
commensurable either. 

But may we say that things are always commensurable 
if the same terms are applied to them without equivoca- 
tion? e.g. a pen, a wine, and the highest note in a scale 
are not commensurable: we cannot say whether any one 
of them is sharper than any other : and why is this ? they 
are incommensurable because it is only equivocally that 
the same term * sharp ' is applied to them : whereas the 
highest note in a scale is commensurable with the leading- 
note, because the term ' sharp ' has the same meaning as 
applied to both. Can it be, then, that the term ' quick * has 10 
not the same meaning as applied to straight motion and to 
circular motion respectively ? If so, far less will it have the 
same meaning as applied to alteration and to locomotion. 

Or shall we in the first place deny that things are always 
commensurable if the same terms are applied to them with- 
out equivocation ? For the term ' much ' has the same 
meaning whether applied to water or to air, yet water and 
air are not commensurable in respect of it:^ or, if this 

' vi. 2. 232* 25 sqq. 

^ The sense is improved by taking the first avixdXrjrd to refer to the 
motions and the second to the straight line and the circle. The 
awkwardness of expression is not un-Aristotelian. The objector 
is supposed to maintain (248* 19) that the two motions must surely be 
commensurable. Nevertheless, says A., this would imply etc. . . . 

^ i. e. a body of water will have more dvvafits though it may have 
the same oyKos as a body of air. 


illustration is not considered satisfactory, ' double ' at any 
rate would seem to have the same meaning as applied to 
each (denoting in each case the proportion of two to one), 
yet water and air are not commensurable in respect of it.^ 

15 But here again may we not take up the same position and 
say that the term ' much ' is equivocal ? In fact there are 
some terms of which even the definitions are equivocal ; 
e.g. if 'much* were defined as * so much and more', 'so 
much ' would mean something different in different cases : ^ 
* equal ' is similarly equivocal ; and * one ' again is perhaps 

20 inevitably an equivocal term; and if 'one' is equivocal, 
so is ' two '. Otherwise why is it that some things ^ 
are commensurable while others* are not, if the nature 
of the attribute in the two cases is really one and the 
same ? 

Can it be that the incommensurability of two things in 
respect of any attribute is due to a difference in that which 
is primarily capable of carrying the attribute ? Thus horse 
and dog are so commensurable that we may say which is 
the whiter, since that which primarily contains the white- 
ness is the same in both, viz. the surface : and similarly 
they are commensurable in respect of size. But water and 
speech are not commensurable in respect of clearness,^ 
since that which primarily contains the attribute is different 

25 in the two cases. It would seem, however, that we must 
reject this solution, since clearly we could thus make all 
equivocal attributes univocal and say merely that that 
which contains each of them is different in different cases : 
249* thus * equality ', ' sweetness,' and ' whiteness ' will severally 
always be the same, though that which contains them is 
different in different cases. Moreover, it is not any casual 
thing that is capable of carrying any attribute : each single 

' e. g. two cubic feet of air will have twice the dvvafiLs of one cubic 
foot of air but not twice the dvvafxn of one cubic foot of water. 

^ Reading in 1. 18 a comma after en (cf. Mef. 1021* 6). 

' e. g. two cubic feet of air and one cubic foot of air. 

* e. g. two cubic feet of air and one cubic foot of water : the double- 
ness in the two cases is not identical. Cf. above. 

^ The attribute in question is still \(vk6tt}s, which can be applied in 
Greek not only to iTrnos and kvcop but also to vd<op and (f^copij : but 
a change of word is necessary in English. 

BOOK VII. 4 249* 

attribute can be carried primarily only by one single 

Must we then say that, if two things are to be com- 
mensurable in respect of any attribute, not only must the 
attribute in question be applicable to both without equivoca- 
tion, but there must also be no specific differences either in 
the attribute itself or in that which contains the attribute — 
that these, I mean, must not be divisible in the way in 5 
which colour is divided into kinds ? Thus in this respect 
one thing will not be commensurable with another, i. e. we 
cannot say that one is more coloured than the other where 
only colour in general and not any particular colour is 
meant ; but they are commensurable in respect of whiteness. 

Similarly in the case of motion : two things are of the 
same velocity if they occupy an equal time in accomplishing 
a certain equal amount of motion. Suppose, then, that in 
a certain time an alteration is undergone by one half ^ of 
a body's length and a locomotion is accomplished by the 
other half: can we say that in this case the alteration is 10 
equal to the locomotion and of the same velocity ? That 
would be absurd, and the reason is that there are different 
species of motion. And if in consequence of this we must 
say that two things are of equal velocity if they accomplish 
locomotion over an equal distance in an equal time, we 
have to admit the equality of a straight line and a circum- 
ference.^ What, then, is the reason of this? Is it that 
locomotion is a genus or that line is a genus? (We may 15 
leave the time out of account, since that is one and the 
same.) If the lines are specifically different, the loco- 
motions also differ specifically from one another:^ for 
locomotion is specifically differentiated according to the 

^ The argument clearly requires that the two parts represented by 
TO n€v and TO be should be equal : cf. laov roaovdi above. 

' This seems to be the general sense of the sentence eoor' ft . . . 
TTfpicfxpTjs. But the connexion of thought is so obscure that I am in- 
clined to suspect a lacuna, e. g. coare to (wto eldos Kivr}<r((t)s del dvai 
eKartpco, d laoTaxrj (CTTni. dXX' ei ktX. 

' Reading in 1. 1 5 (with Simplicius) xpovos 6 avTos' av be rc3 cibci rj aWa, 
K(n fKclva etbei bia(f)€pei. The ordinary reading of the MSS. and 
of Bekker is said by Simplicius to have been introduced from the 
second text. 


249* PHYSIC A 

specific differentiation of that over which it takes place. 
(It is also similarly differentiated, it would seem, accordingly 
as the instrument of the locomotion is different: thus if 
feet are the instrument, it is walking, if wings it is flying ; 
but perhaps we should rather say that this is not so, and 
that in this case the differences in the locomotion are 
merely differences of posture in that which is in motion.^) 
We may say, therefore, that things are of equal velocity 

20 if in an equal time they traverse the same magnitude : and 
when I call it ' the same ' I mean that it contains no specific 
difference and therefore no difference in the motion that 
takes place over it. So we have now to consider how 
motion is differentiated : and this discussion serves to show 
that the genus is not a unity but contains a plurality latent 
in it and distinct from it, and that in the case of equivocal 
terms sometimes the different senses in which they are used 
are far removed from one another, while sometimes there 
is a certain likeness between them, and sometimes again 
they are nearly related either generically or analogically, 
with the result that they seem not to be equivocal though 
they really are. 

25 When, then, is there a difference of species? Is an 
attribute specifically different if the subject is different 
while the attribute is the same, or must the attribute itself 
be different as well } And how are we to define the limits 
of a species ? What will enable us to decide that particular 
instances of whiteness or sweetness are the same or different ? 
Is it enough that it appears different in one subject from 
what it appears in another? Or must there be no same- 
ness at all ? And further, where alteration is in question, 
how is one alteration to be of equal velocity with another? 
One person may be cured quickly and another slowly, and 

30 cures may also be simultaneous : so that, recovery of health 

being an alteration, we have here alterations of equal 

249^ velocity, since each alteration occupies an equal time. But 

what ^ alteration ? We cannot here speak of an * equal ' 

* Reading en 1. 17 . . . aXXt] 1. 19 as parenthetical. 

' i. e. what qualification are we to introduce into our definition of 
TO l(TOTax€S in aXXoiaxris corresponding to laop or ravrov /xe'ye^os (249* 
19) in the case of (^iopa ? Thus ti will be accusative. 

BOOK VII. 4 249 

alteration : what corresponds in the category of quality to 
equality in the category of quantity is * likeness '. However, 
let us say that there is equal velocity where the same change 
is accomplished in an equal time. Are we, then, to find 5 
the commensurability in the subject of the affection or in 
the affection itself? In the case that we have just been 
considering it is the fact that health is one and the same 
that enables us to arrive at the conclusion that the one 
alteration is neither more nor less than the other, but that 
both are alike. If on the other hand the affection is 
different in the two cases, e. g. when the alterations take 
the form of becoming white and becoming healthy respec- 
tively, here there is no sameness or equality or likeness 
inasmuch as the difference in the affections ^ at once makes 
the alterations specifically different, and there is no unity 10 
of alteration any more than there would be unity of locomo- 
tion under like conditions.^ So we must find out how 
many species there are of alteration and of locomotion 
respectively. Now if the things that are in motion — that 
is to say, the things to which the motions belong essentially 
and not accidentally — differ specifically, then their respec- 
tive motions will also differ specifically : if on the other 
hand they differ generically or numerically, the motions 
also will differ generically or numerically as the case may 
be. But there still remains the question whether, supposing 15 
that two alterations are of equal velocity, we ought to look 
for this equality in the sameness (or likeness) of the affec- 
tions, or in the things altered, to see e. g. whether a certain 
quantity of each has become white. Or ought we not 
rather to look for it in both ? That is to say, the altera- 
tions are the same or different according as the affections 
are the same or different,^ while they are equal or unequal 
according as the things altered are equal or unequal.^ 

And now we must consider the same question in the 
case of becoming and perishing : how is one becoming of 20 
equal velocity with another ? They are of equal velocity 

^ ravra '. SC. ro XevKaivo/xevou and to vyi(i(6fievov. 
^ SC. if there are two locomotions of different species. 
^ Reading in 1. 18 to ovto ^ /ii) ro avTo {to avro avro E), and in 1. 19 
(uTov r)y avicrov. 

64516 O 


if in an equal time there are produced two things that are 
the same ^ and specifically inseparable, e. g. two men (not 
merely generically inseparable as e.g. two animals). 
Similarly one is quicker than the other if in an equal time 
the product is different in the two cases. I state it thus ^ 
because we have no pair of terms that will convey this 
* difference ' in the way in which unlikeness is conveyed.^ 
If we adopt the theory that it is number that constitutes 
being, we may indeed speak of a 'greater number' and 
a ' lesser number ' * within the same species, but there is 
no common term that will include both relations,^ nor are 
25 there terms to express each of them separately in the same 
way as we indicate a higher degree or preponderance of 
an affection by ' more ', of a quantity by * greater '. 

Now since wherever there is a movent, its motion 5 
always acts upon something, is always in something, and 
always extends to something (by * is always in something ' 
I mean that it occupies a time : and by * extends to some- 
thing' I mean that it involves the traversing of a certain 
amount of distance : for at any moment when a thing is 
causing motion, it also has caused motion, so that there 
must always be a certain amount of distance that has been 
traversed and a certain amount of time that has been 
30 occupied).^ If, then, A the movent have moved B a 
250^ distance F in a time A, then in the same time the same 
force A will move JB twice the distance T, and in J A it 
will move J B the whole distance F : for thus the rules of 
proportion will be observed. Again if a given force move 
5 a given weight a certain distance in a certain time and 

* i. e. in the matter of completeness of development : there is no 
sufficiently specialized term for Aristotle to use. Cf. the sequel. 

^ sc. use these general terms t6 avro and erepov. 

' i. e. dWoiaaeis are (rvfi^Xqrai in respect of ofioioTrjs and avofioi6Tr]s : 
and the relation of duofioioTijs is indicated by the use of the two terms 
fiaWov and tjttov. 

* i. e. instead of merely using the single term erepov, 

^ Aristotle has as a matter of fact just used irfpoTrjs for this, but he 
feels that this is really too wide a term. 

* Reading \eya> 1. 28 . . . ttoo-w 1. 30 as a parenthesis, followed by a 
comma (so Bonitz). 


BOOK VII. 5 250' 

half the distance in half the time/ half the motive power 
will move half the weight the same distance in the same 
time. Let E represent half the motive power A and Z 
half the weight B : then the ratio between the motive 
power and the weight in the one case is similar and pro- 
portionate to the ratio in the other, so that each force will 
cause the same distance to be traversed in the same time. 

But if E move Z a distance T in a time A, it does not 10 
necessarily follow that E can move twice Z half the distance 
r in the same time. If, then, A move B a distance F in 
a time A, it does not follow that E, being half of A, will 
ill the time A or in any fraction of it cause B ^ to traverse 
a part of T the ratio between which and the whole of T is 
proportionate to that between A and E (whatever fraction 
of A E may be) : ^ in fact it might well be that it will 15 
cause no motion at all ; for it does not follow that, if 
a given motive power causes a certain amount of motion, 
half that power will cause motion either of any particular 
amount or in any length of time : otherwise one man might 
move a ship, since both the motive power of the ship- 
haulers and the distance that they all cause the ship to 
traverse are divisible into as many parts as there are men. 
Hence Zeno's reasoning is false when he argues that there 20 
is no part of the millet that does not make a sound: for 
there is no reason why any such part should not in any 
length of time fail to move the air that the whole bushel 
moves in falling.* In fact it does not of itself move even 
such a quantity of the air as it would move if this part were 
by itself: for no part even exists otherwise than potentially. 

If on the other hand we have two forces each of which 25 
separately moves one of two weights a given distance in 
a given time, then the forces in combination will move the 
combined weights an equal distance in an equal time : for 
in this case the rules of proportion apply. 

^ Reading in 1. 5 a comma after ^/ztVet and not after Kivel (so Bonitz). 

"^ Omitting rfjv in 11, 12, 13, with Simp., and reading in 1. 12 oarj, 
with EHK. 

^ Both the text and the exact sense of this sentence are somewhat 
doubtful. In 1. 14 I read <rt) -r^y, with Prantl, and omit rj, with EFK. 

* Reading in 1. 22 Trea-cov, with Hbc. 

O 2 


Then does this hold good of alteration and of increase 
also ? Surely it does, for in any given case we have a 
30 definite thing that causes increase and a definite thing that 
suffers increase, and the one causes and the other suffers 
a certain amount of increase in a certain amount of time. 
Similarly we have a definite thing that causes alteration 
and a definite thing that undergoes alteration, and a certain 
amount, or rather degree,^ of alteration is completed in 
250^ a certain amount of time : thus in twice as much time 
twice as much alteration will be completed and conversely 
twice as much alteration will occupy twice as much time : 
and the alteration of half of its object will occupy half as 
much time and in half as much time half of the object will 
be altered : or again, in the same amount of time it will be 
altered twice as much. 

On the other hand if that which causes alteration or 
increase causes a certain amount of increase or alteration 
5 respectively in a certain amount of time, it does not neces- 
sarily follow that half the force will occupy twice the time 
in altering or increasing the object, or that in twice the 
time the alteration or increase will be completed by it : ^ 
it may happen that there will be no alteration or increase 
at all, the case being the same as with the weight. 

^ lit. ' a certain amount in respect of more or less ' : the qualifi- 
cation is added because aAXotWis is not measured by quantity in the 
strict sense like <^opa but by degree : in this case we say fxaXXov or 
rjTTov where in the other case we say iielC^u or eXarrov. Cf. above 
249^ 26. 

^ It seems necessary to read in 1. 5 ''^ tJuktv ev dnrXaarla /cat eV 
8nrXa(TL<p tj^j-ktv. Only so will the point made correspond to that 
made about weight in *I2-I9. 



I It remains to consider the following question. Was there 
ever a becoming of motion before which it had no being, 
and is it perishing again so as to leave nothing in motion ? 
Or are we to say that it never had any becoming and is 
not penshmg, but always was and alw ays will be ? Is it 
in fact an immortal never'-lailing property of things that 
are, a sort of life as it were to all naturally constituted 
things ? 

Now the existence of m <7tio" "^ asserted by all who have 15 
anything to say about nature, because they all ^ concern 
themselves with the construction of the world and study 
the question of becoming and perishing, which processes 
could not come about without the existence of motion. 
But those who say that there is an infinite number of , 
worlds, some of which are in process of becoming while 
otKers are in process of perishing, assert that there is always 20 
motion (for these processes of becoming and perishing of 
the worlds necessarily involve motion), whereas those 
who hold that there is only one worlds whether ever- 
lasting or not,^ make corresponding assumptions in regard 
to motion. If then it is possible that at any time nothing 
should be in motion, tKis must come about m one of two 
ways : either in the manner described b y Anaj caggra s , who 
says that all things were together anda^restjpr an infinite 25 
period of time, and that then Min d introduced motion_arid 
separated them ; or in the manner described by Empedocles^^ 
according to whom the universe is alternately m motion 
and at rest — in motion, when Love is making the one out 
'oTmariy, 0?^ Strife is making many out of one, and at rest 

^ Reading in 1. 17 Trao-ij/. Bekker's naa-av is a misprint. 

^ em i) fir) aei. in 1. 22 is difficult. As Simplicius says, the words 
really stand {or eva Kal del t6u avrov r] eva fxeu, oik df\ 8e. We should 
probably read eva (J) del) h fit] aei, with (apparently) Themistius. 


in the intermediate periods of time— his account being as m, 
follows : W^ 

30 ' Since ^ One hath learned to spring from Manifold, 
And One disjoined makes Manifold arise, 
251 Thus they Become, nor stable is their life: 
But since their motion must alternate be, 
Thus have they ever Rest upon their round ' : 

for we must suppose that he means by this that they 

1; alterna te from th e one motion to the other.^ We must 

• ^ ' — " — — «. 

consider, then, how this matter stands, for the discovery of 
the truth about it is of importance, not only for the study 
of nature, but also for the investigation of the First 

Let us take our start from what we have already ^ laid 
down in our course on Physics.'* Motion, we say, is the 

10 fulfilment of the mova ble in so far as it is movable. Each 
kind of mo tion , therefore, necessarily i nvolves~ the presenc e 
of t h e thip g-.< ^ that arf> rapa hlenf that mntton. In fact, even A 
apart from the definition of motion, every one would admit 
that in each kind of motion it is that which is capable of 
that motion that is in motion : thus it is that which is 
capable of alteration that is altered, and that which is 

15 capable of local change that is in locomotion : and so there 
mus t be something capabk of being burned before there 
can be a process of being burned, and something capable 
of burning before there can be a process of burning. More- 
o ver, these thi ngs also must either ^ have abeginning_.before 

* Reading in 1. 29 Xiyav ^ouro)?^ fiep . . .', with Diels (fr. 17. 9-13 = 
26. 8-12). 

^ i. e. from motion towards ep to motion towards noWd and vice 
versa. But the last two lines quoted from Empedocles do not naturally 
bear this meaning : he seems to be insisting first on the rotation and 
then on the perfnanence of the rotation : he does not here say any- 
thing about the fiera^v xpovn in which occurs that yjpefxia which as 
Aristotle says makes Kiurjcns to cease altogether. — Reading in 1. 4 to 
yap Tj de rtiS' dWdaa-ovTii ivOevhi cKflcre Xeyeii' avrov vnoK-qnrioVj with 

' iii. I. 

* The title of the whole eight books of this treatise (or, rather, 
course of lectures) is ^vaiKrj 'AKpoaais. When Aristotle refers to 
TO. cf)vaiKd or TO. rrepl (pvaeats he usually means the first four books only : 
books V, VI, and VI II are referred to as to. nepl Kivqatas. Cf. 267'' 21. 

BOOK VIII. I 251* 

whi ch they had no being, or they must be eternal. Now 
if there was a becoming of every movable thing, jt follow s 
that before the mo tion in que stion another change or 
motion must have taken place in which thai whicEwas 

capable of being moved of mcausing motionhadits 
becoming. To suppose, on the other hand, that these 20 1 
i-hinor<; wprp ir| hpinpr throughout all previous time without I 
there being an y motio n appears unreasonable on a moment's I 
thought, and still more unreasonable, we shall find, on 
further consideration. For if we are to say that, while 
there are on the one hand things that are movable, and 
on the other hand things that are motive, there is a time 
when there is a first movent and a first moved, and 
another time when there is no such thing but only some- 
thing that is at rest, then this thing that is at rest must 25 
previously have been in process of change : for there must 
have been some cause of its rest, rest ^ being the privation 
of motion. Therefore, before this first chang e thert^ will be 
a previous change. For some things cause motion in only 
one way, while others can produce either of two contrary 
motions : thus fire causes heating but not cooling, whereas 30 
it would seem that knowledge may be directed to two 
contrary ends while remaining one and the same. Even in 
the former class, however, there seems to be something 
similar, for a cold thing in a sense causes heating by turning 
away and retiring, just as one possessed of knowledge 
voluntarily makes an error when he uses his knowledge in 
the reverse way.^ But at any rate all thing s that are 251 
^ca£ablg respectively of affecting and being afiected, oj^of^ 
causing motion and being moved,, are capable of it not_ 
under aU conditions , but only when they are in a^garticulax — 
condition and approach one another : so it is on the 
a pproach of one thing to anot her that the one cause s 

^ Simplicius in his commentary has ^pf/zi'a here though we cannot be 
sure that he is quoting verbally from Aristotle. But A. uses r]pefxr)<Tis 
to mean not only ' coming to rest ' but also ' being at rest ', which must 
be the meaning here as we are professedly only dealing with a state of 
rest. Cf. V. 6. 231*2. 

^ i. e. by means of his knowledge he can be sure of giving a wrong 
opinion and thus deceiving some one. 

251^ PHYSIC A 

motion and the other is rn ov^^,^"'^ when they are present 
under such conditions as rendered the one motive and the 

5 other movable. So if the motion was not always in process, 
it is clear that they must have been in a OundiLloilliot such 
as to render them capable^ respectively of being moved and 
of causing motion, and one or other of them must have 
been in process of change : for in what is relative this is 
a necessary consequence: e. g. if one thing is double another 
when before it was not so, one or other of them, if not both, 
must have been in process of change. It follows, then, 
t hat there will be a process of change p revious to the first. 

lo (Further, how can there be any * before ' and ' after ' 
without the existence of time ? Or h ow can there be any 
time without the existence of motio n ? If._thcn^ time is 
The number o f motion o r itself a kind of motion, it follows 
that, if there is alwav, sJ:ime ^motion mu st also be eternal . 
But so far as time is concerned we see that all with one 
exception are in agreement in saying that it is uncreated : 

15 in fact, it is just this ^ that enables Democritus to show that 
all things cannot have had a becoming : forji^e, he says, 
is uncreated. Jlato alone asserts the creation of time , 
saying ^ That it had a becoming together with the universe, 
the universe according to him having had a becoming. 
Now si nce time cannot exist and is unt hink able apart Jrom 

20 the moment, and the moment is a kind of middle-point, 
uniting as it does in itself both a beginning and an end, 
a beginning of future time and an end of past time, it 
follows that there must always be time : for the extremity 
of the last period of time that we take must be found in 
some moment, since time contains no point of contact * for 

25 us except the moment. Therefore, since the moment is 
both a beginn ing _and an end^ here must always be ti me 
on both sides of it. But if this is true of time, it is evi dent 

^ Reading in 1. 4 ws rjv, and in 1. 6 as ^v dvvd[xeva, with E. Cf. 
Met. 1048*6. 

2 Reading in 1. 16 tovtov, with EH. 

^ Aristotle is thinking of a passage in the Timaetis (38 B). 

" It is difficult to give the exact force of Xa^eiv. Aristotle means 
that we can only ' lay hold of ' or ' have at command ' the present 
moment, since all the rest of time is either no longer or not yet 
in existence. 

BOOK VIII. I 251^ 

that it must also be true of motion, time being a kind of / 
affection of motion.) 

The same reasoning will also serve to show the im- 
perishability of motion : just as a becoming of motion 
would involv e, as we saw, th e existence of a p rocess of 30 
c hange p revious to the first, in the same way a perishing 
' of motioj i would mvolve t he existence of a process of c hange 
subsequent to the last : for when a thing ceases to be 
moved, it does not therefore at the same time cease to be 
movable — e. g. the cessation of the process of being burned 
does not involve the cessation of the capacity of being 
burned, since a thing may be capable of being burned 
without being in process of being burned — noi*, when a 
thing ceases to be movent, does it therefore at the same 
time cease to be motive. Again, the destructive agent will 252* 
have to be destroyed, after what it destroys has been 
destroyed,^ and then that which bas_ _the capacity ofL 
de stroying it will have to be destroyed afterwards , (so_thai 
there w jll be a process of change subseq u ent to th^ last,) 
for bein g destroyed also is a kind of chang e. If, then, the 
view which we are criticizing involves these impossible 
consequences, it is clear tha t motion is eternal and cannot 
have existed at one time and not at another : in fact, such 
a view can hardly be described as anything else than 

And much the same may be said of the view that such 5 
is the ordinance of nature and that this must be regarded 
as a principle, as would seem to be the view of Empedocles 
when he says that the constitution of the world is of neces- 
sity such that T.nveand Strife alterna tely predom in ate an d 
cause motion^ while in the intermediate period of time 
there is a state of rest. Probably also those who, like 10 
Anaxagoras, assert a single principle (of motion ^) would 
hold this view. But that which is produced or directed by / 
u ature can never be anything disorderly : for natu re is / 

^ Reading in 1. i /cat ro (pOapTiKov S/7 . . . (pdapij, with E. 

^ It is necessary to insert these words, as Anaxagoras is of course 
a pluralist, and Aristotle is only thinking of the place assigned to 
vovs in his system as the sole cause of motion in contradistinction to 
the two causes (0tXia and vflKos) asserted by Empedocles. 


everywhere the cause of order. Moreover, there is no ratio 
in the relation of the infinite to the infinite, whereas order 
always means ratio. But if we say that there is first 
a state of rest for an infinite time, and then motion is^ 

i 5_started at some momen t, and that the fact that it is this 
rather tha n a previous moment is of no importance, and 
involves no order, then we can no longer say that it is 
nature's work: for if anything is olf _a certain, rhararfpr 
ll n atura lly, it either ^ is s o, invai jably and is not sometimes of 

" this and sometimes of another character (e. g. fire, which 
travels upwards naturally, does not sometimes do so and 
sometimes not) or there is a ratio^ in the variation. It 

20 would be_ b£tter, therefore, to say witli"' Empedocles and 
any one else who may have maintained such a theory as 
his that the universe is^alternately at rest and in motion : 
for in a system of this kind we have at once a certain 

^order. But even here the holder of the theory ought not 
only to assert the fact : he ought also to explain the cause 
of it : i. e. he should not make any mere assumption or lay 
down any gratuitous axiom, but should employ either 

2 5 inductive or demonstrative reasoning. The Love and 
Strife postulated by Empedocles are not in themselves 
causes of the fact in question, nor is it of the essence of 
either that it should be so, the essential function of the 
former being to unite, of the latter to separate. If he is to 
go on to explain this alternate predominance, he should ^ 
a dduce cases where such a state o f thingsexists,__as__he 
pomts to the fact that among mankind we have something 
that unites men, namely Love, while on the other hand 

30 enemies avoid one another: thus from the observed fact 
that this occurs in certain cases comes the assumption that 
it occurs also in the universe. The n, again, some argument 
i s ne eded to explain why the predominance of each of the 
two forces lasts for an equal period of time. But it is 
a wrong assumption to suppose universally that we have 
an adequate first principle in virtue of the fact that some- 
thing always is so or always happens so. Thus Democritus 
reduces the causes that explain nature to the fact that! 
^ Reading in 1. 17 ^. 

BOOK VIII. I 252^ 

things happened in the past in the same way as they 
happen now : but he does not think fit to seek for a first 35 . 
principle to explain this * always ' : so, while his theory is 252^ 
" right in so iar as it is applied to certain individual cases, 
he is wrong in making it of universal application. Thus, 
a triangle always has its angles equal 10 two rigHt angles, 
but there is nevertheless an ulterior cause of t he ete rnity^ 
of t his truth, w hereas first princip les are eternal and have 
no u lterior cause . Let this conclude what we have to say 5 
in support of our contention that t here never was a time 
when there was not motion, and never will be a time when 
there will not be motion. 

2 The arguments that may be advanced against this 
position are not difficult to dispose of. The chief considera- 
tions that might be thought to indicate that motion may 
exist though at one time it had not existed at all are the 

First, it maybe said that no process of change is eternal: 
for the nature of all change is such that it proceeds 10 
from something /o something, so that every process of 
change must be bounded by the contraries that mark its 
course, and no motion can go on to infinity. 

Secondly, we see that a thing that neither is in motion 
nor contains any motion within itself can be set in motion ; 
e. g. inanimate things that are (whether the whole or some 
part is in question) not in motion but at rest, are at some 
moment set in motion : whereas, if motion cannot have 15 
a becoming before which it had no being, these things 
ought to be either always or never in motion. 

Thirdly, the fact^ is evident above all in the case of 
animate beings : for it sometimes happens that there is 
no motion in us and we are quite still, and that nevertheless 
we are then at some moment set in motion, that is to say 
it sometimes happens that we produce a beginning of 
motion in ourselves spontaneously without anything having 20 
set us in motion from without. We see nothing like this 
in the case of inanimate things, which are always set in 

' sc. TO Kiurjaiv elvai irore fxr) ovaav. 


motion by something else from without : the animal, on 
the other hand, we say, moves itself: therefore, if an animal 
is ever in a state of absolute rest, we have a motionless 
thing in which motion can be produced from the thing 
itself, and not from without. Now if this can occur in an 

25 animal, why should not the same be true also of the universe 
as a whole? If it can occur in a small world ^ it could 
also occur in a great one : and if it can occur in the world, 
it could also occur in the infinite ; that is, if the infinite could 
as a whole possibly be in motion or at rest. 

Of these objections, then, the first-mentioned — that 

30 motion to opposites is not always the same and numeri- 
cally one — is a correct statement ; in fact, this may be said 
to be a necessary conclusion, provided that it is possible 
for the motion of that which is one and the same to be not 
always one and the same. (I mean that e. g. we may 
question whether the note given by a single string is one 
and the same, or is different each time the string is struck, 
^ although the string is in the same condition and is moved 

35 in the same way.) But still, however this may be, there is 
nothing to prevent there being a motion that is the same 
253^ in virtue of being continuous and eternal : we shall have 
something to say later ^ that will make this point clearer. 

As regards the second objection, no absurdity is involved 
in the fact ^ that something not in motion may be set in 
motion, that which caused the motion from without being 
at one time present, and at another absent. Nevertheless, 
how this can be so remains matter for inquiry ; how it 
comes about, I mean, that the same motive force at one 
time causes a thing to be in motion, and at another does 
4 5 not do so : for the difficulty raised by our objector really 
amounts to this — why is it that some things are not always 
at rest, and the rest always in motion ? 

The third objection may be thought to present more 
difficulty than the others, namely, that which alleges that 
motion arises in things in which it did not exist before, and 

* Cf. Democr. fr. 34. 2 chapter 8. 

* i. e. this fact does not prove the theory of dlSios Kiptja-is to be 



BOOK VIII. 2 253^ 

adduces in proof the case of animate things: thus an 
animal is first at rest and afterwards walks, not having ,0 
been set in motion apparently by anything from without. 
This, however, is false : for we observe that there is always 
some part of the animal's organism in motion, and the cause 
of the motion of this part is not the animal itself, but, it 
may be, its environment. Moreover, we say that the 
animal itself originates not all of its motions but its loco- 
motion. So it may well be the case — or rather we may 15 
perhaps say that it must necessarily be the case — that many ' 
motions are produced in the body by its environment, and 
some of these set in motion the intellect or the appetite, 
and this again then sets the whole animal in motion : this 
is what happens when animals are asleep : though there is 
then no perceptive motion in them, there is some motion 
that causes them to wake up again. But we will leave 30 
this point also to be elucidated at a later ^ stage in our 

3 Our enquiry will resolve itself at the outset into a con- 
sideration of the above-mentioned problem — what can be 
the reason wh y some thing s in the w orld at one time are in 
motion and at another are at rest again? Now one of 
three things must be true : either all things are always at 
rest J or all things are always in motion, or some things are 25 
in motion and others at rest: and in this last case again 
either the things that are in motion are always in motion 
and the things that are at rest are always at rest, or they are 
all constituted so as to be capable alike of motion and of 
rest ; or there is yet a third possibi lity rem ^iinin p;- — it may 
be that some things in the world are always motionless, 
others always in motion, while others again admit of both 
conditions. This last is the account o f the matter that we 30 
must give : f or herein lies t he sol ution of all the difficulties 
raised and the conclusio n of the investigation upon which 
we are engaged. 


* Chapter 6. 

253'' PHYSICA 

To maintain that all things are at rest/ and to disregard 
sense-perception in an attempt to show the theory to be 
reasonable,^ would be an instance of intellectual weakness : 
it would call in question a whole system, not a particular 
35 detail : moreover, it would be an attack not only on the 
physicist but on almost all sciences and all received 
253^ opinions, since motion plays a part in all of them. Further, 
just as in arguments about mathematics objections that 
involve first principles do not affect the mathematician — 
and the other sciences are in similar case — so, too, objec- 
tions involving the point that we have just raised do not 
5 affect the physicist : for it is a fundamental assumption 
with him that motion is ultimately refer? ^^q to "?t"*-^ 
^erselX ^ 

The assertion that all things are in motion we may 

, fairly regard as equally false, though it is less subversive 

' of physical science : * for though in our course on physics ^ 

it was laid down that rest no less than motion is ultimately 

referable to nature herself, nevertheless ® motion is the 

characteristic fact of nature : m oreover, the view is actually 
10 held by some that not merely some things but all things 
in the world grp tn mntinn and ^lways in motion , though 
we cannot apprehend the fact by sense-perception. Although 
the supporters of this theory do not state clearly what kind 
of motion they mean, or whether they mean all kinds, it 
is no hard matter to reply to them: thus we may point 

^ The Greek as it stands is not quite logical : the dinvoias appaxrrla 
is not TO TidvT rjpefjLelv but to ttcivt rjpefjLdv \eyeiv. Some such word as 
Xey"!^ must be supplied from C^relv following. 

^ The words Cn'^elv Xoyov mean to seek an explanation or rationale 
of the theory, to give a rational account of it. 

^ ///. ' nature is the original cause of motion ' : i. e. motion is an 
ultimate fact in the constitution of the world. See i. 2. 184^ 25 sqq. 

* ///. * less contrary to the investigation *, sc. physical investigation. 

^ ii. I. 192^ 21. See note on 251*9 above. 

^ Reading in 1. 9 o/xcoy. It is impossible to get any sense out of 
ofxoiois, the reading of all the M SS. The two words are often confused : 
moreover Pacius has opaa and mentions no other reading. Even so 
the sense given to ^vo-ikov is somewhat strained : it must mean that 
whereas ^pe/xi'a is a mere a-TcprjaLS of motion, klvtjo-is is a positive fact in 
nature, (fivais being conceived of as emphatically a process. We might 
perhaps get this sense more easily by reading ovx op-oicas : ' motion is 
natural in a different sense ', i. e. in a more special sense. 

BOOK VIII. 3 253^ 

out that there cannot be a continuous prore f^.s either of 
increase or of decrease : that which comes between the two 
has to be included.^ The theory resembles that about the 15 
stone being worn away by the drop of water or split by 
plants growing out of it : if so much has been extruded or 
removed by the drop, it does not follow that half the 
amount has previously been extruded or removed in half 
the time : the case of the hauled ship is exactly comparable : 
here we have so many drops setting so much in motion, 
but a part of them will not set as much in motion in any 
period of time. The amount removed is, it is true, divisible 
into a number of parts, but no one of these was set in 20 
motion separately : they were all set in motion together. 
It is evident, then, that from the fact that the decrease is 
divisible into an infinite number of parts it does not follow 
that some part must always be passing away : it all passes 
away at a particular moment. Similarly, too, in the case 
of any alteration whatever if that which suffers alteration 
is infinitely divisible it does not follow from this that the 
same is true of the alteration itself, which often occurs all 25 
at once, as in freezing. Again, when any one has fallen ill, 
there must follow a period of time in which his restoration 
to health is in the future: the process of change cannot 
take place in an instant : yet the change cannot be a change 
to anything else but health.^ The assertion, therefore, 
that alteration is continuous is an extravagant c alling into 
question of the obvious : for alteration is a change from 30 
one contrary to another. Moreover, we notice that a stone 
becomes neither harder nor softer.^ Again, in the matter 
of locomotion, it would be a strange thing if a stone could 
be falling or resting on the ground without our being able 
to perceive the fact. Further, jtJs a l aw of nature that 
^arth and ^"^^ ntVi^r ^Hicff s hould remain in their prop er 

^ i. e. a thing cannot go on increasing or decreasing to infinity : 
there comes a time when it either remains constant or changes to the 
contrary process, and the two processes must be separated by at least 
a moment of rjpffxia (to fxeaop). 

^ Thus vyiavaisj a particular form of aXXolaais, is not o-vvexrjs. 

^ An argument from ordinary experience : a stone retains the same 
degree of hardness at least for a very long period : it cannot therefore 
be always changing in this respect. 


35 places and be moved fro m th em only by violence: fr om 

the fact then that some of them are in their proper places 

it follows that in respect of place also all things cannot be 

254^ in motion. These and other similar arguments, then, should 

convince us that it is impossible either that all things are 

^always in motion or that all thmgs are always at rest. 

Nor again can it be that some things are always at rest , 
ot hers always in motion, and nothing sometimes at rest and 
5 sometimes in motion. This theory must be pronounced 
impossibl£-On the same grounds as those previously men- 
tioned ; viz. that we see the above- mentioned changes 

I occurring in the case of th e same t hings.^ We may further 
point out that the defender of this position is fighting 
against the obvious, for on this theory there can be no 
such thing as increase : nor can there be any such thing as 
compulsory motion, if it is impossible that a thing can be at 

10 rest before being set in motion unnaturally.^ This theory, 
then, does awaj^ with ^ becoming and perishing. Moreover, 
motion, it would seem, is generally thought t o be a sort of 
becoming and perishing, tor that to which a thing changes 
comes to be,-* or occupancy of it comes to be,^ and that 
from which a thing changes ceases to be, or there ceases 
to be occupancy of it. _It is clea r, therefore, that there are 

cases of 0CC3 *=;inna1 mofi/->t^ onH n^Qgir>r|p1 rpgf-. 

15 We have now to take the assertion that all things are 
sometimes at rest and sometimes in motion and to confront 
it with the arguments previously advanced. We must 
take our start as before from the possibilities that we 
distinguished just above. Either all things are at rest, or 
all things are in motion, or some things are at rest and 
others in motion. And if some things are at rest and 

^ i. e. we make the same appeal to sense-perception : we observe 
the same thing to be now in motion, now at rest (e. g. a falling stone) 
and vice versa. 

"^ The clause 6t /tx'7 .. • n-porepov refers only to ^iaios Kiprjais. The 
reason why the theory does away with av^rjais is not stated, because 
what has been said above (253^ 13), that av^Tjais cannot be a-wex^^t 
applies here too. 

^ sc. because neither yeveais nor (f)6opd can be crvvexrjs. 

* sc. in yepecris proper and dXXoiwa-is. 

® sc. in (fjopd. 

BOOK VIII. 3 254" 

others in motion, then it must be that either all things are 20 
sometimes at rest and sometimes in motion, or some things 
are always at rest and the remainder always in motion,^ 
or some of the things are always at rest and others always 
in motion while others again are sometimes at rest and 
sometimes in motion. Now we have said before that it is 
impossible that all things should be at rest : nevertheless 
we may now repeat that assertion. We may point out 
that, even if it is really the case, as certain persons assert,^ 25 
that the existent is infinite and motionless, it certainly does 
not appear to be so if we follow sense-perception : many 
things that exist appear to be in motion. Now if there is 
such a thing as false opinion or opinion at all, there is also 
motion : and similarly if there is such a thing as imagina- 
tion, or if it is the case that anything seems to be different 
at different times : for imagination and opinion are thought 
to be motions of a kind.^ But to investigate this question 30 
at all — to seek a reasoned justification of a belief with 
regard to which we are too well off to require reasoned 
justification — implies bad judgement of what is better and 
what is worse, what commends itself to belief and what 
does not, what is ultimate and what is not. It is likewise 
impossible that all things should be in motion or that some 
things should be always in motion and the remainder 
always at rest. W e_have sufficient groun d for rejecting 35 
all these th eories in the single f act that we see some tnmgs 
that aTe sometime s Itt motion and som etimes at rest. . It is 254*^ 
evident, therefore, that it is no less impossible that some 
things should be always in motion and the remainder 
always at rest than that all things should be at rest or that 
all things should be in motion continuously. It remains, 
then, to consider whether all things are so constituted as 
to be capable both of being in motion and of being at rest, 
or whether, while some things are so constituted, some are 5 

* Repeating in 1. 22 r\ to. fjiev del rjpefxuv TO. S' del Kiv€i(rdai before 
avT&v, a simple and easy correction, to make the enumeration com- 
plete. Prantl inserts the words after avrcov, but the other position 
seems slightly better and palaeographically easier. 

^ Melissus is meant ; cf. 185*32. 

3 Ci.De An. iii. 3. 428^11. 

•45. i« P 

254^ PHYSIC A 

always at rest and some are always in motion: for it is 
this last view that we have to show to be true. 

Now of things that cause motion or suffer motion, to 4 
some the motion is accidenta l, to others essenti al : thus it 
is accidental to what merely belongs to or contains as 
a part a thing that causes motion or suffers motion, 

10 essential to a thing that causes motion or suffers motion 
not merely by belonging to such a thing or containing it 
as a part. 

Of things to which the motion is essent ial some derive 
their motion from themselves, others from something else : 
and in some cases their motion is natura l, in others yiolent 
and unnatural. Thus in things that derive their motion 

15 fromlHem selves, e.g. all animals, the motion is natural (for 
when an animal is in motion its motion is derived from 
itself) : and whenever the source of the motion of a thing 
is in the thing itself we say that the motion of that thing 
is natural. Therefore the animal as a whole moves itself 
naturally : but the body of the animal may be in motion 
unnaturally as well as naturally : it depends upon the kind ^ 
of motion that it may chance to be suffering and the kind of 

20 element ^ of which it is composed. And the motion of things 
that derive their motion from something else is in some 
cases natural, in others un natural : e. g. upward motion of 
earthy things and downward motion of fire are unnatural. 
Moreover the parts of animals are often in motion in an 
unnatural way, their positions^ and the character of the 
motion * being abnormal. The fact that a thi n^ that is in 

25 motion derives its motion from something is most evident 

/ in things that are in motion unnaturally , because in such 

cases it is clear that the motio n is derived from som ething 

other than the thing itselT ! Next to things that are in 

motion unnaturally those whose motion while natural is 

^ e.g. the motion of jumping natural to the animal as a whole 
is unnatural to the body qua body, which is yerjpov and naturally has 
a downward tendency. 

^ i. e. the material of which a body is composed may be so light as 
naturally to have an upward tendency. 

^ e. g. a man may walk on his hands. 

* e. g. a man may roll along the ground instead of walking. 


BOOK VIII. 4 254^ 

derived from themselves — e.g. animals — make this fact 
clear : for here the uncertainty is not as to whether the 
motion is derived from something but as to how we ought 
to distinguish in the thing between the movent and the 
moved. It would seem that in animals, just as in ships 30 
and things not naturally organized , fHat which causes 1/ 
motion is separate from that which siifypr^mo^i on^ anH that \j 
"it is only i l l thia sense that the anT maTasa whole causes 
its own motion. 

The greatest difficulty, however, is presented by the 
remaining case of those that we last distinguished. Where 
things d erive their motio n from s omething else we dis- 
tinguished the cases in which the motion is ^unn ^tnr^l t we 35 
are left with those that are to be contrasted with the others i^^ 

by reason of the fact that the motion is natural. It is in 255^ 
these cases that difficulty would b e experienced in deciBin^ 
whence the moti on is deriv ed, e.g. in the case of light and 
heavy things. When these things are in motion to posi- 
tions the reverse of those they would properly occupy, their 
motion is violent : wh en they are in motion to their proper 
positions — the light thing up and the heavy thing down — 
their motion is natural ;^. hut in this latter case it is no 
longer evident, as it is when the motion is unnatural, 
whence their motion is derived . It is impossible to say 5 
that their motion is derived from themselves : this is 
a characteristic of life and peculiar to living things. 
Further, if it were, it would have been in their power to 
stop themselve s (I mean that if e.g. a thing can cause 
itself to walk it can also cause itself not to walk), and so, 
since on this suppositio n fire itself _£Ossesses the power of 
upwar d locomot ion, it is clear that it should also possess 
the power of downward locomot ion.^ Moreover if things 10 
move themselves, it would be unreasonable to suppose 
that in only one kind of motion is their motion derived 
from themselves. Again, how can anything of continuous 
and naturally connected substance move itself? In so fa r 
as a thing k nnp anH rontinuous not merely in virtue of 
contact, i t is impassiv e : it is only in so far as a thing is 
divided that one part of it is by nature active and another 

P 2, ^ 


15 passive. Therefore none of the things^ that we are now 
considering move themselve s (for they are of naturally con- 
nected substance) , nor does anything el se that isconiiiuuwje : 
in each case the movent must be separate from the moved, 
as we see to be the case with inanimate things when an 
animate thing moves them. It is the fact that thes e 
things^ also always derive their motion from something : 
what it is would become evident if we were to distinguish 
the different kinds of ^hm*^*^ - 

20 The above-mentioned distinctions can also be made in 
the case of things that caus e motio n : some of them are 
capable of c ausing motion unnaturall y (e. g. the lever is not 
naturally capable of moving the weight), others naturally 
(e. g. what is actually hot is naturally capable of moving ^ 
what is potentially hot) : and similarly in the case of all 
other things of this kind. 

In the same way, too, what is potentially of a certain 
quality or of a certain quantity or in a certain place is 

25 naturally movable when it contains the corresponding 
principle in itself and not accidentally (for the same thing 
may be both of a certain quality and of a certain quantity, 
but the one is an accidental, not an essential property of 
the other *). So when fire or earth is moved by something 
the motion is vi olent when it is unnatur al, a nd natur al 
when it brmcfs to actuality the proper ac tivities^ that 

30 they potentially possess. But the fact that the term 
' potentially ' is used in more than one sense is the reason 
why it is not evident whence such motions as the upward 
motion of fire and the downward motion of earth are 
derived. One who is learning a science potentially knows 
it in a different sense from one who ^5vhile already possess- 
ing the knowledge is not actually exercising it. Wher- 
ever we have something capable of acting and something 

* SC. nvp and the like (to. Kara cfivaip Kivovfxeva). 
^ SC. Til Kara (f)v(nv Kivovyava. 

^ i. e. causing to become hot. 

* i. e. a thing may, in the process of becoming ttoiov^ incidentally 
become TToo-oi/, and vice versa: but the becoming ttoo-ov is irrelevant to 
the change or motion from noiov to iroiov or from ttoO to irov. 

" SC. upward motion and downward motion respectively. 


BOOK VIII. 4 255^ 

capable of being correspondingly acted on, in the event 
of any such pair being in contact what is potential becomes 35 
at times actual:^ e.g. the learner becomes from one poten- ^55 
tial something another potential something : for one who 
possesses knowledge of a science but is not actually exe r- 
cising it knows the science potentially in a sense. thr> ngF> 
not in the same sense as he knew it potentially before he 
le arnt it7 And when he is in this condition, if something 
does not prevent him, he actively exercises his knowledge: 
otherwise he would be in the contradictory state of not 
knowing. In regard to natural bodies also the case is similar. 5 
Thus what is cold is potentially hot : then a change takes 
place and it is fire, and it burns, unless something prevents 
and hinders it. So, too, with heavy and light : light is gene- 
rated from heavy, e. g. air from water (for water is the first 
thing that is potentially light), and air is actually light, and 10 
will at once realize its proper activity as such unless some- 
thing prevents it. The activity of lightness consists in the 
light thing being in a certain situation, namely high up : ^ 
when it is in the contrary situation, it is being prevented 
from rising. The case is similar also in regard to quantity 
and quality. But, be it noted, this is the question we are 
f rying to answer — how can we account for the motion of 
light things and heavy tKings to their proper situations? 
The reason for it is that they have a natural tendency 15 
respectively towards a certain position^ and jbhis const itutes 
the essence oi hghtness and heaviness , the former being 
determined by an upward, the latter by a downward, 
tendency. As we have said, a thing may be potentially 
light or heavy in more senses than one. Thus not only 
when a thing is water is it m a sense potentially light, but 
when it has become air it may be still potentially light : for 

* The sentence is awkwardly expressed, dft and eViort seeming to 
contradict one another, but I do not think any alteration in the text 
is necessary. Certainly it will not do to omit fVtore, without which the 
statement would not be true : e. g. to produce iTrio-TrjiJLr] something more 
than the mere contact of the teacher's mind with the learner's mind is 
needed. I take dei to mean that there is no exceptional c/ass of 
noir^TKiov and naBrjriKnv that as such does not conform to the rule : 
eVioTc virtually means in ' favourable circumstances '. 

^ i. e. above anything that is heavier. 


it may be that through some hindrance it does not occupy 

20 an upper position, whereas, if what hinders it is removed, 
it realizes its activity and continues to rise higher. The 
process whereby what is of a certain quality changes to 
a condition of active existence is similar: thus the exercise 
of knowledg e follows at o nce upon the possession of it 
unless something prevents it. So, too, what is of a certain 
quantity extends itself over a certain space unless some- 
thing prevents it.^ The thing in a sense is and in a sense 
is not moved by one who moves what is obstructing and 

25 preventing its motion (e. g. one who pulls away a pillar 
from under a roof or one who removes a stone from a wine- 
skin in the water is the accidental cause of motion : ^ and 
in the same way the real cause of the motion of a ball 
rebounding from a wall is not the wall but the thrower.^ 
So it is clear that in all these rases the thin p; - does not 

30 move itself, but it contains within itself the source o f 
motion — not of moving something or of causing motion, 
but of suffering it.* 

If then the motion of all things that are in motion is 
either natur al or unnatur al and violen t, an d all things 
whose motion is violent and unnatural a re moved by some - 
thing^ and something other than themselves, and ag ^in al l 
thing^s whose motion is natural are moved by (somethipg — 
both those that are moved by themselves and those that 

35 are not moved by themselves (e. g. light things and heavy 
256^ things, which a re moved either by that which brought the 
thin g into existence as such and made it light and heavy, o r 
by that which released what; was hin derin^^ and p re ventinpf — 
it) ; then all things th at are in motion must be moved by 
something. ^ " 

Now this may come about in either ofj wgaay^ Either 5 
the movent is not itself responsible for the motion, which 

^ i. e. it may be possibly compressed so that it does not occupy the 
amount of space that such a noa-ov would normally occupy : in that 
case it is dvpdfxet noaov in the second sense. 

^ The real cause here is the upward or downward tendency. 

' In this case the wall is an instance of a Kara (Tv/i^e^rfKos kivovv. 

* i. e. the quality of being affected by or responsive to the activity of 



BOOK VIII. 5 356^ 

is ip ^- pc referred to som ething else which moves the mo- 
vent, or t he movent is itself res ponsible for__the_motion^5 ^ 
Further, in the latter case, either the moventlmmediately 
precedes the last thing in the series,^ or there may be 
one or more interm ediate links : e. g. the stick moves the 
stone and is moved by the hand, which again is moved by 
the man : in themanjLOwever, we have reached a movent 
that is not so in virtue_oj^beingjiiov£d_by_jo^ 
else. Now we say that the thing is moved both by the 
last and by the first movent in the series, but more 
strict ly by the first, since the first movent moves the last, 10 
whereas the last does not move the first, and the first will 
move the thing without the last, but the last will not 
move it without the first : e. g. the stick will not move 
anything unless it is itself moved by the man. If Jjien- 
everything that is in motion mus t be moved by something , 
and the ^iovent must either itselt be move H hy gnmp- 
thing else or not, and in the former case there must be 15 
some^jirsFniovent that is not itself moved by _a jiything__ 
else, while in the case of the immediate movent being 
of this kind there is no need of an intermediate movent 
that is also moved ^ (for it i s impossi ble that there should 
be an infinite series of movents, each of which is itself 
moved by something else,^ s ince in an infinite series there I 
is no first term) — if then eve rything that is in moti on.i^ fi 
moved by something, and the first movent is moved but 20 j 
not by anything else, it must be moved by itse lf. I 

This same argument may also be stated in another way 
as follows. Every movent moves something and moves 
it _with something, either with itself or with something else: 
e. g. a man moves a thing either himself or with a stick, 

^ i. e. the thing that is moved. 

^ The argument is stated so concisely that it is perhaps hardly 
clear : but the reasoning appears to be as follows. Z {t6 eaxnrov, the 
thing whose motion is to be accounted for) must be moved directly 
either by JC (a kivovv ovx vtt aWov Kiuovfievov) or by V (a kivovv vtt' 
(iXXou Kivovn(vov). Now Y implies an ultimate X, though P", Y" may 
intervene : but X does not necessarily imply Y in order to move Z : 
otherwise if Y is necessary in order to enable X to move Z^ Y' will be 
necessary to enable it to move Y, and so on ad infinitu7n. 

' Reading in 1. 17 t6 kivovv kcu Kivovfievov with EK. 

.256* PHYSICA 

and a thing is knocked down either by the wind itself or by 
25 a stone propelled by the wind. But it is impossible for 
that with wh ich a thing is m oved to move it withou t being 
Inov ed by that whic h imparts motion by its own agency : ^ 
on the other hand, i £ a thing imparts motion by its own 
agency, it is not necessar y that tnere should be anything , 
,J ^lse^with which it imparts motion , whereas if there is a 
different thing with which it imparts motion, there must 
be something that imparts motion not with something else 
but with itself, or else there will be an infinite series. 
If, then, anything is a movent while being itself moved, 
30 the series must stop somewhere and not be infinite. Thus, 
if the stick moves something in virtue of being moved by 
the hand, the hand moves the stick : and if something else 
moves with the hand^ the hand also is moved by some- 
thing different from itself. So w hen motion by means of 
an Instrument is at ea ch stage caused by somethin g different 
from the ins tnunent^jbh must always be preceded by 
something else ^ which imparts motion with itself. There- 
jore, if this la st move nt is m motion and there isliothing 
256 else that moves it^ it must move itself . So this reasoning 
^ also shows that, when a thing is moved, if it is not moved 

f~ immediately by something that moves itself, th^sengsbrijngs^ 
us at some time or other to a movent of this kin d. 

And if we consider the matter in yet a third way we 
shall get this same result as follows. If everything that is 
5 in motion is moved by something t hat is in motion, either 
thisbeing in_ giQtion is an accidental attribute of th e 
movents in question, so that each of them moves something 
while being itself in motion, but not always because it is 
itself in motion, or it is not an accidental but an essentL|l 
attribu te^ Let us consider the former alternative. If then 
it is an accidental attribut e, it is not necessary that that 
which is in motion should be in motion : and if this is so 
it is clear that there may be a time when nothing that 
exists is in motion, since the accidental is not necessary 

* ai/To is written in 1. 25 for avjov to avoid the possible misinterpre- 
tation of Tov avTov. C(. 257^ 13, 27, 258^ 23, 259* I. 
^ Reading in 1. 31 ravTij. 


BOOK VIII. 5 256^ 

but co ntingent. Now if we assume the existence of a possi- 10 
bility, any conclusion that we thereby reach will not be an 
impossibility, though it may be contrary to fact. But the 
non-existence of motion is an impossibility : for we have 
shown above ^ that there must always be motion. 

Moreover, the conclusion to which we have been led is 
a reasonable one. For ther e must be three thin gs — the 
moved, the movent, an d the instrument of motion . Now 15 
the moved must be in motio n, but it need not move any- 
thing else: the instr ument of motion must both move 
something else and be itself in motion (for it changes 
together with the moved, with which it is in contact 
and continuous, as is clear in the case of things that 
move other things locally, in which case the two things 
must up to a certain point ^ be in contact) : and the 
movent — that is to say, that which causes motion in such 
a manner that it is not merely the instrument of motio n — 
must be unmoved. Now we have visual experience of the 20 
last term in this series, namely that which has the capacity 
of being in motion, but does not contain a motive principle, 
and also of that which i s in motion but is mov ed by itself 
and Qot by anything else ^ : it is reasonable, therefore, not 4 . 
to say necessary, to suppose the existence ^o£_di^_JhinJ I v 
term also, that which causes motion but is itself unmoved. J- 
So, too, Anaxagoras is right when he _says that Mind is 25 

^ Chapter i. 

^ i. e. not necessarily continuously : e. g. a thing thrown continues its 
course after contact with the thrower has ceased. 
^ I am convinced that Bekker's reading (which is that of two MSS. 
including the best) is right — 6 KLvelrai fxeu, ovx W aAXou 8e aXX' v(f>' avrov. 
Prantl reads 6 Kivel /uei/, vtt' aWov 8e (^KtueiTai) aXX* ovx ^4"^ avrov. For the 
transposition of ovx there is MS. authority : but the substitution of Kivel 
for Kivelrai and the insertion of Kivelrai later are alterations of Prantl's 
own, based as it seems to me on a complete misunderstanding of 
Aristotle's meaning. Apparently he would equate the middle term 
here with the ^aKTJ]pla of the previous illustration. But there is no 
essential difference between the XiOos and the ^aKTr)pia as regards their 
motion, and we have no right at all to infer from their existence the 
existence of a kivovv dKivrjrov : the most that we could infer euXd-ytop 
would be the existence of an avTOKivr^Tov. As I read the passage, from 
the admitted existence of what is avTOKlvrjrou (e. g. a stone) and of 
what is both klvovv and Kivovfievov (e. g. an animal, which as moving 
itself shows the amalgamation of both principles) Aristotle infers by 
iivaXoyia that presumably what is kipovp only also exists. 

256'' PHYSICA 

impassive and unmixed^nce he makes it the principle of 

motion : for it could cause motion in this sense^^^iy by 
l^ging its elf unmoye d, and have supreme control only by 

WewttHrow take the second alternative. If the niasifittt 
is not accidentally b ut necessarily in motion — so that, 
if it were not in motion, it would not move anythin g — 
then the movent, in so far as it is in motion, must be in 
30 motion in one of two ways : it is moved either as that is 
which is moved ^ with the same kind of motion, or with 
a different kind — either that which is heating, I mean, is 
itself in process of becoming hot, that which is making 
healthy in process of becoming healthy, and that which is 
causing locomotion in process of locomotion, or else that 
which is making healthy is, let us say, in process of loco- 
motion, and that which is causing locomotion in process of, 
say, increase. But it is evident t hat this is impossible. 
For if we adopt the first assumption we have to make it 
apply within each of the very lowest species into which 
257^ motion can be divided : e. g. we must say that if some one ^ 
is teaching some lesson in geometry, he is also in process 
of being taught that same lesson in geometry, and that 
if he is throwing he is in process of being thrown in just 
the same manner. Or if we reject this assumption we 
must say that one kind of motion is derived from another ; 
e. g. that that which is causing locomotion is in process of 
5 increase, that which is causing this increase is in process 
of being altered by something else, and that which is 
causing this alteration is in process of suffering some 
different kind of motion. But the series must stop some- 
where, since the kinds of motion are limited ; and if we 
say that the process is reversible, and that that which is 
causing alteration is in process of locomotion, we do no 
more than if we had said at the outset that that which is 
causing locomotion is in process of locomotion, and that 
10 one who is teaching is in process of being taught : for it is 

* SC. as apxr) KtvrjO-etos. 

"^ Reading in 1. 30 is- to {coare ro E). 

2 The neuter would sound absurd here in English. 

BOOK VIII. 5 257' 

clear tha t everything that is moy frl '*= "inxr^^H hy tVip 
movent that is further ba ck i n the series a s well as by 
that which immediately moves it : in fa ct the earlier 
mov ent is that which m ore stric tly moves it. But this is of 
course impossible : for it involves the consequence that one 
who is teaching is in process of learning what he is teaching, 
whereas teaching necessarily implies possessing knowledge, 
and learning not possessing it. Still more unreasonable is 
the consequence involved that, since everything that is 15 
moved is moved by something that is itself moved by 
something else,^ everything that has a capacity for causing 
motion has as such a corresponding capacity for being 
moved : i. e. it will have a capacity for being moved in the 
sense in which one might say that everything that has 
a capacity for making healthy, and exercises that capacity,^ 
has as such a capacity for being made healthy, and that 
which has a capacity for building has as such a capacity 
for being built. It will have the capacity for being thus 
moved either immediately or through one or more links (as 
it will if, while everything that has a capacity for causing 
motion has as such a capacity for being moved by some- 
thing else, the motion that it has the capacity for suffering 20 
is not that with which it affects what is next to it, but 
a motion of a different kind ; e. g. that which has a capacity 
for making healthy might as such have a capacity for 
learning : ^ the series, however, could be traced back, as we 
said before, until at some time or other we arrived at the 
same kind of motion). Now the first alternative is impos- 
sible, and the second is fantastic : * it is absurd that that 

* It is necessary to insert * by something else ' in view of the 
possibility admitted below (257*27) that to Kivovfievov TvponTov uvto 
€avTo KiVT](Tei. 

^ The words koI vyid(ov in 1. 17 seem pointless and irrelevant, 
and there is no trace of them in SimpHcius. 

^ Reading in 1. 21 (with three MSS. including the best) na6r]TiKQv. 

* Alexander (quoted by Simplicius) interpreted this to mean that 
while both alternatives are impossible, the second has the additional 
characteristic of being TrXaa-fiuTades. Simplicius himself, however, 
considers that the second alternative, while certainly TrXao-pzTcofief, is 
not logically impossible, since it might be denied that Kivrjo-eis are 
nenepaa-iJLepai or that a thing Kifetrai /jloWov vtto tov Trporepov tChv 
KivovvT(ov. If Simplicius is right, the connexion is very loose, since the 



which has a capacity for causing alteration should as such 
25 necessarily have a capacity, let us say, for increase. It is 
not necessary, therefore, that that which is moved should 
alw ays be moved by something else that is itself moved by 
somethi ng else : so there will be an end to the series. 
Consequently the first thing that is m motion will derive 
its motion either from something that is at rest or from 
itself. But if there were any need to consider which 
of the two, that which moves itself or that which is mov ed 
by something else, is th e^ cause and principle of motion, 
30 every o ne would decide fo r the former : for that which is 
its elf independently a cause is always prior as a cause ^ to 
that which is so only in virtue of being itself dependent 
upon something else that makes it so. 

We must therefore make a fresh start and consider the 
question ; if a t hing moves itself, in w hat sense and in what 
mann er does it do s o ? Now evervthinp- that is in motion 
must be infinite ly divisible, for it has been^shown^ali;eady ^ 
257^ in our general course on Physics,^ that everything that is 
essentially in mot ion is continu ous. Now it is impossible 
that that which moves itself should in its e n t i r e tyi„n3JQ3i£— 
itself ; for then, w hile being specifically one and indivisible . 
it would as a whole both undergo and cause the same 
locomotio n or alteration : thus it would at the same time 
5 be both teaching and being taught (the same thing), or 
both restoring to and being restored to the same health. 
Moreover, we have * established the fact that it is the 
movable that is moved ; and this is potentially, not actually, 
in motion, but the potential is in process to actuality, and 
motion is an incomplete actuality of the movable. The 
movent on the other hand is already in activity : e. g. it 1s 
that which is hot that produces heat : in fact, that which 

second alternative has just been distinctly declared to be only a special 
case of the first. 

^ This must be the sense, whether we read with Bekker in 1. 30 

aiTiov oei nporepov Or with EK net nporepov ahiov I in either case amov 
is wanted both as subject and as predicate. 

^ The reference is apparently to vi. 4. 234^ 10 sqq. 

^ See note on 251* 9. 

* Ch. I. 251^9 sqq. 

BOOK VIII. 5 257^ 

produces the form ^ is always something that possesses it. 
Consequently (if a things can move itself as a whole), the lo 
same thing in respect of the s ame thing ^ may be at the 
same time both hot and not hot. So, too, in every other 
case where the movent must be described by the same 
name in the same sense as the moved.^ Therefore when 
a thing moves itself* it is one pa rt of it that is the moven t 
and anoth er part that is moved. But it is not self-moving ^ 
in the sense that each of the two parts is moved by 
the other part : the following considerations make this 
evident. In the first place, if each of the two parts is to 15 
move the other, there will be no first movent. If a thing 
is move d by a se ries of movents, tha t which is earlier in, 
the series is mor e the cause of its being moved than t hat 
jvhich comes next^ a nd will be more truly the movent : for 
we found that there are two kinds of move nt, that which 
is itself moved b y something else a nd that which deriv es 
its motion from itsel f: and that which is further from the 
thing that is moved is nearer to the principl e of motion 
than jhat which is interm ediate.^ _In the second place, 20 
there is no necessity for the movent part to be moved by 
anything but itself: so it can only be accidentally that the 
other part moves it in return. I take then the possible 
case of its not moving it : then there will be a part that is 
moved and a part that is an unmoved movent. In the 
third place, there is no necessity for the movent to be 
moved in return L, on the contrary the necessity that there 
should always be motion makes it necessary that there 
should be some movent that is either unmoved or moved » 
by itself. In the fourth pla ce we sho\ilr| |h en have a thing^ 2 .^ 
under g oing the same motion tha t it is causing — that which 
is producing heat, therefore, being heated. But as a matter 

M. e. any particular characteristic such as heat, 

"^ i. e. the whole of itself: there is no question of one part of a thing 
heating another part. 

^ i.e. in respect of the imparted characteristic: thus ro Bepfiahov 
and TO depfiaivofxevov both have the predicative depfxov applied to them 
in the same sense {(rvvajvvpoas). 

* Cf. 256* 25 n. 

** Reading in 1. 14 klvovv, with EK Simp. 

^ sc. between t6 noppo)T€pov and t6 Kipovfxcvov, 


of fact that which primarily moves itself^ cannot contain 

either a single part that moves itself or a number ofparts 

each of w hich moves itself. For, if t he whole is moved by 

/ / itself, it must be moved either bj^ ^some part o t its elt or as 

^ 3 ^a whole by itself as a whole. If, then, it is moved in virtue 
of som e part of it being moved by that part itself, it is this 
part that will be the primary self-movent, since, if this part 
is separated from the whole, the part w ill still move itself, 
but the whole will do so no longer. If on the other hand 
t he whole is moved by itself as a whole, it must be acci-. 
dentally that the parts move themselvesT and therefore, 
their self-motion not being necessary, we may take the case 
258^ of their not being moved by themselves. There fore in the 
whole of the thing we may distinguish that which imparts 
motion without itself being moved and that which is moved : 

y^ fo i^only in this way is it possible for a thing to be self-^ 

I mov gdT Further, if the whole moves itself we may distii>_ 
guish in it that which imparts the motion an d that which 
IS moved: so while we say that AB is moved by itself, we 
5 may also say that it is moved by A. And since that^vhich 
irn parts m otion may be either a thing that is moved by 
something else or a thing that is unrnoved* and that which 
7s moved may be either a thing that imparts motion to 
something else or a thing that does not, that which moves 
itself mus t be composed of something that is unmoved bu t 

j imparts m otion and also of something that is moved but 
does not necessarily impart motion but may or may not do 
so. Thus l et A be something tha t imparts motion but is 
unmoved, B something that is moved by A and moves F, 

10 r something that is moved by B but moves nothing (granted 
that we eventually arrive at F we may take it that there is 
only one intermediate term, though there may be more). 
Then the whole ABF moves itself. But if I take away F ^ 
A B will move itself. - A imparting motion and B being 
moved, whereas F will not move itself or in fact be moved 

15 at all. Nor again will BF move itself apart from A : for B 
imparts motion only through being moved by_something 
else^ no tjthrough being moved by any part of itself. So 
1 Cf. 256^2511. 


BOOK VIII. 5 258* 

only AB move s itself. _ Th at which moves itself, therefore , 
must comprise something that imparts motion but is un- 4 
moved and something that is moved but do es not neces- |l 
sarily move 'anything else : and each of these two things, 20 
or at any rate one of them,^ must be jn contact with the 
other. _If, then, that which imparts motion is a continuous 
substance — that which is moved must of course be so — it 
is clear that it is not throug h some part of the whole being 
of such a nature as to be capable ot moving itself that the 
whole moves itself: it moves itself as a whole , b oth being 
moved and imparting motion through containing a part 
that imparts motion a nd a part that is moved. It does 25 
not impart motion as a whole nor is it moved as a whole : 
it is A alone that imparts motion and B alone that is 
moved. It is not true, further, that T is moved by A, 
which is impossible.^ 

Here a difficulty arises : if something is taken away from 
A (supposing that that which imparts motion but is un- 
moved is a continuous substance), or from B the part that 
is moved, will the remainder of A continue to impart 
motion or the remainder of B continue to be moved ? If 3° 
so, it will not be AB primarily that is moved by itself, 
since, when something is taken away from AB, the remain- 
der of AB will still continue to move itself. Perhaps we 
may state the case thus: there is nothing to prevent each 258^ 
of the two parts, or at any rate one of them, that which 
is moved, being divisible though actually undivided, so 
that if it is divided it will not continue in the possession of 
the same capacity : and so there is nothing to prevent self- 

^ If both are corporeal, the two things will be mutually in contact : 
but if one is incorporeal and the other not, the first may be said to be in 
contact with (dnreadai) the second, but not vice versa. So here the 
Kivovv d<ivr]Tou may be said anTcaOaL tov Kivovfxevov, but to Kivovfievov 
cannot be said aimdOai tov klvovvtos aKLvrjTov 6e. See de Gen. et Corr, 
i. 6. 323-^ 25 sqq. 

'^ This sentence comes in awkwardly here, and I am inclined to 
think that it should be omitted. It was not known to Alexander, 
nor did it occur in most of the MSS. known to Simplicius. The best of 
our MSS. omits it. The point of the sentence, if it is kept, seems to 
be that in AB we have one complete avroKivrjrov : A may accidentally 
through B impart motion to r : but r is irrelevant to the axiTOKivTjTop 
that we are considering. 



motion residing primarily in things that are potentially 

From what has been said, then, it is evident that that 
5 which primarily imparts motion is unmoved : for,' whether 
the series is closed at once by that which is in motion but 
moved by something else deriving its motion directly from 
the first unmoved, or whether the motion is derived from 
what is in motion but moves itself and stops its own 
motion, on both suppositions we have the result that in 
I all cases o f things being in motion that which primari ly 

I imparts m ntir>n i«; nnmnvpH. ^ 

I o. Since there must always be motion without intermission, 6 
^ M- '-♦^^^ ^ ifliere must necessarily be something, one thing or it may be 

'fKL plurality ,"'that hr iSt Impaftg m6tiofi, and this first movent 
fm ust be unm oved^ Now the question whether each "of 
the things that are unmoved but impart motion ^ is eterna l 
is irrelevant to our present argument : but the following 

^ considerations will make it clear that there must necessarily 

- be some such thing^ ^ which, while it has the capacity of 
moving snmpthirig^^el se, is itself unmoved and exempt troni 

5 all change^^ which can affect it neither in an unqualified nor 
m an accidental sense.^ Let us suppose, if any one likes, 
that in the case of certain things * it is possible for them at 
different times to be and not to be, without any process of 
becoming and perishing (in fact it would seem to be neces- 
sary, if a thing that has not parts at one time is and at 
another time is not,^ that any such thing should without 
undergoing any process of change at one time be and at 

^ e. g. individual ^vxai- 

^ Omitting in 1. 14 t^s before €kt6s with Simplicius and three MSS. 
one of which has re for r^y and another koI before Trdarjs : any one of 
these variations will give the sense required. Simplicius gives no hint 
of a reading Tr)s cktos nera^oXrjs, which would have to be taken as 
a loose genitive after dKivrjTou — * unmoved in respect of all external 
change': this, though possible, is not quite the sense required: we 
want to have exemption from fxera^oXr} clearly marked as an additional 
attribute, more extensive than exemption from Kivrjais. 

* i. e. neither directly nor indirectly : e. g. a man walking n^ra^aWei 
a-rrXas, a man sailing in a ship /xerajSaXXei Kara o-u/Li/3e/3;;Kor. 

* sc. yjrvxni I Aristotle is answering an objection to the effect that 
here we may find an aKLvijTos dpxn Kivrjatas that is not didios. 

^ Reading in 1. 19 a comma before avev and not before 6t€. 

BOOK VIII. 6 258* 

another time not be). And let us further suppose it 30 
possible that some principles that are unmoved but capable 
of imparting motion at one time are and at another time 
are not. Even so, this cannot be true of all such principles, 
since there must clearly be something that causes things 
that move themselves ^ at one time to be and at another not 
to be. For, si nce nothing that has not par ts can be in 
jngtiwi, that which. mQycsutseJl„fnnst as a -jaL&lfi— have 35 
ma gnitucl ?, though nnthing th^t w^ hnw^ c-tiH mnk^^ this 
necessarily true of ever3r,-mQveat. — So-^the fact that some 
things become and others perish, and that this is so con- 
tinuously, cannot be caused by any one of those things 
that, though they are unmoved, do not always exist: nor 
again can it be caused by any of those which move certain 
particular things, while others ^ move other things. The \ 
eternity and con tinuity of the process cannot be caused 1 
either by any one of them singly or by the sum of them, 1 
because this causal relation must be eternal and necessary, 30! 
whereas the sum of these movents is infinite and they do 
not all exist together. It is clear, then, that though there 
may be countless instances of the perishing of some prin- 
ciples that are unmoved but impart motion, and though 259^ 
many things that move themselves^ perish and are suc- 
ceeded by others that come into being, and though one'- 
thing that is unmoved moves one thing vi^hile another 
moves another, ne vertheless there is some thing that com- 
prehends themjilj^_and that as something apa rt from each 
one of them, and thi s it is that is the cause of the fact that 
some things are and others are not and of the continuous 
process of change : an d this causes the motion of the 5 
other movents, while they are the causes of the motion of 
other things. Motion, then, being eternal, th e first movent, 
if there is but one, will be eternal also : it there are more 
than one, there will be a Plura lity o f such eternal moventsT * 
We ought, however, to suppose that there is one rather 
t han ma ny, and a finite rather than an mnnite number. 

1 Cf. 256*25 n. 

"^ Reading in 1. 29 rav for toutcdi', with Simp. 
3 Cf. 256* 25 n. 
643-ia Q 



When the consequences of either assumption are the same,^ 
we should always assume that things are finite rather than 
10 infinite in number, since in things constituted by nature 
that which is finite and that which is better ought, if 
possible, to be present rather than the reverse : and here 
it is sufiicient to assume only one movent, the first of 

i unmoved thing s, wh ich being eternal Will be^the princip le 
of motion to everything else ^ ~~" 

The following argument also makes it evident that the 
first movent must be something that is one and ete rnal. 
15 We have shown ^ that there mu st always be motion. That 
being so, motion must also be continuous , because jvhat is 
always is continuous, whereas what is merely m succession 
is not continuous. But further, if motion is continuous, it 
is one: and it is one only if the movent and the moved 
that constitute it are each of them one, since in the event 
of a thing's being moved now by one thing and now by 
another the whole motion will not be continuous but 

Moreover a conviction that there is a first unmoved some- 

^thin£_may be reached not only from the foregoing argu- 
ments, but also by considering again the principles operative 
in movents. Now it is evident that among existing things 
there are some that are sometimes in motion a nd sometim es 
at res t. This fact has served above ^ to make it clear that 
it is not true either that all things are in motion or that 
all things are at rest or that some things are always at rest 
35 and the remainder always in motion : on this matter proof 
is supplied by things that fluctuate between the two and 
have the capacity of being sometimes in motion and s ome- 
time s at rest. The existence of things of this kind is clear 
to all : * but we wish to explain also the nature of each of 
the other two kinds an d show that there are some thing s 
that_are al way^_un m nved and some things that are always 

* i.e. when either will equally explain the facts. 
^ Chapter i. 

^ Chapter 3. 

* The apodosis to the eVei clause does not begin till 259^ 3 (ravTa 
B^ ktX.}, 

BOOK VIII. 6 259* 

in motion. In the course of our argument directed to this 
Tnd^ we established the fact t hat everything that is in motion aq 
is moved by somethin g^aL ^^d that th e^ movent is either 
unmove d or in motion, and that , if it is in mot ion, it (§ 
moved eith er by itsel f or by something else and so on 
thr oughout the series ; ^ and so we proceeded to the posi- 
tion^ that t he first principle that directly^ causes thing s 
that are in motion to be moved is t hat which moves itself, 
and the first princ iple of the whole series^ is the unmoved . \ 
Further it is evident from actual observation that there are 259* 
things that have the characteristic of moving themselves, 
e. g. the animal kingdom and the whole class of living 
things.'' This being so, then, t he view was suggested '^ 
that perhaps it may be possible for motion to come to be 
in a thing w it hout having been in p^i^^^"^^ at all before, 
because we see this actually occurring in animals: they are 5 
unmoved at one time and then again they are in motion, as 
it seems. We must grasp the fact, therefore, t hat animals _ 
m ove themselves^ only wit h one kind nf mntinn^Q and 
t hat this is not strictly originated by them. The causeof 
it is not derived from the animal itself: it is connected 
with other natural motions in animals, which they do not 
experience through their own instrumentality, e. g. increase, 
decrease, and respiration: these are experienced by every 10 
anima l while it is at rest a nd not in motionjn^res pect of 
the m^ti^n i^^t up by itff 0^^" HgP"^,y * ^^ here the motion is 
caused by the atmosphere and by many things that enter 
into the animal : thus in s ome cases the cause is nourish- 
ment : when it is being digested animals sleep, and when 
it is being distributed through the system they awake and 

^ Chapter 4. 

^ del. i.e. if a particular klvovv derives its motion from another 
Kivovv the same question arises with regard to the second kivovv, and 
so on. 

' Chapter 5. 

* Kivovixi: voiv fxev in 1. 33 can hardly stand. It may have displaced 
7rpo(Tfxns jueV, which Simp, seems to read, or Kivrjacois. 

^ sc. Ktvovjxeva and o avTo iavTo Kivel together. 

•^ efiylrvxn, including plants. ' 253* 7 sqq. 

* Reading in 1. 7 avrd, with Simp. 

^ sc. locomotion. ^° sc. locomotion. 



move themselves, the first principle of this motion being 
\ thus originally derivedlrom outside. Therefore anirnals 

\^^ _ar^jiot.. 9,1 ways in continuous niotioh by their own agency : 

15 it is something^ else that moves them , itself being in motion 
and changing as it comes into relation with each several 
thing that moves itself (Moreover in all these self-moving 
things the first move nt and cause of their self-motion ^ is 
itself moved by itsej/ ,^ though in an accidental sense : that ' 
is to say, the body changes its place, so that that which is 
in the body changes its place also and is a self-movent 

20 through its exercise of leverage.^) Hence we may con- 
fidently conclude that if a thing belongs to the class of 
unmoved movents that are also themselves moved acci- 

r dentally, it is impossible that it should cause continu ous 

: motion. So the necessity that there should be motion 
/^^^^ continuously requires that there should be a first movent ' 
that is unmoved even accidentally.^ if. as we have said,^ 

I5 there is to be in the world of things an unceasing and 
V ij undying motion, and the world is to rerpain ^ permanently 

i I self-contained and within the same limits: for if the first 

I, f principle is permanent, the universe must also be per- 
hlhanent, since itl? continuous with the first principle. (We 
must distinguish, however, between accidental motion of 
a thing by itself and such motion by something else, the 
former being confined to perishable things, whereas the 
latter belongs also, to certain first principles of heavenly 
30 bodies, of all those, that is to say, that experience more 
than one locomotion.''') 

^ SC. r/ \lrvxr}. 

^ i. e. it is not a true aKivrjTov after all. 

' Reading in 1. 19 (with three MSS.) Ka\ rf} noxKeia : the ordinary 
reading koL to iv rrj fxoxXeia seems meaningless. The sense appears to 
be that the soul may be said to move itself by means of the body, the 
body acting as a sort of lever. 

* Reading in 1. 24 koi Kara crvn^e^rjKos : the fifj before /caret is omitted 
by one MS. and erased in another : also it clearly was not read by 
Simplicius. It might quite easily have been inserted by some one who, 
not understanding the construction, thought that the words following 
icai must denote another attribute in addition to dKivrjTov, 

^ Chapter i. 

^ Reading in 1. 26 fievilp, with Themistius. 

"^ SC. the planets. 

BOOK VIII. 6 259^ 

And further, if there is alway s something of this natur e, 
a movent that is itself unmoved and eternal^ th en that 260* 
whi ch is first moved by it must be eterna l. Indeed this 
is clear also from the consideration that there would other- 
wise be no becoming and perishing and no change of any- 
kind in other things, which require something that is in 
motion to move them : for the motion imparted by the ^-^ 
unmoved will always be imparted in the same way and be 
one and the same, since t he unmove3~3oes not itself change 
in relation to that which is moved by it. But that ^ which 5 
is mo ved by something^ that, though it is in motion, is 
moved directly by the unmoved stands in varying rela- 
tions to the things that it moves, so tl\a t^ the moti on 
that it c auses will not be always the same : by reason of" 
the fact that it occupies contrary positions or assumes 
contrary forms at different times it will produc e contrar^r 
motions in each several thing that it moves and will 10 
cau se it to be at on e time at rest and at anot her time in 

The foregoing argument, then, has served jo clear up the \ 
point about which we raised a difficulty at the outset "^—^ ' 
why is it that instead of all things being either in motion 
or at rest, or some things being always in motion and the 
remainder always at rest, there are things that are some - ^ 
times in motion and sometimes no t ? The cause of this is 
now plajn : it is becaus e, while some things are moved b y 
a n eternal unmoved moven t and are t herefore alway s 
in motion,* other things are moved by a mQvenMhaLisJn^5 
Qiotion and cha nging, so that they too must change. But 
the unmoved movent, as. has been said, since it remains 
perman ^ tly simple and unvaryi ng^and in the same state, 
will cause motion that is one and simple. 

^ e. g. any one of the heavenly bodies. 

^ sc. 6 ovpavos^ which imparts motion to terrestrial things through 
the medium of the various heavenly bodies. I see no reason to depart 
from the reading adopted by Bekker with most MSS. : to my mind 
this reading will account for the reading of K and of Simplicius 
(adopted by Prantl) rh di Kivovfievov vno tov aKivr^rov ^ Kivovfieuov more 
easily than vice versa, 

^ Chapter 3. 

* Reading in 1. 15 5t6 del Kimrat, with EK Them. Phil. Simp. 


20 This matter will be made clearer, however, if we start 7 
afresh from another point. We must consider whether it 
is or is not possible that there should be a continuous 
motion, and, if it is possible, which this motion is, and 
which is the primary motion : for it is plain that if there 
must always be motion, and a particular motion is primary 

25 and continuous, then it is this motion that is imparted by 
the first movent, and so it is necessarily one and the same 
and continuous and primary. 

Now of the three kinds of motion that there are — motion 
in respect of magnitude, motion in respect of affection, and 
motion in respect of place — it is this last, which we call 
locomotion, that must be primary. This may be shown as 
follows. It is impossible that there should be increase 

30 without the previous occurrence of alteration : for that 
which is increased, although in a sense it is increased by 
what is like itself, is in a sense increased by what is unlike 
itself: thus it is said that contrary is nourishment to 
contrary : ^ but growth is effected only by things becoming 
like to like. There must be alteration, then, in that there 
260^ is this change from contrary to contrary. But the fact 
that a thing is altered requires that there should be some- 
thing that alters it, something e.g. that makes the potentially 
hot into the actually hot : so it is plain that the movent 
does not maintain a uniform relation to it but is at one 
time nearer to and at another farther from that which is 
5 altered : and we cannot have this without locomotion. If, 
therefore, there must always be motion, th ere must alsQ 
always be locom otion as the primary motion, and, if there 
is a primary as distinguished from a secondary form of loco- 
motion, it must be the primary form. Again, all affections 
have their origin in condensation and rarefaction : thus 

10 heavy and light, soft and hard, hot and cold, are con- ^ 
sidered to be forms of density and rarity. But condensa- ^ 
tion and rarefaction are nothing more than combination 
and separation, processes in accordance with which sub- 
stances are said to become and perish : and in being com- 
bined and separated things must change in respect of place. 
^ Cf. De An, ii. 4. 416*21 sqq. 

BOOK VIII. 7 260^ 

And further, when a thing is increased or decreased its 
magnitude changes in respect of place. 

Again, there is another point of view from which it will 15 
be clearly seen that locom otion is primary. As in the case 
of other things so too in the case of motion the word 
* primary ' may be used in several senses. A thing is said 
to be prior to other things when, if it does not exist, the 
others will not exist, whereas it can exist without the 
others: and there is also priority in time and priority in 
perfection of existence. Let us begin, then, with the first 
sense. Now there must be motion continuously, and there 20 
may be continuously either continuous motion or successive 
motion, the former, however, in a higher degree than the 
latter: moreover it is better that it should be continuous 
rather than successive motion, and we always assume the 
presence in nature of the better, if it be possible: since, 
then, continuous motion is possible (this will be proved 
later : ^ for the present let us take it for granted), and no 
_other motion can be contin uous except locomotion, I0CO335 
mo tion must be primary . For there is no necessity for the 
subject of locomotion to be the subject either of increase or 
of alteration, nor need it become or perish : on the other 
hand there cannot be any one of these processes without 
the existence of the continuous motion imparted by the 
first movent. 

Secondly, locomotion must be primary in time : for this 
is the only motion possible for eternal things. It is true 30 
indeed that, in the case of any individual thing that has 
a becoming, locomotion must be the last of its motions: for 
after its becoming it first experiences alteration and increase, 
and locomotion is a motion that belongs to such things 
only when they are perfected. But there must previously 261* 
be something else that is in process of locomotion to be the 
cause even of the becoming of things that become, without 
itself being in process of becoming, as e. g. the begotten is 
preceded by what begot it : otherwise becoming might be 
thought to be the primary motion on the ground that the 
thing must first become. But though this is so in the case 5 
^ Chapters. 


of any individual thing that becomes, nevertheless before 
anything becomes, something else must be in motion, not 
itself becoming but being, and before this there must again 
be something else. And since becoming cannot be primary — 
for, if it were, everything that is in motion would be perish- 
able — it is plain that no one of the motions next in order 

lo can be prior to locomotion. By the motions next in order 
I mean increase and then alteration, decrease, and perishing. 
All these are posterior to becoming : consequently, if not 
even becoming is prior to locomotion, then no one of the 
other processes of change is so either. 

Thirdly, that which is in process of becoming appears 
universally as something imperfect and proceeding to a first 
principle : and so what is posterior in the order of becoming 
is prior in the order of nature. Now all things that go 
through the process of becoming acquire locomotion last. 

15 It is this that accounts for the fact that some living things, 
e. g. plants and many kinds of animals, owing to lack of 
the requisite organ, are entirely without motion, whereas 
others acquire it in the course of their being perfected. 
Therefore, if the degree in which things possess locomotion 
corresponds to the degree in which they have realized their 
natural development, then this motion must be prior to all 

20 others in respect of perfection of existence : and not only 
for this reason but also because a thing that is in motion 
loses its essential character less in the process of locomotion 
than in any other kind of motion : it is the only motion 
that does not involve a change of being in the sense in 
which there is a change in quality when a thing is altered 
and a change in quantity when a thing is increased or 
decreased. Above all it is plain that this motion, motion 
in respect of place, is what is in the strictest sense produced 

25 by that which moves itself; but it is the self-movent that 
we declare to be the first principle of things that are moved 
and impart motion and the primary source to which thing 
that are in motion are to be referred. 

It is clear, then, from the foregoing arguments that loco- 
m otion is the primary motion. We have now to show 
which kind of locomotion is primary. The same process 




BOOK VIII. 7 261^ 

of reasoning will also make clear at the same time the 
truth of the assumption we have made both now and at 
a previous stage ^ that it is poss ible that there should be 30 
a motion that is continuous an d eternal. N uw it i& cluar 
Trom the following considerations t hat no other than loco- 
mot ion can be continuous. Every other motion and change 
is from an opposite to an opposite : thus for the processes 
of becoming and perishing the limits are the existent and 
the non-existent, for alteration the various pairs of contrary 
affections, and for increase and decrease either greatness 35 
and smallness or perfection and imperfection of magnitude : 
and changes to the respective contraries are contrary 
changes. Now a thing that is undergoing any particular 261^ 
kind of motion, but though previously existent has not 
always undergone it, must previously have been at rest so 
far as that motion is concerned. It is clear, then, that for 
the changing thing the contraries will be states of rest.^ 
And we have a similar result in the case of changes that 
are not motions : ^ for becoming and perishing, whether 
regarded simply as such without qualification or as affect- 
ing something in particular, are opposites : therefore pro- 5 
vided it is impossible for a thing to undergo opposite 
changes at the same time, the change will not be continuous, \ 
but a period of time will intervene between the opposite 
processes. The question whether these contradictory 
changes are contraries or not makes no difference, provided 
only it is impossible for them both to be present to the 
same thing at the same time : the point is of no importance 
to the argument.* Nor does it matter if the thing need 10 
not rest in the contradictory state, or if there is no state of 
rest a^ a contrary to the process of change : ^ it may be true 

^ 253a 29. Omit the second r6 in 1. 29, with EK Simp. 

^ Hence the Kivrja-is in question cannot be a-wexfjs!. 

'It seems necessary to translate fifra^oXav here in this way: Aristotle 
has been dealing with nera^oXai all along, but so far only with such of 
them as are also Kiptjaeis : he now extends his results to include 
ficra/SoXai that are not Ki.vr)a(ts in the strict sense, namely yeveais and 
(fiOopd, which also proceed from duuKeifitvov to avriKeifuvov, though in 
this case the dvTiKdniva are not ivavria. 

* Reading in 1. 10 Xoyo). Bekker's oXw is apparently a mere slip. 

^ Reading in 1. 11 ^era/SoXry hp^iiia^ with HI. 


that the non-existent is not at rest, and that perishing is 
a process to the non-existent. All that matters is the 
intervention of a time : it is this that prevents the change 
from being continuous : so, too, in our previous instances ^ 
the important thing was not the relation of contrariety but 
the impossibility of the two processes being present to 

15 a thing at the same time. And there is no need to be 
disturbed by the fact that on this showing there may be 
more than one contrary to the same thing, that a particular 
motion will be contrary both to rest and to motion in the 
contrary direction. We have only to grasp the fact that 
a particular motion is in a sense the opposite both of 
a state of rest and of the contrary motion, in the same way 
as that which is of equal or standard measure is the 
opposite both of that which surpasses it and of that which 

20 it surpasses, and that it is impossible for the opposite 
motions or changes to be present to a thing at the same ^ 
time. Furthermore, in the case of becoming and perishing m 
it would seem to be an utterly absurd thing if as soon as 
anything has become it must necessarily perish and cannot 
continue to exist for any time: and, if this is true of 
becoming and perishing, we have fair grounds for inferring 

25 the same to be true of the other kinds of change, since it 
would be in the natural order of things that they should be 
uniform in this respect. 

Let us now proceed to maintain that it is possible that 8 
there should be an infinite motion that is single and con- 
tinuous, and that this motion is rotato ry motion. The 
motion of everything that is in process of locomotion is 
either rotatory or rectilinear or a compound of the two : 
consequently, if one of the former two is not continuous, 
30 that which is composed of them both cannot be continuous 
either. Now it is plain that if the locomotion of a thing is 
rectilinear and finite it is not continuous locomotion : for 
the thing must turn back , and that which turns back in 
a straight line undergoes two contrary locomotions, since, 
so far as motion in respect of place is concerned, upward 

^ sc. the instances of Kivr)<Teis given above. 

BOOK VIII. 8 261^ 

motion is the contrary of downward motion, forward motion 
of backward motion, and motion to the left of motion to 35 
the right, these being the pairs of contraries in the sphere 
of place. But we have alread y^ defined single and con- 262^ 
tinuous motion to be motion of a single thing in a single 
period ot time and operating within a sphere admitting of 
no further specific differentiation (for we have three things 
to consider, first that which is in motion, e.g. a man or 
a god, secondly the * when' of the motion, that is to say, 
the time, and thirdly the sphere within which it operates, 
which may be either place or affection or essential form or 
magnitude) : and contraries are specifically not one and the 5 
same but distinct : and within the sphere of place we have 
the above-mentioned distinctions. Moreover we have an 
indication that motion from A to B is the contrary of 
motion from B to A '-^ in the fact that, if they occur at the 
same time, they arrest and stop each other. And the 
same is true in the case of a circle : the motion from A 
towards B is the contrary of the motion from A towards T ^ : 
for even if they are continuous and there is no turning back 10 
they arrest each other,^ because contraries annihilate or 
obstruct one another. On the other hand lateral motion 
is not the contrary of upward motion.^ But what shows 
most clearly that rectilinear motion cannot be continuous , 
is the fact that turning back necessarily implies coming to 
a stand, not only when it is a straight line that is traversed, 
but also in the case of locomotion in a circle (which is 15 
not the same thing as rotatory locomotion: for, when 
a thing merely traverses a circle, it may either proceed on 
its course without a break or turn back again when it has 
reached the same point from which it started). We may 
assure ourselves of the necessity of this coming to a stand 

A » < B ^ 


* Reading in 11. 10, 11 commas after yap and dvdKaiMyjris. 
° sc. here we haveithe opposite conclusion from the fact that these 
two motions do not interfere with each other. 


not only on the strength of observation, but also on 
theoretical grounds. We may start as follows : we have 
three points, starting-point, middle-point, and finishing- 

20 point, of which the middle-point in virtue of the relations 
in which it stands severally to the other two is both a 
starting-point and a finishing-point, and though numerically 
one is theoretically two. We have further the distinction 
between the potential and the actual. So in the straight 
line in question any one of the points lying between th< 
two extremes is potentially a middle-point : but it is no| 
actually so unless that which is in motion divides th< 
line by coming to a stand at that point and beginning i1 

35 motion again : thus the middle-point becomes both 
starting-point and a goal, the starting-point of the lattei 
part and the finishing-point of the first part of the motioi 
This is the case e. g. when A in the course of its locomo^ 
tion comes to a stand at B and starts again towards F 
but when its motion is continuous A cannot either hav( 
come to be or have ceased to be at the point B : it cai 

30 only have been there at the moment of passing, its passag< 
not being contained within any period of time except 
the whole ^ of which the particular moment is a dividing-^ 
point. To maintain that it has come to be and ceased t< 
be there will involve the consequence that A in the coun 
of its locomotion will always be coming to a stand : for it 
262^ is impossible that A should simultaneously have come t< 
be at B and ceased to be there, so that the two things musj 
have happened at different points of time, and therefore 
there will be the intervening period of time : consequently' 
A will be in a state of rest at B, and similarly at all other 
points, since the same reasoning holds good in every case. 
5 When to A, that which is in process of locomotion, B, the 
middle-point, serves both as a finishing-point and as a 
starting-point for its motion, A must come to a stand at B, 
because it makes it two just as one might do in thought. 
However, the point A is the real starting-point at which ^ 
the moving body has ceased to be, and it is at T that it ^ 

^ Omitting r<S ABF in 1. 31, with EK. 

BOOK VIII. 8 26a* 

has really come to be when its course is finished and it 
comes to a stand. So this is how we must meet the diffi- 
culty that then arises, which is as follows. Suppose the line 10 
E is equal to the line Z, that A proceeds in continuous loco- 
motion from the extreme point of E to T, and that, at the 
moment when A is at the point B, A is proceeding in 
uniform locomotion and with the same velocity as A from 
the extremity of Z to H : ^ then, says the argument, A will 
have reached H before A has reached T : for that which 
makes an earlier start and departure must make an earlier 
arrival : the reason, then, for the late arrival of A is that 15 
it has not simultaneously come to be and ceased to be at 
B : otherwise it will not arrive later : for this to happen it 
will be necessary that it should come to a stand there. 
Therefore we must not hold that there was a moment 
when A came to be at B and that at the same moment A 
was in motion from the extremity of Z : for the fact of A's 
having come to be at B will involve the fact of its also 20 
ceasing to be there, and the two events will not be simul- 
taneous, whereas the truth is that A is at B at a sectional 
point of time and does not occupy time there. In this 
case, therefore, where the motion of a thing is continuous,^ 
it is impossible to use this form of expression.^ On the 
other hand in the case of a thing that turns back in its 
course we must do so. For suppose H in the course of its 
locomotion proceeds to A and then turns back and proceeds 
downwards again : * then the extreme point A has served 


"^ The MSS. in 1. 22 vary between r^y a-wexovs (sc. Kivrjaeas) and 
Tov (Tvvexovs (Bekker) with which it is difficult to see what word 
to supply. I suspect the true reading to be tov a-wcx^s (sc. kipov- 


^ sc. to speak of it as yeyovos at any intermediate point. 


as finishing-point and as starting-point for it, one point thus 
25 serving as two : therefore H must have come to a stand 
there : it cannot have come to be at A and departed from 
A simultaneously, for in that case it would simultaneously 
be there and not be there at the same moment. And here 
we cannot apply the argument used to solve the difficulty 
stated above : we cannot argue that H is at A at a sectional 
point of time and has not come to be or ceased to be there. 
30 For here the goal that is reached is necessarily one that is 
actually, not potentially, existent. Now the point in the 
middle is potential : but this one is actual, and regarded 
from below it is a finishing-point, while regarded from 
above it is a starting-point, so that it stands in these 
263^ same two respective relations to the two motions.^ There- 
fore t hat which turns back in traversing a rectili near 
course must in so doing come to a stand. Consequently 
there cannot be a continuous rectilinear motion that is 

The same method should also be adopted in replying to 
5 those who ask, in the terms of Zeno's argument,^ whether 
we admit that before any distance can be traversed half 
the distance must be traversed, that these half-distances 
are infinite in number, and that it is impossible to traverse 
distances infinite in number — or some on the lines of this 
same argument put the questions in another form, and 
would have us grant that in the time during which a motion 
is in progress it should be possible to reckon a half-motion 
before the whole for every half-distance that we get, so that 
we have the result that when the whole distance is traversed 
10 we have reckoned an infinite number, which is admittedly 
impossible. Now when we first discussed the question of 
motion we put forward a solution * of this difficulty turning 

^ i. e. it is TeXevrrj in relation to the first (upward) part of the motion 
(up to A) and dpxr) in relation to the second (downward) part (down 
from A). 

^ Reading in I. 3 enl rrjs evdcias didiov. Bekker's reading eVt diSiop 
T^s ev6eias is apparently a mere slip. 

3 Kai d^iovvras in 1. 5 seems to be a gloss introduced under the 
influence of d^iovvres, 1. 7. 

* vi. 2. 233^21 sqq., and vi. 9. 

BOOK VIII. 8 263^ 

on the fact that the period of time occupied in traversing 
the distance contains within itself an infinite number of 
units: there is no absurdity, we said, in supposing the 
traversing of infinite distances in infinite time, and the 
element of infinity is present in the time no less than in 
the distance. But, although this solution is adequate as 15 
a reply to the questioner (the question asked being whether 
it is possible in a finite time to traverse or reckon an infinite 
number of units), nevertheless as an account of the fact and 
explanation of its true nature it is inadequate. For suppose 
the distance to be left out of account and the question asked 
to be no longer whether it is possible in a finite time to 
traverse an infinite number of distances, and suppose that 20 
the inquiry is made to refer to the time taken by itself (for 
the time contains an infinite number of divisions) : then 
this solution will no longer be adequate, and we must apply 
the truth that we enunciated in our recent discussion, stating 
it in the following way. In the act of dividing the con- 
tinuou s distance i nto two halves one point is treated as 
two, since we make it a startmg-pomt and a finishing-point : 
and this same result is also produced by the act of reckon- 25 
ing halves as well as by the act of dividing into halves. 
But if divisions are made in this way, neither the distance 
nor the motion will be continuous : f o r motion if it is to be 
continuous must relate t o what is continuous: and though ^ 
what is co ntinuous contains anlnfinite number of halves, 
they are not actual but potential halves. If the halves 
ar e made actual, we shall get not a continuous but an 
intermittent motion. In the case of reckoning the halves, 30 
it is clear that this result follows : for then one point 
must, be^jec koned as two : it will be the tinishing-poirvrof263^ 
the one half and the starting-point of the other, if we 
reckon not the one continuous whole but the two halves. 
Therefore to the question _jvhether it is possible to pass 
through an infinite number of units either of time or of 
distance we must reply that in a sense it is and in a sense it 
is not. If the units are actual, it is not possible : if t hey a re? 
potential, it is possible. For in the course of a continuous 
^motion the traveller has traversed an infinite number of 

263*^ PHYSICA 

units in an accidental sense but not in an unqualified sense : 
for though it is an accidental characteristic of the distance 
to be an infinite number of half-distances, this is not its 
real and essential character. It is also pl ain that_u nless 

lo we hold that the point of time' that divides earlier from 
later always belongs only to the later so far as the thing is 
concerned, we shall be involved in the consequence that 
the same thing is at the same moment existent and not 
existent, and that a thing is not existent at the moment 
when it has become. It is true that the point is common 
to both times, the earlier as well as the later, and that, 
while numerically one and the same, it is theoretically not 
so, being the finishing-point of the one and the starting-point 
of the other : but so far as the thing is concerned it belongs 

15 to the later stage of what happens to it. Let us suppose 
a time ABr^ and a thing A, A being white in the time A 
and not-white in the time B. Then A is at the mo ment_r 
white and not- white : for if we were right in saying that it is 
white during the whole time A, it is true to call it white at 
any moment of A, and not-white in B, and T is in both A 

ao and B. We must not allow, therefore, that it is white in 
the whole of A, but must say that it is so in all of it except 
the last moment F. T belongs already to the later period,^ 
and if in the whole of A not- white was in process of becom- 
ing and white of perishing, at T the process is complete. 
And so r is the first moment at which it is true to call the 
thing white or not-white respectively.^ Otherwise a thing 
gjnayjbe non-existent at the moment when it has become 
and existent at the moment when it has perished : or else 

2 ^ it must be possible for a thing at the same time to be white 
and not white and in fact to be existent and n on-existent. 
Further, if anythitlg Ihafexists after having been previously 
non-existent must become existent and does not exist when 
it is becoming, time cannot be divisible into time-atoms. 

* Reading in 1. 15 AFB. Bekker has ABr, apparently a slip. The 
first and third letters denote periods of time, the second the moment 
that divides them. 

^ Reading in 1. 21 toO varepov, with (apparently) Phil. Simp. 

^ Only the latter case has been mentioned above. 

BOOK VIII. 8 a63*> 

For suppose that A was becoming white in the time A and 
that at another time B, a time-atom consecutive with the last 
atom of A, A has already become white and so is white at 
that moment : then, inasmuch as in the time A it was 30 
becoming white and so was not white and at the moment B 
it is white, there must have been a becoming beween A 
and B and therefore also a time in which the becoming 
took place. On the other hand, those who deny atoms of 264* 
time (as we do) are not affected by this argument : accord- 
ing to them A has become and so is white at the last point 
of the actual time in which it was becoming white : and this 
point has no other point consecutive with or in succession 
to it, whereas time-atoms are conceived as successive. More- 
over it is clear that if A was becoming white in the whole 
time A, the time occupied by it in having become white in 5 
addition to having been in process of becoming white is no 
more than all that it occupied in the mere process of 
becoming white.^ 

These and such-like, then, are the arguments for our 
conclusion that derive cogency from the fact that they 
have a special bearing on the point at issue. If we look at 
the question from the point of view of general theory, the 
same result would also appear to be indicated by the 
following arguments. Everything who se motion is con- 
tinuous must , on arriving at any point m the course of its 10 
locomotion, have been previo usly also in process of loco- 
motion to that point, if it is not torced out ot its path by 
anything : e. g. on arriving at B a thing mu st also have 
been in proc ess of locomotion^to B, and that not merely 
when it was near to B, but from the moment of its starting 
on its course, since there can be no reason for its being so 
at any particular stage rather than at an earlier one. So, 
too, in the case of the other kinds of motion. Now we are 
to suppose that a thing proceeds in locomotion from A to 
r and that at the moment of its arrival at F the continuity 15 
of its motion is unbroken and will remain so until it has 

^ sc. and therefore t6 ev a yeyove cannot be xpo»'o$'j since it makes no 
addition to the total : it is merely a (rrjfidov xpovov. 

648-ie R 

264* PHYSIC A 

arrived back at A. Then when it is undergoing locomo- 
tion from A to r it is at the same time undergoing 
also its locomotion to A from F : consequently it is simul- 
taneously undergoing two contrary motions, since the 
two motions that follow the same straight line are contrary 
to each other. With this consequence there also follows 
another : we have a thing that is in process of change from 
a position in which it has not yet been : so, inasmuch as 
this is impossible, the thing must come to a stand at T. 

20 Therefore the motion is not a single motion, since m otion 
that is interrupted by stationariness is not single. 

Further, the following argument will serve better to 
make this point clear universally in respect of every kind 
of motion. If the motion undergone by that which is in 
motion is always one of those already enumerated, and the 
state of rest that it undergoes is one of those that are 
the oppositcs of the motions (for we found ^ that there 
could be no other besides these), and moreover that which 
is undergoing but does not always undergo a particular 

25 motion (by this I mean one of the various specifically 
distinct motions, not some particular part of the whole 
motion) must have been previously undergoing the state 
of rest that is the opposite of the motion, the state of rest 
being privation of motion ; ^ then, inas much as the tw o 
motions that follow the same straight line are contrary 
^motions, a n d it is impossible for a thing to underg o 
simultaneously two contrary motions, that which is under- 

30 going locomotion from A to T cannot also simultaneously 
be undergoing locomotion from T ^ to A : and since the 
latter locomotion is not simultaneous with the former but 
is still to be undergone, before it is undergone there 
must occur a state of rest at T : for this, as we found,* is 
the state of rest that is the opposite of the motion from F. 
The foregoing argument, then, makes it plain that the 
motion in question ^ is not continuous. 

^ V. 2. 

' Reading in 1. 28 a colon before d, with Bonitz. 

^ Reading in 1. 30 r. Bekker's A is apparently a mere slip. 

* V. 6. 229^ 28 sqq. 

* SC. 17 en\ rrjs evdeias. 

BOOK VIII. 8 264* 

Our next argument has a more special bearing than the 264^ 
foregoing on the point at issue. We will suppose that 
there has occurred in something simultaneously a perishing 
of not-white and a becoming of white. Then if the altera- 
tion to white and from white is a continuous process and 
the white does not remain any time, there must have 5 
occurred simultaneously a perishing of not-white, a be- 
coming of white, and a becoming of not -white: for the 
time of the three will be the same. 

Again, from the continuity of the time in which the 
motion takes place we cannot infer continuity in the motion, 
but only successiveness : in fact, how could contraries, 
e. g. whiteness and blackness, meet in the same extreme 
point ? ^ 

On the other hand, in motion o n a circular line we shall 
find singleness and continuity : ior here we are met by no 
impossible consequence: that which is in motion from A 10 
will in virtue of the same direction of energy be simul- 
taneously in motion to A (since it is in motion to the point 
at which it will finally arrive), and yet will not be undergoing 
two contrary or opposite motions : for a motion to a point 
and a motion from that point are n ot always con traries or 
opposites : they are contraries only if they are on the same ^ 
straight line (for then they are contrary to one another in 15 
respect of place, as e. g. the two motions along the diameter 
of the circle, since the ends of this are at the greatest 
possible distance from one another), and they are oppo- 
sites only if they are along the same line.^ Therefore 
in the case we are now considering there is nothing to 
prevent the motion being continu ous and free from all 
intermission : for rotatory motion is motion of a thing from _ 
its place to its place,'^ whereas rectilinear motion is motion a o 
from its place t o another place. 

^ sc. as would be necessary if there is to be a-wexa-a between the 
two contrary processes. 

^ i. e. they must traverse the same course in opposite directions, 
though their dpx^ and reXfVTT] need not be nXelarop dnexovcrai as in the 
case of ivavTiai Kivrja-fis, which, however, are of course included in the 
term avriKeifievai. 

^ Reading in U. 18-19 «*'^ «^^o- 

64516 R 2 


264^ PHYSIC A 

Moreover the pr ogress of rotatory motion is never 
^localized within certain fixed limits, whereas that of recti- 
linear motion repeatedly is so.^ Now a motion that is 
always shifting its ground from moment to moment can be 
continuous : but a motion that is repeatedly localized within 
certain fixed limits cannot be so, since then the same thing 
would have to undergo simultaneously two opposite 
motions. So, too, there cannot be continuous motion in 

25 a semicircle or in any other arc of a circle, since here also 
the same ground must be traversed repeatedly and two 
contrary processes of change must occur. The reason is 
t hat in these motions the sta rting-point and the termina- 
tion d o not coincide , where as m motion over a circle the y 
do coincide, and so this is the only perfect motion.^ 

This differentiation also provides another means of show- 
ing that the other kinds of motion cannot be continuous 

30 eithe r : for in all of them we find that there is the same 
ground to be traversed repeated TNT: thus in alteration there 
are the intermediate stages of the process, and in quantita- 
tive change there are the intervening degrees of magnitude : 
and in becoming and perishing the same thing is true. It 
makes no difference whether we take the intermediate 
stages of the process to be few or many, or whether we 
265* add or subtract one : for in either case we fin d tha t there 
is still the same ground to be traversed repeatedly . More- 
over it is plain from what has been said that those ghysicists_ 
who assert that all sensible things are always in motion 
are wrong: for their motion must be one or other of the 

~5 matTonrjust mentioned : in fact they mostly conceive it as 
alteration (thi ngs are always in flux an d decay, they say), 
and they go so far as to speak even of becoming and 
perishing as a process of alteration. On the other hand, 
our argument has enabled us to assert the fact, applying 
universally to all motions , that no motion admits of con- 
tinuity except rotatory motion : consequently neither aJtera- 

^ i. e. the apxh and TeXevrf) of the line are fixed extreme points, and 
the motion is repeatedly taking place between them, whereas on the 
circle there are no such points. 

^ Because finite lines may be extended, whereas a circle is once for 
all complete. 


BOOK VIII. 8 265* 

tion nor in crease^ admits of continuity^ _ We neeci now say 10 
no more in support of the position th at there is no process 
of ch ange that admits of infinity or continuity except 
rotatory locomotion . 

9 It can now be shown plainly that rotation is the primary 

loc o motion. Every locomotion, as we said before,'^ is eithe"? 

rot atory or rectilinea r or a compound of the two : and the 15 

two Yormer must be prior to the last, since they are the 

elements of which the latter consists. Moreover rotatory 

locomotion is prior to re ctilinear locomotion, b ecause it is 

more simple and complete, wnich may be shown as follows. 

The straight ime traversed, in rectilinear motion cannot be 

infinite: for there is no such thing as an infinite straight 

line ; and even if there were, it would not be traversed by 

anything in motion : for the impossible does not happen 

and it is impossible to traverse an infinite distance. On 20 

the other hand rectilinear motion on a finite straight line is 

if it turns back a composite motion, in fact two motions, 

while if it does not turn back it is incomplete and perishable : 

and in the order of nature, of definition, and of time alike 

the complete is prior to the incomplete and the imperishable 

to the perishable. Again, a motion tha t admits of being 

eternal is prior to one that does not. Now_rotatory motion 25 

can be eternal : b^t ^ other motion, whether locomotion 

or motion of any other kind, can be so, sin ce in all of them 

rest must occur, and with the occurrence of rest the motion 

has perished. Moreover the result at which we have 

arrived, that rotatory motion is single and continuous , and 

rectilinear motion is not, is a reasonable one. I n rectilinear 

motion we have a definite start ing-point , finis hing-point, 

and middle^point, which all have their place in it in such 30 

a way that there is a point from which that which is in 

motion can be said to start and a point at which it can be 

said to finish its course (for when anything is at the limits 

of its course, whether at the starting-point or at the 

finishing-point, it must be in a state of rg st^)- On the 

^ av^rja-is and (jidiaris regarded as one process. 

2 Ch. 8. 261^ 28. 

^ And therefore the motion must have limits. 


other hanf^ in rtmilar motion there are no such definite 
points : for why should any one point on the l ine be a limit 
rather than any other i* Any one point as much as any 
other is alike starting-point, middle-point, and finishing- 
point, so that we can say of certain things ^ both that they 
are always and that they never are at a starting-point and 
265^ at a finishing-point (so that a revolving sphere, while it is 
in motion, is also in a sense at rest, for it continues to 
occupy the same place). The reason of this is that in 
this case all these characteristics belong to the centre : that 
is to say, the centre is a like starting-pointy middle-poin t, 
an d finishing^ point of the space traversed ; consequently 

5 since this point is not a point on the circular line, th ere is 
no point at which that which is in process of locomotion 
ca n be in a sta te of rest as havin g traversed its course, 
because in its locomotion it is proceeding always about 
a central po int and not to an extreme point : therefore it 
remains still, and the wKole is in a sense always a t rest a s 
well ^as^ continuously in niotion? Our next point gives 
a convertible result : on the one hand, because rotation is 
the measure ^ of motions it must be the primary motion 

10 (for all things are measured by what is primary) : on the 
other hand, because rotation is the primar y motion it is 
the measure of all other motions. Again, rotatory motion^ 
is also the only motion that admits of bei n^ regular. In 
rectilinear locomotion the motion of things in leaving the 
starting-point igjiot uniform with their motion in approach- 
ing the finishing-point, since the velocity of a thing always 
increases proportionately as it removes ^ itself farther from 
its position of rest : on the other hand rotatory motion is 
the only motion whose course is natur ally such that'll has 

i fijio starting-point or finishing-point in itself but is determined 
from elsewhere. 

As to locomotion being the primary motion, this is 

^ sc. things that rotate about an axis. 

^ Cf. iv. 14. 223^ 19 sqq. 

^ I translate ac^ior/^rat as a true middle in order to bring out the 
fact that this remark refers only to things that are in motion Kara 
<t>v(Tiv : the motion of things that are moved napa ^vcriv^ e. g. of a stone 
thrown upwards, becomes slower : cf. v. 6. 230^ 23 sqq. 


BOOK VIII. 9 265* 

a truth that is attested by all who have ever made mention 
of motion in their theories : they all assign their first prin- 
ciples of motion to things that impart motion of this kind. 
Thus ' separation ' and ' combination ' are motions in respect 
of place, and the motion! imparted by 'Love' and 20 

* Strife ' ^ takes these forms, the latter ' separating ' and the 
former * combining '. Anaxagoras, too, says that * Mind ', 
his first movent, ' separates '. Similarly those ^ who assert 
no cause of this kind but say that ' void ' accounts for 
motion — they also hold that the motion of natural sub- 25 
stance is motion in respect of place : for their motion that 

is accounted for by * void ' is locomotion, and its sphere of 
operation may be said to be place. Moreover they are 
of opinion that the primary substances are not subject to 
any of the other motions, though the things that are com- 
pounds of these substances are so subject : the processes 
of increase and decrease and alteration, they say, are effects 
of the ' combination ' and ' separation ' of * atoms *. It is 30 
the same, too, with those who make out that the becoming 
or perishing of a thing is accounted for by * density ' or 

* rarity ' : * for it is by ' combination ' and * separation ' that 
the place of these things in their systems is determined. 
Moreover to these we may add those who make Soul the 
cause of motion : * for they say that things that undergo 
motion have as their first principle 'that which moves 
itself ' : and when animals and all living things move them- 
selves, the motion is motion in respect of place. Finally it 266^ 
is to be noted that w e^ say that a thing * is in motion ' in 

the strict sen se of the term onl y when its motion is motion 

inj^espect of place: if a thincr 15; fn prr >rpt;t; r>f jrirr^ac e or 

decr ease or is undergoing some alteration while rem aining 

at rest in the same place , we say that it is in motion _ia- 

some particular respe ct : we do not say that it * is ii LPiQtiQn ' 

jwithout Qualification. 5 

Our present position, then, is this : We have argued that 

^ The motive forces in the system of Empedocles. 
"^ Leucippus and Democritus. 

^ The early Ionian school : Thales, Anaximenes, and Heraclitus, 
the last two of whom are known to have employed these terms. 
* Plato and the Platonists. 


there always was motion and al ways will be f pntinn 
throughout all time, and we have explained what is the 
first principle of this eternal motion : we have explained 
further which is the primar y motion^ and which is the only 
moti on tK a t can be etern al : and we have pronounced thelirst 
movent to be unmoved. 

lo We have now to assert that the first movent must be 
without parts and w itho ut ma^nitudeyS ep^innin^ with the lo 
establishment of the premisses on which this conclusion 

One of these premisses is that nothing finite can cause 
motion during an infinite time. We have three things, the 
movent, the moved, and thirdly that in which the motion 
takes place, namely the time: and these are either all 
infinite or all finite or partly — that is to say two of them 

15 or one of them — finite and partly infinite. Let A be the 
movent, B the moved, and T the infinite time. Now let us 
suppose that A ^ moves E, a part of B. Then the time occu- 
pied by this motion cannot be equal to T : for the greater 
the amount moved, the longer the time occupied.^ It 
follows that the time Z ^ is not infinite. Now we see 
that by continuing to add to A I shall use up A and 

20 by continuing to add to E I shall use up B : but I shall 
not use up the time by continually subtracting a corre- 
sponding amount from it, because it is infinite. Conse- 
quently the duration of the part of T which is occupied by 
all A in moving the whole of B, will be finite. Therefore 
a finite thing cannot impart to anything a n infinite m otion^ 
It is clear, then, that it is impossible for th e finite to cause 
motion during an infinite time. 

25 It has now to be shown that i n no case is it possible for . 
an infinite force to reside in a finite magnitude. This can 
be shown as follows : we take it for granted that the greater 
force is always that which in less time than another does 
an equal amount of work when engaged in any activity — 

^ sc. a part'of A. 

^ Clearly A must be a larger fraction of A than E is of B. 
^ The time occupied by A in moving E to the same extent as B is 
moved by A. Read in 1. 19 6 to Z. 

BOOK VIII. lo a66» 

in heating, for example, or sweetening or throwing ; in fact, 
in causing any kind of motion. Then that on which the 
forces act must be affected to some extent by our supposed 
finite magnitude possessing an infinite force as well as by 
anything else, in fact to a greater extent than by anything 
else, since the infinite force is greater than any other. But 30 
then there cannot be any time in which its action could 
take place. Suppose that A is the time occupied by the 
infinite power in the performance of an act of heating or 
pushing, and that AB^ is the time occupied by a finite 
power in the performance of the same act : then by adding 
to the latter another finite power and continually increasing 266^ 
the magnitude of the power so added I shall at some time or 
other reach a point at which the finite power has completed 
the motive act in the time A : for by continual addition to 
a finite magnitude I must arrive at a magnitude that 
exceeds any assigned limit, and in the same way by con- 
tinual subtraction I must arrive at one that falls short of 
any assigned limit. So we get the result that the finite 
force will occupy the same amount of time in performing 
the motive act as the infinite force. But this is impossible. 5 
Therefo re nothing finite can possess an infinite force. So 
it is also impossible fora finite force to reside in an infinite 
mag nitude. It is true that a greater force can reside in 
a lesser magnitude : but the superiority of any such greater 
force can be still greater if the magnitude in which it resides 
is greater. Now let AB be an infinite magnitude. Then 
Br ^ possesses a certain force that occupies a certain time, 
let us say the time EZ,^ in moving A. Now if I take 10 
a magnitude twice as great as BF, the time occupied by 
this magnitude in moving A will be half of EZ (assuming 
this to be the proportion *) : so we may call this time ZH. 
That being so, by continually taking a greater magnitude 
in this way I shall never arrive at the full AB, whereas 

^ Reading in 1. 33 iv t<§ fi' AB, with Simplicius. 

^ sc. a part of AB. 

^ E being presumably the time occupied by AB in moving A. 

* He assumes that the force increases proportionately to the 
magnitude, so that the time decreases proportionately. This simpli- 
fies the argument, though of course it is not essential to it. 

266'' PHYSICA 

I shall always be getting a lesser fraction of the time '^ 
originally given. Therefore the force must be infinite, 

15 since it exceeds any finite force. Moreover the time 
occupied by the action of any finite force niust also Tje 
finite : for if a given force moves something in a certain 
time, a greater force will do so in a lesser time, but still 
a definite time, in inverse proportion.^ B ut a force mus t 
always be infinite — just as a number or a magnitude is — if 

30 It exceeds all definit e limits. This point may also be 
proved in another way — by taking a finite magnitude in 
which there resides a force the same in kind as that which 
resides in the infinite magnitude, so that this force will 
be a measure of the finite force residing in the infinite 

25 It is plain, then, from the foregoing arguments that it is 
impn<;<;ih|fi ff>r an ir^f^nifp fpf^^ e to reside in a finite ma^ ai- 
tude or fnr a finitf* fnrre- t o res j^e in an infinite magnitude. 
But before proceeding to our conclusion it will be well to 
discuss a difficulty that arises in connexion with locomotion. 
If everything that is in motion w ith the exception of things 
that move themselves is moved by something else, l iow is 
it that some things , e. g. things thrown, continue to be in 
motion when their movent is no longer in contact with 

30 them ? If we say that the movent in such cases moves 
something else at the same time, that the thrower e. g. also 
moves the air, and that this in being moved is also a movent, 
then it would be no more possible for this second thing 
than for the original thing to be in motion when the 
original movent is not in contact with it or moving it '. all 
the things moved would have to be in motion simultaneously 
and also to have ceased simultaneously to be in motion 
267* when the original movent ceases to move them, even if, 

* i. e. greater force : lesser force = time occupied by lesser force : 
time occupied by greater force. 

^ The argument is left incomplete : the point is that then either the 
finite magnitude is the measure of the infinite magnitude (which is 
impossible) or it is a measure of so much of the infinite n.agnitude as 
can be said to possess the force, the rest not possessing any force, in 
which case it is not justifiable to say that it is the infinite magnitude 
that possesses the finite force. 

BOOK VIII. lo 267^ 

like the magnet, it makes that which it has moved capable 
of being a movent.^ Therefore, while we must accept this 
explanation to the extent of saying that the o riginal movent 
gives the power of being a movent either to air ^ or to 
water or to something else of the kind, naturally adapted 
for imparting and undergoing motion, we must say further 5 
tjiat this th ing does not cease simultaneously to impart 
motion and to undergo motion : it ceases to be in motion 
at the moment when its movent ceases to move it, but it 
still re mains a movent , and so it causes something else^ 
consecutive with it to be in motion, and of this again the 
same may be said. The motion begins to cease when the 
motive force produced in one member of the consecutive 
series is at each stage* less than that possessed by the 
preceding member, and it finally ceases when one member 
no longer causes the next member to be a movent but only 
causes it to be in motion. The motion of these last two — 10 
of the one as movent and of the other as moved — must 
cease simultaneously, and with this the whole motion 
ceases. Now the things in which this motion is produced 
are things that admit of being sometimes in motion and 
sometimes at rest, and the motion is not continuous but 
only appears so : for it is motion of things that are either 
successive or in contact, there being not one movent but 
a n umber of mo vents consecutive with one another: and 15 
so motion of this kind takes place in air and water. Some 
say^ that it is * mutual replacement': but we must 
recognize that the difficulty raised rannnt he finWeA nfhpr- 
wise than in the way we have d escribed.^ So far as they 

* Reading in 1. I (with H Simp.) TroteT, Sxnrcp 17 Xi'^os-, olov Kivelv, 
which seems clearly indicated by the next sentence : KLvel gives no 
satisfactory sense and seems to contradict Trava-rjrai immediately pre- 
ceding. The point is that the magnet can attract one piece of iron 
through the medium of another. 

Reading in 1. 3 olop re Kivelv rj t6v depa [toiovtov]. 
^ Reading in 1. 7 Kivel n aX\o, with K. 

* Reading in 1. 8 orav del eKdrTOiv, with EK Simp., and in 1. 9 
eyyivrjTai, with FH Them. Simp. 

" Cf. PI. Tzm. 59 A, 79B, c, E, 80 c. 

■ ^ i. e. dvTLneplaTaa-is may be a fact, but it does not in itself constitute 
an explanation. (Simplicius defines dvrnrepiaTaais thus : dvTmepia-Taa-is 
ecTTiVf OTov e^(odovfievov tivos aafxaros vno (rcifiaros dvTaWayrj yevrjrai Ta>v 


are affected by * mutual replacement ', all the members 
of the series are moved and impart motion simultaneously, 
so that their motions also cease simultaneously : but our 
present problem co ncerns the appearance of r ontinnpyg^ 

20 motio n m a smgle thin g, and therefore, since it cannot be 
moved throughout its motion by the same movent, ^the 
question is. w hat ; moves i t ? 

Resuming our main argument, we proceed from the 
positions that there must be continuous motion i n the 
world of things, that this is a^singlejnotion, that a single 
motion m ust be a motion of a magnitude ( for that which is 
without magnitude cannot be in motion), and that the 
magnitude must be a single magnitude moved by a single 
movent (for otherwise there will not be continuous motion 
but a consecutive series of separate motions), and^ that if 
the movent is a single thing, it is either itself in motion or 

25 itself unmoved : if, then, it is in motion, it will have to be 
subject to the same conditions as that which it moves, that 
is to say it will itself be in process of change and in being 
267^ so will also have to be moved by something : so we have 
a series tViaj^rr|]]gt rr>mf; to an end, and a point will be 
reacHeH^t which motion is imp arted by something that is 
unnio yed. Thus we have a movent that has no need to 
change along with that which it moves but will be able 
to cause motion always (for the causing of motion under 
these conditions*"lnv6Tves no effort): and this motion 
alone is regular, or at least it is so in a higher degree 
than anjrother, since the movent is never subj ect to any 
5 change . So, too, in order that the motion may continue to 
be of the same charact er, the moved must not be^sub- 
ject to chan^ in respect of its relation to the movent.^ 

TOTTCov, Ka\ TO fx€v c^coBrjcrav iv t<o tov i^aOrjOevros arfj totto), to de e^adrjdev 
TO npO(Te)(es i^(o6fj Ka\ iKelvo to e)(6fxevoVf OTav irXeiova ^, eois ap to €(r\aTov 
iv T(o Tona yeurjTai tov rrpaTov e^codrjaavTos. 

^ Reading 8i in 1. 24, and a colon after 6v in 1. 25 (so Bonitz). 

^ SC. fir) avfifM€Ta^d\\ov. 

2 Reading in 1. 5 (with three MSS. and almost certainly Simplicius) 
iicelvo. It is hard to see how any satisfactory sense can be got out of 
eKeipoVj since TO Kivovfievov obviously n€Ta^aX\€i npos (= viro) tov 
KLvovvTos : the point is that /Mera^oX^ must always be the same /xera- 
^okrjy namely KVK\o<f)opia, Cf. 1. 17. 

BOOK VIII. lo 267* 

Moreover ^ the movent must occupy either the centre or 
the circumference, since these are the first principles from 
which a sphere is derived. But the things nearest the 
movent are those whose motion is quickest, and in this case 
it is the motion of the circumference ^ that is the quickest : 
therefore the movent occupies the circumference. 

There is a further difficulty in supposing it to be possible 
for anything that is in motion to cause motion continuously 
and not merely in the way in which it is caused by some- jo 
thing repeatedly pushing (in which case the continuity 
amounts to no more than successiveness). Such a movent 
must either itself continue ^ to push or pull or perform both 
these actions, or else the action must be taken up by some- 
thing else and be passed on from one movent to another 
(the process that we described before as occurring in the 
case of things thrown, since the air or the water, being 
divisible, is a movent only in virtue of the fact that 
different parts of the air are moved one after another *) : 
and in either case the motion cannot be a single motion, 15 
but only a consecutive series of motions. Jheonly 
continuous motion, then, is t hat which is caused by the ^ 
unmoved movent: and this m otion is continuous because 
the movent remains always invariable, so that its relation 
to that which it moves remains also invariable and con- 

Now that these points are settled, it i s clear that the firsts 
unmoved movent cannot have any magnitude. For if it 
has magnitude, this must be either a^ fi nite or an infinite 
magnitude. Now we have already'' proved in our course' 20 
on Physics^ that there cannot be an infinite magnitude: 
and we hav e now proved that it 1§ impossible for a Hnite 

^ Reading in 1. 6 8' rj, with FI. 

^ Reading in 1. 9 kvkXov with HK Simp. If oXov be kept, the 
general sense will have to be the same, but it is in that case very much 
obscured : in particular the reference of e/cet in the next clause becomes 
very awkward. 

^ Reading in 1. 12 Set dei, with EK. 

* Reading in 1. 13 el diaiperos S>v 6 dqp 77 to uScop kivu aWos a«, with 

^ iii. 5. 

' See note on 251*9. 


magnitude to have an infinite foi'ce . and also that it is 

im possible for a thing to be moved bv a finite magnitud e 

during an infinite time. But the first movent causes a 

• motion that is eternal and does cause it during an infinite 

/f5 time. It is clear, therefore, t hat the first movent is in- 

11 jiivisible and is without parts and without magnitude. 


84^-99^ = 184^-199^, 0^-67^ = 2ooa-267^ 

'Above', 'up' 88*24, 5^) 32, 12* 

' Achilles ' (Zeno's argument) 39** 

Actuality (ivepyeia) 91'' 28, !»» 3I. 

Cf. Fulfilment. 
Addition 90^6, 4* 7, 6* 15, ^3. 
Air 12« 12, 13*26, 16^18. 
Alteration (dXXoiwo-if) 90^ 8, I* 12, 

23^ 10, 26* 26, ^2, 41* 32, 45^ 4, 

46^2, 12,47*19,60*33. 
'Always' 21^3, 59* 16. 
Anaxagoras 87*22, 26, 89*17, 3* 

20,5^1, 13*24, 50^24, 52*10, 

56^ 24, 65^ 22. 
Anaximander 87*21, 3^14. 
Animal 52^22, 53*12, 54^15, 


Antiphon 85*17, 93* 12. 

Ants 99* 23. 

' Apart ' 26^ 22. 

Aristotle — works referred to : — 
Physics 1*26, 51*9, 53^8, 57* 
34, 63*11, 67^21; De Gen. et 
Corr. 92^ 2, 93^ 21, 13* 5 ; Met. 
91^ 29, 92* 35 , 94^ 1 4 ; On Philo- 
sophy 94* 36. 

'Arrow, the' (Zeno's argument) 

Art93*l6, 31, 94*21, ^i, 99*15- 

Ashes, absorbed by water 13^ 21. 
Astronomy 93^ 26, 94* 8. 
' At some time ' 22* 25-9. 
Atom 65^ 29 ; time-atoms 63^27. 
Atomic magnitudes 87* 3. 

Becoming. Cf. Coining into being. 
'Before')('behind' 88*15, 5^32; 

' before ')(' after' 23*9. 
'Below '88* 25, 1*7,5^32, 12*26. 

29^7, 61^34. 

' Between ' 26^ 23, 27* 10, 31^ 9. 
Bisection %^^% 7^ii, 39^22. 
Body 4^ 5, 20,5^31, 53*16; natural 
bodies 8^ 8. 

Carrying 43* 17, ^ 17. 

Cask 13" 17. 

Categories 85*31, 0^28, I* 10, 

^27, 25^5, 27^ 5» 42*35. , 
Causes, the 94** 16-95*' 30» 9^ 25, 

98* 14-^ 15 ; internal cause 97^ 

Centre 65^ 3. 

Chance 95^ 31-98* 13, 99^ 23. 

Change (/xeraSoX^) 86*15, 1*8, 
24* 21-26^ 17, 29* 25, 36* 14, ^2, 
52^ 10, 65* II ; everything that 
changes, divisible 34^ 10-35^ 5 ; 
no part of it first 36* 34 ; differ- 
ence between change and mo- 
tion 29* 30 ; no change infinite 
41*26; all change is in time 
22^30-23* 15. 

Chaos (Hesiod) 8^ 31. 

Children 84^12, 47^19. 

Circle 17*19,40*29,48^6; human 
affairs form a circle 23^ 24 ; 
squaring of 85* 16 ; motion in 
a circle, rotation 48* 20, 61^29, 
62*15,64^18, 65*14. 

Circular motion, rotation {kvkKo- 
((>opLa, irepi(}iopd) 23^ 1 9, 33, 
27** 18, 65* 13-*' 16. 

Clepsydra 13*27. 

Coincidence 99*1 ; in time 18*25. 

Combination 43^8-11, 60^ 11, 65^ 

Coming into being, becoming 91^ 
13, 23^21, 25*13-26*16, 30*31, 
49^ 20 ; in the full sense 86* 14, 
93^21, 25* 13; )( passing away 
I* 14, 58^ 17. 


Complete 7* 9, 65^ 23. 
Compulsory, violent 15* I, 2, 30* 

29,30, 54*9. 
Condensation 87^ 15. 
Confused masses 84* 22. 
Contact 2» 7, 8, 26^ 23, 27* 15,31* 

22 ; )( organic union 13*9, 27* 


Contentious argument 85^8, 86*6. 

Contiguous 27^6, 36^ 12, 27^ 8. 

Continuity 86* 28. 

Continuous 85^10, 0^18, 11*30, 
17*3, 19* 12, 27*10-^2, 31*21, 
32^ 24, 33a 25, 34a 8, 39a 22, 42b 

Contraries, the, principles 88* 19; 
locally contrary 26^ 32 ; con- 
trary nourished by contrary 60* 
31 ; more than one contrary to 
the same thing 61^ 16. 

Contrariety 87* 20, 29* 23 ; local 
30^ 1 1, 61^ 36 ; natural 17* 23. 

Coriscus 19^21, 27^32. 

Cosmogony 96* 22, 50^ 16. 

Decrease i* 14, 26* 31, 41^ i, 53^ 

Defect— excess 87* 17, 89^ 11. 
Democritus 84^ 21, SS^ 22, 94* 20, 

3*20,33,13*34,51^16, 52*34. 
Density 60'* 10. 
Diagonal 21^24, 22* 5. 
Dialectical difficulty 2* 22. 
Diameter 64^15. 
Dimensions 9*4. 
Distance 2^ 17. 

Divinest of visible things 96*33. 
Division 4* 7, 6* 1 5, ^ 4, 22* 19, 24* 

9, 33*20, 36^15, 62*30, 63* 21. 

Earth, spherical? 93^30; at rest 

14^ 32 ; moves downward 14'' 14. 
Element, letter (o-rotxetov) 84* 11, 

87*26, 88^28, 89^27, 95*16, 

4^33 ; three in number 89^ 16. 
Empedocles 87^ 22, 88^ 18, 89* 15, 

94*20, 96*20, 98^32, 50*26, 

End 94*27-35, ^32, 95*24, 98* 

24, ^3,99*8, 30,0*22,33. 
Equivocal terms 49* 23. 
Essence 85^9, 94*21, ^27, 95* 

20, 98^ 8. 
Eternal 3^ 30, 63* 3. 
Europe 24^21. 
Even, the, infinite 3* 11. 
Excellence 46* 13, ^ 3, 47* 7. 

Excess 87* 16, 89^ 10, 15^ 17. 
Extension (dida-Taais) 4^20. Cf. 

'Fast' 18^15. 

* Father ', use of word by children 

Finite 84^18, 89*15, 5*31, 37^ 

.27, 59* 9> 66^ 25-67^ 23. 
Fire, moves upward 14^ 14 ; rare 

17* I ; (Heraclitus) 5* 4. 
Flood 22* 23, 26. 
Force. Cf. Potency, 
Form (fiSos) 87* 20, 93* 31, 94^ 26, 

7^1, 9*21, ^23, 10*21. Cf. 

Forms, the 3*8 ; theory of 93^ 36. 

* Fortunate stones * (Protarchus) 

97^ 10. 
Fortune, good 97* 26. 
Fulfilment, actuality (eW6Xe;i^etn) 

93^*7, 0^26, 1*10, ^31, 2*11, 


Genus 89* 14, i^ 19, 9* 4, 10* 18. 
Geometer 85* I, 16. 
Geometry 94* 10. 
Gnomons 3* 14. 
Good 92* 17. 

Great and Small 87* 17, 92* 7, 3* 

Harmonics 94* 8. 

Heavenly sphere, heaven, uni- 
verse ipvpavo^) 96*33, 17*13, 
51^19; inhales 13^24; in a 
grain 21* 22 ; = the All 12^ 17 ; 
' outside the heaven ' 3* 7, ** 25 ; 
heavenly bodies 59^ 30. 

Heavy 1*8, 5^ 15, 27, 12* 25, 17^ 
17, 55b 16, 6oi> 9. 

Heraclitus 85*7, ^20, 5*3. 

Hermes 90^ 8. 

Hesiod 8^ 29. 

Homogeneous bodies 88* 13, 12^ 
5 ; (of Anaxagoras) 3*21. 

Iliad 22* 23. 
Immobility 2* 4, 28^ 3. 
Immovable, unmoved (a/cti/»;ro?) 

26^ 10, 58b 14, 60* 3, 6i* 16 ; in 

mathematics 98* 1 7. 
*In', ambiguous 10*14-24; * in 

itself 10*25. 
Incomparable speeds 17* 10. 
Increase, magnification {av^r]^ 

av^yais) 6^28, 7^29, 8*22, II* 


15, 26*31, 4i*33» 60*29, 61* 

Indivisible 31^ 3, 32* 24, 41* 26. 
Induction 85* 14, 24^30, 29^3, 

52*24; 'inductively ' 10^8. 
Infinite 87^8, 0^17, 2^30-8*23, 

33* I9» 37^24, 50^18, 67^20; 

series 56* 28, 29. 
Infinity 3*12. 
Instinct, animal 99* 26. 
Intelligence 98* 10. 
Interval, extension (Siao-riy/Lta) 2* 

18,11^7,14*5. ^ 
Inverse proportion 15"* 31, 66'' 18. 
*Is', ambiguous 85*21, 6*21; 

* what just is ' 86* 33-87* 8. 

Knowable to us )( by nature 84* 16. 
Knowledge 47^ 10. 

'Lately' 22^12. 
Left 5^33» 29^8, 61^35. 
Length9*5, 29^7, 63*14. 
Letter. Cf. Element. 
Leucippus 13*34. 
Lever 55*22. 
Leverage 59^20. 

* Light' 1*8, 5^27, 12*25, 17^18, 

55^11, 60^9. 

Limit, termination (nepas) 85^ 18, 
9*9, 18*23,64^27. 

Line 94* 10, 20^30, 22* 16, 31*25, 
^ 9> 33^ 16 ; not composed of 
points 15^ 19, 31* 24, 41* 3 ; in- 
divisible lines 6* 18. 

Living things 55* 7, 59^ 2, 65^34. 

Locomotion 1*7, 15, 8*32, ^8, 
11*15, 14^13, i9i>3o, 26*33, 
41^20,43*8-16, 60*28-61^31, 
65* 13,^17-66*9. 

* Long ago' 22^14. 

Love — Strife (Empedocles) 50^ 

28, 52*26, 65^21. 
Lyceum 19^21. 
Lycophron 85^ 28. 

Magnet 67* 2. 

Magnification. Cf. Increase. 

Magnitude 6*16, 19*11, 33*14, 
39*21, 67^21; atomic magni- 
tudes 87*3, 88*12; mathe- 
matical magnitudes 3^25. 

Man begets man 93^ 8, 12, 94^ 13, 
98*26, 2* II. 

Mathematical magnitudes 3^ 25 ; 
lines 94* 10, 22* 15. 

Mathematician 93^ 23-31. 

Mathematics 94* 8, 98* 17, o* 15 ; 
objects of 8^ 23. 

Matter 90^25, 91*10, 92*3-31, 
93* 29, o* 14, ^8, 7* 22-35, 9^9- 
10*21, 11^36, 13*6, 14*13, 


Melissus 84^16, 85*9-32, ^17, 
86*6, 7*15, 13^12, 14*27. 

Middle 19* 27, 29^ 19, 62* 20-^31. 

Mind (Anaxagoras) 3* 31, 50^ 26, 
56^ 25, 65^ 22. 

Mixture 87* 23 ; * everything 
mixed in everything 87^1. 

Moment. Cf. * Now '. 

Motion, movement {Kivr]fsis) o^ 12- 
2^29,27^ 23, 35* 11,51*10, 61* 
33 ; contrary motions 29* 7- 
"22 ; ' one motion ' 27^ 3, 42* 30, 
62*1, 67*22; 'one motion* 
simpliciter 28^ i ; primary mo- 
tion 8*31, 43*11,60*23,61*21, 
66* I ; motion denied by Zeno 
39^ 5-40^ 7 ; does not prove the 
existence of a void 14*22 ; com- 
parability of motions 48* 10- 
50^ 7 ; why some things are 
moved and others not 53* 22- 
54^ 6 ; motion implies a mover 
42* 14, 54^ 7-56* 3 ; implies two 
subjects 29^ 29 ; is eternal 50^ 
11-52^6; is in time 22^30-23* 
15; doubly divisible 34^21- 
35^ 5 ; which kind of motion 
can be infinite? 61*30, ^27- 
63* 3 ; three kinds of motion 
92^ 14, 25^7, 26* 16, 43*6, 60* 
26, 61*9; being moved by 
something else 43* 1 5 ; motion 
in strict sense 66* i. 

' Movable' and 'mover', ambigu- 
ous 24*26-34. 

Movent and moved have no inter- 
mediary 43* 5 ; first movent 43* 
3 ; the first movent unmoved 
56*4-58^9; indivisible and 
without magnitude 66* 10-^ 26; 
natural 55*29. 

Natural 93*33, 61^25; contra- 
rieties 17*23; bodies ^8\ 
alterations 30^ 4. 

Nature 84*15, 87"^ T, 89*27, 92^ 
8-93^ 21, 94* 12-28, 96^ 22, 98* 
4,99^30, 0^12, 50^15, 52*12, 
53^5, 60^23, 61*14, 65*22; 
= matter 91*8, ^34, 93* 9-30 ; 
by nature, according to nature. 


naturally 97^ 34, 98^ 35» 99* 18, 
26, o* 16, 14^ 14, 15* 2, 30a 19- 
31^17,50^14,54^17, 59^11. 

Necessary, the 98^ 11. 

Necessity 96^ 13, 99^ 34- 

* Now ', present, moment (vvv) 
18*6-27, ^25, 19^12-20*21, 
22*33, 31^10, 33^33-34^24, 
37*6-25, 39^2, 41*24, 51*' 20, 
62* 30. 

'Number', two senses of 19^6, 
23* 24 ; the smallest number 
20* 27. 

Olympic games 6* 24. 

*One', ambiguous 85^6, 27 3; 
*all things are one' 85*22; 
' what is just one ' 86* 34 ; plu- 
rality of ones 7^ 7. 

Optics 94*8, II. 

Order 88* 24, 96* 28, 52* 12 ; ab- 
sence of 90^ 15. 

Organic union 13* 9, 27* 17. 

'Ox-progeny, man-faced * (Empe- 
docles) 98^32, 99^5, II. 

Parmenides 84^16, 85*9, ^18, 
86*7, 22, 88*20, 92*.j;>*15. 

Paron 22^18. 

Part 85^ II-16, 10*16, 18* 7, 50* 

Passing away, perishing, being 
destroyed {(f)6opa) 1*15, 3^9, 
22^25, 25*18-35,46*16,58^18. 

Past time 22^ i, 34* 14. 

Patiency 2* 23-^ 20. 

Perceptive motion 53* 19. 

Perfection 46^ 2, 47* 2. 

Perishing. Cf. Passing- away. 

Physical lines 94*10; branches' 
of mathematics 94* 7. 

Physicist 93^23, 94*15-^13,98* 
22,0*32,3^3, 53*35, ^5 ; the 
physicists 84^17, 86*20, 87*12, 
28, 35, 3*16, ^15, 5*5,27,6^ 
23, 13° I, 65*3. 

Physics 93^29, 51*9, 67^21. 

Place 5^3, 8*27-13*11, 26^22; 
dissimilar 5*20 ; proper 53^34 ; 
differences of 5^ 31-6* 7. 

Plant Z']^ 16, 90^ 4, 92^10, 99* 24, 
^10, 61*16. 

Plato 87*17,3*4, 8, 15,6^27,51^ 
17 ; Timaeus 9^ 11, 10*2 ; un- 
written teaching 9^ 15. 

Pleasures 47* 8. 

Point 12^24, '15^ 18, 20*10, 20, 

Polyclitus 95* 34, ^11. 
Position 88*23, 54^24. 
Potency, potentiality, force {hlva- 

fiis) 91^ 28, 2* 12, 8^22, 55*31, 

57^ 7, 66* 26. 
Present. Cf. ' Now \ 
'Presently', 'just' 22^7. 
Principle 89* 30 ; one or more } 

84^15, 89*11-^29; moving 

principles 98* 36 ; contraries 

are principles 88* 19. 
Prior 60^ 1 7. 
Privation 91^15, 92*3, 93^19, 

Protarchus 97 ^^ 10. 
Pulling 43* 17, ^ 14, 44*8. 
Pushing 43* 17, 44*7. 
Pythagoreans 3*4, 4*33, 13^23, 

22^ 18. 

Qualitative change (cVepoicoo-iy) 17^ 

26. Cf. Alteration. 
Quality 85*34, i* 5, 26* 27, 28. 
Quantity 1*6. 

' Raiment ' = ' dress ' 85^ 20, 2^ 

Rare 88* 22, 16^ 30, 17^ 12. 
Rarefaction 87*15, 12^3, 17*12, 

Rarity 16^ 22. 
Rectilinear 61^29, 62*13-63*3, 

64* 28, b 19. Cf. Straight line. 
Reduction 6^13, 29, 31, 7*23, 

Regular 23* i, ^19, 28^ 16, 20, 

Relative, relation 0^28, 25^11, 

Replacement, mutual 8^ 2, 15* 15, 

67a 16, 18. 
Rest (fjpffiiaj rjpefiijais) 2*4, 5* 17, 

21^8, 26^15, 29*8, ^23-30* 10, 

30*20, ^10, 15, 18, 31*2, 51* 

26, 64* 24. Cf. Stationariness. 
Rest, coming to {fjpefxrja-ts) 26* 7, 

Rings, endless 7* 2. 
Rotation. Cf. Circle, Circular, 


' Same, the ' 24* 2. 
Sardinia, the sleepers of 18^ 24. 
Saw o* 10. 
Seed-mass 3*21. 


Self-moved 58* 2. 

Sense, sense-perception 89* 7, 44^ 

Shape, form {nop(f)lj) 90^ 20, 93* 

30,^19, 98^3, 99*31, 1*4,45^ 

7, 46» I. Cf. Form. 
Shapelessness 88^20, 90^ 15. 
Ship, hauling of co* 18, 53^ 18. 
Ship-building 99^29. 
Slowness 28^29. 
Snub 86^ 22, 94a 6. 
Snubness 94* 13. 
' Somewhere ' 8* 29, 12^ 9-27. 
Soul 65^ 32 ; and time 23* 17, 21. 
Space 8^7, 9*8, ^12, 15. 
Sphere 18^ i, 6, 40*29, 65^2. 
Sphinx 8*31. 
Spider 99* 22, 27. 
Spiral 28^ 24. 

Spontaneity 95^31-98* 13 ; deri- 
vation of the word 97^ 30. 
Starts 32*9, 41* 4. 
State 93* 25, 45b 7, 46a 10. 
Stationariness {a-rda-is) 92^ 14, 95* 

23,28^6,64*21. Ci. Rest. 
' Stones, fortunate ' (Protarchus) 

97^ 10. 
Straight line 17* 20, 48* 13, ^ 5 ; 

path 27b 18. Cf. Rectilinear. 
Strife (Empedocles) 50^' 28, 52* 

26, 65^21. 
String (proverb) 7* 17. 
Subject. Cf. Substratu7n. 
Substance 85* 23, 31, 89* 29, ^23, 

92b 34. 
Substratum, subject (InoKdfj.evov) 

87*13, 89*31, 90^2, 24, 91*8, 

32,93*29, 8*1,25*3-^3. 
* Succession, in ' 26^ 34, 27* 4, 18, 

31*23, 59*17. 
'Suddenly' 22^ 15. 
Sun, man begotten by 94^ 13. 
Surface 93^ 24, 9* 8. 
Swallow 99* 26. 

Teeth 98^ 24. 

Termination. Cf. Limit. 

' That for the sake of which ' 

94* 27, 36, b 32, 98* 24, b 3, o* 

Throwing 43* 20, 57* 3. 

Time 17^29-24*17, 31^10, 34* 
14, 36*36, ^20, 39*8, 21, b 8, 
41*3, 15, 51^11-28, 62*30, '^ 21, 
63*15-23, 64*4, ^7; 'the 
wisest of all things ' 22^ 17 ; 
continuous and infinite 32* 23- 

* Together' 26^21, 43*4. 

* Together, all things were ' 

(Anaxagoras) Z']^ 29, 3* 25, 50^ 

Torch-race 28* 28. 
Troy 22* 26, ^ II. 
Twirling, rotation (8iV»ja-if) 14*32, 

Two, the number 20* 27. 

Universal 89* 5. 

Universe. Cf. Heavenly sphere, 

Unmoved. Cf. Immovable. 
Untraversable 7^ 29. 
*Up'. Ci. Above. 

* Vain, in ' 97^ 22-32, 3^ 5. 
Velocity, equal, uniform 16* 20, 

32*20,^16, 36^35v37*i, ^27, 

38*4,49*8, 13, 29, «> 20. 
Vessel = transportable place 9^ 

29, 12* 14. 
Void 88* 23, 8^ 26, 13* 12-17^ 28, 

65^ 24. 
Vortex 96* 26. 

Walking 27^ 18, 28* 17, 49* 17. 
Weight 15*25, 50*9. 
Wineskins, straining 13*26. 
Whole, universe {o\ov) 95*21, 

7*9, 16^35, 18*33,28^x4. 
' Whole-natured ' (Empedocles) 

World, little )( big 52'* 26 ; out- 
side the world 6^23; worlds 
96* 25, 3^ 26, 50^ 19. 

Xuthus 16^26. 

Zeno 9*23, 10^22, 33*21, 50*20, 
63* 5 ; arguments about mo- 
tion 39^ 10. 

Zeus 98^18. 





J. L. STOCKS, M.A., D. S. O. 




Oxford University Press 

London Edinburgh Glasgoiv Copenhagen 

Neiv Tork Toronto Melbourne Cape Toivn 

Bombay Calcutta Madras Shanghai 
Humphrey Milford Publisher to the Umveksity 


This translation was begun many years ago in co-opera- 
tion with Mr. H. B. Wallis of the Board of Education. 
Unfortunately he was obliged to turn to other work, but 
his original draft formed the basis of nearly half my 
version of the book. 

Rather full textual notes are given throughout, the text 
of Prantl being taken as basis. (A complete table of the 
passages dealt with will be found in the Index, s.v. Text.) 
For this purpose I have collated the Vienna MS., J, from 
a photograph, and the reading of this MS. is noted in each 
case, either explicitly or by implication. 

Mr. Ross's generous conception of an editor's responsi- 
bilities has been of the greatest service. He has saved me 
from many mistakes and has made many useful suggestions 
for the improvement of the translation. A few of his 
suggestions will be found recorded in the foot-notes as his ; 
but for the most part he is merged in his translator. 

J. L. S. 
3 1 J/ March, \^'X'X. 




1. The subject of inquiry 268* 

2. That in addition to the four elements, earth, water, air, and 

fire, there is. a fifth element, the movement of which is 
circular 268^ 

3. That this body is exempt from alteration and decay . . 269^ 

4. That the circular movement has no contrary . . . 270^ 

5. That no body is infinite.— (i) Not the primary body, or fifth 

element 271^ 

6. (ii) None of the other elements 273^^ 

7. (iii) In general, an infinite body is impossible . . . 274^ 

8. That there cannot be more than one Heaven. — (i) Proved 

from a consideration of the natural movements and places 

of the elements 276* 

9. (ii) Proved by the principles of form and matter, the three 

different senses of the term * heaven ' being explained. 
Corollary. — There is no place or void or time outside the 
Heaven 277^ 

10. That the Heaven is ungenerated and indestructible. — 

(i) Review of previous theories 279^' 

11. (ii) Definition of the terms 'ungenerated' and * indestructible', 

and of their opposites 280* 

12. (iii) Proof of the thesis 281* 


1. Corroboration of this result 283^ 

2. Of the sense in which the spatial oppositions, up and down, 

right and left, can be attributed to the Heaven . . 284^ 

3. Why there is a plurality of movements and of bodies within 

the Heaven 286* 

4. That the Heaven is perfectly spherical .... 286*^ 

5. Why the first Heaven revolves in one direction rather than 

the other 287^ 

6. That the movement of the first Heaven is regular . . 288* 

7. Of the stars. — (i) That they are not composed of fire . . 289* 

8. (ii) That their movement is due to the movement of circles 

to which they are attached 289^^ 

9. (iii) That no * harmony of the spheres ' resuhs from their 

movement 290^ 

10. (iv) Of their order 291* 

268^ DE CAELO 

matter and in that to which they are applied, body alone 
among magnitudes can be complete. For it alone is de- 
termined by the three dimensions, that is, is an 'all'.^ 
But if it is divisible in three dimensions it is every way 
35 divisible, while the other magnitudes are divisible in one 
dimension or in two alone : for the divisibility and continuity 
of magnitudes depend upon the number of the dimensions, 
one sort being continuous in one direction, another in two, 
another in all. All magnitudes, then, which are divisible 
are also continuous. Whether we can also say that what- 
30 ever is continuous is divisible does not yet, on our present 
grounds, appear. One thing, however, is clear. We cannot 
268^ pass beyond body to a further kind, as we passed from 
length to surface, and from surface to body. For if we 
could, it would cease to be true that body is complete 
magnitude. We could pass beyond it only in virtue of 
a defect in it ; and that which is complete cannot be 
5 defective, since it has being in every respect.^ Now bodies 
which are classed as parts of the whole ^ are each complete 
according to our formula, since each possesses every dimen- 
sion. But each is determined relatively to that part which 
is next to it by contact, for which reason each of them 
is in a sense many bodies. But the whole of which they are 
parts must necessarily be complete, and thus^ in accordance 
10 with the meaning of the word, have being, not in some 
respects only, but in every respect.* 

The question as to the nature of the whole, whether it is 2 
infinite in size or limited in its total mass, is a matter for 

^ Body alone is so determined, and only what is so determined is 
a totality (an ' all ')• Put a comma, instead of a full stop, after Tpialv. 
The words tovto fi' fW) nav are difficult to interpret. Prantl makes 
TovTo predicate, and translates as though we had t6 nav instead of Trar. 
Simplicius gives no help. 

"^ To be incomplete or defective is to lack being in some respect. 

^ i. e. the elements. 

* The 'parts' or elements are bodies, and therefore complete in the 
sense just given to the word. They are, however, only parts, and as 
such limited in their being by the juxtaposition of other parts. This 
suggests a development of the notion of completeness which will make 
the term ' complete ' applicable only to the unrestricted being of the 

BOOK I. 2 268^ 

subsequent inquiry.^ VVe will now speak of those parts of 
the whole which are specifically distinct.^ Let us take 
this as our starting-point. All natural bodies and magni- 15 
tudes we hold to be, as such, capable of locomotion; for ' 
nature, we say, is their principle of movement.^ But all 
movement that is in place, all locomotion, as we term it, 
is either straight or circular or a combination of these two, 
which are the only simple movements. And the reason of 
this is that these two, the straight and the circular line, are 20 
the only simple magnitudes. Now revolution about the 
centre is circular motion, while the upward and downward 
movements are in a straight line, ' upward ' meaning 
motion away from the centre, and 'downward' motion 
towards it. All simple motion, then, must be motion 
either away from or towards or about the centre. This 
seems to be in exact accord with what we said above : ^ -55 
as body found its completion in three dimensions, so its 
movement completes itself in three forms. 

Bodies are either simple or compounded of such ; and by 
simple bodies I mean those which possess a principle of 
movement in their own nature, such as fire and earth with 
their kinds, and whatever is akin to them.^ Necessarily, 
then, movements also will be either simple or in some sort 30 
compound— simple in the case of the simple bodies, com- 269^ 
pound in that of the composite — and in the latter case the 
motion will be that of the simple body which prevails in the 
composition. Supposing, then, that there is such a thing as 
simple movement, and that circular movement is an instance 
of it, and that both movement of a simple body is simple and 

^ See c. vii. 

^ i. e. the elements, which represent the ultimate distinctions of kind 
among bodies. 

' Cf. P/iys. 192^20. 

"* Reading rjKoXovdqKevai Kara Xoyov with all MSS. except E. 

^ Ta Tovrap e'ldq ('with their kinds') can hardly mean h'nds 0/ fire 
and earth (e.g. sandy and stony earth, flame and glowing coal), as 
Simplicius supposes, for there is no variety of movement corresponding 
to this variety of kind. Rather, as Alexander supposes, the phrase is 
a generalizing formula {durl too KadaXou nav irvp . . . koI KadoXov Traaav 
ytjv) : fire and its kind, earth and its kind, and other species of the 
same genus (viz. air and water, and the ' fifth body' of which the stars 
are made). 

B 2 

269* DE CAELO 

simple movement is of a simple body (for if it is movement 

5 of a compound it will be in virtue of a prevailing simple 
element), then there must necessarily be some simple body 
which revolves naturally and in virtue of its own nature ^ 
with a circular movement. By constraint, of course, it may 
be brought to move with the motion of something else 
different from itself, but it cannot so move naturally, since 
there is one sort of movement natural to each of the simple 
bodies. Again, if the unnatural movement is the contrary 

ro of the natural and a thing can have no more than one con- 
trary, it will follow that circular movement, being a simple 
motion, must be unnatural, if it is not natural, to the body 
moved. If then (i) the body, whose movement is circular, 
is fire or some other element, its natural motion must be the 
contrary of the circular motion. But a single thing has 
a single contrary ; and upward and downward motion are 

15 the contraries of one another.^ If, on the other hand, 
(2) the body moving with this circular motion which is 
unnatural to it is something different from the elements, 
there will be some other motion which is natural to it. 
But this cannot be. For if the natural motion is upward, 
' it will be fire or air, and if downward, water or earth. 
^ Further, this circular motion is necessarily primary. For the 

20 perfect is naturally prior to the imperfect, and the circle is 
a perfect thing. This cannot be said of any straight line : 
— not of an infinite line ; for, if it were perfect, it would 
have a limit and an end : nor of any finite line ; for in 
every case there is something beyond it,^ since any finite 
line can be extended. And so, since the prior movement 

25 belongs to the body which is naturally prior, and circular 
movement is prior to straight, and movement in a straight 
line belongs to simple bodies — fire moving straight upward 
and earthy bodies straight downward towards the centre — 
since this is so, it follows that circular movement also must 

^ Reading icwrov with all MSS. except E. 

^ Therefore neither of these can be a/so the contrary of circular 
motion. Thus there is fio simple motion opposed as contrary 10 the 

' Reading nacrav yap iari ti cktos (iari is omitted by E alone). 

BOOK I. 2 269* 

be the movement of some simple body.^ For the move- 
ment of composite bodies is, as we said, determined by that 
simple body which preponderates in the composition. 30 
These premises clearly give the conclusion that there is in 
nature some bodily substance other than the formations we 
know, prior to them all and more divine than they. But it 
may also be proved as follows. We may take it that all 
movement is either natural or unnatural, and that the 
movement which is unnatural to one body is natural to 
another — as, for instance, is the case with the upward and 
downward movements, which are natural and unnatural to 35 
fire and earth respectively. It necessarily follows that 269 
circular movement, being unnatural to these bodies, is the 
natural movement of some other. Further, if, on the one 
hand, circular movement is natwal to something, it must 
surely be some simple and primary body which is ordained 
to move with a natural circular motion, as fire is ordained 5 
to fly up and earth down. If, on the other hand, the 
movement of the rotating bodies about the centre is 
Mtnatural^ it would be remarkable and indeed quite in- 
conceivable that this movement alone should be continuous 
and eternal, being nevertheless contrary to nature. At any 
rate the evidence of ail other cases goes to show that it is 
the unnatural which quickest passes away. And so, if, as 10 
some say, the body so moved is fire, this movement is just 
as unnatural to it as downward movement ; for any one can 
see that fire moves in a straight line away from the centre. 
On all these grounds, therefore, we may infer with con- 
fidence that there is something beyond the bodies that are ^^ 
about us on this earth, different and separate from them ; 
and that the superior glory of its nature is proportionate to 
its distance from this world of ours.'^ 

^ From his premises Aristotle is here entitled to conclude, not 
merely that circular movement is the movement of a simple body, but 
also that it is the movement of a simple body prior to the other simple 
bodies. Prantl therefore inserts nporepov after twos and appeals to 
Simplicius's paraphrase for corroboration. Simplicius, however, not 
only does not corroborate the conjecture but actually points out that 
this part of the conclusion is suppressed {onep as aa(pes napfjKe). The 
insertion of npoTepov does not really make the argument any clearer. 

2 Cf. Plato, P/uredo, iiiB. 

269'' DE CAELO 

In consequence of what has been said, in part by way of 3 
assumption and in part by way of proof, it is clear that not 

20 every body either possesses lightness or heaviness. As 
a preliminary we must explain in what sense we are using 
the words ' heavy ' and * light ', sufificiently, at least, for our 
present purpose : ^ we can examine the terms more closely 
later, when we come to consider their essential nature.^ Let 
us then apply the term 'heavy ''to that which naturally 
moves towards the centre, and ' light ' to that which moves 
naturally away from the centre. The heaviest thing will be 

25 that which sinks to the bottom of all things that move 
downward, and the lightest that which rises to the surface 
of everything that moves upward. Now, necessarily,^ every- 
thing which moves either up or down possesses lightness or 
heaviness or both — but not both relatively to the same 
thing : for things are heavy and light relatively to one 
another ; air, for instance, is light relatively to water, and 

30 water light relatively to earth. The body, then, which 
moves in a circle cannot possibly possess either heaviness 
or lightness. For neither naturally nor unnaturally can it 
move either towards or away from the centre. Movement 
in a straight line certainly does not belong to it ftaturally, 
since one sort of movement is, as we saw, appropriate to 
each simple body, and so we should be compelled to identify 

35 it with one of the bodies which move in this way. Suppose, 
then, that the movement is tmnatural. In that case, if it is 
270^ the downward movement which is unnatural, the upward 
movement will be natural ; and if it is the upward which is 
unnatural, the downward will be natural. For we decided 
that of contrary movements, if the one is unnatural to any- 
thing, the other will be natural to it. But since the natural 
movement of the whole and of its part —of earth, for in- 

5 stance, as a whole and of a small clod — have one and the 
same direction, it results, in the first place, that this body 
can possess no lightness or heaviness at all (for that would 
mean that it could move by its own nature either from or 

^ Reading iKavm wy TrptJy (wj is omitted by E alone). 

2 Below, Bk. IV, cc. i-iv. 

^ Reading avayKx] 8rj {de is in F alone). 

BOOK I. 3 270 

towards the centre, which, as we know, is impossible) ; 
and, secondly, that it cannot possibly move in the way 
of locomotion by being forced violently aside in an upward 
or downward direction. For neither naturally nor un- 10 
naturally can it move with any other motion but its own, 
either itself or any part of it, since the reasoning which 
applies to the whole applies also to the part. 

It is equally reasonable to assume that this body will be 
ungenerated and indestructible and exempt from increase 
and alteration, since everything that comes to be comes into 
being from its contrary and in some substrate, and passes 75 
away likewise in a substrate by the action of the contrary 
into the contrary, as we explained in our opening discussions.^ 
Now the motions of contraries are contrary. If then this 
body can have no contrary, because there can be no con- 
trary motion to the circular, nature seems justly to have 20 
exempted from contraries the body which was to be un- 
generated and mdestructible. For it is in contraries that 
generation and decay subsist. Again, that which is subject 
to increase increases upon contact with a kindred body, 
which is resolved into its matter.^ But there is nothing out 25 
of which this body can have been generated.^ And if it is 
exempt from increase and diminution,"^ the same reasoning 
leads us to suppose that it is also unalterable. For altera- 
tion is movement in respect of quality; and qualitative 
states and dispositions, such as health and disease, do not 
come into being without changes of properties. But all 
natural bodies which change their properties we see to be 30 
subject without exception to increase and diminution. This 
is the case, for instance, with the bodies of animals and 

^ Phys. I. vii-ix. For the phrase, cf. 311* 12. 

^ Omitting Kai to cpdivov (jidtuei (1. 23). These words are omitted by 
three representative MSS. (EFJ), are not referred to by Simplicius or 
Themistius, and are an awkward intrusion in the sentence since 
what follows applies only to increase. For the doctrine, cf. De Gen. et 
Corr. I. V. 

^ Increase is effected by generation of one kindred body out of 
another. This body has no contrary out of which it can be generated. 
Therefore it cannot increase. 

* Reading a^euov with H (so Prantl). All other MSS. have 
ucpOapTov ; but the rare «0(9itoi/ would be easily altered to the commoner 
word. Simplicius has acbdaprov, but explains that cf^diais is a kind of 
(f)6opd and so a^Oaprov may be used for a(fidLrov. 

27o^ DE CAELO 

their parts and with vegetable bodies, and similarly also 
with those of the elements. And so, if the body which 
moves with a circular motion cannot admit of increase 

35 or diminution, it is reasonable to suppose that it is also 
270^ The reasons why the primary body is eternal and not sub- 
ject to increase or diminution, but unaging and unalterable 
and unmodified, will be clear from what has been said to any 
one who believes in our assumptions. Our theory seems to 
5 confirm experience and to be confirmed by it For all men 
have some conception of the nature of the gods, and all who 
believe in the existence of gods at all, whether barbarian or 
Greek, agree in allotting the highest place to the deity, 
surely because they suppose that immortal is linked with 
immortal and regard any other supposition as inconceivable. 

10 If then there is, as there certainly is, anything divine, what 
we have just said about the primary bodily substance was 
well said. The mere evidence of the senses is enough to 
convince us of this, at least with human certainty. For in 
the whole range of time past, so far as our inherited records 

15 reach,^ no change appears to have taken place either in the 
whole scheme of the outermost heaven or in any of its 
proper parts. The common name, too, which has been 
handed down from our distant ancestors even to our own 
day, seems to show that they conceived of it in the fashion 
which we have been expressing. The same ideas, one must 

20 believe, recur in men's minds not once or twice but again 
and again. And so, implying that the primary body is 
something else beyond earth, fire, air, and water, they gave 
the highest place a name of its own, aither^ derived from the 
fact that it * runs always ' ^ for an eternity of time. Anaxa- 

25 goras, however, scandalously misuses this name, taking 
aithej' as equivalent to fire."^ 

It is also clear from what has been said why the number 

^ Simplicius says he 'has been told' that there are written astro- 
nomical records {auT^wa^ rr/pi^afj? avaypivmov^) in Egypt for the past 
630,000 years and in Babylon for the past 1,440,000 years. 

^ i. e. aiOrip from aei Biiv. The derivation was suggested by Plato 
{Cratyltis, 410 B). 

^ i.e. deriving al6f]p from a'lBcLv. Cf. Bk. Ill, 302^4. 

BOOK I. 3 270^^ 

of what we call simple bodies cannot be greater than it is. 
The motion of a simple body must itself be simple, and we 
assert that there are only these two simple motions, the 
circular and the straight, the latter being subdivided into 30 
motion away from and motion towards the centre. 

4 That there is no other form of motion opposed as 
contrary to the circular may be proved in various ways. 
In the first place, there is an obvious tendency to oppose 
the straight line to the circular. For concave and convex 35 
are not only regarded as opposed to one another, but they 271^ 
are also coupled together and treated as a unity in oppo- 
sition to the straight. And so, if there is a contrary 
to circular motion, motion in a straight line must be re- 
cognized as having the best claim to that name. But the 
two forms of rectilinear motion are opposed to one another 
by reason of their places ; for up and down is a difference 5 
and a contrary opposition in place.^ Secondly, it may be 
thought that the same reasoning which holds good of the 
rectilinear path applies also to the circular, movement from 
^ to ^ being opposed as contrary to movement from B to 
A. But what is meant is still rectilinear motion. For that is 
limited to a single path, while the circular paths which pass to 
through the same two points are infinite in number.^ Even 
if we are confined to the single semicircle and the opposition 
is between movement from C to D and from D to C along 
that semicircle, the case is no better. For the motion is the 
same as that along the diameter, since we invariably regard 
the distance between two points as the length of the straight 
line which joins them."* It is no more satisfactory to con- 
struct a circle and treat motion along one semicircle as 15 
contrary to motion along the other. For example, taking 

^ The point of this elliptical argument seems to be that, while the 
generally admitted case of contrary opposition (viz. that of upward 
and downward motion) rests on a contrary opposition of places (viz. 
above and below), no such ground can be suggested for the opposition 
of circular to rectilinear motion. 

2 Fig. I. ^ 3 YiQ^ jj^ 

271^ DE CAELO 

a complete circle, motion from E to F on the semicircle G 
may be opposed to motion from F to E on the semicircle 
I/} But even supposing these are contraries, it in no way 
follows that the reverse motions on the complete cir- 

20 cumference are contraries. Nor again can motion along 
the circle from ^ to ^ be regarded as the contrary of 
motion from A to C:'^ for the motion goes from the same 
point towards the same point, and contrary motion was 
distinguished as motion from a contrary to its contrary.^ 
And even if the motion round a circle is the contrary of the 
reverse motion, one of the two would be ineffective : for 
both move to the same point, because ^ that which moves 

25 in a circle, at whatever point it begins, must necessarily 
pass through all the contrary places alike. (By contrarieties 
of place I mean up and down, back and front, and right 
and left ; and the contrary oppositions of movements are 
determined by those of places.) One of the motions, then, 
would be ineffective, for if the two motions were of equal 
strength,* there would be no movement either way, and if 

30 one of the two were preponderant, the other would be 
inoperative. So that if both bodies were there, one of 
them, inasmuch as it would not be moving with its own 
movement, would be useless, in the sense in which a shoe 
is useless when it is not worn. But God and nature create 
nothing that has not its use.^ 

1 Fig. III. 


"^ Phys. V. V, 229^21. 

^ Reading ort for the 'in of our MSS. after Simplicius, who had both 
readings before him. 

* Prantl's alteration of -yap into ap is not needed. The yap refers 
back to the remark 'one of the two would be ineffective'. That 
remark is therefore repeated in the text. 

^ The bearing of this argument is clear if it is remembered that the 
assertion of the existence of a certain movement necessarily involves 
for Aristotle the assertion of the existence of a body which naturally 
exhibits the movement. Similarly the assertion that a movement is 
inoperative involves the assertion that a body is inoperative. 

BOOK I. 5 271* 

5 This bemg clear, we must go on to consider the questions 271 
which remain. First, is th ere an infinite body ^ g tllf 
ma^ioritY- aLihe ancient philo sopliers thought, or is this an 
impossibihty ? The decision of this question, either way, is 
not unimportant, but rather all-important, to our search for 5 
the truth.^ It is this problem which has practically always 
been the source of the differences of those who have written 
about nature as a whole. So it has been and so it must 
be; since the least initial deviation from the truth is 
multiplied later a thousandfold.^ Admit, for instance, the 10 
existence of a minimum magnitude, and you will find that 
the minimum which you have introduced, small as it is, causes 
the greatest truths of mathematics to totter. The reason 
is that a principle is great rather in power than in extent ; ^ 
hence that which was small at the start turns out a giant at 
the end. Now the conception of the infinite possesses this 
power of principles, and indeed in the sphere of quantity 
possesses it in a higher degree than any other conception ; so 15 
that it is in no way absurd or unreasonable that the assump- 
tion that an infinite body exists should be of peculiar 
moment to our inquiry. The infinite, then, we must now 
discuss, opening the whole matter from the beginning. 

Every body is necessarily to be classed either as simple 
or as composite ; ^ the infinite body, therefore, will be either 
simple or composite. But it is clear, further, that if the simple 20 
bodies are finite, the composite must also be finite, since 
that which is composed of bodies finite both in number and 
in magnitude is itself finite in respect of number and 
magnitude : its quantity is in fact the same as that of the 
bodies which compose it. What remains for us to consider, 
then, is whether any of the simple bodies can be infinite in 
magnitude, or whether this is impossible. Let us try the 25 
primary body first, and then go on to consider the others. 

The body which moves in a circle must necessarily be 
finite in every respect, for the following reasons, (i) If the 
body so moving is infinite, the radii drawn from the centre 

^ Reading rj]v rrepl ttjs with FHMJ. The phrase recurs in this form 
in Mef. 993* 30. 

^ After Plato, Cratyliis, 436 D. 

^ The eo-Tot of all other MSS. is preferable to E's uvau 

271^ DE CAELO 

30 will be infinite.^ But the space between infinite radii is 
infinite : and by the space between the radii I mean the 
area outside which no magnitude which is in contact with 
the two lines can be conceived as falling.^ This, I say, will 
be infinite : first, because in the case of finite radii it is always 

272* finite ; and secondly,^ because in it one can always go on to 
a width greater than any given width ; thus the reasoning 
which forces us to believe in infinite number, because there is 
no maximum, applies also to the space between the radii. 
Now the infinite cannot be traversed, and if the body is 
infinite the interval between the radii is necessarily infinite : 
5 circular motion therefore is an impossibility. Yet our eyes 

., tell us that the heavens revolve in a circle, and by argument 
also we have determined that there is something to which 
circular movement belongs. 

(2) Again, if from a finite time a finite time be subtracted, 
what remains must be finite and have a beginning. And if 
10 the time of a journey has a beginning, there must be 
a beginning also of the movement, and consequently also 
of the distance traversed. This applies universally. Take 
a line, ACE, infinite in one direction, E, and another line, 
BBy infinite in both directions.* 'Let ACE describe a circle, 

* 'The centre', when not in any way qualified, means the centre 
of the earth, which is taken by Aristotle to be also the centre of all the 
revolutions of the heavenly bodies. He cannot here mean the centre 
of the supposed infinite body, since to that no shape has yet been given. 

^ The last phrase {ol fir]8€v eanv e^oa Xa^elv) seems to have been mis- 
understood by Prantl. A comparison of this passage with others in 
which what is practically the same phrase occurs (esp. Ale/. 1021^12, 
1055* 12) shows (a) that ov is governed by e^o) (' outside which '), and 
(d) that the phrase is roughly equivalent to reXetoi/. The point here 
is that by 8uiaTrjfxa he means, not a straight line spanning the interval 
between the radii, but the whole area enclosed between the two radii 
and the portion of the circumference which connects their extremities. 
In 1. 30 read, after duia-Trjixa, de rather than yup, which is in E alone. 

^ Reading m with the MSS. ; Prantl's eVei seems to have nothing 
to recommend it. It will then be necessary to put a full-stop after 
8ia(TTrj[jLaTos in 1. 3. This sentence gives, of course, a second reason 
for taking the duiaTqfxa to be infinite. 

* Fig. IV. ■,- . 



BOOK I. 5 272^ 

revolving upon C as centre. In its movement it will cut 15 
BB continuously for a certain time. This will be a finite 
time, since the total time is finite in which the heavens 
complete their circular orbit, and consequently the time 
subtracted from it, during which the one line in its motion 
cuts the other, is also finite. Therefore there will be 
a point at which ACE began for the first time to cut BB, 
This, however, is impossible.^ The infinite, then, cartnot 
revolve in a circle ; nor could the world, if it were infinite.^ 20 

(3) That the infinite cannot move may also be shown as 
follows. Let ^ be a finite line moving past the finite line, 
B. Of necessity A will pass clear of B and ^ of ^ at the 
same moment; for each overlaps the other to precisely the 25 
same extent. Now if the two were both moving, and 
moving in contrary directions, they would pass clear of one 
another more rapidly ; if one were still and the other 
moving past it, less rapidly ; provided that the speed of the 
latter were the same in both cases. This, however, is clear : 
that it is impossible to traverse an infinite line in a finite 
time. Infinite time, then, would be required. (This we 30 
demonstrated above in the discussion of movement.^) And 

^ In this argument the ascertained fact that the revolution of the 
heavens occupies a Hmited time is used to prove the finitude of its 
path and consequently also of the body itself. BB represents an 
infinite line drawn within the infinite body and therefore 'traversed' by 
that body in its revolution. But there can be no point at which the 
contact of A CE with BB either begins or ends, while there is a time 
within which the revolution is completed. Therefore the revolving 
body is not infinite. — Possibly the centre of the movement oi ACE 
should be A (as in F and Simpl.) rather than C 

"^ Movement of the 'world' {Koay-o^) is here used for movement of 
the 'heaven* (oupaj/oy). Either KOCT/uoy stands for the heavenly body, 
as in Nic. Eth. 1141^ i, or the movement and the infinity are treated 
for the moment as attributes of the whole. 

^ Aristotle refers to the Physics, here and elsewhere, as continuous 
with the De Caelo. Different parts of the Physics are referred to by 
different names. Simplicius (p. 226, 19) observes that Phys. I-IV are 
cited as 'the discussion of principles' (Trfpi apy^wv) and Phys, V-VIII 
as 'the discussion of movement' (Trept xivi^o-ews). In Phys. VIII, 
257* 34} Aristotle refers back to an earlier passage as occurring tV toIs- 
KaBoknv Tot's Trepl (j)va(a)s ', and Simplicius, commenting on this {Comm. 
in Phys. p. 1233, 30), ' infers' that Phys. I-V are the Trtpi (fivcrecos and 
Phys. VI-VIII the Trfpl Kivr-io-ews. But his inference is false. The 
reference is not, as he thought, to V. iv. The principle had been 
asserted earlier, viz. in III. i. The ' general considerations concerning 
nature' may therefore be identified with the 'discussion of principles', 
and the Physics may be divided in the middle, i.e. at the end of 
Book IV. — The reference in this passage is to Phys. VI. vii. 

272* DE CAELO 

it makes no difference whether a finite is passing by an 

272^ infinite or an infinite by a finite. For when A is passing B^ 

then B overlaps ^ A, and it makes no difference whether B 

is moved or unmoved, except that, if both move, they pass 

clear of one another more quickly. It is, however, quite 

possible that a moving line should in certain cases pass one 

which is stationary quicker than it passes one moving in an 

5 opposite direction. One has only to imagine the movement 

to be slow where both move and much faster where one is 

stationary. To suppose one line stationary, then, makes no 

difficulty for our argument, since it is quite possible for^ to 

pass ^ at a slower rate when both are moving than when only 

10 one is. If, therefore, the time which the finite moving line 

takes to pass the other is infinite, then necessarily the time 

occupied by the motion of the infinite past the finite is also 

infinite. For the infinite to move at all is thus absolutely 

impossible ; since the very smallest movement conceivable 

must take an infinity of time. Moreover the heavens 

certainly revolve, and they complete their circular orbit in 

15 a finite time ; so that they pass round the whole extent of 

any line within their orbit, such as the finite line AB. The 

revolving body, therefore, cannot be infinite. 

(4) Again, as a line which has a limit cannot be infinite, 
or, if it is infinite, is so only in length,^ so a surface cannot 

^ Reading KaKelvrj TrapaWaTTei €K€lv7]v with FHMJ. The alternative 
to TrnpaWciTTeij nap', rests upon the sole authority of E : for L has 
TTopaXXaTTr]. Ilap' is intolerable, since it must stand for ^epfna irapd 
and thus attributes movement to B, of which in the same sentence it is 
said that it may be unmoved. 

2 The reading is doubtful. It is difficult to attach any other sense 
to the possession of ixipas ('limit') than a denial of infinity; in which 
case dXX' e'inep, fVi p.r]Kos means 'or if a finite line is infinite, it is so in 
length '. The antecedent thus appears to contradict both itself and 
the consequent. Simplicius preserves a variant for inX prJKos, eVi 
Odrepa. ('A finite line can only be infinite, if at all, in one direction '.) 
— Perhaps, however, the text is correct. The sentence may be para- 
phrased as follows. A limited line cannot be infinite : lines, in fact, 
can only be infinite, if at all, in that respect in which they are un- 
limited : but there is nothing in the nature of ' line ' to determine the 
length of any given line : consequently, it is only in respect to length 
that infinity is ever ascribed to lines. (Mr. Ross suggests that »/ should 
be read instead of rjs in 1. 17. 'A line cannot be infinite in that respect 
in which it is a limit.' The line is the limit of the plane, i. e. a limit 
in respect of breadth. Similarly the plane is the limit in respect of 
depth. This correction has support from the translation of Argyropylus 
('ex ea parte qua finis est'), and is probably right.) 

BOOK I. 5 


be infinite in that respect in which it has a limit; or, indeed, / 
if it is completely determinate, in any respect whatever. 
Whether it be a square or a circle or a sphere, it cannot be 20 
infinite, any more than a foot-rule can. There is then no 
such thing as an infinite sphere or square or circle, and 
where there is no circle there can be no circular movement, 
and similarly where there is no infinite at all there can be 
no infinite movement ; and from this it follows that, an 
infinite circle being itself an impossibility, there can be no 
circular motion of an infinite body. 

(5) Again, take a centre C, an infinite line, AB^ another 25 
infinite line at right angles to it, E^ and a moving radius, 
CD} CD will never cease contact with E^ but the position 
will always be something like CE^ CD cutting E at F,^ 
The infinite line, therefore, refuses to complete the circle.^ 

(6) Again, if the heaven is infinite and moves in a circle, 30 
we shall have to admit that in a finite time it has traversed 
the infinite. For suppose the fixed heaven infinite, and that 
which moves within it equal to it. It results that when 
the infinite body has completed its revolution, it has 
traversed an infinite equal to itself in a finite time. But 273^ 
that we know to be impossible. 

(7) It can also be shown, conversely, that if the time of 
revolution is finite, the area traversed must also be finite ; 

^ Also, of course, infinite. 
2 Fig. V. 

^ The 'infinite line' is the infinite radius CD, which is unable to 
complete the circle owing to its inability to extricate its outer extremity 
from that of the other infinite, E. The MSS. vary between kvkXcoi 
(EL), kvkXo) (M), and kvkXov (HFJ : the last, however, has cot stipra- 
scriptinn). In FMJ TrepUuxL follows instead of preceding kvkXov {kCkXco 
M). Perhaps kvkXuv irfpUio-iv should be read with FJ, though either 
reading will give the sense required. 

273^ DE CAELO 

but the area traversed was equal to itself; therefore, it is 
itself finite.^ 
5 We have now shown that the body which moves in 
a circle is not endless or infinite, but has its limit. 

Further, neither that which moves towards nor that 6 
which moves away from the centre can be infinite. For the 
upward and downward motions are contraries and are there- 
fore motions towards contrary places. But if one of a pair 

lo of contraries is determinate, the other must be determinate 
also. Now the centre is determined ; for, from whatever 
point the body which sinks to the bottom starts its down- 
ward motion, it cannot go farther than the centre. The 
centre, therefore, being determinate, the upper place must 
also be determinate. But if these two places are determined 

15 and finite, the corresponding bodies must also be finite. 
Further, if up and down are determinate, the intermediate 
place is also necessarily determinate. For, if it is indeter- 
minate, the movement within it will be infinite^; and 
that we have already shown to be an impossibility.^ The 
middle region then is determinate, and consequently any 
body which either is in it, or might be in it, is determinate. 

20 But the bodies ^which move up and down may be in it, 
since the one moves naturally away from the centre and 
the other towards it. 

From this alone it is clear that an infinite body is an 
impossibility ; but there is a further point. If there is no 
such thing as infinite weight, then it follows that none of 
these bodies can be infinite. For the supposed infinite 

35 body would have to be infinite in weight. (The same argu- 
ment applies to lightness : for as the one supposition 
involves 'infinite weight, so the infinity of the body which 
rises to the surface involves infinite lightness.) This is 

^ The preceding six arguments start from the hypothesis of an 
infinite body and show the difficulties involved in the consequent 
assumption of an infinite path and in the infinite time needed for its 
completion. The converse argument starts from known finite time of 
revolution and argues from that to the finitude of the path traversed 
and of the body which traverses it. -J 

^ Reading €17 rj^Kirrion with FHMJ Simpl. % 

3 PAys.Vin. vul 

BOOK I. 6 273* 

proved as follows. Assume the weight to be finite, and 
take an infinite body, AB, of the weight C. Subtract from 
the infinite body a finite mass, BB, the weight of which 30 
shall be E. E then is less than (7, since it is the weight of 
a lesser mass.^ Suppose then that the smaller goes into the 
greater a certain number of times, and take BF bearing 273^^ 
the same proportion to BD which the greater weight bears 
to the smaller. For you may subtract as much as you 
please from an infinite. If now the masses are propor- 
tionate to the weights, and the lesser weight is that of the 
lesser mass, the greater must be that of the greater. The 5 
weights, therefore, of the finite and of the infinite body are 
equal. Again, if the weight of a greater body is greater 
than that of a less, the weight of GB will be greater than 
that of FB ; ^ and thus the weight of the finite body is 
greater than that of the infinite. And, further, the weight 
of unequal masses will be the same, since the infinite and 
the finite cannot be equal. It does not matter whether the 10 
weights are commensurable or not. If {a) they are incom- 
mensurable the same reasoning holds. For instance, 
suppose E multiplied by three is rather more than C: the 
weight of three masses of the full size oi BD will be greater 
than C. We thus arrive at the same impossibility as 15 
before. Again {b) we may assume weights which are com- 
mensurate ; for it makes no difference whether we begin 
with the weight or with the mass. For example, assume 
the weight E to be commensurate with C^ and take from 
the infinite mass a part BD of weight E. Then let a mass 
BF be taken having the same proportion to BD which the 20 
two weights have to one another. (For the mass being 
infinite you may subtract from it as much as you please.) 
These assumed bodies will be commensurate in mass and 
in weight alike. Nor again does it make any difference to 
our demonstration whether the total mass has its weight 
equally or unequally distributed. For it must always be 
possible to take from the infinite mass a body of equal 25 

' Fig. VI. ^ G F D B 
, , , , 

273^ DE CAELO 

weight to BD by diminishing or increasing the size of the 
section to the necessary extent.^ 

From what we have said, then, it is clear that the weight 
of the infinite body cannot be finite. It must then be 
infinite. We have therefore only to show this to be im- 
possible in order to prove an infinite body impossible. But 
30 the impossibility of infinite weight can be shown in the 
following way. A given weight moves a given distance in 
a given time ; a weight which is as great and more moves 
the same distance in a less time, the times being in inverse 
274^ proportion to the weights. For instance, if one weight is 
twice another, it will take half as long over a given move- 
ment. Further, a finite weight traverses any finite distance 
in a finite time. It necessarily follows from this that 
infinite weight, if there is such a thing, being, on the one 
5 hand, as great and more than as great as the finite,^ will 
move accordingly, but being, on the other hand, compelled 
to move in a time inversely proportionate to its greatness, 
cannot move at all.^ The time should be less in proportion 
as the weight is greater. But there is no proportion be- 
tween the infinite and the finite ; proportion can only hold 
between a less and a greater finite time. And though you 
may say that the time of the movement can be continually 
10 diminished, yet there is no minimum.* Nor, if there were, 

^ Delete comma after BA. 

' There can be no doubt that the comma should follow, not precede, 
Koi €TL (1. 5). The phrase roa-ovBe oaov to nfirfpaa-fxivov ku\ en is 
parallel to the roaovrov koX en of 273^31. Bonitz (Jn^f. 291*7) takes 
Km €Ti in this way, but appears to interpret the phrase as indicating 
the distance moved, which is impossible. — For the use of koi en 
cf. Met. 1021*6. 

^ Because, as explained in the following sentences, there is no time 
for it to move in. The argument is : the infinite may (fj-ev) be regarded 
loosely as something exceedingly great, in which case it follows simply 
that it moves exceedingly fast : so far there is no difficulty: but {8e) 
as soon as you begin to specify /1020 great it is and Aow fast it moves 
the difficulties become insuperable. 

■* aXX' del ev eXdrTuvi is probably an opponent's objection. It is 
an application of the argument mentioned in 272*1. We talk of 
number as infinite, A. says there, because there is no maximum. 
^ Similarly the advocate of infinite weight says, 'At any rate the weight 
can be increased and'the time proportionately diminished ad injinitum '. 
But the motion of the infinite, to be conceivable, must according to 
Aristotle occupy a tii)ie\ and any time, however snjall, will be' a time 
in which the given movement could be effected by a finite body. 

BOOK I. 6 274^ 

would it help us. For some finite body could have been 
found greater than the given finite in the same proportion 
which is supposed to hold between the infinite and the 
given finite ; ^ so that an infinite and a finite weight must 
have traversed an equal distance in equal time. But that 
is impossible. Again, whatever the time, so long as it is 
finite, in which the infinite performs the motion, a finite 15 
weight must necessarily move a certain finite distance in 
that same time. Infinite weight is therefore impossible, 
and the same reasoning applies also to infinite lightness. 
Bodies then of infinite weight and of infinite lightness are 
equally impossible. 

That there is no infinite body may be shown, as we have 
shown it, by a detailed consideration of the various cases. 20 
But it may also be shown universally, not only by such 
reasoning as we advanced in our discussion of principles ^ 
(though in that passage we have already determined univer- 
sally the sense in which the existence of an infinite is to be 
asserted or denied), but also suitably to our present purpose 
in the following way. That will lead us to a further 
question. Even if the total mass is not infinite, it may 25 
yet be great enough to admit a plurality of universes. The 
question might possibly be raised whether there is any 
obstacle to our believing that there are other universes 
composed on the pattern of our own, more than one, 
though stopping short of infinity. First, however, let us 
treat of the infinite universally. 

^ What difficulty there is in this sentence is due to the elliptical 
expression and to the tacit inference from a proportion between the 
times to a proportion between the bodies. What is known is the ratio 
between the imaginary minimum time assigned to the infinite body 
and some other finite time. A. speaks of this known ratio as a ratio 
between the infinite body and another body. The argument is : take 
any other finite body [erepov) : its ratio to the infinite may be deter- 
mined by their respective times : but another finite body (aWo n 
TTcirfpaaiJLevov) could be found in the same ratio (on the basis of 
a comparison of times) to the first. Thus a finite body will cover the 
same distance as the infinite body in the same time, which is absurd. — 
The comma after Xoyco in 1. 11 should be deleted. fxelCou belongs to 
the predicate both of the relative clause and of the main sentence. 
Neither Simplicius nor Alexander (as reported by Simplicius) seems 
to have interpreted the words quite correctly. 

- P/ijfs. 111. iv-viii (see n. on 272* 30). Read dpqixevovs with FM. 

C 2 

274^ DE CAELO 

30 Every body must necessarily be either finite or infinite, 7 
and if infinite, either of similar or of dissimilar parts. If its 
parts are dissimilar, they must represent either a finite or 
an infinite number of kinds. That the kinds cannot be 
infinite is evident, if our original presuppositions remain 
274^ unchallenged. For the primary movements being finite in 
number, the kinds of simple body are necessarily also finite, 
since the movement of a simple body is simple, and the 
simple movements are finite, and every natural body must 
5 always have its proper motion. Now if ^ the infinite body is 
to be composed oi 2i finite number of kinds, then each of its 
parts must necessarily be infinite in quantity, that is to 
say, the water, fire, &c., which compose it. But this is 
impossible, because, as we have already shown, infinite 
weight and lightness do not exist. Moreover it would be 
necessary also that their places should be infinite in extent, 

10 so that the movements too of all these bodies would be in- 
finite. But this is not possible, if we are to hold to the , 
truth of our original presuppositions and to the view that 
neither that which moves downward, nor, by the same 
reasoning, that which moves upward, can prolong its move- 
ment to infinity. For it is true in regard to quality, 
quantity, and place alike that any process of change is 

15 impossible which can have no end. I mean that if it is im- 
possible for a thing to have come to be white, or a cubit 
long, or in Egypt, it is also impossible for it to be in process 
of coming to be any of these. It is thus impossible for a 
thing to be moving to a place at which in its motion it can 
never by any possibility arrive. Again, suppose the body 
to exist in dispersion, it may be maintained none the less 
that the total of all these scattered particles, say, of fire, is 

20 infinite,^ But body we saw to be that which has exten- 
sion every way. How can there be several dissimilar ele- 
ments, each infinite? Each would have to be infinitely 
extended every way. 

It is no more conceivable, again, that the infinite should 
exist as a whole of similar parts. For, in the first place, 

* Reading el'ye with FHMJ. 

2 * As Anaxagoras seems to have supposed ' (Simpl.). 


BOOK I. 7 274*^ 

there is no other (straight) movement beyond those men- 
tioned : we must therefore give it one of them. And if so, 
we shall have to admit either infinite weight or infinite 25 
lightness. Nor, secondly, could the body whose movement 
is circular be infinite, since it is impossible for the infinite 
to move in a circle. This, indeed, would be as good as 
saying that the heavens are infinite, which we have shown 
to be impossible. 

Moreover, in general, it is impossible that the infinite 30 
should move at all. If it did, it would move either natur- 
ally or by constraint : and if by constraint, it possesses also 
a natural motion, that is to say, there is another place, 
infinite like itself, to which it will move. But that is 

That in general it is impossible for the infinite to be acted 
upon by the finite or to act upon it may be shown as 

(i. The infinite cannot be acted upon by the finite^ Let 275^ 
A be an infinite, B a finite, C the time of a given movement 
produced by one in the other. Suppose, then, that A was 
heated, or impelled, or modified in any way, or caused to 
undergo any sort of movement whatever, by B in the time 
C, Let D be less than B\ and, assuming that a lesser 
agent moves a lesser patient in an equal time, call the quan- 5 
tity thus modified by D, E. Then, as D is to B^ so is E 
to some finite quantum. We assume that the alteration of 
equal by equal takes equal time, and the alteration of less 
by less or of greater by greater takes the same time, if the 
quantity of the patient is such as to keep, the proportion 
which obtains between the agents, greater and less. If so, i© 
no movement can be caused in the infinite ^ by any finite 
agent in any time whatever. For a less agent will produce 
that movement in a less patient in an equal time, and the 
proportionate equivalent of that patient will be a finite 

^ Because an infinite place cannot exclude, or be ' other ' than, any 
finite place. This argument applies to natural as well as unnatural 
movement : for a body moves naturally in the effort to reach its place. 
— Read roTroy aWo? \<roi with EL, confirmed by Simplicius (ro-no^ tcroy 
aWoi, 239, 24).^ 

* Read Kiv^drjaeTai with Simplicius and all MSS. except E. 

275^ DE CAELO 

quantity, since no proportion holds between finite and 

(2. The infinite cannot act upon the finite.) Nor, again, can 

15 the infinite produce a movement in the finite in any time 
whatever. Let A be an infinite, j5^ a finite, C the time of 
action. In the time (7, D will produce that motion in a 
patient less than B^ say F. Then take E^ bearing the same 
proportion to D as the whole BF bears to F. E will pro- 
duce the motion in BF in the time C. Thus the finite and 

20 the infinite effect the same alteration in equal times. But 
this is impossible ; for the assumption is that the greater 
effects it in a shorter time. It will be the same with any 
time that can be taken, so that there will be no time in which 
the infinite can effect this movement. And, as to infinite time, 
in that nothing can move another or be moved by it. For 
such time has no limit, while the action and reaction have. 
(3. There is no inter actiojt between infinites^ Nor can 

25 infinite be acted upon in any way by infinite. Let A and B 
be infinites, CD being the time of the action of A upon B. 
Now the whole B was modified in a certain time, and the 
part of this infinite, E^ cannot be so modified in the same 
time, since we assume that a less quantity makes the move- 
ment in a less time. Let E then, when acted upon by A^ 

30 complete the movement in the time D. Then, as D is to 
CD^ so is E to some finite part of ^. This part will neces- 
sarily be moved by A in the time CD, For we suppose 
that the same agent produces a given effect on a greater 
275^ and a smaller mass in longer and shorter times, the times 
and masses varying proportionately. There is thus no 
finite time in which infinites can move one another. Is 
their time then infinite? No, for infinite time has no end, 
but the movement communicated has. 

5 If therefore every perceptible body possesses the power ^ 
of acting or of being acted upon, or both of these, it is im-^ 
possible that an infinite body should be perceptible. All 
bodies, however, that occupy place are perceptible. There 
is therefore no infinite body beyond the heaven. Nor again 
is there anything of limited extent beyond it. And so 

* Called BF a few lines below. 


BOOK I. 7 275^ 

beyond the heaven there is no body at all. For if you 
suppose it an object of intelligence, it will be in a place — 10 
since place is what ' within ' and ' beyond ' denote — and 
therefore an object of perception. But nothing that is not 
in a place is perceptible.^ 

The question may also be examined in the light of more 
general considerations as follows. The infinite, considered 
as a whole of similar parts, cannot, on the one hand, move 
in a circle. For there is no centre of the infinite, and that 
which moves in a circle moves about the centre. Nor again 15 
can the infinite move in a straight line. For there would 
have to be another place infinite like itself to be the goal of 
its natural movement and another, equally great, for the 
goal of its unnatural movement. Moreover, whether its 
rectilinear movement is natural or constrained, in either 
case the force which causes its motion will have to be 20 
infinite. For infinite force is force of an infinite body, and 
of an infinite body the force is infinite. So the motive body 
also will be infinite. (The proof of this is given in our dis- 
cussion of movement,^ where it is shown'that no finite thing 
possesses infinite power, and no infinite thing finite power.) 
If then that which moves naturally can also move unnatur- 
ally, there will be two infinites, one which causes, and 25 
another which exhibits the latter motion. Again, what is 
it that moves the infinite ? If it moves itself, it must be 
animate. But how can it possibly be conceived as an 
infinite animal ? And if there is something else that moves 
it, there will be two infinites, that which moves and that 
which is moved, differing in their form and power.^ 

^ These sentences are rather disjointed and read more like rough 
notes than a finished argument. The final remark seems inconsequent. 
We should expect : ' but what is not perceptible cannot occupy 
a place ' ; so that the hypothesis that the body beyond the heaven 
is voijTov contradicts itself. The main point, however, is that all these 
connected attributes are inapplicable to an object of intelligence like 
the Platonic ddos. 

2 Pkfs.VUl.x. 

^ The last argument (from ' Again, what is it ... ') is not a mere 
repetition of the preceding. The preceding sentence shows that an 
infinite disturbing force is needed to account for any unnatural move- 
ment of an infinite body. Finally, it is suggested that even the natural 
or normal movement of such a body would presuppose an independent 
infinite force. Again, the foregoing argument applied only to rectilinear 

275'' DE CAELO 

30 If the whole is not continuous, but exists, as Democritus 
and Leucippus think, in- the form of parts separated by- 
void, there must necessarily be one movement of all the 
multitude. They are distinguished, we are told, from one 
275a another by their figures ; but their nature is one, like many 
pieces of gold separated from one another. But each piece 
must, as we assert, have the same motion. For a single 
clod moves to the same place as the whole mass of earth, 
and a spark to the same place as the whole mass of fire. 
So that if it be weight that all possess, no body is, strictly 
5 speaking, light ; and if lightness ^ be universal, none is 
heavy. Moreover, whatever possesses weight or lightness 
will have its place either at one of the extremes or in the 
middle region. But this is impossible while the world is 
conceived as infinite. And, generally, that which has no 
centre or extreme limit, no up or down, gives the bodies no 
10 place for their motion ; and without that movement is 
impossible. A thing must move either naturally or un- 
naturally, and the two movements are determined by the 
proper and alien places. Again, a place in which a thing 
rests or to which it moves unnaturally, must be the natural 
15 place for some other body, as experience shows. Neces- 
sarily, therefore, not everything possesses weight or lightness, 
but some things do and some do not. From these argu- 
ments then it is clear that the body of the universe is not 

We must now proceed to explain why there cannot be 8 
more than one heaven — the further question mentioned 
above.^ For it may be thought that we have not proved 
20 universally of bodies that none whatever can exist outside 

movement, since unnatural circular movement has been shown to be 
impossible : but the last argument would apply equally to circular 
movement. The remark * i f it moves itself, it must be animate' 
implies that it is incorrect to think of the natural movement of the 
elements as self-movement. It is only movement uninfluenced by 
any sublunary body. That self-movement is impossible Aristotle has 
already shown in Phys. VII. 

^ Prantl misprints ff for et. 

^ In 1. 18 Prantl's Xeyofieu seems to be a misprint for Xeyco/zfv. — 
* Heaven ' here stands of course for world {oiipapos = Koo-fioi,), — The 
reference is to c. vi (274^24). 

BOOK I. 8 276^ 

our universe, and that our argument applied only to those 
of indeterminate extent. 

Now all things rest and move naturally and by con- 
straint. A thing moves naturally to a place in which it 
rests without constraint, and rests naturally in a place ta 
which it moves without constraint. On the other hand, ^5 
a thing moves by constraint to a place in which it rests by 
constraint, and rests by constraint in a place to which it 
moves by constraint. Further, if a given movement is due 
to constraint, its contrary is natural. If, then, it is by con- 
straint that earth moves from a certain place to the centre 
here, its movement from here to there will be natural, and 
if earth from there rests here without constraint, its move- 
ment hither will be natural. And the natural movement 30 
in each case is one.^ Further, these worlds, being similar in 
nature to ours, must all be composed of the same bodies as 
it. Moreover each of the bodies, fire, I mean, and earth 
and their intermediates, must have the same power as in 276^ 
our world. For if these names are used equivocally, if the 
identity of name does not rest upon an identity of form in 
those elements and ours, then the whole to which they 
belong can only be called a world by equivocation. Clearly, 
then, one of the bodies will move naturally away from the 5 
centre and another towards the centre, since fire must be 
identical with fire, earth with earth, and so on, as the frag- 
ments of each are identical in this world. That this must 
be the case is evident from the principles laid down in our 
discussion of the movements ; ^ for these are limited in 
number, and the distinction of the elements depends upon 
the distinction of the movements. Therefore, since the 10 
movements are the same, the elements must also be the 
same everywhere. The particles of earth, then, in another 
world move naturally also to our centre and its fire to our 
circumference. This, however, is impossible, since, if it 
were true, earth must, in its own world, move upwards, and 15 
fire to the centre ; in the same way the earth of our world 

^ Reading /xw d' fj with EF^M Alex. The ydp of the other MSS. 
and Simpl. is misleading and suggests an argument where there is 
none. The principle is simply stated for future use. 

* Above, cc. ii-iv. 

276^ DE CAELO 

must move naturally away from the centre when it moves 
towards the centre of another universe.^ This follows from 
the supposed juxtaposition of the worlds. For either we 
must refuse to admit the identical nature of the simple 

20 bodies in the various universes, or, admitting this, we must 
make the centre and the extremity one as suggested. This 
being so, it follows that there cannot be more worlds than 

To postulate a difference of nature in the simple bodies 
according as they are more or less distant from their proper 
places is unreasonable. For what difference can it make 
whether we say that a thing is this distance away or that ? 

25 One would have to suppose a difference proportionate to 
the distance and increasing with it, but the form is in fact 
the same. Moreover, the bodies must have some movement, 
since the fact that they move is quite evident.^ Are we to 
say then that all their movements, even those which are 
mutually contrary, are due to constraint ? No, for a body 
which has no natural movement at all cannot be moved by 

30 constraint. If then the bodies have a natural movement, 

^ In 1. 17 the comma which Prantl places after (f)vaLv should be 
placed instead after fxea-op. It is needed in this place in order to show 
that the following clause {8ia to . . . aXXtjXovs) is explanatory of the 
dvdyKr} of 1. 1 4, not of (j)epea6aL in 1. 1 6. 

^ If there is one centre and one extremity, there is only one heaven 
or world. (Read tovtov S' oVrof, ddvvaTou kt\. Prantl's dronov is 
found only in F and J, and in both it is preceded by tov, which shows 
that it is an adscript intended to explain the meaning of tovtov.) — The 
argument of the chapter down to this point is a single redtcctio ad 
absurdum, Simplicius tries unsuccessfully to interpret it as a series 
of reductions. The remainder of the chapter reasserts the conclusion 
here drawn by closing up various pathways of escape. In truth there 
is only one way of escape, as Aristotle here says, viz. to deny the 
identity of the fire and earth in the other worlds with that in our own ; 
but the contention takes a variety of forms — (i) 'distance makes 
a difference ' ; (2) ' they have no movement, or only movje by con- 
straint ' ; (3) ' the goal of their movement is only the same m kind 2iS 
that of the corresponding elements here '. These suggestions are 
refuted in what follows. 

^ Throughout this paragraph when Aristotle speaks of ' the bodies ' 
he is thinking of the fire, earth, &c., supposed to constitute another 
Koa-fjLos. He is not proving over again the proposition that the four 
elements have each a natural motion, but considering what would be 
their motion in another world existing beside our own. The empirical 
evidence of movement here appealed to must be that of the fire and 
earth of this world ; but a thing that did not move would not be 
a body at all. 

BOOK I. 8 276'' 

the movement of the particular instances of each form must 
necessarily have for goal a place numerically one, i. e. a 
particular centre or a particular extremity. If it be sug- 
gested that the goal in each case is one in form but 
numerically more than one, on the analogy of particulars 277* 
which are many though each undifferentiated in form, we 
reply that the variety of goal cannot be limited to this 
portion or that but must extend to all alike.^ For all are 
equally undifferentiated in form, but any one is different 
numerically from any other. What I mean is this : if the 5 
portions in this world behave similarly both to one another 
and to those in another world, then the portion which is 
taken hence will not behave differently either from the 
portions in another world or from those in the same world, 
but similarly to them, since in form no portion differs from 
another. The result is that we must either abandon our 
present assumptions or assert that the centre and the 10 
extremity are each numerically one. But this being so, the 
heaven, by the same evidence and the same necessary 
inferences, must be one only and no more. 

A consideration of the other kinds of movement also 
makes it plain that there is some point to which earth and 
fire move naturally. For in general that which is moved 
changes from something into something, the starting- 15 
point and the goal being different in form, and always 
it is a finite change.^ For instance, to recover health 
is to change from disease to health, to increase is to 
change from smallness to greatness. Locomotion must be 
similar: for it also has its goal and starting-point — and 
therefore the starting-point and the goal of the natural 
movement must differ in form — ^just as the movement of 
coming to health does not take any direction which chance 20 

^ Read tm fiev t« 6' ov with FLJ Simpl. The meaning is that since 
none but a 'numerical' difference can be postulated between the 
portions (e.g. of earth) in this world and those in another, and since 
a difference of goal can only be justified by a difference in the body, 
we should have to suppose a distinct goal for every single portion of 
earth; which is absurd. 

^ A full-stop, rather than a comma, is needed after fierajBo'KT} in 1. 16. 
Three principles are laid down and all are illustrated in the case of 
locomotion. But the instances of health and increase are used only 
to illustrate the first. 

277^ DE CAELO 

or the wishes of the mover may select-;^ Thus, too, fire and 
earth move not to infinity but to opposite points ; and since 
the opposition in place is between above and below, these 
will be the limits of their movement.^ (Even in circular 
movement there is a sort of opposition between the ends of 
the diameter, though the movement as a whole has no 
25 contrary : so that here too the movement has in a sense an 
opposed and finite goal.) There must therefore be some 
end to locomotion : it cannot continue to infinity. 

This conclusion that local movement is not continued to 
infinity is corroborated by the fact that earth moves more 
quickly the nearer it is to the centre, and fire the nearer it 
30 is to the upper place. But if movement were infinite speed 
would be infinite also ; and if speed then weight and light- 
ness. For as superior speed in downward movement 
implies superior weight, so infinite increase of weight neces- 
sitates infinite increase of speed .^ 
277^ Further, it is not the action of another body that makes 
one of these bodies move up and the other down ; nor is it 
constraint, like the ' extrusion ' of some writers.* For in 
that case the larger the mass of fire or earth the slower 
would be the upward or downward movement ; but the fact 

^ 11. 18-19, the full-stop after not should be deleted, and the words 
del opa . . . (pepfadai should be marked as a parenthesis. Locomotion, 
like healing, has a determinate direction, and that involves a difference 
of form between its two terms. 

^ The remarks which follow concerning circular motion are a kind 
of footnote and would be best marked as a parenthesis. 

' In I. 29 it is tempting to read el b' els aneipov rjv for d 6' aneipov rjvf 
but no evidence of such a reading survives. The sense of the para- 
graph is plain. We observe an increase of speed in a falling body as 
it approaches the earth. The explanation, on our view, is the proximity 
of the goal. But if there is no goal, the movement, and with it the 
increase of speed, is capable of continuing to infinity. But infinite 
speed means infinite weight, which has already (c. vi) been proved 
impossible. The Greek of the last sentence is puzzling and may be 
corrupt. Accepting the text of Bekker and Prantl, we must translate 
as follows : ' as that which by reason of speed is lower than another 
body would be presumed speedy by reason of weight, so if there were 
infinite increase of weight there would also be infinite increase of 
speed.' (The alteration of an accent is required : ^upei for ^apel in 
1. 32.) The sentence is clumsy, but it gives the required sense. 
Simplicius seems to have interpreted the passage as above. In 1. 31 
irepov is found in F alone, all the other MSS. giving erepov ; but 
hepov must be right. 

* The atomists, Leucippus and Democritus. 

BOOK I. 8 277^ 

is the reverse : the greater the mass of fire or earth the 
quicker always is its movement towards its own place. 5 
Again, the speed of the movement would not increase 
towards the end if it were due to constraint or extrusion ; 
for a constrained movement always diminishes in speed as 
the source of constraint becomes more distant, and a body 
moves without constraint to the place whence it was moved 
by constraint. 

A consideration of these points, then, gives adequate 
assurance of the truth of our contentions. The same could 
also be shown with the aid of the discussions which fall 10 
under First Philosophy,^ as well as from the nature of the 
circular movement, which must be eternal both here and in 
the other worlds. It is plain, too, from the following con- 
siderations that the universe must be one. 

The bodily elements are three, and therefore the places of 
the elements will be three also ; the place, first, of the body 15 
which sinks to the bottom, namely the region about the 
centre ; the place, secondly, of the revolving body, namely 
the outermost place, and thirdly, the intermediate place, • 
belonging to the intermediate body. Here in this third 
place will be the body which rises to the surface ; since, if 
not here, it will be elsewhere, and it cannot be elsewhere : 
for we have two bodies, one weightless, one endowed with 
weight, and below is the place of the body endowed with 20 
weight, since the region about the centre has been given to 
the heavy body. And its position cannot be unnatural to 
it, for it would have to be natural to something else, and 
there is nothing else. It must then occupy the intermediate 
place. What distinctions there are within the intermediate 
itself we will explain later on. 

We have now said enough to make plain the character and 
number of the bodily elements, the place of each, and fur- 
ther, in general, how many in number the various places are. 25 

9 We must show not only that the heaven is one,^ but 
also that more than one heaven is impossible, and, further, 

^ i.e. Metaphysics. Cf. Met. A. 8. 

"^ Prantl misprints ^h'SorXd^. For ovpavcs read 6 ovpavos with M. 
J, like EH L, omits the word ovpavos altogether. 

277^ DE CAELO 

that, as exempt from decay and generation, the heaven 
is eternal. We may begin by raising a difficulty. From 

3c one point of view it might seem impossible that the 
heaven should be one and unique,^ since in all formations 
and products whether of nature or of art we can distinguish 
the shape in itself and the shape in combination with matter. 
278^ For instance the form of the sphere is one thing and the 
gold or bronze sphere another ; the shape of the circle 
again is one thing, the bronze or wooden circle another. 
For when we state the essential nature of the sphere or 
circle we do not include in the formula gold or bronze, 
5 because they do not belong to the essence, but if we 
are speaking of the copper or gold sphere we do in- 
clude them. We still make the distinction even if we 
cannot conceive or apprehend any other example beside 
the particular thing. This may, of course, sometimes be 
the case : it might be, for instance, that only one circle 
could be found ; yet none the less the difference will 
remain between the being of circle and of this particular 
circle, the one being form, the other form in matter, 

10 i. e. a particular thing. Now since the universe is per- 
ceptible it must be regarded as a particular ; for every- 
thing that is perceptible subsists, as we know, in matter. 
But if it is a particular, there will be a distinction between 
the being of ' this universe ' and of ' universe ' unqualified. 
There is a difference, then, between 'this universe' and 
simple 'universe'; the second is form and shape, the first 

15 form in combination with matter ; and any shape or form 
has, or may have, more than one particular instance. 

On the supposition of Forms such as some assert, this 
must be the case, and equally on the view that no such 
entity has a separate existence. For in every case in 
which the essence is in matter it is a fact of observation 
that the particulars of like form are several or infinite in 

20 number. Hence there either are, or may be, more heavens 

^ More correctly : that the heaven should be necessarily one and 
unique. The argument here set out only attempts to prove the 
possibility of more than one world, and Aristotle replies by proving 
the impossibility of more than one. Alexander (cited by Simpl.) 
points out this defect in the statement. 

BOOK I. 9 278^ 

than one.^ On these grounds, then, it might be inferred 
either that there are or that there might be several heavens. 
We must, however, return and ask how much of this argu- 
ment is correct and how much not. 

Now it is quite right to say that the formula of the 
shape apart from the matter must be different from that 
of the shape in the matter, and we may allow this to be 25 
true. We are not, however, therefore compelled to assert 
a plurality of worlds. Such a plurality is in fact impossible 
if this world contains the entirety of matter, as in fact 
it does. But perhaps our contention can be made clearer 
in this way. Suppose ' aquilinity ' to be curvature in the 
nose or flesh, and flesh to be the matter of aquilinity. 30 
Suppose, further, that all flesh came together into a single 
whole of flesh endowed with this aquiline quality. Then 
neither would there be, nor could there arise, any other 
thing that was aquiline. Similarly, suppose flesh and bones 
to be the matter of man, and suppose a man to be created 
of all flesh and all bones in indissoluble union. The 35 
possibility of another man would be removed. Whatever 
case you took it would be the same. The general rule 278^ 
is this : a thing whose essence resides in a substratum 
of matter can never come into being in the absence of 
all matter.^ Now the universe is certainly a particular 
and a material thing : if however it is composed not of 
a part but of the whole of matter, then though the being 5 
of ' universe ' and of * this universe ' are still distinct, yet 
there is no other universe, and no possibility of others 
being made, because all the matter is already included 
in this. It remains, then, only to prove that it is composed 
of all natural perceptible body. 

First, however, we must explain what we mean by ' heaven ' 10 
and in how many senses we use the word, in order to make 
clearer the object of our inquiry, (a) In one sense, then, we call 

^ The 01 before ovpaioi is attributed only to E, and to it * dubio '. 
J has it. But the article does not seem to be required here. In 
corresponding passages in this chapter it is omitted. 

^ Read nvoi vXrjs. The omission of tiu6s in E must be a mere slip. 
All the other MSS., as well as Simpl., have iiucs vXrjs, and E is full of 
small omissions. 

278^ DE CAELO 

* heaven ' the substance of the extreme chxumference of the 
whole, or that natural body whose place is at the extreme 
circumference. We recognize habitually a special right to 

15 the name * heaven' in the extremity or upper region, which 
we take to be the seat of all that is divine.^ (d) In another 
sense, we use this name for the body continuous with the 
extreme circumference, which contains the moon, the sun, 
and some of the stars ; these we say are ' in the heaven '. 
(c) In yet another sense we give the name to all body 

30 included within the extreme circumference, since we habi- 
tually call the whole or totality 'the heaven '. The word, 
then, is used in three senses. 

Now the whole included within the extreme circumference 
must be composed of ^// physical and sensible body, because 
there neither is, nor can come into being, any body outside 

25 the heaven. For if there is a natural body outside the 
extreme circumference it must be either a simple or a com- 
posite body, and its position must be either natural or 
unnatural. But it cannot be any of the simple bodies. 
For, first, it has been shown ^ that that which moves in a circle 

30 cannot change its place. And, secondly, it cannot be that 
which moves from the centre or that which lies lowest. 
Naturally they could not be there, since their proper places 
are elsewhere ; and if these are there umiaturally^ the 
exterior place will be natural to some other body, since 
a place which is unnatural to one body must be natural 
to another : but we saw that there is no other body besides 

35 these.^ Then it is not possible that any simple body should 
279^ be outside the heaven. But, if no simple body, neither can 
any mixed body be there : for the presence of the simple 
body is involved in the presence of the mixture. Further 
neither can any body come into that place : for it will do so 
either naturally or unnaturally, and will be either simple 
5 or composite ; so that the same argument will apply, since 
it makes no difference whether the question is *does A 

^ Place a full-stop after (pajxev. In the next line crui/e^fs should be 

2 Read to fxev yap. The jueV is wanted, and is omitted by E alone. 
The reference is to cc. ii and iii above. 
■' c. ii above. 

BOOK I. 9 279' 

exist ? ' or * could A come to exist ? ' From our arguments 
then it is evident not only that there is not, but also that there 
could never come to be, any bodily mass whatever outside 
the circumference. The world as a whole, therefore, includes 
all its appropriate matter, which is, as we saw, natural 
perceptible body. So that neither are there now, nor have 
there ever been, nor can there ever be formed more heavens 10 
than one, but this heaven of ours is one and unique and 

It is therefore evident that there is also no place or void 
or time outside the heaven. For in every place body can 
be present ; and void is said to be that in which the presence 
of body, though not actual, is possible; and time is the ^5 
number of movement. But in the absence of natural body 
there is no movement, and outside the heaven, as we have 
shown, body neither exists nor can come to exist. It is 
clear then that there is neither place, nor void, nor time, 
outside the heaven. Hence whatever is there, is of such 
a nature as not to occupy any place, nor does time age it ; 
nor is there any change in any of the things which lie beyond ao 
the outermost motion ; they continue through their entire 
duration unalterable and unmodified, living the best and 
most self-sufficient of lives. As a matter of fact, this word 
' duration ' possessed a divine significance for the ancients, 
for the fulfilment which includes the period of life of any 
creature, outside of which no natural development can fall, 
has been called its duration. On the same principle the 25 
fulfilment of the whole heaven, the fulfilment which includes 
all time and infinity, is ' duration ' — a name based upon the 
fact that it is always^ — duration immortal and divine. 
From it derive the being and life which other things, 
some more or less articulately but others feebly, enjoy. 30 
So, too, in its discussions concerning the divine, popular 
philosophy"^ often propounds the view that whatever is 

^ i. e. aloav is derived from det cSi/. 

' Aristotle refers apparently under this name to elementary hand- 
books of philosophy current among his audience. It is usual to 
identify them with the i^arepiKoX \6yoi, as Simpl. does in his com- 
mentary on this passage. See Bonitz, Ind. Ar.^ s. v. 'ApKTToreXrjSf 

645.20 D 

279^ DE CAELO 

divine, whatever is primary and supreme, is necessarily 
unchangeable. This fact confirms what we have said. 
For there is nothing else stronger than it to move it — 
35 since that would mean more divine — and it has no defect 
279^ and lacks none of its proper excellences. Its unceasing 
movement, then, is also reasonable, since everything ceases 
to move when it comes to its proper place, but the body 
whose path is the circle has one and the same place for 
starting-point and goal. 

Having established these distinctions, we may now pro- 10 
5 ceed to the question whether the heaven is ungenerated 
or generated, indestructible or destructible. Let us start 
with a review of the theories of other thinkers ; for the 
proofs of a theory are difficulties for the contrary theory.^ 
Besides, those who have first heard the pleas of our 
adversaries will be more likely to credit the assertions 
10 which we are going to make. We shall be less open 
to the charge of procuring judgement by default. To 
give a satisfactory decision as to the truth it is necessary 
to be rather an arbitrator than a party to the dispute. 

That the world was generated all are agreed, but, genera- 
tion over, some say that it is eternal, others say that it is 
destructible like any other natural formation.^ Others 
15 again, with Empedocles of Acragas and Heraclitus of 
Ephesus, believe that there is alternation in the destructive 
process, which takes now this direction, now that, and 
continues without end.^ 

^ Prantl misprints tvv ivavriav for tcou ivavriwv in 1. 6. 

2 The former view, according to Alexander {ap. Simpl.), is that of 
Orpheus (i.e. of Orphic cosmogony), Hesiod, and Plato, while the 
latter is that of Democritus and his school, 

^ Cf. Burnet, E.G.P.^ P- I57 (§ 77)- Heraclitus and Empedocles 
are agreed in believing in periodic changes in the constitution of our 
world as a whole. For both, the world exists, as it were, in a succession 
of lives (below, 280* 14) ; and the view is a kind of compromise 
between that which regards it as eternal and that which gives it 
a single life ended by annihilation. The phrase 'alternation in the 
destructive process' is somewhat inaccurate, since the alternation 
may be described as between generation and destruction (Empedocles' 
Love and Strife, Stoic BioKoafirjais and fKnvpaxns). But it is intelligible. 
Aristotle is here classing the theory for convenience with those that 
hold to a destructible world, and the antithesis is between destruction 
aiiKms and destruction with alternation. Later he explains that this 

BOOK I. lo 279^ 

Now to assert that it was generated and yet is eternal is 
to assert the impossible ; for we cannot reasonably attribute 
to anything any characteristics but those which observation 
detects in many or all instances. But in this case the facts 20 
point the other way : generated things are seen always to 
be destroyed. Further, a thing whose present state had no 
beginning and which could not have been other than it was at 
any previous moment throughout its entire duration, cannot 
possibly be changed.^ For there will have to be some cause 
of change, and if this had been present earlier it would have 
made possible another condition of that to which any other 
condition was impossible. Suppose that the world was formed 35 
out of elements which were formerly otherwise conditioned 
than as they are now. Then (i) if their condition was always 
so and could not have been otherwise, the world could never 
have come into being.^ And (2) if the world did come into 
being, then, clearly, their condition must have been capable 
of change and not eternal : after combination therefore they 
will be dispersed, just as in the past after dispersion they 
came into combination, and this process either has been, 
or could have been, indefinitely repeated. But if this is so, 30 
the world cannot be indestructible, and it does not matten 
whether the change of condition has actually occurred or 
remains a possibility. 

Some of those who hold that the world, though in- 
destructible, was yet generated, try to support their case 
by a parallel which is illusory.^ They say that in their 
statements about its generation they are doing what 
geometricians do when they construct their figures, not 35 
implying that the universe really had a beginning, but 

alternation is not cpdopd at all. Burnet in his first edition proposed to 
excise (pBeipofievov, but the suggestion is now tacitly retracted. In 
his later editions Burnet wrongly states that what is here in 
question is the eternity of the first heaven. That has already been 
proved in c. iii, and the first heaven would not be referred to as 
6 Koaiios. 

^ A comma is required after alcova in 1. 22, unless the comma after 
tX^iv in the preceding line is deleted. 

' The close coordination of el fieu (in 1. 25) with d 84 (in 1. 26) 
demands a comma, rather than a full-stop, after eyevero. 

' Simpl. refers the following argument to Xenocrates and the 

D a 

28o^ DE CAELO 

280^ for didactic reasons facilitating understanding by exhibiting 
the object, like the figure, as in course of formation. The 
two cases, as we said, are not parallel ; for, in the construc- 
tion of the figure, when the various steps are completed 
the required figure forthwith results ; but in these other 
demonstrations what results is not that which was required.^ 
5 Indeed it cannot be so ; for antecedent and consequent, as 
assumed, are in contradiction. The ordered, it is said,^ 
arose out of the unordered ; and the same thing cannot 
be at the same time both ordered and unordered ; there 
must be a process and a lapse of time separating the two 

10 states. In the figure, on the other hand, there is no 
temporal separation.^ It is clear then that the universe 
cannot be at once eternal and generated. 

To say that the universe alternately combines and dissolves 
is no more paradoxical than to make it eternal but vary- 
ing in shape. It is as if one were to think that there was now 

15 destruction and now existence when from a child a man is 
generated, and from a man a child- For it is clear that when 
the elements come together the result is not a chance system 
and combination, but the very same as before — especially 
on the view of those who hold this theory, since they say 
that the contrary is the cause of each state.* So that if 

20 the totality of body, which is a continuum, is now in this 
order or disposition and now in that, and if the combination 
of the whole is a world or heaven, then it will not be the 
world that comes into being and is destroyed, but only 
its dispositions. 

If the world is believed to be one, it is impossible to 

^ i.e. the geometricians can truly write Q. E.F. at the end of their 
construction, but these cosmogonists cannot. The figure, or world, 
constructed should be ' the same ' {t6 avro) as that demanded in the 

^ Cp. Plato, Ttmaeus 30 A. 

^ The construction of the cosmogonist cannot be a mere didactic 
device like that of the geometrician ; for the attributes successively 
assumed in the construction of the world cannot exist simultaneously 
as those assumed by the geometrician do. 

* Here Aristotle clearly refers to Empedocles, rather than to 
Hcraclitus. The two causes of Empedocles are Love and Strife 
{(f)iXia and velKos), and since these are two it follows, Aristotle argues, 
that the world would merely oscillate between two arrangements or 

BOOK I. lo 280' 

suppose that it should be, as a whole, first generated and 
then destroyed, never to reappear ; since before it came 
into being there was always present the combination prior 25 
to it, and that, we hold, could never change if it was never 
generated. If, on the other hand, the worlds are infinite 
in number the view is more plausible. But whether this 
is, or is not, impossible will be clear from what follows. 
For there are some who think it possible both for the 
ungenerated to be destroyed and for the generated to 30 
persist undestroyed.^ (This is held in the Timaeus^ 
where Plato says that the heaven, though it was generated, 
will none the less exist to eternity.) So far as the heaven 
is concerned we have answered this view with arguments 
appropriate to the nature of the heaven : on the general 
question we shall attain clearness when we examine the 
matter universally.^ 

II We must first distinguish the senses in which we use the 280* 
words 'ungenerated' and 'generated', 'destructible' and 
' indestructible '.'^ These have many meanings, and though 

^ In 1. 29 Prantl misprints k/xi for kuL 

^ A colon instead of a full-stop is needed after Ti/iai&). The reference 
is to Plato, Timaetis 31. Plato is quoted as authority for the in- 
destructible-generated not for the ungenerated-destructible, as the 
context shows. 

^ The general question is the mutual relations of the terms 'generated ', 
* ungenerated ', ' destructible ', ' indestructible ', which have so far been 
considered only in their application to the heaven. The terms are 
discussed universally, i.e. apart from any special application, in 
cc. xi and xii. The combination attributed to Plato is refuted at the 
end of that discussion (283* i ff.). Simplicius found the argument of 
the last paragraph of this chapter (11. 23 ff.) somewhat obscure. It 
deals, provisionally and subject to further investigation, with the view 
that the world is subject both to generation and to destruction in the 
sense in which the man Socrates is. Simpl. is probably right in 
supposing that under this head Aristotle is thinking of the atomists. 
Their infinite worlds were successive, if also co-existent. Aristotle 
here argues that if that out of which the world was formed had the 
capacity to give birth to a world, then that into which the world is 
destroyed will have the same capacity. Thus the theory of world- 
annihilation is dismissed as absurd, while the infinite succession of 
destructible worlds is left open. But the refutation even of the first 
of these views, and therefore a fortiori of the second, cannot be 
regarded as complete until the whole problem of generation and 
destruction has been examined. 

* It is unfortunate that 'generated' and 'destructible' are not 
similar grammatical forms as the Greek y^vriTo^ and (f)dapT6y are. 
But from the analysis given by Aristotle it will be seen that in 
meaning the Greek verbal adjective tends to approximate to the past 

28o'^ DE CAELO 

it may make no difference to the argument, yet some con- 
fusion of mind must result from treating as uniform in its 
5 use a word which has several distinct applications. The 
character which is the ground of the predication will 
always remain obscure. 

The word ' ungenerated ' then is used (a) in one sense 
whenever something now is which formerly was not, no 
process of becoming or change being involved. Such' is the 
case, according to some, with contact and motion, since 
there is no process of coming to be in contact or in motion. 
{b) It is used in another sense, when something which is 

^o capable of coming to be, with or without process, does not 
exist ; such a thing is ungenerated in the sense that its 
generation is not a fact but a possibility, (c) It is also 
applied where there is general impossibility of any generation 
such that the thing now is which then was not. And ' im- 
possibility ' has two uses : first, where it is untrue to say 
that the thing can ever come into being, and secondly, 
where it cannot do so easily, quickly, or well. In the 

15 same way the word ' generated ' is used, (a) first, where 
what formerly was not afterwards is, whether a process of 
becoming was" or was not involved, so long as that which 
then was not, now is ; (d) secondly, of anything capable of 
existing, 'capable' being defined with reference either to 
truth or to facility ; (c) thirdly, of anything to which the 
passage from not being to being belongs,^ whether already 
actual, if its existence is due to a past process of becoming, 

20 or not yet actual but only possible. The uses of the words 
' destructible ' and ' indestructible ' are similar. ' Destruc- 
tible ' is applied (a) to that which formerly was and after- 
wards either is not or might not be, whether a period of 
being destroyed and changed intervenes or not ; - and (/;) 

participle, and therefore it is not worth while to insist on 'generable', 
' ungenerable ' for yevrjros, ayevrjros. 

^ For eau J] -yeVfo-is- read iav fi ycveats. (M has rj 17, but all Other 
MSS. have rj.) The correction was suggested by Haydnck (Greifs- 
wald Gymnasium Program, 187 1, p. ij). 

^ The evidence afforded by Simpl. and the MSS., together with the 
difficulty of establishing a precise correspondence between this defini- 
tion of (pdapTov and the parallel uses of 'ungenerated' (d) and 
'generated' (a), might lead one to doubt the soundness of the text 
at this point ; but it is guaranteed by Aristotle's own citation at 
281'' 27. 

BOOK I. II 280' 

sometimes we apply the word to that which a process of 
destruction may cause not to be ; and also (c) in a third 
sense, ^to that which is easily destructible, to the 'easily- 25 
destroyed ', so to speak.^ Of the indestructible the same 
account holds good. It is either {a) that which now is and 
now is not, without any process of destruction, like contact, 
which without being destroyed afterwards is not, though 
formerly it was ; or (d) that which is but might not be, or 
which will at some time not be, though it now is.^ For you 
exist now and so does the contact ; yet both are destructible, 30 
because a time will come when it will not be true of you 
that you exist, nor of these things that they are in contact. 
Thirdly (c) in its most proper use, it is that which is, but is 
incapable of any destruction such that the thing which now 
is later ceases to be or might cease to be ; or again, that 
which has not yet been destroyed, but in the future may 
cease to be.^ For indestructible is also used of that which 281^ 
is destroyed with difficulty.^ 

^ Aristotle carelessly omits to mention the other and more exact 
kind of possibility. Cf. ' ungenerated ' (c) and 'generated* (d). 

^ The third ^ (in 1. 29) is not coordinate with the two which precede 
it (11. 26, 28), and it would be well to mark this by putting a colon 
instead of a comma after elaiv in 1. 28. Simplicius read rj koX ovk in 
1. 29, and the addition of mi would be an improvement. 

^ Omit the ovk inserted by Prantl before eV6e;^d/zfj/oi/. The ov be 
which Prantl's note attributes to Simplicius is found only in one 
inferior MS. and is not printed in Heiberg's text of the commentary. 
J also has no word between icjidapfxevov and (pdexof^fvop, nor had 

* Read Xeyerm yap for Xeyerai de, and place a colon instead of a full- 
stop before Xeyerai. This alteration is conjectural, but it is preferable 
to Hayduck's excision of J) koI . . . elvai (11. 33, 34), and without some 
alteration the Greek will not give a satisfactory sense. The account 
given of * indestructible ' is closely parallel to that given of ' un- 
generated ' above. Sense (a) of * indestructible ' (11. 26-28) turns on 
the absence of process, like sense (a) of ' ungenerated ', even repeating 
the same instance, touch. In sense (d) (11. 28-31) 'indestructible' 
covers all that has not been destroyed, as ' ungenerated ' in sense (^) 
covers what has not yet come into being : as ' ungenerated ' includes 
all possible existents which are now non-existent, so 'indestructible' 
includes all possible non-exlstents which are now existent. There 
remains the third and proper sense, viz. potentiality or possibility, 
subdivided in the case of ' ungenerated ', according to an ambiguity 
in the word possible, into (i) strict and final impossibility {tS fifj 
aXT)Bes chai eiVeii'), (ii) popular or 'practical' impossibility (rw firj 
pqkas pT]d€ raxv rj Ka\a>s). The third Sense of 'indestructible' is 
introduced by to de pciXiara Kvpt<os in 1. 31, and its subdivision 
is effected by fj kuI in 1. 33. The words before rj Kai assert the final 

28i^ DE CAELO 

This being so, we must ask what we mean by * possible ' 
and ^ impossible '. For in its most proper use the predicate 
' indestructible ' is given because it is impossible that the 
thing should be destroyed, i. e. exist at one time and not at 

5 another. And ' ungenerated ' also involves impossibility 
when used for that which cannot be generated, in such 
fashion that, while formerly it was not, later it is. An in- 
stance is a commensurable diagonal. Now when we speak 
of a power ^ to move 2 or to lift weights, we refer always to 
the maximum. We speak, for instance, of a power to lift 
a hundred talents or walk . a hundred stades — though 
a power to effect the maximum is also a power to effect any M 

10 part of the maximum — since we feel obliged in defining the ^ 
power to give the limit or maximum. A thing, then, which 
is capable of a certain amount as maximum must also be 
capable of that which lies within it. If, for example, a man 
can lift a hundred talents, he can also lift two, and if he can 
walk a hundred stades, he can also walk two. But the 

15 power is of the maximum, and a thing said, with reference 
to its maximum,^ to be incapable of so much is also in- 
capable of any greater amount. It is, for instance, clear 
that a person who cannot walk a thousand stades will also 
be unable to walk a thousand and one. This point need 
not trouble us, for we may take it as settled that what is, in 
the strict sense, possible is determined by a limiting maxi- 

20 mum. Now perhaps the objection might be raised that 

removal of the possibility of non-existence, and the following clau 
relaxes the requirement as popular use demands. Even if the possi 
bility of destruction has not been finally removed, a thing may be 
called 'indestructible' in this sense if it has not been destroyed. 
^ For {\eyeTin yap) what is not easily destroyed is called indestructible.' 
By calling this the proper sense, whether in its stricter or more 
popular use, Aristotle must mean that the verbal adjective in -tos 
should not in precise speech be allowed to approximate, as it often 
does, to a past participle passive. (Simplicius's interpretation of this 
passage is quite inadmissible, but he was confused by faulty MSS.) 

* ' Power ' [dvmfiii) must be taken throughout as the noun corre- 
sponding to the adjective ' possible * {dvmTop}. 

^ The MSS. have KivrjOfjvai (rrddia (Karov ('to move a hundred 
stades'). The translation omits the reference to distance, which 
seems clearly out of place. The words arddia cKarov, which occur 
more than once in the context, probably got their place in this clausi 
through a copyist's mistake. 

^ Prantl misprints vTTfp^aXrjv for vTrfp^oXrjv. 



BOOK I. II 281^ 

there is no necessity in this, since he who sees a stade need 25 
not see the smaller measures contained in it, while, on the 
contrary, he who can see a dot or hear a small sound will 
perceive what is greater. This, however, does not touch 
our argument. The maximum may be determined either 
in the power or in its object.^ The application' of this is 
plain. Superior sight is sight of the smaller body, but 
sup^ior speed is that of the greater body. 

12 Having established these distinctions we can now proceed 
to the sequel. If there arc things capable both of being 
and of not being, there must be some definite maximum 
time of their being and not being ; a time, I mean, during 30 
which continued existence is possible to them and a time 
during which continued non-existence is possible. And 
this is true in every category, whether the thing is, for ex- 
ample, * man ', or ' white ', or ' three cubits long ', or whatever 
it may be. For if the time is not definite in quantity, but 
longer than any that can be suggested and shorter than 
none, then it will be possible for one and the same thing to 281^ 
exist for infinite time and not to exist for another infinity. 
This, however, is impossible. 

Let us take our start from this point. The impossible 
and the false have not the same significance. One use of 
* impossible ' and ' possible ', and ' false ' and ' true ', is hypo- 5 
thetical. It is impossible, for instance, on a certain 
hypothesis that the triangle should have its angles equal to 
two right angles, and on another the diagonal is commen- 
surable. But there are also things possible and impossible, 
false and true, absolutely. Now it is one thing to be abso- 
lutely false, and another thing to be absolutely impossible. 
To say that you are standing when you are not standing is 
to assert a falsehood, but not an impossibility. Similarly 10 

* i. e. sometimes the maximum is an actual maximum (determined 
' in the object', cVi toO Trpay/naToc), e. g. in the case of weigh t-Hfting, 
where the largest weight lifted serves to define the power ; sometimes 
it is an actual minimum, determined as maximum ' in the power ' (eVi 
rrjs 8vvdiJL€(os), e. g. in the case of vision, where the smallest object seen 
serves to define the capacity. Cf the distinction between the fieaov 
Tov TrpdynaTos (or Kara to npdyiui) and the fieaov Trpos fjfxas in E//i. Nic. 

28i^ DE CAELO 

to say that a man who is playing the harp, but not singing, 
is singing, is to say what is false but not impossible. To 
say, however, that you are at once standing and sitting, or 
that the diagonal is commensurable, is to say what is not 
only false but also impossible. Thus it is not the same- 
thing to make a false and to make an impossible hypothesis ;^ 

15 and from the impossible hypothesis impossible results follow. 
A man has, it is true, the capacity at once of sitting and 
of standing, because when he possesses the one he also 
possesses the other ; but it does not follow that he can at 
once sit and stand, only that at another time he can do the 
other also. But^ if a thing has for infinite time more than 
one capacity, another time is impossible and the times must 

20 coincide. Thus if anything which exists for infinite time is 
destructible, it will have the capacity of not being. Now if 
it exists for infinite time let this capacity be actualized ; ^ 
and it will be in actuality at once existent and non-existent. 
Thus a false conclusion would follow because a false assump- 
tion was made, but if what was assumed had not been 

25 impossible its consequence would not have been im- 

Anything then which always exists is absolutely im- 
perishable. It is also ungenerated, since if it was generated 
it will have the power for some time of not being. For as 
that which formerly was, but now is not, or is capable at 
some future time of not being, is destructible, so that which 
is capable of formerly not having been is generated.^ But 
in the case of that which always is, there is no time for such 

30 a capacity of not being, whether the supposed time is finite 

^ Cf. A7tal. Prio7'. 34* I fif. for this distinction. There should be 
a colon rather than a full-stop after ahvvaTov. The production of like 
consequences is of course not peculiar to the impossible hypothesis : 
it applies equally to the false hypothesis. See loc. cit. 

^ Read el de with FHMJ for el 8t}. There is no semblance of 
inference. Simplicius makes the connexion antithetical. 

^ For eo-rai read earo) with all MSS. (except E) and Simpl. The 
fjifj eliai which follows dvvarai in FHMJ must have been a copyist's 

* The assumption in this case was both false and impossible. 

^ The words are taken in their ' most proper ' sense, as the qualifica- 
tion 'absolutely' in 1. 25 suggests; viz. as conveying a strict and 
demonstrable possibility or impossibility. See foregoing chapter. 

BOOK T. 12 281^ 

or infinite ; for its capacity of being must include the finite 
time since it covers infinite time.^ 

It is therefore impossible that one and the same thing 
should be capable of always existing and of always not- 
existing.^ And 'not always existing', the contradictory, is 
also excluded. Thus it is impossible for a thing always to 
exist and yet to be destructible. Nor, similarly, can it be 282^ 
generated. For of two attributes if B cannot be present 
without A^ the impossibility of A proves the impossibility 
of B. What always is, then, since it is incapable of ever 
not being, cannot possibly be generated. But since the 
contradictory of ' that which is always capable of being ' is 5 
' that which is not always capable of being ' ; while ' that 
which is always capable of not being' is the contrary, 
whose contradictory in turn is *that which is not always 
capable of not being ', it is necessary that the contradictories 
of both terms should be predicable of one and the same 
thing, and thus that, intermediate between what always is 
and what always is not, there should be that to which being 
and not-being are both possible ; for the contradictory of 10 
each will at times be true of it unless it always exists. 
Hence that which not always is not will sometimes be and 
sometimes not be ; and it is clear that this is true also of 
that which cannot always be but sometimes is and therefore 
sometimes is not.^ One thing, then, will have the power 
of being and of not being, and will thus be intermediate 
between the other two. 

Expressed universally our argument is as follows. Let 
there be two attributes, A and B^ not capable of being 15 
present in any one thing together, while either A or C and 

^ In 1. 29 after \xr] ilvai a full-stop is required instead of a comma. 
The construction of the following clauses is difficult. The translation 
given above proceeds on the hypothesis that no stop is required after 
act ov (1. 30) and that ^warov , . , ware \xr] elvoL is equivalent to dwarov 
fitj (tvat. I cannot find another case of dwarbv coo-re, but similar uses 
of ware are fairly common in Aristotle (see Bonitz, In^. Ar., p. 873* 20). 
ovr aTTdpov ovre TTfTrepaa-fievov (sc. xpovov) is a loose epexegesis of ovK 
(o-Tiv iv « xpovco^ and perhaps should be preceded by a comma. 

^ Km aei /xi; eiVm is the reading of FJ Simpl. Since the omission of 
au in the other MSS. is easily accounted for, it seems best to accept 
this. (J at the first attempt omitted the khi.) 

^ After TTore ov a comma, not a colon. 

282^ DE CAELO 

either B ox D are capable of being present in everything. 
Then C and D must be predicated of everything of which 
neither A nor B is predicated. Let E lie between A and 
B ; for that which is neither of two contraries is a mean 
between them. In E both C and D must be present, for 

3o either ^ or 6' is present everywhere and therefore in E. 
Since then A is impossible, C must be present, and the 
same argument holds of D} 

Neither that which always is, therefore, nor that which, 
always is not is either generated or destructible. And clearly 
whatever is generated or destructible is not eternal. If it were, 
it would be at once capable of always being and capable of 

25 not always being, but it has already been shown ^ that this 
is impossible. Surely then whatever is ungenerated and in 
being must be eternal, and whatever is indestructible and 
in being must equally be so."' (I use the words ' ungen- 
erated ' and ' indestructible ' in their proper sense, ' un- 
generated' for that which now is and could not at any 
previous time have been truly said not to be ; ' indestruc- 
tible ' for that which now is and cannot at any future time 

30 be truly said not to be.^) If, again, the two terms are 
coincident,^ if the ungenerated is indestructible, and the in- 
destructible ungenerated, then each of them is coincident 

^ The four letters A BCD are to be allotted as follows : yi is ' that 
which is always capable of being ' = ' what always is ', B is its 
contrary, 'that which is always capable of not being '= 'what always 
is not ', C is its contradictory, ' that which is not always capable of 
being ', and D is the contradictory of B^ ' that which is not always 
capable of not being '. C and I) might also be described by the terms 
' what not always is' and 'what not always is not' respectively. 

2 281b 18 ff. 

' The question-mark should come at the end of the line after ov be, 
preceded by a comma at ehai. 

* 1. e. each term has its third sense as defined in chapter xi 

^ The term ' coincidence ' is used in this passage to express the 
mutual involution (called by later writers avraKoXovka) of predicates. 
This mutual involution is here described by Aristotle in terms which 
- mean that the two terms ' follow ' or ' accompany ' one another. But 
later on (e. g. in 282^ 10, 27, 32) he frequently says simply that one 
predicate ' follows ' another when he means that the two terms are 
mutually involved. To avoid confusion I have expressed the relation 
in terms of coincidence throughout. — The 7 following the parenthesis 
introduces an alternative proof to the same effect as that which 
preceded the parenthesis. 

BOOK I. 12 282^ 

with 'eternal'; anything ungenerated is eternal and anything 282^ 
indestructible is eternal. This is clear too from the defini- 
tion of the terms. Whatever is destructible must be 
generated ; for it is either ungenerated or generated, but, if 
ungenerated, it is by hypothesis ^ indestructible. Whatever, 
further, is generated must be destructible. For it is either 
destructible or indestructible, but, if indestructible, it is by 5 
hypothesis ^ ungenerated. 

If, however, ' indestructible ' and ' ungenerated ' are not 
coincident, there is no necessity that either the ungenerated 
or the indestructible should be eternal. But they must be 
coincident, for the following reasons. The terms ' gener- 
ated ' and * destructible ' are coincident ; this is obvious 
from our former remarks, since between what always is and 10 
what always is not there is an intermediate which is neither, 
and that intermediate is the generated and destructible. 
For whatever is either of these is capable both of being and 
of not being for a definite time: in either case, I mean, 
there is a certain period of time during which the thing is 
and another during which it is not. Anything therefore 
which is generated or destructible must be intermediate. ^5 
Now let A be that which always is and B that which 
always is not, C the generated, and D the destructible. 
Then C must be intermediate between A and B. For in 
their case there is no time in the direction of either limit,^ 
in which either A is not or B is. But for the generated 

* 281^25 ff. But Aristotle proceeds to give a proof of the mutual 
involution of these terms. If the destructible is generated and the 
generated is destructible, it follows that the ungenerated is eternal 
and the indestructible is eternal, and this is the thesis set out for proof 
in 282^^ 25. But the proof here given of the antecedent depends on the 
assumption that ' ungenerated ' and ' indestructible ' are coincident, 
which assumption is now proved. Aristotle's procedure, however, is 
needlessly complicated. Having proved the coincidence of ' generated ' 
and 'destructible' by assuming the coincidence of 'ungenerated ' and 
' indestructible ', he now proves the coincidence of the latter by 
proving (on other lines) the coincidence of the former. 

^ i. e., in effect, ' neither in the past nor in the future '. But time, of 
course, has no limit. The notion of limit is transferred to the in- 
destructible-ungenerated from the destructible-generated. The being 
of the latter class is necessarily limited in both directions, by birth on 
one side and death on the other, and the same terms limit its not- 
being. These two limits of finite existence are used to describe the 
two directions of infinite existence. 

282^ DE CAELO 

20 there must be such a time either actually or potentially, 
though not for A and B in either way. C then will be, and 
also not be, for a limited length of time, and this is true also 
of D, the destructible. Therefore each is both generated 
and destructible. Therefore ' generated ' and * destruc- 
tible * are coincident. Now let E stand for the ungenerated, 

25 F for the generated, G for the indestructible, and H for the 
destructible. As for F and H, it has been shown that they 
are coincident. But when terms stand to one another as 
these do, F and H coincident, E and F never predicated of 
the same thing but one or other of everything, and G and 

30 H likewise, then E and G must needs be coincident. For 
suppose that E is not coincident with G, then F will be, 
since either ^ or F is predicable of everything. But of that 
of which F is predicated H will be predicable also. H\v\\\ 
283* then be coincident with G, but this we saw to be impossible. 
And the same argument shows that G is coincident with E, 
Now the relation of the ungenerated {E) to the generated 
{F) is the same as that of the indestructible {G) to the de- 
structible {H). To say then that there is no reason why 
anything should not be generated and yet indestructible or 

5 ungenerated and yet destroyed, to imagine that in the one 
case generation and in the other case destruction occurs 
once for all, is to destroy part of the data.^ For (i) every- 
thing is capable of acting or being acted upon, of being or 
not being, either for an infinite, or for a definitely limited 
space of time ; and the infinite time is only a possible alter- 
native because it is after a fashion defined, as a length of 

10 time which cannot be exceeded. But infinity in one 
direction is neither infinite nor finite. (2) Further, why, 
after always existing, was the thing destroyed, why, after 
an infinity of not being, was it generated, at one moment 
rather than another? If every moment is alike and the 
moments are infinite in number, it is clear that a generated 
or destructible thing existed for an infinite time. It has 

^ Aristotle now proceeds to apply his results to the refutation of the 
view attributed in 280* 30 to Plato's Timaeus. He there promised to 
give a clearer demonstration of its absurdity when the terms 'generated', 
' ungenerated ', &c. should be investigated on their own account and 
apart from the special case of the heaven. 


BOOK I. 12 - 283' 

therefore for an infinite time the capacity of not being 
(since the capacity of being and the capacity of not being 15 
will be present together)/ if destructible, in the time before 
destruction, if generated, in the time after generation. If 
then we assume the two capacities to be actualized, oppo- 
sites will be present together.^ (3) Further, this second 
capacity will be present like the first at every moment, so 
that the thing will have for an infinite time the capacity 
both of being and of not being ; but this has been shown 
to be impossible.^ (4) Again, if the capacity is present prior 20 
to the activity, it will be present for all time, even while the 
thing was as yet ungenerated and non-existent, throughout 
the infinite time in which it was capable of being generated. 
At the time, then, when it was not, at that same time it had 
the capacity of being, both of being then and of being there- 
after, and therefore for an infinity of time.* 

It is clear also on other grounds that it is impossible 35 
that the destructible should not at some time be destroyed. 
For otherwise it will always be at once destructible and in 
actuality indestructible,^ so that it will be at the same time 

* The words aixa yap . . . Koi (Ivai are plainly parenthetical, since the 
TO /ieV, TO he which follow explain the clause which precedes them. 
They should be enclosed in brackets and the colon after xpovov deleted. 

' Read a dvifarai. Prantl's note is incorrect. The facts are as 
follows: a dvvarai FM Simpl., a hvpavrai EL, abvvara HJ. Bekker 
prints the last, though attested by only one of his MSS. 

^ The third argument is distinct from the second in that the second 
arrives at an absurdum by actualizing the capacity, while the third 
points out that the co-presence of two such capacities has already 
been admitted to be impossible. Cf. 282*5, 'that which is always 
capable of being ' is the contrary of ' that which is always capable of 
not being *. Alexander seems to have maintained that our third argu- 
ment was not a distinct argument at all ; but the short account of his 
view given by Simpl. is not convincing. 

^ A colon is required after vanpov. Aristotle is proving that the 
capacity was present for infinite time, which in argument (3) he 
assumed as evident without proof. 

^ Prantl's note as to the reading in 1. 26 is inaccurate. The words 
KOA acf)dapTop (not Koi (fiBapTov) were lacking in the MSS. used both by 
Alexander and by Simpl. ; and they interpreted the sentence without 
those words to mean — *it will be at once eternal and in actuality 
destructible ' ; but * in actuality destructible ' means * destroyed ', and 
therefore the assertion is not justified by the context. Alex., how- 
ever, suggested the insertion of the words /cat a^daprov, and Simpl. 
says he ' has come across * a manuscript in which the words are found. 
Ka\ acpdapTov seems to have been added to E upon revision, but all our 
other MSS. have the words, and it is best to retain them in the text. 

283^ DE CAELO 

capable of always existing and of not always existing. 
Thus the destructible is at some time actually destroyed. 
The generable, similarly, has been generated, for it is capable 
of having been generated and thus also of not always 
30 We may. also see in the following way how impossible it 
is either for a thing which is generated to be thenceforward 
indestructible, or for a thing which is ungenerated and has 
always hitherto existed to be destroyed. Nothing that is by 
chance can be indestructible or ungenerated, since the pro- 
283 ducts of chance and fortune are opposed to what is, or comes 
to be, always or usually, while anything which exists for a 
time infinite either absolutely or in one direction, is in exist- 
ence either always or usually. That which is by chance, then, 
is by nature such as to exist at one time and not at another. 
But in things of that character the contradictory states 
5 proceed from one and the same capacity, the matter of the 
thing being the cause equally of its existence and of its non- 
existence. Hence contradictories would be present together 
in actuality.^ 

* The end of this paragraph from koI el yevtirov seems to be a short 
statement of the parallel argument with regard to generation. If this 
is so we require a full-stop instead of a comma after (fydaprov. to 
(f)3apT6v can hardly be the subject of yeyovev, as Prantl's stopping 
suggests. The last words, koI prj del opa emu, are unsatisfactory, 
since, though they draw a true consequence, it is one more directly 
appropriate to (f)6opd than to yeveais. It is tempting to read koL pf] de\ 
apa pr) eivai. We should then have the relevant consequence and 
a more precise parallelism between the two arguments. — The point 
of the paragraph as a whole is to remove the possibility of an escape, 
by means of a doctrine of unrealized possibilities, from the conclusion 
already drawn that what is generated is also destructible. (Simpl. 
appositely quotes Tmiaeus 41 a, B, where the permanence of the world- 
order depends on the will and promise of the Demiurge.) Aristotle 
always maintains that an unrealized possibility in this sense is 

"^ For Prantl's kcli apa read apa. The Kai is omitted by FMJ Simpl. — 
The notions of 'chance' {to avTopuTop) and 'fortune' (rvxr)) are fully 
discussed in F/tys. II. iv-vi, the exclusion of the 'necessar>'' and the 
' usual ' (283^ 32) being explained in II. v. It is there plainly implied 
that chance had actually been suggested by earlier writers as the 
generative cause of the world (196^33, 198^10). The reason why 
they had recourse to this notion would be that chance means a cause 
quite external to the nature of the thing considered; and thus the 
chance generation or destruction of the world would not involve the 
consequence that in general and as such the world was either generated 
or destructible. Aristotle's reply to the suggestion is simply that 
chance necessarily implies intermittent being, so that a chance- 

BOOK I. 12 283^ 

Further, it cannot truly be said of a thing now that it 
exists last year, nor could it be said last year that it exists 
now.^ It is therefore impossible for what once did not 
exist later to be eternal. For in its later state it will possess 
the capacity of not existing, only ^ not of not existing at 
a time when it exists — since then it exists in actuality — but 10 
of not existing last year or in the past. Now suppose it to 
be in actuality what it is capable of being. It will then be 
true to say now that it does not exist last year. But this is 
impossible. No capacity relates to being in the past, but 
always to being in the present or future. It is the same 
with the notion of an eternity of existence followed later 
by non-existence. In the later state the capacity will be ^5 
present for that which is not there in actuality.^ Actualize, 
then, the capacity. It will be true to say now that this 
exists last year or in the past generally. 

Considerations also not general like these but proper to 
the subject show it to be impossible that what was formerly 
eternal should later be destroyed or that what formerly was 
not should later be eternal. Whatever is destructible or 20 
generated is always alterable. Now alteration is due to 
contraries, and the things which compose the natural body 
are the very same that destroy it.'^ 

eternal is a contradiction in terms. (' Fortune ' is a name for chance 
within the sphere of conduct ; and anything which can bs caused by- 
chance could also, according to Aristotle, be caused either by intelli- 
gence, as in the case of conduct, or by nature, as here. See Phys. 1. c.) 

^ For l(TTi, IfTTiv read %(TTi, eariv. — The concluding argument is 
introduced very abruptly, by a formula which shows that in Aristotle's 
mind the suggestion here criticized is only another form of the appeal 
to chance just dealt with. The suggestion is that a capacity may be 
limited in respect of time of fulfilment. Aristotle refutes it by assuming 
that its authors admit (a) that the possession of the capacity is not 
limited in time, and {d} that any capacity may be actualized. 

^ Before n\r)v a comma is required instead of Prantl's full-stop. 

^ ov must be taken to stand for iK^ivov o, as in Simpl.'s paraphrase. — 
The meaning is that after the thing has ceased to be it still retains its 
capacity of existing at any time previous to that event. 

* A comma is required after evapriois and, for avpia-Tarai, avvia-Tarai. 


283^26 That th e heaven as a whole neither came into beings 1 
nor admits of destruction, as some assert, but is one and 
eternal, wit h no en d or beg^inning of it s total duration, con- 

30 taining and embracmg in itself the infinity of time , we may- 
convince ourselves not only by the arguments already set 
forth but also by a consideration of the views of those who 
differ from us in providing for its generation. If our view 
is a possible one, and the manner of generation which they 
284^ assert is impossible, this fact will have great weight in con- 
vincing us o f the immortality and eternity of the world. 
Hence it is well to persuade oneself of the truth of the 
ancient and truly traditional theories, that there is som e 
immortal and divine thing which pQssessesmovement, but 

5 movement such as has no limit and is rather itselt the limit 
of all other movement. A limit is a thing which contains; 
and this motion^, being perfect, contains those imperfect 
motions which have a limit and a goal, having it self no 
b eginning or end, but unceasing through the infinity of 

loTime, and oi otner movements, to some the cause of their 
beginning, to others offering the goal. The ancients gave 
to the Gods the heaven ^ or upper place, as being alo ne im- 
morta l ; and our pres ent arg^ument testifies that it is ind e- 
structible and ungenerated. Further, it is unaffected by 

15 any mortal discomfort, and, in addition, effortless; for it 
needs no constraining necessity to keep it to its path, and 
prevent it from moving with some other movement more 
natural to itself. Such a constrained movement would 
necessarily involve effort — the more so, the more eternal it 
were— and would be inconsistent with perfection. Hence 
we must not believe the old tale which says that the world 

20 needs some Atlas to keep it safe — a tale composed, it would 
seem, by men who, like later thinkers, conceived of all the 

^ Omit 17 KVK\o(Popia. The words are found only in L, and though 
harmless are quite superfluous. There is no reference to KVK\o(f)opia 
in Simpl.'s paraphrase. 

BOOK II. I 384* 

upper bodies as earthy and endowed with weight, and 
therefore supported it in their fabulous way upon animate 
necessity. We must no more believe that than follow Em- 
pedocles when he says that the world, by being whirled 
round, received a movement quick enough to overpower its 35 
own downward tendency, and thus has been kept from 
destruction all this time. Nor, again, is it conceivable that 
it should persist eternally by the necessitation of a soul.^ 
For a soul could not live in such conditions painlessly or 
happily, since the movement involves constraint, being im- 30 
posed on the first body, whose natural motion is different, 
and imposed continuously.^ It must therefore be uneasy 
and devoid of all rational satisfaction ; for it could not even, 
like the soul of mortal animals, take recreation in the bodily 
relaxation of sleep. An Ixion's lot must needs possess it, 35 
without end or respite. If then, as we said, the view already 284^ 
stated of the first motion is a possible one, it is not only 
more appropriate so to conceive of its eternity, but also on ~ 
this hypothesis alone are we able to advance a theory con- 
sistent with popular divinations of the divine nature.^ But 5 
of this enough for the present. 

2 Since there are some who say that there is a right and 
a left in the heaven, with those who are known as Pythago- 
reans — to whom indeed the view really belongs — we must 
consider whether, if we are to apply these principles to the 
body of the universe, we should follow their statement of 10 
the matter or find a better way. At the start we may say 

^ The cosmic motions must not be regarded as imposed upon the 
body of the cosmos by a world-soul as the human soul imposes move- 
ment on the human body. Such a notion necessarily implies constraint 
on the^part of the body and effort on the part of the'soul, and there- 
fore the movement could not be eternal. Aristotle has in mind, no 
doubt, the world-soul of the Timaeus. 

"^ Read eiTrep Kivfi (fiepeadai 7re(f)VK6Tos . . . aXXws koi Kive7 avvcx^^i 
with all MSS. except E. Simpl.'s paraphrase supports this reading.— 
The remarks which follow as to the absence of ' rational satisfaction ' 
recall verbally Plato, Timaeus 36 E Qdav apxh^ rfp^aro [fj -^vxf) — the 
world-soul] aTraixTTov Ka\ €fi(f)popns ^iov npos tov avpiravTa xpovov. 

^ By ' divination' (p.nvTfia) Aristotle means, not any religious practice 
of prophecy or the like, but simply the inspired guesses of common 

sense — rqu Koivfjv ravrrju evpoiav riv ep^o/iifi/ TTfpi Trjs dnovias Kai fxaKapio- 
TTjTos TOV deiov (Simpl.). 

E a 

284^^ DE CARLO 

that, if right and left are applicable, there are prior princi- 
ples which must first be applied. These principles have 
been analysed in the discussion of the movements of 
animals,^ for the reason that they are proper to animal 

15 nature. For in some animals we find all such distinctions 
of parts as this of right and left clearly present, and in 
others some ; but in plants we find only above and below. 
Now if we are to apply to the heaven such a distinction of 
parts, we must expect, as we have said, to find in it also that 

20 distinction which in animals is found first of them all. 
The distinctions are three,^ namely, above and below, front 
and its opposite, right and left — all these three oppositions 
we expect to find in the perfect body — and each may be 
called a principle. Above is the principle of length, right 

25 of breadth, front of depth. Or again we may connect them 
with the various movements, taking principle to mean that 
part, in a thing capable of movement, from w^hich move- 
ment first begins. Growth starts from above, locomotion 
fi'om the right, sense-movement from in front (for front is 

30 simply the part to which the senses are directed). Hence 
we must not look for above and below, right and left, front 
and back, in every kind£of body, but only in those which, 
being animate, have a principle of movement within them- 
selves. For in no inanimate thing do we observe a part 
from which movement originates. Some do not move at 

35 all, some move, but not indifferently in any direction ; fire, 
285^ for example, only upward, and earth only to the centre. 
It is true that we speak of above and below, right and 
left, in these bodies relatively to ourselves. The reference 
may be to our own right hands, as with the diviner, or to 
some similarity to our own members, such as the parts of 
5 a statue possess ; or we may take the contrary spatial 
order, calling right that which is to our left, and left that 
which is to our right. ^ We observe, however, in the things 

^ De Incessu Afiiin.^ cc. iv, v. 

^ Prantl misprints -yav for -ydp. 

^ Bekker and Prantl are probably right in regarding the words 
which follow h^iiov (viz. Ka\ . . . efxirpoadev) as spurious, though they are 
found in all MSS. except E. There is no trace of them in Simpl. 
or Them. 

BOOK II. 2 285' 

themselves none of these distinctions ; indeed if they are 
turned round we proceed to speak of the opposite parts as 
right and left, above and below, front and back. Hence it 10 
is remarkable that the Pythagoreans should have spoken of 
these two principles, right and left, only, to the exclusion of 
the other four, which have as good a title as they. There 
is no less difference between above and below or front and 
back in animals generally than between right and left. 15 
The difference is sometimes only one of function,^ some- 
times also one of shape ; and while the distinction of above 
and below is characteristic of all animate things, whether 
plants or animals, that of right and left is not found in 
plants. Further, inasmuch as length is prior to breadth, if 
above is the principle of length, right of breadth, and if the 20 
principle of that which is prior is itself prior, then above 
will be prior to right, or let us say, since * prior ' is am- 
biguous, prior in order of generation.^ If, in addition*, 
above is the region from which movement originates, right 
the region in which it starts, front the region to which it is 
directed, then on this ground too above has a certain original 25 
character as compared with the other forms of position. 
On these two grounds, then, they may fairly be criticized, 
first, for omitting the more fundamental principles, and 
secondly, for thinking that the two they mentioned were 
attributable equally to everything. 

Since we have already determined that functions of this 
kind belong to things which possess a principle of move- 
ment,^ and that the heaven is animate and possesses a prin- 30 
ciple of movement,** clearly the heaven must also exhibit 

* The right and left hands, for instance, differ in function but not 
in shape. It is implied that the difference of function underlies all 
the oppositions and determines the differences of shape where these 
occur. The differences of function are summarized above, 284^ 25-30. 

- For the four main kinds of 'priority', see Cat. ch. xii (i4*26ff.). 
Additional distinctions are made in Met. A, ch. xi. 

^ i. e. to animals. This is laid down at the beginning of the present 
chapter, 283^ 13, where reference is made to the De Incessti Animalium, 
Cf. also Phys. VIII. 4, 254^7. 

* Bk. I, 279*28, where it is stated to be the source of all life and 
movement. The term ' animate ' (e/i>/^uxos) has not hitherto been 
applied to it. The notion that the stars are ' inanimate ' is rejected 
below, 292* 20. 

285^ DE CAELO 

above and below, right and left. We need not be troubled 
by the question, arising from the spherical shape of the 
world, how there can be a distinction of right and left 
285^ within it, all parts being alike and all for ever in motion. 
We must think of the world as of something in which right 
differs from left in shape as well as in other respects, which 
subsequently is included in a sphere. The difference of 
function will persist, but will appear not to by reason 
5 of the regularity of shape. In the same fashion must 
we conceive of the beginning of its movement. For even 
if it never began to move, yet it must possess a prin- 
ciple from which it would have begun to move if it had 
begun, and from which it would begin again if it came to 
a stand. Now by its length I mean the interval between 

10 its poles, one pole being above and the other below ; for 
two hemispheres are specially distinguished from all others 
by the immobility of the poles.^ Further, by ' transverse ' 
in the universe we commonly mean, not above and below, 
but a direction crossing the line of the poles, which, by 
implication, is length: for transverse motion is motion 

15 crossing motion up and down. Of the poles, that which we 
see above us is the lower region, and that which we do not 
see is the upper. For right in anything is, as we say, the 
region in which locomotion originates, and the rotation of 
the heaven originates in the region from which the stars 
rise. So this will be the right, and the region where they 

30 set the left. If then they begin from the right and move 
round to the right, the upper must be the unseen pole. For 
if it is the pole we see, the movement will be leftward, 
which we deny to be the fact. Clearly then the invisible 
pole is above. And those who live in the other hemisphere 

35 are above and to the right, while we are below and to the 
left. This is just the opposite of the view of the Pythago- 
reans, who make us above and on the right side and those 
in the other hemisphere below and on the left side ; the fact 

' The unmoving poles mark out one among the infinite possible 
bisections of the sphere as natural and intelligible. We thus arrive, 
as explained in what follows, at an 'upper' and a 'lower' hemi- 

BOOK II. 2 285^ 

being the exact opposite.^ Relatively, however, to the 
secondary revolution, I mean that of the planets, we are 
above and on the right and they are below and on the left. 30 
For the principle of their movement has the reverse posi- 
tion, since the movement itself is the contrary of the other : 
hence it follows that we are at its beginning and they at its 
end. Here we may end our discussion of the distinctions 286^ 
of parts created by the three dimensions and of the conse- 
quent differences of position. 

3 Since circular motion is not the contrary of the r everse 
_ circular motion , we must consider why there is more than 
one motion, though we have to pursue our inquiries at 5 
a distance — a distance created not so much by our spatial 
position as by the fact that our senses enable us to perceive 
very few of the attributes of the heavenly bodies. But let 

^ Heath {Artstarchiis, pp. 231-2) summarizes the argument as 
follows: '"Right" is the place from which motion in space starts; 
and the motion of the heaven starts from the side where the stars rise, 
i. e. the east ; therefore the east is " right " and the west " left ". If 
now (i) you suppose yourself to be lying along the world's axis with 
your head towards the north pole, your feet towards the soiith pole, 
and your right hand towards the east, then clearly the apparent motion 
of the stars from east to west is over your back from your right side 
towards your left ; this motion, Aristotle maintains, cannot be called 
motion " to the right ", and therefore our hypothesis does not fit the 
assumption from which we start, namely that the daily rotation " begins 
from the right and is carried round towards the right [inX to. be^ia) ". 
We must therefore alter the hypothesis and suppose (2) that you are 
lying with your head towards the south pole and your feet towards the 
north pole. If then your right hand is to the east, the daily motion 
begins at your right hand and proceeds over the front of your body 
from your right hand to your left.' Heath points out that to us this 
still gives a wrong result : the motion across your front will still be 
from right to left ; but he accepts Simpl.'s explanation that movement 
to the front is regarded as rightward and motion to the back as left- 
ward — 17 yap eVi he^ia navrois as to efnrpoa-Oev eari. If this is true, 
Heath's account is satisfactory. It is curious that the notion of right- 
ward movement also gives trouble in the cosmology of Plato. Heath 
has an entirely different solution of that difficulty, in which the 
ordinary sense of 'to the right' is preserved (pp. 160-3). In view of 
the solution of the present passage quoted above, perhaps there is 
something after all to be said for the assertion of Proclus {In Timaeum 
220 e), quoted by Heath only to be dismissed, that cVt Sf ^ta does not 
mean eiV to hi^iov but is confined to circular motion and means 'the 
direction of a movement imparted by the right hand ' (e(^' a to dt^iov 
Kivei). The discrimination of right and left in circular motions is 
peculiarly difficult and ambiguous, as every child knows ; and some 
such use of en\ de^td may have been the Greek solution of the termino- 
logical problem. 


not that deter us. The reason must be sought in the 
following facts. Ev erything which has a function exists 
for its function. The activity of God is immortality, i. e. 

10 eternal life.^ Therefore the mov ement of that which is 
divine must be eterna l. But such is the heaven, v iz. 
a divine body^ and for that reason to it is given the circular 
body whose nature it is to move always in a circle .'^ Why, 
then, is not the whole body of the heaven of the same 
character as that part ? Because there must be something 
at rest at the centre of the revolving bod y ; and of that 

15 body no part can be at rest, either elsewhere or at the 
centre. It could do so only if the body's natural movement 
were towards the centre. But the circular movement is 
jiaturalr since otherwise it could not be eternal : for 
nothing unnatural is eternal.^ The unnatural is subse- 
quent to the natural, being a derangement of the natural 

20 which occurs in the course of its generation.* Earth then 
has to exis t ; for it i s earth which is at rest at the ce ntre. 
(At present we may take this for granted : it shall be ex- 
plained later.^) But if earth must exist, so must fire . For, 
if one of a pair of contraries naturally exists, the other, if 
it is really contrary, exists also naturally. In some form it 

25 must be present, since the matter of contraries is the same. 
Also, the positive is prior to its privation (warm, for in- 
stance, to cold), and rest and heaviness stand for the priva- 

* The argument is clear. ' God ' or ' divine ' means * eternal *. All 
body has motion. Therefore the notion of a divine body necessarily 
involves the notion of an eternal movement. — Simpl. says wrongly that 
Oeos here stands for delov crcofMa. 

^ The nature of the circular motion, and the reasons why it alone is 
compatible with immutability and the other divine attributes, have 
been explained in Bk. I, chaps, iii and iv. — The adjective 'circular* 
(e'yKVKXios) here and in several other passages of this book is trans- 
ferred from the motion to the body endowed with it. 

^ The body which is at the centre cannot be of the same nature, and 
endowed with the same motion, as that which is at the extremity ; for 
the actual position and movement of one or the other would in that 
case be unnatural. There must therefore be a body whose natural 
position is at the centre and whose natural movement is towards the 

* All change involves 'derangement' {eKama is), Phys. 222^16; 
cf. Phys. 241'' 2. eKaraais is opposed to TcXet'coffis ('fulfilment', or 
movement of a thing towards its ideal nature), P/tys. 246*17, ^2, 


^ See ch. xiv. 


BOOK IT. 3 286^ 

tion of lightness and movement. But further, if fire and 
earth exist, the intermed iate bodies ^ must exist also : for 
each element stands in a contrary relation to every other. 30 
(This, again, we will here take for granted and try later to 
explain.^) With these four elements, generation clearly is 
involved, since n one of them can be eterna l : for contraries 
interact with one' another and destroy one another. Further, 
it is inconceivable that a movable body should be eternal, 
if its movement cannot be regarded as naturally eternal : 35 
and these bodies we know to possess movement.^ Thus we 286'' 
see that^ generation is necessarily involved. But if so, there 
must be at least on e other circular motion : for a single move- 
ment of the whole heaven would necessitate an identical re- 
lation of the elements of bodies to one another.* This matter 5 
also shall be cleared up in what follows : but for the present so 
much is clear, that the reason why t her e is mor e than one 
circular body isthe necessity of generation, which follows 
on the presence of fire, which, with that of the other bodies, 
follows on that of earth ; and earth is required because 
eternal movement in one body necessitates eternal rest in 

4 The shape of the hea ven is of necessity s pherical ; for 10 
that is the shape most appropriate to its substance and also 
by nature primary. 

^ viz. air and water. 

^ See De Gen. et Corr. II. iii, iv. 

^ Retaining the MSS. reading, which is confirmed by Simpl. and 
Them., rovrav 6* 'icm Kivr^cris. If these words are taken to mean ravra 
8' eVrt KivTjTa, the argument, though summarily stated, is complete 
and Prantl's conjecture is unnecessary. If it is granted that the 
sublunary elements move, generation is admitted, unless it can be 
shown that their movement is such as to be naturally eternal. But 
it has already been shown {Phys. 26i*3iff.) that the rectilinear 
movements must be intermittent. 

* A. is proving the necessity of the secondary revolution, i. e. that 
of the planets. ' If, he argues, * there were only the movement of the 
fixed stars, and sun and moon were set in it and carried along with it, 
the varieties of summer and winter and the other seasons would 
disappear and the daily interchange would not follow its accustomed 
course. For if the sun were set in Cancer, we should have perpetual 
summer, and if it were set in Capricorn, perpetual winter: there 
would be no generation or destruction, not even the varied phases of 
the moon ' (Simpl.). The further discussion promised here is to be 
found in De Gen. et Corr. II. x. 


286^ DE CAELO 

First, let us consider generally which shape is primary 
among planes and solids alike. Every plane figure must 

15 be either rectilinear or curvilinear. Now the rectilinear is 
bounded by more than one line, the curvilinear by one only. 
But since in any kind the one is naturally prior to the 
many and the simple to the complex, _the circle will be the 
first of plane figures . Again, if by complete, as previously 

ao defined,^ we mean a thing outside which no part of itself 
can be found, and if addition is always possible to the 
straight line but never to the circular, clearly the line which 
embraces the circle is complete. If then the complete is 
prior to the incomplete, it follows on this ground also that 
the circle is prima ry among fignrpQ And the sphere holds 
the same position among solid s. For it alone is embraced 

25 by a single surface, while rectilinear solids have several. 
The spher e is amo ng solids what the circle is among- plane 
figures. Further, those who divide bodies into planes and 
generate them out of planes ^ seem to bear witness to the 
truth of this. Alone ^ among solids they leave thje sphere 

30 undivided, as not possessing more than one surface : for the 
division into surfaces is not just dividing a whole by cutting 
it into its parts, but division of another fashion into parts 
different in form.* It is clear, then, that the sphere is first 
of solid figures. 

If, again, one orders figures according to their numbers, 

35 it is most natural to arrange them in this way. The circle 

287^ corresponds to the number one, the triangle, being the sum 

of two right angles, to the number two. But if one is 

assigned to the triangle, the circle will not be a figure 

at all. 

* Phys. III. 207a 8. For the terms of the definition cf. sup. 271^ 31. 
This notion of * perfect ' (or ' complete ') is presupposed in the opening 
chapter of this treatise. — In 1. 19 read rtiiv avrovi the tS)v is omitted 
only in E and F. 

^ Cf. PAys. VI. I and m/. Bk. Ill, ch. i for further criticisms of 
these theories. The theory criticized is that expressed by Timaeus 
the Pythagorean in Plato's dialogue of that name. (So Simpl. on 

' Prantl's fxovT] is a misprint for fiovrjv. 

* Both sphere and circle can of course be divided into parts, but 
they cannot be geometrically analysed into constituents not themselves 
spherical or circular. The geometrical analysis requires that the 
constituent or * part * shall be different in form from the whole. 

BOOK II. 4 287^ 

Now the first figure belongs to the first body, and the 
first body is that at the farthest circumference. It follows 
that the body which revolves with a circular movement 
must be spherical. The same then will be true of the body 5 
continuous with it : for that which is continuous with the 
spherical is spherical. The same again holds of the bodies 
between these and the centre. Bodies which are bounded 
by the spherical and in contact with it must be, as wholes, 
spherical ; and the bodies below the sphere of the planets 
are contiguous with the sphere above them. The sphere 
then will be spherical throughout ; for every body within it 10 
is contiguous and continuous with spheres. 

Again, since the whole revolves, palpably and by 
assumption, in a circle, and since it has been shown that 
outside the farthest circumference there is neither void nor 
place, from these grounds also it will follow necessarily that 
the heaven is spherical. For if it is to be rectilinear in 
shape, it will follow that there is place and body and void ^5 
without it. For a rectilinear figure as it revolves never 
continues in the same room, but where formerly was body, 
is now none, and where now is none, body will be in 
a moment because of the projection at the corners. 
Similarly, if the world had some other figure with unequal 20 
radii, if, for instance, it were lentiform, or oviform, in every 
case we should have to admit space and void outside the 
moving body, because the whole body would not always 
occupy the same room.^ 

Again, if the motion of the heaven is the measure of all 
movements whatever in virtue of being alone continuous 
and regular and eternal, and if, in each kind, the measure is 25 
the minimum, and the minimum movement is the swiftest, 
then, clearly, the movement of the heaven must be the 
swiftest of all movements. Now of lines which return upon 
themselves^ the line which bounds the circle is the shortest; 

' This depends, as Simpl. observes, after Alexander, on the position 
of the axis of revolution. In the case of a perfect sphere alone the 
position of the axis is immaterial. 

^ Reading a(f)* invrov €(}i eouTo, with Simpl. and the consensus of the 
MSS. The Tov and to in Prantl's text are conjectural insertions. 
J has a<fi avTov €<f> avro. 

287^ DE CAELO 

and that movement is the swiftest which follows the 
shortest line.^ Therefore, if the heaven moves in a circle 

30 and moves more swiftly than anything else, it must 
necessarily be spherical. 

Corroborative evidence may be drawn from the bodies 
whose position is about the centre. If earth is enclosed by 
water, water by air, air by fire, and these similarly by the 
upper bodies — which while not continuous are yet contiguous 
287^ with them ^ — and if the surface of water is spherical, and that 
which is continuous with or embraces the spherical must 
itself be spherical, then on these grounds also it is clear 
that the heavens are spherical. But the surface of water 
5 is seen to be spherical if we take as our starting-point the 
fact that water naturally tends to collect in a hollow place — 
' hollow ' meaning * nearer the centre '. Draw from the 
centre the lines AB, AC, and let their extremities be joined 
by the straight line BC. The line AD, drawn to the base 
of the triangle, will be shorter than either of the radii.^ 

10 Therefore the place in which it terminates will be a hollow 
place. The water then will collect there until equality is 
established, that is until the line AE is equal to the two 
radii. Thus water forces its way to the ends of the radii, 
and there only will it rest : but the line which connects the 
extremities of the radii is circular : therefore the surface of 
the water BE C is spherical. 

15 It is plain from the foregoing that the universe is 
spherical. It is plain, further, that it is turned (so to speak) 
with a, finish which no manufactured thing nor anything 

* This is true if equality of effort (dno rrjs avr^s dwdfxeuis Simpl.) is 
postulated. In a word, the underlying notion is rather the compara- 
tive economy than the comparative swiftness of movements. — For the 
origin of this argument Simpl. refers to Tim. 2il B. 

2 'Continuous', 'contiguous', and the related terms are defined in 
Phys. V. iii. If these bodies were continuous with the heavenly body 
they would have to move with the same motion as it. 

BOOK II. 4 287^ 

else within the range of our observation can even approach. 
For the matter of which these are composed does not 
admit of anything like the same regularity and finish as 
the substance of the enveloping body ; since with each step 20 
away from earth the matter manifestly becomes finer in the 
same proportion as water is finer than earth. 

5 Now there are two ways of moving along a circle, from A 
to B or from A to C,^ and we have already explained ^ thai 
thes e movements are n ot contrary to one another. But 
nothing which concerns the eternal can be a matter of 25 . 
chance or spontaneity, and the heaven and its circular 
motion are eternal. We must therefore ask why this 
motion takes one direction and not the other. Either this 
is itself an ultimate fact or there is an ultimate fact behind 
it. It may seem evidence of excessive folly or excessive zeal 
to try to provide an explanation of some things, or of every- 30 
thing, admitting no exception. The criticism, however, is not 
always just : one should first consider what reason there is 
for speaking, and also what kind of certainty is looked for, 
whether human merely or of a more cogent kind.^ When 
any one shall succeed in finding proofs of greater precision, 288^ 
gratitude will be due to him for the discovery, but at 
present we must be content with a probable solution.* If 
nature always follows the best course possible, and, just as 
upward movement is the superior form of rectilinear move- 
ment, since the upper region is more divine than the lower. 5 
so forward movement is superior to backward, then front 
and back exhibits, like right and left, as we said before ' and 

* D/""'^^ ^f ^ 's the ' right from which movement starts, 

°f ^ A why should the movement be towards B rather than 

I J towards C? Probably, answers Aristotle, because 

^^— ^ movement towards B is ' forward ' and movement 

towards C ' backward ' motion. 

2 I. iv. 

^ Bekker and Prantl prefer L's KapTepiKonTepov to the Kapreparepov of 
all other MSS. It is difificult to imagine why. There is good Platonic 
parallel for the use of Kaprepos in this connexion {Phaedo 77 A, Theaet. 
169 B). 

^ A similar caution is repeated at the beginning of ch. xii, 291^25. 
For this use of 0ati/d/x6»/oj/ cf. Bonitz, Ind. Ar. 809*24. 
^ Reading, with Prantl, e^^^ ^') ftTrep, and accepting his punctuation. 

288^ DE CARLO 

as the difficulty just stated itself suggests, the distinction of 
prior and posterior, which provides a reason and so solves 
our difficulty. Supposing that nature is ordered in the 
10 best way possible, this may stand as the reason of the fact 
mentioned. • For it is best to move with a movement simple 
and unceasing, and, further, in the superior of two possible 

We have next to show that the movement of the heaven 6 
15 is regular and not irregular. 1 his applies only to the first " 
heaven and the first movement ; for tJie_J ower s pheres 
exhibit a composition of several movements into one. If the 

movement is uneven, clearly there will be acceleration, 
maximum speed, and retardation, since these appear in all 
20 irregular motions. The maximum may occur either at the 
starting-point or at the goal or between the two ; and we 
expect natural motion to reach its maximum at the goal, 
unnatural motion at the starting-point, and missiles midway 
between the two.^ But circular movement, having no be- 

The passage as punctuated by Bekker is untranslatable. The apo- 
dosis undoubtedly begins at the word ex^t. EL give c^^* ^^ firrfp, the 
remaining MSS. e^^i einep. — The existence of a 'front' and *back' in 
the world was asserted in ch. ii. The priority of * up ', ' right ', and 
'front' over 'down', 'left', and 'back' is assumed in the same 
chapter, 284^ 24.— The gist of the present rather involved and hesita- 
ting statement is that the only way to account for the direction of 
the heavenly movements is by means of these oppositions and the 
priority commonly attributed in each to one term over the other. 

^ It appears from Meteorologica I. iv, 341^ — 342* that meteors and 
shooting stars come under the notion of ' missiles ' or ' things thrown '. 
Their motion is compared to that of the stone of a fruit when it is 
made to fly through the air by being squeezed out from between the 
fingers. Ordinary throwing, e. g. of a stone or javelin, would of course 
also be included. — Simpl. and, by his report, Alexander are much 
puzzled by the statement in the text. Simpl. makes the wild sugges- 
tion that A. here regards animal movements as 'missile' motion, in 
that they are neither upward nor downward but horizontal. Alex, 
suggests that ' missile ' movements may be said to have their maximum 
between goal and starting-point, because every earthly body has its 
goal either up or down, and the whole of the ' missile ' movement, 
from beginning to end, takes place in the middle region. Alex, is 
probably right. It is to be remembered that all movement is either 
natural or unnatural, and that ' missile ' movement can only be 
distinguished in principle as a mixture of the two ; further that the 
body thrown must be composed of one or more of the four elementary 
bodies. ' Throwing ' is thought of as a forced horizontal motion put 
upon one of these bodies, each of which has a ' goal ', down (or up), 
and a ' starting-point ', up (or down). In such a motion the maximum 

BOOK 11. 6 288^ 

ginning or limit or middle in the direct sense of the words, 
has neither whence nor whither nor middle : for in time it 
is eternal, and in length it returns upon itself without a 25 
break. If then its movement has no maximum, it can 
have no irregularity^ ._since irregularity is produced by re- 
tardation and acceleration. Further, since everything that 
is moved is moved by something, the cause of the irregu- 
larity of movement must lie either in the mover or in the 
moved or in both. For if the mover moved not always 30 
with the same force, or if the moved were altered and did 
not remain the same, or if both were to change, the result 
might well be an irregular movement in the moved. But 
none of these possibilities can be conceived as actual in the 
case of the heavens. As to that which is moved, we have 
shown that it is primary and simple and ungenerated and 288*^ 
indestructible and generally unchanging ; and the mover 
has an even better right to these attributes. It is the 
primary that moves the primary, the simple the simple, 
the indestructible and ungenerated that which is indestruc- 
tible and ungenerated. Since th^n that which is moved, 5 
being a body, is nevertheless unchanging, how should the 
mover, which is incorporeal, be changed ? 

It follows then, further, that the motion cannot be 
irregular-.r- For if irregularity occurs, there must be change 
either in the movement as a whole, from fast to slow and 
slow to fast, or in its parts. That there is no irregularity in 
the parts is obvious, since, if there were, some divergence 10 
of the stars would have taken place ^ before now in the 
infinity of time, as one moved slower and another faster : 
but no alteration of their intervals is ever observed. Nor 
again is a change in the movement as a whole admissible. 
Retardation is always due to incapacity, and incapacity is 
unnatural. The incapacities of animals, age, decay, and the 15 
like, are all unnatural, due, it seems, to the fact that the 

cannot be said to be attained at either terminus, since neither terminus 
is involved, but only 'between the two'. This means that in the case 
of natural motion ' goal ' must be taken to be the natural place of the 
body, which is also the 'starting-point' of unnatural motion in the 
same body. In 'throwing', therefore, there is neither starting-point 
nor goal, but all is in the intermediate region. 
* For yeyovei read eyeyovei with FHLMJ. 

288^ DE CAELO 

whole animal complex is made up of materials which differ 
in respect of their proper places, and no single part occupies 
its own place. If therefore that which is primary contains 

20 nothing unnatural, being simple and unmixed and in its 
proper place and having no contrary, then it has no place 
for incapacity, nor, consequently, for retardation or (since 
acceleration involves retardation) for acceleration. Again, 
it is inconceivable that the mover should first show in- 
capacity for an infinite time, and capacity afterwards for 
another infinity. For clearly nothing which, like incapacity, 

25 is unnatural ever continues for an infinity of time ; nor does 
the unnatural endure as long as the natural, or any form of 
incapacity as long as the capacity.^ But if the movement 
is retarded it must necessarily be retarded for an infinite 
time.^ Equally impossible is perpetual acceleration or 
perpetual retardation. For such movement would be in- 
finite and indefinite,^ but every movement, in our view, 

30 proceeds from one point to another and is definite in 
character. Again, suppose one assumes a minimum time 
in less than which the heaven could not complete its move- 
ment. For, as a given walk or a given exercise on the harp 
cannot take any and every time, but every performance has 
its definite minimum time which is unsurpassable, so, one 
might suppose, the movement of the heaven could not be 
289^ completed in any and every time. But in that case per- 
petual acceleration is impossible (and, equally, perpetual 
retardation : for the argument holds of both and each),'' 

^ Reading olb' oXco?, with all MSS. except E, which Praiitl follows 
in reading ovS' aWcos. — The effect of aXXco? is to make the unnatural 
one species or department within the general notion of incapacity. 
oXo)? has much more varied uses and enables one to avoid this 

^ i.e. equality of duration must be supposed between the incapacity 
(retardation) and the preceding capacity, as assumed in the foregoing 
argument, in which infinity (sc. in one direction) is attributed to each. 
For if the speed of movement has been everlastingly increasing, and 
now begins to decrease, it is impossible to suppose anything else but 
that it will decrease everlastingly. 

^ viz. in respect of its speed. The hypothesis now considered is 
retardation or acceleration not balanced by its opposite but having 
neither beginning nor end, i.e. infinite in dol/t directions. 

^ Prantl's stopping needs correction. The words d St fu) . . . Oanpov 
should be enclosed within brackets. 

BOOK II. 6 289^ 

if we may take acceleration to proceed by identical or in- 
creasing additions of speed and for an infinite time. The 
remaining alternative is to say that the movement exhibits 5 
an alternation of slower and faster: but this is a mere 
fiction and quite inconceivable. Further, irregularity of 
this kind would be particularly unlikely to pass unobserved, 
since contrast makes observation easy. 

T hat there is one heave n, then, only, and that it is un- 
generated and eternal, and further that its' movement is 
regular, has now been sufficiently explained. 10 

7 We have next to speak of the stars, as they are called, 
of their composition, shape, and movements. It would be 
most natural and consequent upon what has been said that 
each of the stars should be composed of that substance in 1.5 
which their path lies,^ since, as we said, there is an element 
whose natural movement is circular. In so saying we are 
only following the same line of thought as those who say 
that the stars are fiery because they believe the upper body 
to be fire, the presumption being that a thing is composed of 
the same stuff as that in which it is situated. The warmth 
and light which proceed from them are caused by the friction ao 
set up in the air by their motion. Movement tends to 
create fire in wood, stone, and iron ; and with even more 
reason should it have that effect on air, a substance which is 
closer to fire than these.^ An example is that of missiles, 
which as they move are themselves fired so strongly that 
leaden balls are melted ; and if they are fired the surround- 25 
ing air must be similarly affected. Now while the missiles 
are heated by reason of their motion in air, which is turned 
into fire by the agitation produced by their movement,^ 
the upper bodies are carried on a moving sphere, so that, 
though they are not themselves fired, yet the air underneath 30 
the sphere of the revolving body is necessarily heated by its 

^ i. e. of the same substance as the spheres to which their motion 
is due. 

^ A colon is required after the word dfjp in 1. 23. 

^ TrXT/yi^ seems to stand here for the continuous beating of the 
missile upon the air rather than for a single blow. Cf. Simpl. 439. 25 
v7t6 TTJs . . . TrXijyrjs Kai Traparpi-^ewy. The same use recurs below, 

646*20 F 

289^ DE CAELO 

motion, and particularly in that part where the sun is 
attached to it.^ Hence warmth increases as the sun gets 
nearer or higher or overhead. Of the fact, then, that the 
^ 35 stars are neither fiery nor move in fire, enough has been 

289^ Since changes evidently occur not only in the position of 8 
the stars but also in that of the whole heaven, there are 
three possibilities. Either (i) both are at rest, or (2) both 
are in motion, or (3) the one is at rest and the other in 

(i) That both should be at rest is impossible; for, if the 

5 earth is at rest, the hypothesis does not account for the 

observations ; and we take it as granted that the earth is at 

rest. It remains either that both are moved, or that the 

one is moved and the other at rest. 

(Of) On the view, first, that both are in motion, we have the 
absurdity that the stars and the circles move with the same 
speed, i. e. that the pace of every star is that of the circle in 
10 which it moves. For star and circle are seen to come back 
to the same place at the same moment ; from which it 
follows that the star has traversed the circle and the circle 
has completed its own movement, i. e. traversed its own 
circumference, at one and the same moment. But it is 
difficult to conceive that the pace of each star should be 
15 exactly proportioned to the size of its circle. That the pace 
of each circle should ke proportionate to its size is not 
absurd but inevitable : but that the same should be true of 
the movement of the stars contained in the circles is quite 

^ The stars are not themselves ignited because the substance of 
which they are composed cannot be transmuted into any other as fire, 
air, and the other sublunary substances can. It is, however, legitimate 
to object to the above account that fire, not air, is the substance in 
contact with the spheres, and that only with the innermost. How, 
then, is air ignited by the movement of the spheres ? Alex, and 
Simpl. agree that ' air' must in some sense include fire (or vneKKavfxa, 
the ' fuel of fire ' which occupies the outer place) ; but that, even if 
true, will not solve the difficulties. The view here advanced is 
nowhere fully worked out ; but some further suggestions are made 
in Meteor. I. iii and iv. Cf. Heath, Aristarchus, pp. 241-2. It seems 
certain that what Aristotle meant was that the 'fire' which is in 
contact with the spheres is ignited and agitated by their motion and 
the air beneath by it (341*2-3 and 30-31). 


BOOK II. 8 289'' 

incredible. For if, on the one hand, we suppose that the 
star which moves on the greater circle is necessarily swifter, 
clearly we also admit that if stars shifted their position so 
as to exchange circles, the slower would become swifter and 20 
the swifter slower. But this would show that their move- 
ment was not their own, but due to the circles. If, on the 
other hand, the arrangement was a chance combination, the 
coincidence in every case of a greater circle with a swifter 
movement of the star contained in it is too much to believe. 
In one or two cases it might not inconceivably fall out so, 35 
but to imagine it in every case alike is a mere fiction. 
Besides, chance has no place in that which is natural, and 
what happens everywhere and in every case is no matter of 

(3) The same absurdity is equally plain ^ if it is supposed 
that the circles stand still and that it is the stars them- 
selves which move. For it will follow that the outer stars 
are the swifter, and that the pace of the stars corresponds to 3° 
the size of their circles. 

Since, then, we cannot reasonably suppose either that 
both are in motion or that the star alone moves, the remain- 
ing alternative is that the circles should move, while the stars 
are at rest and move with the circles to which they are 
attached. Only on this supposition are we involved in no 
absurd consequence. For, in the first place, the quicker 
movement of the larger circle is natural when all the circles 35 
are attached to the same centre. Whenever bodies are 290^ 
moving with their proper motion, the larger moves 
quicker. It is the same here with the revolving bodies: 
for the arc intercepted by two radii will be larger in the 
larger circle, and hence it is not surprising that the 
revolution of the larger circle should take the same time as 5 
that of the smaller. And secondly, the fact that the 
heavens do not break in pieces follows not only from this 

^ Bekker and Prantl read ravra instead of ra avrd, which is the 
reading of all MSS. and of Simpl. The alteration is unnecessary. 
The difficulty is the same as that pointed out in the preceding argu- 
ment — an unaccountable correspondence between the size of the circle 
and the speed of the star's movement. 

F 2 

290^ DE CAELO 

but also from the proof already given ^ of the continuity 
of the whole. 

Again, since the stars are spherical, as our opponents 
assert and we may consistently admit, inasmuch as we 
construct them out of the spherical body, and since the 

10 spherical body has two movements proper to itself, namely 
rolling and spinning,^ it follows that if the stars have a 
movement of their own, it will be one of these. But neither 
is observed, (i) Suppose them to spin. They would then 
stay where they were, and not change their place, as, by ob- 
servation and general consent, they do. Further, one would 
. expect them all to exhibit the same movement : but the 

15 only star which appears to possess this movement is the 
sun, at sunrise or sunset, and this appearance is due not to 
the sun itself but to the distance from which we observe it. 
The visual ray being excessively prolonged becomes weak 
and wavering.^ The same reason probably accounts for the 
apparent twinkling of the fixed stars and the absence of 

20 twinkling in the planets. The planets are near, so that the 
visual ray reaches them in its full vigour, but when it 
comes to the fixed stars it is quivering because of the dis- 
tance and its excessive extension ; and its tremor produces 
an appearance of movement in the star : for it makes no 
difference whether movement is set up in the ray or in the 
object of vision. 

25 (2) On the other hand, it is also clear that the stars 
do not roll. For rolling involves rotation : but the * face ', 

^ Cf c. iv. But there is no attempt to prove continuity in the 
De Caelo. 

2 By 'spinning' is meant rotation on a stationary axis, by 'rolling' 
a fprward movement in which a body turns completely round in 
a distance equal to its own circumference. See Heath, Aristarchus, 

PP- 233-5- 

^ The term oy\ns ( = visual ray) belongs to pre-Aristotelian psychology. 
Cf. Plato, Meno, 76 C-D. Aristotle's use of it here and elsewhere 
(e.g. Meteor. III. iv, 373^2) seems to commit him 'to the view that 
the eye sees by rays issuing from a native fire within it' (Beare, 
Greek Theories of Elementary Cognition^ p. 66, n. i). But his own 
argument, when dealing with vision, is to the contrary effect. 'In 
seeing we take something in, not give something out' {Top. 105^6); 
and the process is ' from object to eye, not conversely ' (Beare, p. 86). 
Aristotle must be supposed here to. be adopting popular or^Platonic 

BOOK II. 8 290' 

as it is called, of the moon is always seen.^ Therefore, 
since any movement of their own which the stars possessed 
would presumably be one proper to themselves, and no such 
movement is observed in^Ahem, clearly they have no move- 
ment of their own. 

There is, further, the absurdity that nature has bestowed 30 
upon them no organ appropriate to such movement. For 
nature leaves nothing to chance, and would not, while car- 
ing for animals, overlook things so precious. Indeed, 
nature seems deliberately to have stripped them of every- 
thing which makes self-originated progression possible, and 
to have removed them as far as possible from things which 
have organs of movement. This is just why it seems 35 
proper that the whole heaven and every star should be 290' 
spherical. For while of all shapes the sphere is the most 
convenient for movement in one place, making possible, as 
it does, the swiftest and most self-contained motion, for 
forward movement it is the most unsuitable, least of all 5 
resembling shapes which are self-moved, in that it has no 
dependent or projecting part, as a rectilinear figure has, and 
is in fact as far as possible removed in shape from ambu- 
latory bodies. Since, therefore , the heavens have to move 
in one place, anotS^stars are not required to move them- 
selves forward, it is natural that both should be spherical — 10 
a shape which best suits the movement of the one and the 
immobility of the other. 

9 From all this it is clear that the theory that the move- 
ment of the stars produces a harmony, i. e. that the sounds 
they make are concordant, in spite of the grace and 
originality with which it has been stated, is nevertheless 15 
untrue.^ Some thinkers suppose that the motion of bodies 

^ It has been objected to Aristotle that if the moon always shows 
the same side to us it is thereby proved that it does rotate upon its 
axis. But such rotation (incidental, in Aristotle's view, to the move- 
ment of the sphere) is quite different from the rotation involved in 
'rolling*, which Aristotle is here concerned to deny. See Heath, 

P- 235. 

^ The doctrine of the 'harmony of the spheres' is no doubt, as 
Simpl. says, Pythagorean. The most famous statement of the doctrine 
is in Plato's Reptiblic (Myth of Er, 61 7B), and the ratios given to the 
planets in Tiviaetis, 35B, seem to have a musical significance. For 
a discussion of the doctrine see Heath, Aristarclms^ pp. 105-15. 

290^ DE CAELO 

of that size must produce a noise, since on our earth the 
motion of bodies, far inferior in size and in speed of move- 
ment has that effect. Also, when the sun and the moon, 
they say, and all the stars, so great in number and in size, 

20 are moving with so rapid a motion, how should they not 
produce a sound immensely great ? Starting from this 
argument and from the observation that their speeds, as 
measured by their distances, are in the same ratios as 
musical concordances, they assert that the sound given 
forth by the circular movement of the stars is a harmony. 
Since, however, it appears unaccountable that we should 

25 not hear this music, they explain this by saying that the 
sound is in our ears from the very moment of birth and is 
thus indistinguishable from its contrary silence, since sound 
and silence are discriminated by mutual contrast. What 
happens to men, then, is just what happens to coppersmiths, 

♦ who are so accustomed to the noise of the smithy that it 

30 makes no difference to them. But, as we said before, 
melodious and poetical as the theory is, it cannot be a true 
account of the facts. There is not only the absurdity of our 
hearing nothing, the ground of which they try to remove, 
but also the fact that no effect other than sensitive is 
produced upon us. Excessive noises, we, know, shatter the 

35 solid bodies even of inanimate things : the noise of thunder, 
291^ for instance, splits rocks and the strongest of bodies. But 
if the moving bodies are so great, and the sound which 
penetrates to us is proportionate to their size, that sound 
must needs reach us in an intensity many times that of 
thunder, and the force of its action must be immense. 
5 Indeed the reason why we do not hear, and show in our 
bodies none of the effects of violent force, is easily given : 
it is that there is no noise. But not only is the explanation 
evident ; it is also a corroboration of the truth of the views 
we have advanced. For the very difficulty which made 
the Pythagoreans say that the motion of the stars produces 

10 a concord corroborates our view. Bodies which are them- 
selves in motion, produce noise and friction : but those 
which are attached or fixed to a moving body, as the parts 
to a ship, can no more create noise, than a ship on a river 

BOOK II. 9 291* 

moving with the stream. Yet by the same argument one 
might say it was absurd that on a large vessel the motion of 
mast and poop should not make a great noise, and the like 15 
might be said of the movement of the vessel itself. But sound is 
caused when a moving body is enclosed in an unmoved body, 
and cannot be caused by one enclosed in, and continuous with, 
a moving body which creates no friction. We may say, 
then, in this matter that if the heavenly bodies moved in 
a generally diffused mass of air or fire, as every one supposes, 20 
their motion would necessarily cause a noise of tremendous 
strength and such a noise would necessarily reach and 
shatter us.^ Since, therefore, this effect is evidently not 
produced, it follows that none of them can move with the 
motion either of animate nature or of constraint.^ It is as 
though nature had foreseen the result, that if their move- 25 
ment were other than it is, nothing on this earth could 
maintain its character. 

That the stars are spherical and are not self-moved, has 
now been explained. 

10 With their order — I mean the position of each, as 30 
involving the priority of some and the posteriority of 
others, and their respective distances from the extremity — 
with this astronomy may be left to deal, since the astro- 
nomical discussion is adequate.^ This discussion shows 
that the movements of the several stars depend, as regards 
the varieties of speed which they exhibit, on the distance 

^ Prantl misprints diaKvaUv for biaKvaUiv. 

■- If the stars moved in a non-moving medium either with a self- 
originated motion, like that of an animal, or with a motion imposed 
on them by external force, like that of a stone thrown, a great and 
destructive noise would result. There is no such noise or destruction. 
Therefore they do not so move. The Pythagorean doctrine is thus 
used to corroborate a conclusion already reached. It might be 
objected that Aristotle has already postulated friction with another 
substance to account for the brightness of the stars, and that this 
friction might well be expected to be accompanied with noise as in 
the case of missiles on the earth. 

^ The tone of this reference to ' astronomy ', as well as the present 
tense in the verb XeyeToi, suggest that Aristotle is not here referring to 
other works of his own but to contemporary works on astronomy, 
current in the school, by other writers. These sentences also clearly 
imply that * astronomy' is more empirical in its methods than the 
De Caelo. Cf. /;//>«, 291^21.— In 1. 29 Prantl's o is a misprint for ov. 

291^ DE CAELO 

35 of each from the extremity. It is established that the 
outermost revolution of the heavens is a simple movement 
291^ and the swiftest of all, and that the movement of all other 
bodies is composite and relatively slow, for the reason that 
each is moving on its own circle with the reverse motion to 
that of the heavens. This at once leads us to expect that 
the body which is nearest to that first simple revolution 

5 should take the longest time to complete its circle, and that 
which is farthest from it the shortest, the others taking 
a longer time the nearer they are and a shorter time the 
farther away they are. For it is the nearest body which is 
most strongly influenced, and the most remote, by reason 
of its distance, which is least affected, the influence on the 
intermediate bodies varying, as the mathematicians show, 

TO with their distance.^ 

With regard to the shape of each star, the most reasonable 11 
view is that they are spherical. It has been shown ^ that 
it is not in their nature to move themselves, and, since 
nature is no wanton or random creator, clearly she will have 
15 given things which possess no movement a shape particularly 
unadapted to movement. Such a shape is the sphere, since 
it possesses no instrument of movement. Clearly then 
their mass will have the form of a sphere.^ Again, what 

^ In regard to 'order' Aristotle only seeks to explain one point 
which might present a difficulty. It would be natural to expect the 
moon, which is the nearest planet to the earth, to have the slowest 
motion; but in fact it is the swiftest of the planets. His answer is 
that the movement of the planets, being the reverse of that of the 
outer heaven, is hampered by proximity to it ; and the planet nearest 
to the earth is least influenced and therefore moves swiftest. Simpl. 
raises the objection : is not the planetary motion then in some degree 
constrained or unnatural ? He quotes with approval from Alex, the 
reply : ' No : for the planetary sphere is not unwilling. This accords 
with its purpose and desire. It may be necessity, but it is also good, 
and recognized as such.' Simpl. is not altogether satisfied by this 

2 Ch. viii. 

^ Simpl. notes a circle in Aristotle's argument, since he has already 
used the spherical shape of the stars to prove that they have no 
independent motion (c. viii). (The same charge is brought against 
Aristotle by Y)xQ.-^tx, Planetary Systems, p. iii.) He is not satisfied 
with Alex.'s rejoinder that neither of these arguments stands alone. 
The true answer is that the argument of c. viii is explicitly based, in 
respect of the spherical shape of the stars, on a premise borrowed 
from the opposition : see 290* 7. Aristotle's own proof of the matter 
precedes it. This argument is therefore in order. 

BOOK II. II 291^ 

holds of one holds of all, and the evidence of our eyes shows 
us that the moon is spherical. For how else should the 
moon as it waxes and wanes show for the most part 20 
a crescent-shaped or gibbous figure, and only at one mo- 
ment a half-moon? And astronomical arguments^ give 
further confirmation ; for no other hypothesis accounts for 
the crescent shape of the sun's eclipses. One, then, of the 
heavenly bodies being spherical, clearly the rest will be 
spherical also. 

12 There are two difficulties, which may very reasonably 
here be raised, of which we must now attempt to state the 25 
probable solution : ^ for we regard the zeal of one whose 
thirst after philosophy leads him to accept even slight 
indications where it is very difficult to see one's way, as 
a proof rather of modesty than of over-confidence. 

Of many such problems one of the strangest is the 
problem why we find the greatest number of movements in 30 
the intermediate bodies, and not, rather, in each successive 
body a variety of movement proportionate to its distance 
from the primary motion. For we should expect, since the 
primary body shows one motion only, that the body which 
is nearest to it should move with the fewest movements, 
say two, and the one next after that with three, or some 
similar arrangement. But the opposite is the case. The 35 
movements of the sun and moon are fewer than those of 292^ 
some of the planets. Yet these planets are farther from 
the centre and thus nearer to the primary body than they, 
as observation has itself revealed. For we have seen the 
moon, half-full, pass beneath the planet Mars, which 5 
vanished on its shadow side and came forth by the bright 
and shining part.^ Similar accounts of other stars are 

^ See note on 291*32. 

2 See note on 288^2. 

^ Brandis (Berlin Aristotle, vol. IV, 497^13) quotes a scholium to 
the effect that Alexander in his Commentary said it was Mercury, not 
Mars. Both Simpl. and Them., however, give Mars without question. 
If it was Mars, a calculation of Kepler's {Astro7ioinia Nova, 1609, 
p. 323) fixes the date. ' Inveni,' he writes, ' longissima inductione per 
annos L, ab anno quindecimo ad finem vitae Aristotelis, non potuisse 
esse alio die, quam in vespera diei iv Aprilis, anno ante CHRISTI 
vulgarem epocham CCCLVII, cum Aristoteles xxi annorum audiret 

292^ DE CAELO 

given by the Egyptians and Babylonians, whose observa- 
tions have been kept for very many years past, and from 
whom much of our evidence about particular stars is 

TO A second difficulty which may with equal justice be 
raised is this. Why is it that the primary motion includes 
such a multitude of stars that their whole array seems to 
defy counting, while of the other stars ^ each one is separated 
off, and in no case do we find two or more attached to the 
same motion ? ^ 

On these questions, I say, it is well that we should seek 

15 to increase our understanding, though we have but little to 
go upon, and are placed at so great a distance from the 
facts in question. Nevertheless there are certain principles 
on which if we base our consideration we shall not find this 
difficulty by any means insoluble. We may object that we 
have been thinking of the stars as mere bodies, and as units 

20 with a serial order indeed but entirely inanimate ; but 
should rather conceive them as enjoying life and action. 
On this view the facts cease to appear surprising. For it is 
natural that the best-conditioned of all things should have 
its good without action, that that which is nearest to it 
should achieve it by little and simple action, and that which 
is farther removed by a complexity of actions, just as with 

25 men's bodies one is in good condition without exercise at 
all, anotiier after a short walk, while another requires 
running and wrestling and hard training,* and there are yet 

Eudoxum, ut ex Diogene Laertio constat.' Diogenes' date for 
Aristotle's birth is in fact Ol. 99, i (384-3 B. C.) : Aristotle would 
therefore be 27 at the date arrived at. The calculation for Mercury 
does not appear to have been made. 

* See note on 270^ 14. 

* i. e. the planets. 

^ The term (popd (motion) is transferred from the motion itself to the 
sphere which imparts the motion. 

* There seems to be no parallel for the use of the word Koviais 
(tr. ' hard training ') in connexion with the exercises of the palaestra, 
though Koui(TTpa is used in post-Aristotelian writers for the arena. 
Simpl. says the term stands for the training of the wrestler, bia to iv 
Kovii yvfivdCea-Oai ra naXaiaTpiKa. By water (/. of Phil, xxviii, p. 241) 
objects that the third term in the phrase should be a distinct form of 
exercise from running or wrestling, and suggests Ka/coi/rio-fw?. Perhaps 
it is best to keep the text, though there can be no certainty that it is 

BOOK II. 12 292* 

others who however hard they worked themselves could 
never secure this good, but only some substitute for it. To 
succeed often or in many things is difficult. For instance, 
to throw ten thousand Coan throws with the dice would be 30 
impossible, but to throw one or two is comparatively easy.^ 
In action, again, when A has to be done to get B^ B to 
get (7, and C to get D^ one step or two present little 
difficulty, but as the series extends the difficulty grows- 292 
We must, then, think of the action of the lower stars as 
similar to that of animals and plants. For on our earth 
it is man that has the greatest variety of actions — for there 
are many goods that man can secure ; hence his actions are 
various 2 and directed to ends beyond them — while the 
perfectly conditioned has no need of action, since it is itself 5 
the end, and action always requires two terms, end and 
means. The lower animals have less variety of action than 
man ; and plants perhaps have little action and of one kind 
only.^ For either they have but one attainable good (as 
indeed man has), or, if several, each contributes directly to 10 
their ultimate good.* One thing then has and enjoys the 

^ Prantl's Kojov? rests on one MS. (H) and was known as an alterna- 
tive reading to Simpl. Two MSS. (EL) give Xt'ovs, two others (FM) 
Xi'ous r] Ka)oi;y. J has xCkiov^ jj^coXov?, with yiov^ t] Koiiovs in the margin. 
Simpl. thinks the point is the size of the dice {m /ue-yaXwy da-TpaydXav 
fv dficf)OT€pais yipofxevcov rals vTjcrois). Prantl takes the impossibility to 
be a succession of good throws or 'sixes', and therefore prefers 
' Coan ' to ' Chian', which according to Pollux was used for the worst 
throw. The impossibility is clearly the same whether the worst throw 
or the best is intended ; but, since success is implied by the context, 
I have followed Prantl. The double reading Xiovs rj Kioovs may how- 
ever be right. 

* ^ Reading TrpoTrei, with FHMJ and Bekker, for Prantl's TrpdrTdv 

^ The long parenthesis (1. 3 noWSip ydp to 1. 7 eveKo) in Prantl's text 
breaks the structure of the sentence and should be removed. The 
succession of colons which results (for a colon must be marked after 
7rpd^€is]in 1. 3) is best broken by placing full-stops after cfivTwv (1. 2), 
fVfKa (1. 4), eveKa (1. 7). 

* If there is more than one good, e.g. nutriment and propagation, 
each is a constituent of the plant's ' good ' in the final sense. To be 
able to accept something merely as a means to something else, i. e. as 
indirectly good, is a distinctive mark of a higher development. Thus 
the variety here indicated as characteristic of human action lies not 
so much in the superior range of human desires (though that also is 
a fact) as in the variety and complexity of the means by which man 
effects their satisfaction. 

292^ DE CAELO 

ultimate good, other things attain to it, one immediately ^ 
by few steps, another by many, while yet another does not 
even attempt to secure it but is satisfied to reach a point 
not far removed from that consummation. Thus, taking 
health as the end, there will be one thing that always 
possesses health, others that attain it, one by reducing 
flesh, another by running and thus reducing flesh, another 

15 by taking steps to enable himself to run, thus further 
increasing the number of movements, while another cannot 
attain health itself, but only running or reduction of flesh, 
so that one or other of these is for such a being the end.^ 
For while it is clearly best for any being to attain the real 
end, yet, if that cannot be, the nearer it is to the best the 

20 better will be its state. It is for this reason that the earth 
moves not at all and the bodies near to it with few move- 
ments. For they do not attain the final end, but only come 
as near to it as their share in the divine principle permits." 
But the first heaven finds it immediately with a single 

25 movement, and the bodies intermediate between the first 
and last heavens attain it indeed, but at the cost of a multi- 
plicity of movement.* 

As to the difficulty that into the one primary motion 
is crowded a vast multitude of stars, while of the other 
stars each has been separately given special movements 
of its own, there is in the first place this reason for regarding 
the arrangement as a natural one. In thinking of the life 

^ Reading dOvs for iyyvs. Cf. 1. 20 below, iyyvs is in all the 
MSS., but is quite intolerable in view of the general contrast between 
attainment and approximation made here and repeated below. The 
influence of iyyvs in the following line may be supposed to have 
caused its substitution for €v6vi here. Simpl. paraphrases to be bC 
cikiyoiv KivTj(Tf(ou dcpiKuelrai npos to iavTov TeXos, and therefore appears 
not to have had eyyvs in his text. Them., however, has it : * ad illud 
prope per pauca accedit.' 

^ Place a full-stop after iXBe'iv (1. 13), delete bracket, comma after 
laxvavdrjvai (1. 1 7). ' Running ' or ' reduction of flesh ' becomes in such 
a case the ' end ', i. e. the content of purpose, as soon as the true end 
or good is recognized as unattainable. 

^ Simpl. finds this sentence difficult. He did not see that Aristotle 
here, as frequently elsewhere, uses aXXd where «XX* ^ would be 
expected. See Bonitz, In^. Ar. 33^ 15. 

^ The upshot of the argument seems to be this, that the earth and 
the bodies nearest to it move simply, or not at all, because they are 
content with little, and perfection is beyond their reach. 

BOOK II. 12 292^ 

and moving principle of the several heavens one must 
regard the first as far superior to the others. Such z^ 
a superiority would be reasonable. For this single first 
motion has to move many of the divine bodies, while the 
numerous other motions move only one each, since each 293^ 
single planet moves with a variety of motions. Thus, then, 
nature makes matters equal and establishes a certain order, 
giving to the single motion many bodies and to the single 
body many motions. And there is a second reason why 
the other motions have each only one body, in that each of 5 
them except the last, i. e. that which contains the one star,^ 
is really moving many bodies. For this last sphere moves 
with many others, to which it is fixed, each sphere being 
actually a body ; so that its movement will be a joint 
product. Each sphere, in fact, has its particular natural 
motion, to which the general movement is, as it were, 10 
added. But the force of any limited body is only adequate 
to moving a limited body.^ 

The characteristics of the stars which move with a circular 
motion, in respect of substance and shape, movement and 
order, have now been sufficiently explained. 

■13 It remains to s peak of the earth, of its position, of the it; 
question whether it is at rest nr fp motio n, and of ifq shapf;, 
I. As to its position there is some difference of opinion. 
Most people — all, in fact, who regard the whole heaven as 
finite — say it lies at the centre. But the Italian philoso- 20 
phers known as Pythagoreans take the contrary view. At 
the centre, they say, is fire, and the earth is one of the stars, 
creating night and day by its circular motion about the 

* The movements of each planet are analysed into the combination 
of a number of simple spherical motions each contributed by a single 
sphere. The * last ' sphere or motion means the outermost, viz. that 
to which the planet is actually attached. The inner spheres have 
really bodies to move even though they carry no planet : for they 
have to communicate their motion to the sphere or spheres in which 
they are included. 

"^ Prantl seems to find unnecessary difficulty in this sentence. 
These spheres, says Aristotle, have only a limited force, and they 
have enough to do to impart their motion to the outer spheres, and 
through it to the planet : the burden of several planets would be too 
much for them. 


293^ DE CAELO 

centre. They further construct another earth in opposition 

25 to ours to which they give the name counter-earth.^ In all 
this they are not seeking for theories and causes to account 
for observed facts, but rather forcing their observations and 
trying to accommodate them to certain theories and 
opinions of their own. But there are many others who 
would agree that it is wrong to give the earth the central 

30 position, looking for confirmation rather to theory than to 
the facts of observation. Their view is that the most 
precious place befits the most precious thing : but fire, they 
say, is more precious than earth, and the limit than the 
intermediate, and the circumference and the centre are 
limits. Reasoning on this basis they take the view that it 
is not earth that lies at the centre of the sphere, but rather 
293 fire. The Pythagoreans have a further reason. They hold 
that the most important part of the world, which is the 
centre, should be most strictly guarded, and name it, or 
rather the fire which occupies that place, the ' Guard-house 
of Zeus', as if the word 'centre' were quite unequivocal, 
5 and the centre of the mathematical figure were always the 
same with that of the thing or the natural centre. But it is 
better to conceive of the case of the whole heaven as 
analogous to that of animals, in which the centre of the 
animal and that of the body are different. For this reason 
they have no need to be so disturbed about the world, or to 

10 call in a guard for its centre : rather let them look for the 
centre in the other sense and tell us what it is like and 
where nature has set it. That centre will be something 
primary and precious ; but to the mere position we should 
give the last place rather than the first. For the middle is 
what IS defined, and what defines it is the limit, and that 
which contains or limits is more precious than that which 

15 is limited, seeing that the latter is the matter and the 
former the essence of the system. 

II. As to the position of the earth, then, this is the view 

which some advance, and the views advanced concerning 

its rest or motioj jjdiX^ similar. For here too there is no 

general agreement. All who deny that the earth lies at 

1 oj/o/xa is omitted by FHMJ, but is probably right. 

BOOK II. 13 293 

the centre think that it revolves about the centre,^ and not 
the earth only but, as we said before, the counter-earth as 20 
well. Some of them even consider it possible that there 
are several bodies so moving, which are invisible to us 
owing to the interposition of the earth. This, they say, 
accounts for the fact that eclipses of the moon are more 
frequent than eclipses of the sun : for in addition to the 
earth each of these moving bodies can obstruct it. Indeed, 25 
as in any case the surface of the earth is not actually 
a centre but distant from it a full hemisphere, there is no 
more difficulty, they think, in accounting for the observed 
facts on their view that we do not dwell at the centre, than 
on the common view that the earth is in the middle.^ Even 
as it is, there is nothing in the observations to suggest that 
we are removed from the centre by half the diameter of the 30 
earth. Others, again, say that the earth, which lies at the 
centre, is 'rolled', and thus in motion, about the axis of 
the whole heaven. So it stands written in the Timaeus? 

III. There are similar disputes about the shape of the — - 
earth. Some think it is spherical, others that it is flat and 
drum-shaped. For evidence they bring the fact that, as the 294 

* \ir]h' in 1. 18 appears to prove that the comma should be put 
after Keiadai instead of after ovttjv, and that (jiaaiv governs both 

^ Prantl's insertion of tirj in the last clause rests on a misunder- 
standing of the passage. The text is quite sound. — Dreyer {Planetary 
Systems^ p. 45) thinks that the supposed movement would seriously 
affect observations of the sun and the moon. 

^ Timaeus, 40 B. For a discussion of this vexed passage see 
Heath, Aristarchus, pp. 174-8. J has fXkfiaQai kcli Kive7o-6ai (in 
296* 26, however, where the same pair of words recur, it has elWeadai 
K. K.), which decreases the probability, not antecedently very great, 
that the words koX KivelaOai are an insertion. Unless the idea of 
movement is contained in the phrase, the quotation would seem to 
be out of place here. It seems plain that Aristotle considered the 
word iWecrdai ('rolled' in the text) obscure or ambiguous, and added 
the words Koi Kiveia-Oai to indicate his interpretation of it. Alex. 
{apud Simpl.) says that the word used in the Timaeus means 
'pressed' (3ta^6(r^ai), but that it is difficult to contradict Aristotle 
on a point on which he was so much better informed. Simpl. says 
that, spelt with the diphthong ei and a single X, the word does 
connote rotation. He points out that Aristotle promised to speak of 
the earth's motion and rest \ and suggests that, taking koi Kiv^'iadai to 
be a later insertion, one might suppose that Aristotle passes in this 
sentence to the consideration of the view that the earth is at rest. 
But this will hardly do. 

294^ DE CAELO 

sun rises and sets, the part concealed by the earth shows 
a straight and not a curved edge, whereas if the earth were 
spherical the line of section would have to be circular. In 
5 this they leave out of account the great distance of the sun 
from the earth and the great size of the circumference, 
which, seen from a distance on these apparently small 
circles appears straight. Such an appearance ought not to 
make them doubt the circular shape of the earth. But they 
have another argument. They say that because it is at 

lo rest, the earth must necessarily have this shape. For there 
are many different ways in which the movement or rest of 
the earth has been conceived. 

The difficulty must have occurred to every one. It would 
indeed be a complacent mind that fdt no surprise that, 
while a little bit of earth, let loose in mid-air, moves and 

15 will not stay still, and the more there is of it the faster it 
moves, the whole earth, free in mid-air, should show no 
movement at all. Yet here is this great weight of earth, 
and it is at rest. And again, from beneath one of these 
moving fragments of earth, before it falls, take away the 
earth, and it will continue its downward movement with 
. nothing to stop it. The difficulty then, has naturally passed 

20 into a commonplace of philosophy ; and one may well 
wonder that the solutions offered are not seen to involve 
greater absurdities than the problem itself. 

By these considerations some have been led to assert 
that the earth below us is infinite, saying, with Xenophanes 
of Colophon, that it has ' pushed its roots to infinity '} — in 
order to save the trouble of seeking for the cause. Hence 

25 the sharp rebuke of Empedocles, in the words ' if the deeps 

\ of the earth are endless and endless the ample ether — such 

is the vain tale told by many a tongue, poured from the 

mouths of those who have seen but little of the whole '.^ 

^ Diels, Vorsokratiker'^ , 11 A 47 (53, 38 ff.), B 28 (63, 8). Ritter and 
Preller, 103 b. Simpl. cannot find the quotation in the writings of 
Xenophanes, and doubts whether to KaTfn r^f yr\% means ' the under- 
parts of the earth' or 'the ether under the earth'. A fragment 
corroborating the former interpretation survives (no. 28 in Diels). 
Cf. Burnet, E.G.P.^ § 60. 

- Diels, Vors? 21 B 39 (241, 16). Ritter and Preller, 103 b. Burnet, 
E.G.P.3 p. 212. 

BOOK II. 13 294^ 

Others say the earth rests upon water. This, indeed, is the 
oldest theory that has been preserved, and is attributed to 
Thales of Miletus. It was supposed to stay still because it 30 
floated like wood and other similar substances, which are 
so constituted as to rest upon water but not upon air. As 
if the same account had not to be given of the water which 
carries the earth as of the earth itself! It is not the nature 
of water, any more than of earth, to stay in mid-air : it 
must have something to rest upon. Again, as air is lighter 294^^ 
than water, so is water than earth : how then can they think 
that the naturally lighter substance lies below the heavier ? 
Again, if the earth as a whole is capable of floating upon 
water, that must obviously be the case with any part of it. 
But observation shows that this is not the case. Any piece 5 
of earth goes to the bottom, the quicker the larger it is. 
These thinkers seem to push their inquiries some way into 
the problem, but not so far as they might. It is what we 
are all inclined to do, to direct our inquiry not by the 
matter itself, but by the views of our opponents : and even 
when interrogating oneself one pushes the inquiry only 10 
to the point at which one can no longer offer any opposi- 
tion. Hence a good inquirer will be one who is ready in 
bringing forward the objections proper to the genus, and 
that he will be when he has gained an understanding of all 
the differences.^ , 

Anaximenes and Anaxagoras and Democritus give the 
flatness of the earth as the cause of its staying still. Thus, 15 
they say, it does not cut, but covers like a lid, the air 
beneath it. This seems to be the way of flat-shaped 
bodies : for even the wind can scarcely move them because 
of their power of resistance. The same immobility, they 
say, is produced by the flatness of the surface which the 
earth presents to the air which underlies it ; while the air, 

^ The objections must be ' proper to the kind ' or class to which the 
subject of investigation belongs, i.e. scientific, not dialectical or 
sophistical. These thinkers, as Simpl. observes, have failed to investi- 
gate the peculiar characteristics of wood and earth in the genus 
'body', and therefore think that, because wood floats, earth may. 
For the importance of a study of the ' differences ' Simpl. refers to 
Top. I. xviii. 

645.20 G 

294^ DE CAELO 

20 not having room enough to change its place because it is 
underneath the earth, stays there in a mass, like the water 
in the case of the water-clock.^ And they adduce an 
amount of evidence to prove that air, when cut off and at 
rest, can bear a considerable weight. 

Now, first, if the shape of the earth is not flat, its flat- 
n^s cannot be the cause of its immobility. But in their 

25 own account it is rather the size of the earth than its flat- 
ness that causes it to remain at rest. For the reason why 
the air is so closely confined that it cannot find a passage, 
and therefore stays where it is, is its great amount : and 
this amount is great because the body which isolates it, the 
earth, is very large. This result, then, will follow, even if 

30 the earth is spherical, so long as it retains its size. So far 
as their arguments go, the earth will still be at rest. 

In general, our quarrel with those who speak of move- 
ment in this way cannot be confined to the parts ^; it con- 
cerns the whole universe. One must decide at the outset 
whether bodies have a natural movement or not, whether 
there is no natural but only constrained movement. Seeing, 
295^ however, that we have already decided this matter to the 
best of our ability, we are entitled to treat our results as 
representing fact. Bodies, we say, which have no natural 
movement, have no constrained movement ; and where 
. there is no natural and no constrained movement there will 
5 be no movement at all. This is a conclusion, the necessity 
of which we have already decided,^ and we have seen 
further that rest also will be inconceivable, since rest, like 

* Reading wo-Trcp with the MSS. Diels {Vors.^ 25, 32) inserts roO 
before fXfTacrTrjvai (1. 19), a conjecture which has some support in L, 
which has nov in that place. — Experiments with the water-clock are 
frequently mentioned. See esp. Emped. fr. 100 (Diels), Arist. Probl. 
914^26, Burnet, E.G.P.^ Index I s.v. Klepsydra. *The water-clock', 
says Simpl., 'is a vessel with a narrow mouth and a flattish base 
pierced with small holes, what we now call a hyd7'arpax. If this 
vessel is dipped in water while the mouth at the top is kept closed, 
no water runs in through the holes. The massed air inside resists 
the water and prevents its ingress, being unable to change its own 
place. When the mouth at the top is opened the water runs in, the 
air making way for it.' The position of the water beneath the water- 
clock is analogous to that of the air beneath the earth. 

"^ i. e. to the single element earth or to earth and air. 

^ I. ii-iv. 

BOOK II. 13 295' 

movement, is either natural or constrained. But if there is 
any natural movement, constraint will not be the sole prin- 
ciple of motion or of rest. If, then, it is by constraint that 
the earth now keeps its place, the so-called ' whirling ' 
movement by which its parts came together at the centre 10 
was also constrained. (The form of causation supposed 
they all borrow from observations of liquids and of air, 
in which the larger and heavier bodies always move 
to the centre of the whirl. This is thought by all those 
who try to generate the heavens to explain why the earth 
came together at the centre. They then seek a reason for its 15 
staying there ; and some say, in the manner explained, that 
the reason is its size and flatness, others, with Empedocles, 
that the motion of the heavens, moving about it at a higher 
speed, prevents movement of the earth, as the water in 
a cup, when the cup is given a circular motion, though it is 20 
often underneath the bronze, is for this same reason pre- 
vented from moving with the downward movement which 
is natural to it.^) But suppose both the ' whirl ' and its 
flatness (the air beneath being withdrawn ^) cease to pre- 
vent the earth's motion, where will the earth move to then ? 
Its movement to the centre was constrained, and its rest at 
the centre is due to constraint ; but there must be some 
motion which is natural to it. Will this be upward motion 35 
or downward or what ? It must have some motion ; and if 
upward and downward motion are alike to it, and the air 
above the earth does not prevent upward movement, then 
no more could air below it prevent downward movement. 
For the same cause must necessarily have the same effect 
on the same thing.^ 

Further, against Empedocles there is another point which 30 
might be made. When the elements were separated off by 

^ Simplicius seems to be right in considering the portion included 
within brackets in the text as a parenthetic note on divrja-is, interrupt- 
ing Aristotle's argument. 

■^ The sense required is ' withdrawn ', as above, but there} is no 
parallel to the use of vireXdelv in this sense. The MSS. offer no 
variant, and Simpl. paraphrases eKaravros. In the absence of a better 
suggestion I should read vne^eKOovros . 

^ The suggestion clearly is that, consciously or unconsciously, these 
thinkers attributed a natural motion downward to the earth, since 
they gave it a reason for not moving in that direction only. 

G a 

295* DE CAELO 

Hate, what caused the earth to keep its place ? Surely the 
* whirl ' cannot have been then also the cause. It is absurd 
too not to perceive that, while the whirling movement may- 
have been responsible for the original coming together of 
the parts of earth at the centre, the question remains, why 
35 7tow do all heavy bodies move to the earth. For the whirl 
295^ surely does not come near us. Why, again, does fire move 
upward ? Not, surely, because of the whirl. But if fire is 
naturally such as to move in a certain direction, clearly the 
same may be supposed to hold of earth. Again, it cannot 
be the whirl which determines the heavy and the light.^ 
5 Rather that movement caused the pre-existent heavy and 
light things to go to the middle and stay on the surface 
respectively. Thus, before ever the whirl began, heavy and 
light existed ; and what can have been the ground of their 
distinction, or the manner and direction of their natural 
movements? In the infinite chaos there can have been 
neither above nor below, and it is by these that heavy and 
light are determined. 
^o It is to these causes that most writers pay attention : but 
there are some, Anaximander, for instance, among the 
ancients, who say that the earth keeps its place because of 
its indifference.^ Motion upward and downward and side- 
ways were all, they thought, equally inappropriate to that 
which is set at the centre and indifferently related to every 
15 extreme point ; and to move in contrary directions^ at the 
same time was impossible : so it must needs remain still. 
This view is ingenious but not true. The argument would 
prove that everything, whatever it be, which is put at the 

^ Read Ka\ to koxx^ov with all MSS. except E. 

^ Literally 'likeness'. Kranz, Index to Diels, Vors., s. v. o/xoiotj??, 
translates * gleichmassige Lage '. Burnet (who formerly took a dif- 
ferent view) now accepts ' indifference ' as the equivalent of o/ioioT/;? 
in this passage. (E.G.P.^ p. 66, n. i.) Cf. Burnet's note on Plato, 
Phaedo, 109 A 2, where he proposes the translation * equiformity ', 
and the phrase Trpoy ofiolas yavias below (296*' 20). From Aris- 
totle's wording it seems probable that he had the Phaedo in mind 
here. The full phrase there is : rr]v ofioiorrjTa roC ovpavov avrov 
eavrS navrr) /cat r/)? yr^s avrrjs rqv laropponiav. It is to be observed that 
Plato makes ofioioTrjs an attribute of the whole heaven or universe, not 
of the'earth. 

^ Prantl's ivavrlov is a misprint for ivavrlov. 

BOOK II. 13 295^ 

centre, must stay there. Fire, then, will rest at the centre : 
for the proof turns on no peculiar property of earth. But 
this does not follow. The observed facts about earth are 20 
not only that it remains at the centre, but also that it moves 
to the centre. The place to which any fragment of earth 
moves must necessarily be the place to which the whole 
moves ; and in the place to which a thing naturally moves, 
it will naturally rest. The reason then is^-not in the fact 
that the earth is indifferently related to every extreme 
point : for this would apply to any body, whereas move- 25 
ment to the centre is peculiar to earth. Again it is absurd 
to look for a reason why the earth remains at the centre 
and not for a reason why fire remains at the extremity. If 
the extremity is the natural place of fire, clearly earth must 
also have a natural place. But suppose that the centre is 
not its place, and that the reason of its remaining there is this 30 
necessity of indifference — on the analogy of the hair which, 
it is said, however great the tension, will not break under 
it, if it be evenly distributed, or of the man who, though 
exceedingly hungry and thirsty, and both equally,^ yet 
being equidistant from food and drink, is therefore bound 
to stay where he is — even so, it still remains to explain why 35 
fire stays at the extremities. It is strange, too, to ask 296^ 
about things staying still but not about their motion, — why, 
I mean, one thing, if nothing stops it, moves up, and another 
thing to the centre. Again, their statements are not true. 
It happens, indeed, to be the case that a thing to which 5 
movement this way and that is equally inappropriate is 
obliged to remain at the centre.^ But so far as their argu- 
ment goes, instead of remaining there, it will move, only not 
as a mass but in fragments. For the argument applies 
equally to fire. Fire, if set at the centre, should stay there, 
like earth, since it will be indifferently related to every point 10 
on the extremity. Nevertheless it will move, as in fact it 
always does move when nothing stops it, away from the 
centre to the extremity. It will not, however, move in a 

* The structure of the sentence would be made clearer if commas 
were placed after fxev and after de in 1. 33. 

^ The principle is in fact true, if it is properly understood, i. e. seen 
to apply, as explained in what follows, only to indivisible bodies. 

296^ DE CAELO 

mass to a single point on the circumference — the only pos- 
sible result on the lines of the indifference theory — but 

15 rather each corresponding portion of fire to the correspond- 
ing part of the extremity, each fourth part, for instance, to 
a fourth part of the circumference. For since no body is 
a point, it will have parts. The expansion, when the body 
increased the place occupied, would be on the same prin- 
ciple as the contraction, in which the place was diminished. 
Thus, for all the indifference theory shows to the contrary, 

20 earth also would have moved in this manner away from the 
centre, unless the centre had been its natural place. 

We have now outlined the views held as to the shape, 
position, and rest or movement of the earth. 

Let us first decide the question w hether the earth moves 14 

2 5 or is at rest. For, as we said, there are some who make it 

one of the stars, and others who, setting it at the centre, 

suppose it to be ' rolled ' and in motion about the pole as 

axis.^ That both views are untenable will be clear if we 

take as our starting-point the fact that the earth's motion, 

whether the earth be at the centre or away from it, must 

30 needs be a constrained motion. It cannot be the movement 

of the earth itself. If it were, any portion of it would have 

this movement ; but in fact every part moves in a straight 

line to the centre. Being, then, constrained and unnatural, 

the movement could not be eternal. But the order of the 

universe is eternal. Again, everything that moves with the 

35 circular movement, except the first sphere, is observed to 

296^ be passed, and to move with more than one motion. The 

earth, then, also, whether it move about the centre or as 

stationary at it, must necessarily move with two motions. 

But if this were so, there would have to be passings and 

5 turnings of the fixed stars. Yet no such thing is observed. 

The same stars always rise and set in the same parts of the 


^ For tWea-Bai J has eiWeaOai. See note on 293^31. 

^ This passage is examined in Heath, Arisiarchus , pp. 240-1. The 
necessity for two motions appears to rest only on the analogy of the 
planets, which are ' passed ' or left behind by the motion of the sphere 
of the fixed stars. The consequence, that there would be variety in 

BOOK II. 14 296^ 

Further, the natural movement of the earth, part and 
whole alike, is to the centre of the whole — whence the fact 
that it is now actually situated at the centre — but it might 
be questioned, since both centres are the same, which centre 10 
it is that portions of earth and other heavy things move to. 
Is this their goal because it is the centre of the earth or 
because it is the centre of the whole ? The goal, surely, 
must be the centre of the whole. For fire and other light 
things move to the extremity of the area which contains 
the centre. It happens, however, that the centre of the 15 
earth and of the whole is the same. Thus they do move 
to the centre of the earth, but accidentally, in virtue of the 
fact that the earth's centre lies at the centre of the whole. 
That the centre of the earth is the goal of their movement 
is indicated by the fact that heavy bodies moving towards 
the earth do not move parallel but so as to make equal 20 
angles,^ and thus to a single centre, that of the earth. It is 
clear, then, that the earth must be at the centre and im- 
movable, not only for the reasons already given, but also 
because heavy bodies forcibly thrown quite straight upward 
return to the point from which they started, even if they 
are thrown to an infinite distance.^ From these considera- 25 
tions then it is clear that the earth does not move and does — 
not lie elsewhere than at the centre. 

From what we have said the explanation of the earth's 
immobility is also apparent. If it is the nature of earth, as 
observation shows, to move from any point to the centre, as 

the places of rising and setting of the fixed stars, follows from the 
assumption of a second motion, if the second is taken to be obhque to 
the first (Heath, loc. cit.). 

* i. e. at right angles to a tangent : if it fell otherwise than at right 
angles, the angles on each side of the line of fall would be unequal. 
Cf. injf. 311^34, where the argument is repeated. The phrase npbs 
ofioias ycovins, ' at Izke angles ', appears to strike Simpl. as a rather 
strange equivalent for npos 'icras yavias, ' at e^tm/ angles ', borrowed, as 
he says, from those who referred ' angle ' to the category of quality — 
ofioias de eKciXovp ras taas yoivlas ot Tr]V yatviav ino to ttolov dvayovres 
(538, 22). Cf. Burnet's remarks on ofioiorrjs in Phaedo^ 109 A 2, quoted 
in part above in note on 295^ 1 1. 

^ It seems plain that the words koio. a-Tadfirjv ('quite straight') refer 
to the line of the throw, not, as Simpl. supposes, to the line of return. 
But it is difficult to see what independent test Aristotle had of the 
straightness of the throw. 

296^^ DE C AELO 

of fire contrariwise to move from the centre to the extremity, 

30 it is impossible that any portion of earth should move away 
from the centre except by constraint. For a single thing 
has a single movement, and a simple thing a simple : con- 
traiy movements cannot belong to the same thing, and 
movement away from the centre is the contrary of movement 
to it. If then no portion of earth can move away from the 
centre, obviously still less can the earth as a whole so move. 

35 For it is the nature of the whole to move to the point to 

297^ which the part naturally moves. Since, then, it would 

require a force greater than itself to move it, it must needs 

stay at the centre. This view is further supported by the 

contributions of mathematicians to astronomy, since the 

5 observations made as the shapes change by which the order 
of the stars is determined,^ are fully accounted for on the 
hypothesis that the earth lies at the centre. Of the position 
of the earth and of the manner of its rest or movement, our 
discussion may here end. 

I ts shape must necessarily be spherical. For every por- 

10 tion of earth has weight until it reaches the centre, and the 
jostling of parts greater and smaller would bring about not 
a waved surface, but rather compression and convergence ^ 
of part and part until the centre is reached. The process 
should be conceived by supposing the earth to come into 
being in the way that some of the natural philosophers 

15 describe.^ Only they attribute the downward movement 
to constraint, and it is better to keep to the truth and say 
that the reason of this motion is that a thing which possesses 

^ The sense of the sentence is, clearly, 'the phenomena are accounted 
for on the present hypothesis: why change it?' But the precise 
relevance of (apparent) changes of shape does not seem clear. Simpl. 
illustrates by changes which would be necessitated by the hypothesis 
of a moving earth ; but his own paraphrase of Aristotle's words 
implies that the changes in question are observed changes. The 
Greek implies (i) that the order of the stars is settled by the apparent 
shapes or patterns which they make in combination ; (2) that the 
changes of these shapes are accounted for on the hypothesis of a 
stationary earth. 

* crvyxtopeti/ is clearly used here of * convergence *, not, as Prantl 
translates, of 'making way'. So Simpl. paraphrases, o-u/iiTrXaTTerai 
T] avyxapel erepov irepco, 

' The cosmogony which follows is in principle that of Anaxagoras 
(Burnet, E.G.P.^ § 133). 

BOOK II. 14 297^ 

weight is naturally endowed with a centripetal movement. 
When the mixture, then, was merely potential, the things 
that were separated off moved similarly from every side 
towards the centre. Whether the parts which came together 
at the centre were distributed at the extremities evenly, or 20 
in some other way, makes no difference. If, on the one 
hand, there were a similar movement from each quarter of 
the extremity to the single centre, it is obvious that the 
resulting mass would be similar on every side. For if an 
equal amount is added on every side the extremity of the 
mass will be everywhere equidistant from its centre, i.e. the 25 
figure will be spherical. But neither will it in any way 
affect the argument if there is not a similar accession of 
concurrent fragments from every side. For the greater 
quantity, finding a lesser in front of it, must necessarily 
drive it on, both having an impulse whose goal is the centre, 
and the greater weight driving the lesser forward till this 30 
goal is reached. In this we have also the solution of a pos- 
sible difficulty. The eart h, it might be argued, is at the 
centre and spherical in shape j^ if, then, a weight many times 
that of the earth were added to one hemisphere, the centre 
of the earth and of the whole will no longer be coincident. 
So that either the earth will not stay still at the centre, or 
if it does, it will be at rest without having its centre at the 297^ 
place to which it is still its nature to move.^ Such is the 
difficulty. A short consideration will give us an easy 
answer, if we first give precision to our postulate that any 
body endowed with weight, of whatever size, moves towards 
the centre. Clearly it will not stop when its edge touches 5 
the centre. The greater quantity must prevail until the 
body's centre occupies the centre. For that is the goal of 
its impulse. Now it makes no difference whether we apply 

* The words ' at the centre ' in the first clause seem intrusive at first 
sight ; and logically they are indefensible. ' Either the earth will not 
stay still at the centre, or, if it does stay still at the centre, it will not 
have its (new) centre at the centre which is its natural goal ! ' The 
words eVt Tov nea-ov, then, may be an insertion. They are, however, 
more probably due to the desire for a direct contradictory. The view 
is fievei (ttI tou fxcaov : the contradictory is therefore ov fxevet eVi tov 
fiecrov : and the (tnep recalls only the fxevei. ' Either it does not staj/ 
still at the centre or it doesn't stay still at the centre! 

297^ DE CAELO 

this to a clod or common fragment of earth or to the earth 
as a whole. The fact indicated does not depend upon 

lo degrees of size but applies universally to everything that 
has the centripetal impulse. Therefore earth in motion, 
whether in a mass or in fragments, necessarily continues to 
move until it occupies the centre equally every way, the 
less being forced to equalize itself by the greater owing to 
the forward drive of the impulse.^ 

If the earth was generated, then, it must have been 

15 formed in this way, and so clearly its generation was 
spherical ; and if it is ungenerated and has remained so 
always, its character must be that which the initial genera- 
tion, if it had occurred, would have given it. But the 
spherical shape, necessitated by this argument, follows also 
from, the fact that the motions of heavy bodies always 

20 make equal angles,^ and are not parallel. This would be 
the natural form of movement towards what is naturally 
spherical. Either then the earth is spherical or it is at 
least naturally spherical.^ And it is right to call anything 
that which nature intends it to be, and which belongs to it, 
rather than that which it is by constraint and contrary to 
nature. The evidence of the senses further corroborates 
this. How else would eclipses of the moon show segments 

25 shaped as we see them ? As it is, the shapes which the 
moon itself each month shows are of every kind— straight, 
gibbous, and concave — but in eclipses the outline is always 
curved : and, since it is the interposition of the earth that 

^ The argument is quite clear if it is understood that 'greater' and 
' less ' here and in * 30 and in ^ 5 stand for greater and smaller portions 
of one body, the line of division passing through the centre which is 
the goal. Suppose the earth so placed in regard to the centre. The 
larger and heavier division would 'drive the lesser forward*, i.e. 
beyond the centre (* 30) ; it would ' prevail until the body's centre 
occupied the centre' (^5); it would 'force the less to equalize itself, 
i. e. to move on until the line passing through the central goal divided 
the body equally. Simpl. fails to see this. — Alex. {ap. Simpl. 543, 15) 
raises the difficulty that the final movement of the ' less ' will be away 
from the centre, or upward, and hence unnatural. But this is to make 
a perverse abstraction of part from whole. The desire of earth to 
reach the centre can never be fully satisfied, since the centre is 
a geometrical point. 

^ See note on 296^ 20. 

^ Allowing for scruples due to the evident inequalities of the earth's 

BOOK II. 14 297* 

makes the eclipse, the form of this line will be caused by 30 
the form of the earth's surface, which is therefore spherical. 
Again, our observations of the stars make it evident, not 
only that the earth is circular, but also that it is a circle of 
no great size. For quite a small change of position to 
south or north causes a manifest alteration of the horizon. 
There is much change, I mean, in the stars which are over- 298^ 
head, and the stars seen are different, as one moves north- 
ward or southward. Indeed there are some stars seen in 
Egypt and in the neighbourhood of Cyprus which are not 
seen in the northerly regions ; and stars, which in the north 5 
are never beyond the range of observation, in those regions 
rise and set. All of which goes to show not only that the 
earth is circular in shape, but also that it is a sphere of no 
great size : for otherwise the effect of so slight a change of 
place would not be so quickly apparent. Hence one should 
not be too sure of the incredibility of the view of those who 10 
conceive that there is continuity between the parts about 
the pillars of Hercules and the parts about India, and that 
in this way the ocean is one. As further evidence in favour 
of this they quote the case of elephants, a species occurring 
in each of these extreme regions, suggesting that the 
common characteristic of these extremes is explained by 15 
their continuity. Also, those mathematicians who try to 
calculate the size of the earth's circumference arrive at the 
figure 400,000 stades.^ This indicates not only that the 
earth's mass is spherical in shape, but also that as compared 
with the stars it is not of great size. 20 

^ Simpl. gives, for the benefit of ' those who doubt the wisdom of 
the ancients ', a summary account of the methods by which this result 
was attained. — This appears to be the oldest recorded estimate of the 
size of the earth. 400,000 stades = 9,987 geographical miles. Other 
estimates (in miles) are: Archimedes, 7,495; Eratosthenes and Hip- 
parchus, 6,292 ; Poseidonius, 5,992 or 4,494 ; present day, 5,400. 
(These figures are borrowed from Prantl's note on the passage in his 
translation, p. 319.) 


298^ We have already discussed the first heaven and its parts, i 

25 the moving stars within it, the matter of which these are 
composed and their bodily constitution, and we have also 
shown that they are ungenerated and indestructible. Now 
things that we call natural are either substances or functions 
and attributes of substances. As substances I class the 

30 simple bodies — fire, earth, and the other terms of the 
series — and all things composed of them ; for example, 
the heaven as a whole and its parts, animals, again, and 
plants and their parts. By attributes and functions I mean 
the movements of these and of all other things in which 
they have power in themselves to cause movement, and 
298 also their alterations and reciprocal transformations. It is 

' obvious, then, that the greater part of the inquiry into 
nature concerns bodies : for a natural substance is either 
a body or a thing which cannot come into existence without 
5 body and magnitude. This appears plainly from an analysis 
of the character of natural things, and equally from an 
inspection of the instances of inquiry into nature. Since, 
then, we have spoken of the primary element, of its bodily 
constitution, and of its freedom from destruction and 
generation, it remains to speak of the other two.^ In 
speaking of them we shall be obliged also to inquire into 

10 generation and destruction. For if there is generation 
anywhere, it must be in these elements and things com- 
posed of them. 

This is indeed the first question we have to ask: is 

generation a fact or not? Earlier speculation was at 

variance both with itself and with the views here put fbr- 

Vj5 ward as to the true answer to this question. Some removed 

generation and destruction from the world altogether. 

^ Aristotle speaks of the four sublunary elements as-tvvo, because 
generically they are two. Two are heavy, two light : two move up 
and two down. Books III and IV of this treatise deal solely with 
these elements. 

BOOK III. I 298^ 

Nothing that is, they said, is generated or destroyed, and 
our conviction to the contrary is an illusion. So maintained / ^ 
the school of Melissus and Parmenides. But however 
excellent their theories may otherwise be, anyhow they 
cannot be held to speak as students of nature. There may 
be things not subject to generation or any kind of move- 
ment, but if so they belong to another and a higher inquiry 30 
than the study of nature. They, however, had no idea of 
any form of being other than the substance of things per- • 
ceived ; and when they saw, what no one previously had 
seen, that there could be no knowledge or wisdom without 
some such unchanging entities, they naturally transferred j 
what was true of them to things perceived. Others, perhaps f 
intentionally, maintain precisely the contrary opinion to 35 
this. It had been asserted that everything in the world 
was subject to generation and nothing was ungenerated, 
but that after being generated some things remained in- 
destructible while the rest were again destroyed. This had 
been asserted in the first instance by Hesiod and his ' 
followers, but afterwards outside his circle by the earliest 
natural philosophers.^ But what these thinkers maintained 
was that all else has been generated and, as they said, ' is 30 
flowing away ', nothing having any solidity, except one 
single thing which persists as the basis of all these trans- 
formations. So we may interpret the statements of 
Heraclitus of Ephesus and many others.^ And some ^ sub- 
ject all bodies whatever to generation, by means of the 
composition and separation of planes. 299^ 

Discussion of the other views may be postponed.* But 
this last theory which composes every body of planes is, as 

* The reference, according to Simplicius, is to Orphic writings (* the 
school of Orpheus and Musae.us '). 

^ e. g. Thales, Anaximander, Anaximenes. 

'^ ' The view of Timaeus the Pythagorean, recorded by Plato in the 
dialogue named after him' (Simpl.). The theory criticized is certainly 
that advanced in the Thnaeiis^ and is usually attributed to Plato, as 
by Zeller, Ph. d. Gr} II. i, p. 804, but Aristotle probably has also in 
mind certain members of the Academy, particularly Xenocrates 
{lb., pp. 1016 ff.). 

^ Tlie promised discussion is not to be found in the De Caelo nor in 
its sequel, the De Generaiione et Corruptione. But Aristotle has . 
already devoted some attention to these views at the beginning of the 
Physics^ and there is also the discussion of Met, A. 

299^ DE CAELO 

the most superficial observation shows, in many respects in 
plain contradiction with mathematics. It is, however, wrong 

5 to remove the foundations of a science unless you can replace 
them with others more convincing. And, secondly, the same 
theory which composes solids of planes clearly composes 
planes of lines and lines of points, so that a part of a line 
need not be a line. This matter has been already considered 

10 in our discussion of movement, where we have shown that 
an indivisible' length is impossible.^ But with respect to 
natural bodies there are impossibilities involved in the 
view which asserts indivisible lines, which we may briefly 
consider at this point. For the impossible consequences 
which result from this view in the mathematical sphere will 
reproduce themselves when it is applied to physical bodies, 

1 5 but there will be difficulties in physics which are not present 
in mathematics ; for mathematics deals with an abstract 
and physics with a more concrete object. There are many 
attributes necessarily present in physical bodies which are 
necessarily excluded by indivisibility ; all attributes, in fact, 
which are divisible.^ There can be nothing divisible in an 
indivisible thing, but the attributes of bodies are all divisible 

2o in one of two ways. They are divisible into kinds, as colour 
is divided into white and black, and they are divisible per 
accidens when that which has them is divisible. In this 
latter sense attributes which are simple^ are nevertheless 
divisible. Attributes of this kind will serve, therefore, to 
illustrate the impossibility of the view. It is impossible, if 

25 two parts of a thing have no weight, that the two together 
should have weight. But either all perceptible bodies 
or some, such as earth and water, have weight, as these 
thinkers would themselves admit. Now if the point has no 
weight, clearly the lines have not either, and, if they have 
not, neither have the planes. Therefore no body has 

30 weight. It is, further, manifest that their point cannot have 

1 Phys. VI. i. 

^ The reading 8iaiperdi/, though preserved only in one rather inferior 
manuscript, must be preferred on grounds of sense to the ahialp^rov 
of the other manuscripts. The silence of Simplicius seems to cor- 
roborate the reading Smtpfroi/. Possibly the clause is a gloss. 

^ i. e. not divisible into kinds. 

BOOK III. I 299^ 

weight. For while a heavy thing may always be heavier 
than something and a light thing lighter than something, 299^ 
a thing which is heavier or lighter than something 
need not be itself heavy or light, just as a large thing is 
larger than others, but what is larger is not always large. 
A thing which, judged absolutely, is small may none the 
less be larger than other things. Whatever, then, is heavy 5 
and also heavier than something else, must exceed this by 
something which is heavy. A heavy thing therefore is 
always divisible. But it is common ground that a point is 
indivisible. Again, suppose that what is heavy is a dense 
body, and what is light rare. Dense differs from rare in 
containing more matter in the same cubic area. A point, 
then, if it may be heavy or light, may be dense or rare. 10 
But the dense is divisible while a point is indivisible. And 
if what is heavy must be either hard or soft, an impossible 
consequence is easy to draw. For a thing is soft if its 
surface can be pressed in, hard if it cannot ; and if it can 
be pressed in it is divisible. 

Moreover, no weight can consist of parts not possessing 15 
weight. For how, except by the merest fiction, can they 
specify the number and character of the parts which will 
produce weight? And, further, when one weight is greater 
than another, the difference is a third weight ; from which 
it will follow that every indivisible part possesses weight. 
For suppose that a body of four points possesses weight. 
A body composed of more than four points^ will be 
superior in weight to it, a thing which has weight. But the ^o 
difference between weight and weight must be a weight, as 
the difference between white and whiter is white. Here the 
difference which makes the superior weight heavier ^ is the 
single point which remains when the common number, four, 
is subtracted. A single point, therefore, has weight. 

Further, to assume, on the one hand, that the planes can • 

^ Prantl's conjecture ^ rovdi is unsatisfactory. The alternatives are 
(i) to keep the reading of the manuscripts {q roSi), (2) to read rovdl, 
omitting ^. In the latter case the sense remains the same but the 
construction becomes rather easier. 

^ Prantl's conjectural duplication of the words jxid o-ny/xi;, though 
harmless, is unnecessary. 

299^ DE CAELO 

25 only be put in linear contact ^ would be ridiculous. For 
just as there are two ways of putting lines together, namely, 
end to end and side by side, so there must be two ways of 
putting planes together. Lines can be put together so that 
contact is linear by laying one along the other, though not 
by putting them end to end.^ But if, similarly, in putting 
the planes together, superficial contact is allowed as an 

30 alternative to linear, that method will give them bodies 
which are not any element nor composed of elements.^ 
Again, if it is the number of planes in a body * that makes 
300^ one heavier than another, as the Timaeus^ explains, 
clearly the line and the point will have weight. For the 
three cases are, as we said before, analogous.^ But if the 
reason of differences of weight is not this, but rather the 
5 heaviness of earth and the lightness of fire, then some of 
the planes will be light and others heavy (which involves 
a similar distinction in the lines and the points) ; the earth- 
plane, I mean, will be heavier than the fire-plane. In 
general, the result is either that there is no magnitude at 
all, or that all magnitude could be done away with. For 

TO a point is to a line as a line is to a plane and as a plane is 
to a body. Now the various forms in passing into one 
another will each be resolved into its ultimate constituents. 
It might happen therefore that nothing existed except 
points, and that there was no body at all. A further con- 
sideration is that if time is similarly constituted, there would 
be, or might be, a time at which it was done away with. For 

15 the indivisible now is like a point in a line. The same conse- 
quences follow from composing the heaven of numbers, as 
some of the Pythagoreans do who make all nature out of 
numbers. For natural bodies are manifestly endowed with 
weight and lightness, but an assemblage of units can neither 
be composed to form a body nor possess weight. 

^ i. e. so as to form pyramids, cubes, &c. 

^ Grammar requires the readings imriOffMepr], Trpoa-TidefjLevrj instead of 
the eniTLBeixfVTjv, Trpoa-Tidfjjiiuqu of all manuscripts but one (M). 

^ Because they will not be pyramids or instances of any other 
recognized figure. 

* Omitting the to. before tmv ennredayvj which got into E by a simple 
dittography and is found in no other manuscript. 

^ Plato, Tzm. 56 B. 

^ i.e. point : line :: line : plane :: plane : body (as below). 

BOOK III. 2 300^ 

2 The necessity that each of the simple bodies should have 20 
a natural movement may be shown as follows. They mani- 
festly move, and if they have no proper movement they 
must move by constraint : and the constrained is the same 
as the unnatural. Now an unnatural movement presupposes 
a natural movement which it contravenes, and which, how- 25 
ever many the unnatural movements, is always one. For 
naturally a thing moves in one way, while its unnatural 
movements are manifold.^ The same may be shown from 
the fact of rest. Rest, also, must either be constrained or 
natural, constrained in a place to which movement was con- 
strained, naturaHn a place movement to which was natural. 
Now manifestly there is a body which is at rest at the 30 
centre. If then this rest is natural to it, clearly motion to 
this place is natural to it. If, on the other hand, its rest 
is constrained, what is hindering its motion ? Something, 
perhaps, which is at rest : but if so, we shall simply repeat 
the same argument ; and either we shall come to an ultimate 
something to which rest where it is is natural, or we shall 300^ 
have an infinite process, which is impossible. The hindrance 
to its movement, then, we will suppose, is a moving thing — 
as Empedocles says that it is the vortex which keeps the 
earth still — : but in that case we ask, where would it have 
moved to but for the vortex?'^ It could not move in- 
finitely ; for to traverse an infinite is impossible, and im- 5 
possibilities do not happen. So the moving thing must 
stop somewhere, and there rest not by constraint but 
naturally. But a natural rest proves a natural movement 

^ This is in verbal contradiction with the doctrine of Book I, which 
asserts that the unnatural movement is single since it is the contrary 
of the natural, which is single. But it is not difficult to conceive of 
all movements of a body divergent from the one natural path as 
unnatural according to the degree of their divergence, even though, 
strictly construed, the unnatural path is also one. 

"^ This question, {hough relevant to the general problem, is not 
specially relevant to the hypothesis that the obstacle is in movement. 
There is therefore something to be said for an interpretation which, like 
that attributed by Simplicius to Alexander, makes the question refer 
to the supposed moving obstacle instead of to the earth. But 
Alexander's interpretation turns out on examination to create more 
difficulties than it removes : and there is no great objection, after all, 
to supposing that Aristotle refutes the second alternative by an argu- 
ment which refutes both. 

645.20 H 

300*^ DE CAELO 

to the place of rest. Hence Leucippus and Democritus, 
who say that the primary bodies are in perpetual movement 

lo in the void or infinite, may be asked to explain the manner 
of their motion and the kind of movement which is natural 
to them. For if the various elements are constrained by 
one another to move as they do, each must still have 
a natural movement which the constrained contravenes, and 
the prime mover must cause motion not by constraint but 

15 naturally. If there is no ultimate natural cause of move- 
ment and each preceding term in the series is always moved 
by constraint, we shall have an infinite process. The same 
difficulty is involved even if it is supposed, as we 'read in 
the Tintaetis^ XhdX before the ordered world was made the 
elements moved without order. Their movement must 
have been due either to constraint or to their nature. And 

20 i( their movement was natural, a moment's consideration 
shows that there was already an ordered world. For the 
prime mover must cause motion in virtue of its own natural 
movement,^ and the other bodies, moving without constraint, 
as they came to rest in their proper places, would fall into 
the order in which they now stand, the heavy bodies moving 

25 towards the centre and the light bodies away from it. But 
that is the order of their distribution in our world. There 
is a further question, too, which might be asked. Is it pos- 
sible or impossible that bodies in unordered movement 
should combine in some cases into combinations like those 
of which bodies of nature's composing are composed, such, 
I mean, as bones and flesh ? Yet this is what Empedocles 

30 asserts to have occurred under Love. * Many a head ', says 

^ Plato, Tmi. 30 a. 

^ Taking the reading for which Alexander argued— ict^etj/ avro kivov- 
fievov Kara (f)v(Ti.v. I should put a comma after Kivelv and take Kara (f). 
with Kipovfifvov. The hypothesis is that the elements have their 
natural movements ; and the dependent clause avro klv. k. 0. applies 
this hypothesis to the prime mover, as to. KLvovfieva fxfi ^ia applies it to 
the other bodies. Aristotle shows that, on this hypothesis, the present 
world-order would exist : the prime mover would be imparting move- 
ment to the bodies within it, as it does now, and the four elements 
would be moving towards or resting in their proper places, as now. 
If avTo is read, we have a more disputable description of this koo-^xos 
and less use for the words mvovixeuov Kara <f}v(nv. avro is said to be 
the reading of the manuscripts, but neither copyists nor collators are 
to be trusted with a breathing. J has avro (sic). 

BOOK III. 2 300*^ 

he, *came to birth without a neck.'^ The answer to the 
view that there are infinite bodies moving in an infinite is 
that, if the cause of movement is single, they must move 
with a single motion, and therefore not without order ; and 
if, on the other hand, the causes are of infinite variety, their 301* 
motions too must be infinitely varied. For a finite number 
of causes would produce a kind of order, since absence of 
order is not proved by diversity of direction in motions : 
indeed, in the world we know, not all bodies, but only 
bodies of the same kind, have a common goal of movement. 
Again, disorderly movement means in reality unnatural 5 
movement, since the order proper to perceptible things is 
their nature. And there is also absurdity and impossibility 
in the notion that the disorderly movement is infinitely con- 
tinued. For the nature of things is the nature which most 
of them possess for most of the time. Thus their view 
brings them into the contrary position^ that disorder is to 
natural, and order or system unnatural. But no natural 
fact can originate in chance. This is a point which Anaxa- 
goras seems to have thoroughly grasped ; for he starts his 
cosmogony from unmoved things. The others, it is true, 
make things collect together somehow before they try to 
produce motion and separation. But there is no sense in 
starting generation from an original state in which bodies 15 
are separated and in movement. Hence Empedocles 
begins after the process ruled by Love : for he could not 
have constructed the heaven by building it up out of 
bodies in separation, making them to combine by the power 
of Love, since our world has its constituent elements in 
separation, and therefore presupposes a previous state of 
unity and combination.^ 20 

These arguments make it plain that every body has its 
natural movement, which is not constrained or contrary to 
its nature. We go on to show that there are certain bodies ^ 

* Emped. fr. 57, 1. i (Diels, Vors.'"^ 245, 20). 

^ Reading a-vfx^aiv^i, with HMJ, for o-vfi^aiveLv, 

' Putting a comma instead of a full-stop after aroixeiav (I. 19). 

* The proposition to be proved is that some bodies have necessarily 
this kind of impetus. The introduction of necessity shows that we are 
dealing with a universal. Below in 301^ 16, and again in 301^30, we 


301^ DE CAELO 

whose necessary impetus is that of weight and lightness. 
Of necessity, we assert, they must move, and a moved thing 

25 which has no natural impetus cannot move either towards 
or away from the centre. Suppose a body A without weight, 
and a body B endowed with weight. Suppose the weight- 
less body to move the distance CD, while B in the same 
time moves the distance CE, which will be greater since the 
heavy thing must move further. Let the heavy body then 

30 be divided in the proportion CE : CD (for there is no reason 
why a part of B should not stand in this relation to the 
whole). Now if the whole moves the whole distance CE, 
the part must in the same time move the distance CD. 
A weightless body, therefore, and one which has weight 
301^ will move the same distance, which is impossible. And * 
the same argument would fit the case of lightness. Again, 
a body which is in motion but has neither weight nor light- 
ness, must be moved by constraint, and must continue its 
constrained movement infinitely. For there will be a force 
5 which moves it, and the smaller and lighter a body is the 
further will a given force move it. Now let ^, the weight- 
less body, be moved the distance CE, and B, which has 
weight, be moved in the same time the distance CD. 
Dividing the heavy body in the proportion CE : CD, we 

10 subtract from the heavy body a part which will in the same 
time move the distance CE, since the whole moved CD : 
for the relative speeds of the two bodies will be in inverse 
ratio to their respective sizes. Thus the weightless body 
will move the same distance as the heavy in the same time. 

15 But this is impossible. Hence, since the motion of the 
weightless body will cover a greater distance than any that 
is suggested,^ it will continue infinitely. It is therefore 
obvious that every body must have a definite^ weight or 

are told that every body is either light or heavy. Aristotle's readers 
would of course understand that the disjunction only applied uni- 
versally 'beneath the moon'. The more cautious statement in this 
passage allows for the exception of the heavenly body. 

^ Reading irporedevTos, which is given by all manuscripts except M 
and by Simplicius. 

^ i.e. not infinite. bioipKTiihov is here equivalent to iypia-fievop. 
A similar tendency is observable in other derivatives of diopiCeiv, e. g. 
dbiopuTTos. Alexander and Simplicius made great, but not very 

BOOK III. 2 301^ 

lightness. But since ' nature ' means a source of movement 
within the thing itself, while a force is a source of move- 
ment in something other than it or in itself qua other,* and 
since movement is always due either to nature or to con- ao 
straint, movement which is natural, as downward movement 
is to a stone, will be merely accelerated by an external 
force, while an unnatural movement will be due to the force 
alone.'^ In either case the air is as it were instrumental to 
the force. For air is both light and heavy, and thus qttd 
light produces upward motion, being propelled and set in 
motion by the force, and qtid heavy produces a downward 25 
motion. In either case the force transmits the movement 
to the body by first, as it were, impregnating the air/' 
That is why a body moved by constraint continues to move 
when that which gave the impulse ceases to accompany it. 
Otherwise, i. e. if the air were not endowed with this func- 
tion, constrained movement would be impossible. And 
the natural movement of a body may be helped on in the 30 
same way. This discussion suffices to show* (i) that all 
bodies are either light or heavy, and (%) how unnatural 
movement takes place. 

From what has been said earlier ^ it is plain that there 

successful, efforts to interpret the word as qualifying 'body': they 
do not consider the possibility of its qualifying /3apos i) Kov<p6TT}Ta. 
Probably their manuscripts, like FHMJ, had to before diapia-fxepov, 
which would make it difficult or impossible to take dicopLo-nepov in 
that way. 

* Reading rj ^ aXKo. It looks as if Simplicius had this reading (see 
critical note to Heiberg's edition, p. 595, 22) : his interpretation 
requires it. 

- Reading ^arrco in 1. 20, with all manuscripts except F and with 
Simplicius. avTr] in 22 is somewhat vague in reference, but must 
stand for f] dCvafiis avrrj. 

^ 11. 23-5, rre^vKf . . . ^apvs, are grammatically a parenthesis, and 
should be so printed, with a colon in 23 after ^apv<^. For the doctrine 
cf. PA^'s. IV. 8 and VIII. 10. 

^ Simplicius and Alexander, with three of our manuscripts (FHM), 
have €v TovTOLs for €< rovrav. iv tovtois would go with exovai rather 
than with (pavepov, qualifying the application of the second clause. 
The qualification, however, cannot be made very precise, and it is 
best to follow the other three manuscripts. 

° The yap which introduces the next sentence shows that the 
justification of the statement is to come. The thesis follows from 
what was * said earlier ', because in Phys. IV. 6-9 the hypothesis of 
a void was investigated and refuted, and it is here shown that absolute 
generation, or generation of body out of not-body, requires a void. 

30i^ DE CAELO 

cannot be generation either of everything or in an absolute 
sense of anything. It is impossible that everything should 
302^ be generated,, unless an extra-corporeal ^ void is possible. 
For, assuming generation, the place which is to be occupied 
by that which is coming to be, must have been previously 
occupied by void in which no body was.^ Now it is quite 
possible for one body to be generated out of another, air 
5 for instance out of fire, but in the absence of any pre- 
existing mass generation is impossible. That which is 
potentially a certain kind of body may, it is true, become 
such in actuality. But if the potential body was not already 
in actuality some other kind of body, the existence of an 
extra-corporeal void must be admitted. 

10 It remains to say what bodies are subject to generation, 3 
and why. Since in every case knowledge depends on what 
is prj^arv. and the elements are the primary constituents 
of bodies, we must ask which of such bodies ^ are elements, 
and why ; and after that what is their number and character. 

15 The answer will be plain if we first explain what kind of 
' substance an element is. An element, we take it, is a body 
into which other bodies may be analysed, present in them 
potentially or in actuality (which of these, is still disputable), 
and not itself divisible into bodies different in form. That, 
or something like it, is what all men in every case mean by 

20 element. Now if what we have described is an element, 
clearly there rriust be such bodies. For flesh and wood 
and all other similar bodies contain potentially fire and 
earth, since one sees these elements exuded from them ; 
and, on the other hand, neither in potentiality nor in actuality 

25 does fire contain flesh or wood, or it would exude them. 

The nature of the heavenly body and the views of Paimenides and 
Melissus, referred to by Simphcius, are not here in point. 

M.e. a void outside bodies, as distinct from the fragments of void 
which are supposed to be distributed throughout the texture of every 
body. Simplicius attributes the distinction of two kinds of void to the 
authors of the theory themselves. 

"^ Reading in 1. 2 ro yivofievov^ ci eyevtro with Bekker. The manu- 
scripts are confused, and offer many variants. 

' viz. bodies subject to generation. We read nola rCav toiovtcdv with 
the manuscripts, taking tmv toiovtiov as a partitive genitive (after 

BOOK III. 3 302* 

Similarly, even if there were only one elementary body, 
it would not contain them. For though it will be either 
flesh or bone or something else, that does not at once 
show that it contained these in potentiality : the further 
question remains, in what manner it becomes them. Now 
Anaxagoras opposes Empedocles' view of the elements. 
Empedocles says that fire and earth and the related bodies 30 
are elementary bodies of which all things are composed ; 
but this Anaxagoras denies. His elements are the homoeo- 
merous things,^ viz. flesh, bone, and the like. Earth and 302 
fire are mixtures, composed of them and all the other seeds, 
each consisting of a collection of all the homoeomerous 
bodies, separately invisible ; and that explains why from 
these two bodies all others are generated. (To him fire 
and aithcr are the same thing.-) But since every natural 5 
body has its proper movement, and movements are either 
simple or mixed, mixed in mixed bodies and simple in 
simple, there must obviously be simple bodies ; for there 
are simple movements. It is plain, then, that there are 
elements, and why. 

4 The next question to consider is whether the elements ro 
are finite or infinite in number, and, if finite, what their 
number is. Let us first show reason for denying that 
their number is infinite, as some suppose. We begin with 
the view of Anaxagoras that all the homoeomerous bodies 
are elements.^ Any one who adopts this view misapprehends 15 
the meaning of element. Observation shows that even mixed 
bodies are often divisible into homoeomerous parts ; examples 
are flesh, bone, wood, and stone. Since then the composite 

^ 'Homoeomerous' means 'having parts like one another and like 
the whole of which they are parts '. Some confusion is here caused 
by the fact that Aristotle sometimes uses ' homoeomerous * as an 
attribute of the parts of a homoeomerous whole, i. e. as meaning ' like 
one another and like the whole of which they are parts'. That is 
what he means when he says of a body (302^ 16) that it is ' divisible 
into homoeomerous parts' or {ib. 25) that it is 'composed of homoeo- 
merous bodies '. The use of the term 'KenTOficpes (= fxiKpofxepes) is 
complicated by a similar transference from whole to part (cp. 304^9, 

2 Cp. Book I, 270^ 24. 

^ Tovs . . . TToiovvTai must be construed (by a kind of zeugma) with 


302^ ^ DE CAELO 

cannot be an element, not every homoeomerous body can 
be an element ; only, as we said before,^ that which is 

20 not divisible into bodies different in form.^ But even 
taking * element * as they do, they need not assert an 
infinity of elements, since the hypothesis of a finite number 
will give identical results. Indeed even two or three such 
bodies serve the purpose as well, as Empedocles' attempt 
shows. Again, even on their view it turns out that all 

25 things are not composed of homoeomerous bodies. They 
do not pretend that a face is composed of faces, or that any 
other natural conformation is composed of parts like itself.^ 
Obviously then it would be better to assume a finite number 
of principles. They should, in fact, be as few as possible, 
consistently with proving what has to be proved. This is 

-30 the common demand of mathematicians, who always assume 
as principles things finite either in kind or in number.* 
Again, if body is distinguished from body by the ap- 
propriate qualitative difference, and there is a limit to 
303^ the number of differences (for the difference lies in qualities 
apprehended by sense, which are in fact finite in number, 
though this requires proof ^), then manifestly there is neces- 
sarily a limit to the number of elements. 

There is, further, another view — that of Leucippus and 
Democritus of Abdera— the implications of which are also 

^ Above, 302*18. 

^ 'Divisible into homoeomerous parts ' = * homoeomerous wholes' 
(cp. note on 'homoeomerous' at 302*31). The argument is therefore 
as follows : ' homoeomerous ' includes mixed as well as simple bodies ; 
but any one who understood the meaning of the term ' element ' would 
have seen that a mixed body cannot be an element : instead of 
regarding all homoeomerous bodies as elements, he would have 
confined the term to such homoeomerous bodies as are simple. — As 
an argument against Anaxagoras this is ineffective ; for he (a) denied 
that flesh, bone, &c., are mixed; (d) denied that earth, air, fire, and 
water — cited by Simplicius as simple and homoeomerous — are simple. 
Aristotle is content to argue from what he regards as estabhshed fact, 
whether Anaxagoras admits it or not. Anaxagoras would have 
claimed that the suggested criterion of indivisibility kut eldos was 
satisfied by his ofxoiofiep^, and could therefore plead not guilty to the 
charge of misapprehending the meaning of ' element '. 

^ All bodies should be either elements or composed of elements. 
But Anaxagoras, though he makes his elements infinite, is still not 
able to show that every whole is composed of parts like itself. 

* Reading ra nenepaaiiiva (so J, as well as three of Bekker's manu- 

^ The proof of the proposition is given in De Sensu, 6 (445^2off.). 

BOOK III. 4 303' 

unacceptable. The primary masses, according to them, 5 
are infinite in number and indivisible in mass : one cannot 
turn into many nor many into one ; and all things are 
generated by their combination and involution. Now this 
view in a sense makes things out to be numbers or composed 
of numbers.^ The exposition is not clear, but this is its ^o 
real meaning. And further, they say that since the atomic 
bodies differ in shape, and there is an infinity of shapes, 
there is an infinity of simple bodies. But they have never 
explained in detail the shapes of the various elements, 
except so far as to allot the sphere to fire. Air, water, 15 
and the rest they distinguished by the relative size of 
the atom, assuming that the atomic substance was a sort 
of master-seed for each and every element. Now, in 
the first place, they make the mistake already noticed. 
The principles which they assume are not limited in 
number, though such limitation would necessitate no other 
alteration in their theory. Further, if the differences of 
bodies are not infinite, plainly the elements will not be 20 
an infinity.^ Besides, a view which asserts atomic bodies 
must needs come into conflict with the mathematical 
sciences, in addition to invalidating many common opinions 
and apparent data of sense perception. But of these things 
we have already spoken in our discussion of time and move- 
ment.^ They are also bound to contradict themselves. 25 
For if the elements are atomic, air, earth, and water cannot 
be differentiated by the relative sizes of their atoms, since 
then they could not be generated out of one another. The 
extrusion of the largest atoms is a process that will in time 
exhaust the supply ; and it is by such a process that they 
account for the generation of water, air, and earth from one 
another.'* Again, even on their own presuppositions it does 30 

^ Because the atom is practically a mathematical unit, out of which 
bodies are formed by simple addition. Cp. Met. Z. 13, 1039'^ 3 ff. 

'' Cp. 303'^ I. 2 Esp. Phys. VI. 1-2 (231^ 18 if.). 

* Suppose water is being formed out of air ; and suppose that the 
water-atom is larger than the air-atom: what is required on this 
theory is the extrusion from the air of the larger atoms. Conversely, 
if air were being formed out of water, the smaller atoms would be 
extruded from the water. But the supply of large (or small) atoms 
will soon run out, and air not reducible to water (or water not reducible 
to air) will be left. 

303^ DE CAELO 

not seem as if the elements would be infinite in number. 
The atoms differ in figure, and all figures are composed of 
303^ pyramids, rectilinear in the case of rectilinear figures, while 
the sphere has eight pyramidal parts.^ The figures must 
have their principles,^ and, whether these are one or two 
or more, the simple bodies must be the same in number 
as they. Again, if every element has its proper movement, 
5 and a simple body has a simple movement, and the number 
of simple movements is not infinite, because the simple 
motions are only two and the number of places is not 
infinite,^ on these grounds also we should have to deny 
that the number of elements is infinite. 

Since the number of the elements must be limited, it 5 
ro remains to inquire whether there is more than one element. 
Some assume one only, which is according to some * water, 
to others ^ air, to others ^ fire, to others "^ again something 
finer than water and denser than air, an infinite body — 
so they say — embracing all the heavens. 

Now those who decide for a single element, which is 
either water or air or a body finer than water and denser 
'5 than air, and proceed to generate other things out of it 
by use of the attributes density and rarity, all alike fail 
to observe the fact that they are depriving the element 
of its priority. Generation out of the elements is, as they 
say, synthesis, and generation into the elements is analysis, 

^ The pyramids are tetrahedrons; and those produced by triple 
section of a sphere are irregular, having a spherical base. 

^ i. e. there must be a limited number of primary figures to which all 
other figures are reducible. 

^ There are only two places to which movement can be directed, 
viz. the circumference and the centre. By the two simple motions 
Aristotle probably here means motions towards these two places, 
motion up and motion down. Circular motion is not possible beneath 
the moon. 

* Thales and Hippon. 

^ Anaximenes and Diogenes of ApoUonia. 

^ Heracleitus and Hippasus : but see below, 304=* 18, note. 

' Anaximander. This identification has been rejected by many 
modern scholars. See Bonitz, Jnd. 50*33, Diels, Vors.^ 18, 10 and 
416, I, Burnet, E.G.P? § 15. Diels follows Zeller in attributing the 
view to a certain Idaios of Himera, whom Aristotle never mentions 
by name and of whom hardly anything is known. Burnet refers the 
passage to Anaximander. 

BOOK III. 5 303'' 

so that the body with the finer parts must have priority 
in the order of nature. But they say that fire is of all 20 
bodies the finest. Hence fire will be first in the natural 
order. And whether the finest body is fire or not makes 
no difference ; anyhow it must be one of the other bodies 
that is primary and not that which is intermediate.^ Again, 
density and rarity, as instruments of generation, are equiva- 
lent to fineness and coarseness, since the fine is rare, and 
coarse in their use means dense. But fineness and coarse- 25 
ness, again, are equivalent to greatness and smallness, since 
a thing with small parts is fine and a thing with large parts 
coarse. For that which spreads itself out widely is fine, 
and a thing composed of small parts is so spread out. In 
the end, then, they distinguish the various other substances 
from the element by the greatness and smallness of their 30 
parts. This method of distinction makes all judgement rela- 
tive. There will be no absolute distinction between fire, water, 
and air, but one and the same body will be relatively to 
this fire, relatively to something else air.^ The same 3^4^ 
difficulty is involved equally in the view which recognizes 
several elements and distinguishes them by their greatness 
and smallness. The principle of distinction between bodies 
being quantity, the various sizes will be in a definite ratio, 
and whatever bodies are in this ratio to one another must be 5 
air, fire, earth, and water respectively. For the ratios of 
smaller bodies may be repeated among greater bodies.'' 

Those who start from fire as the single element, while 
avoiding this difficulty, involve themselves in many others. 
Some of them give fire a particular shape, like those who 10 
make it a pyramid, and this on one of two grounds. The 
reason given may be — more crudely — that the pyramid is 
the most piercing of figures as fire is of bodies,* or — more 

' i. e. the rarest or finest body is the true element, as being the true 
starting-point of the process of generation or synthesis ; and a body 
denser than fire and rarer than earth, like air or water, or finer than 
water and denser than air, like Anaximander's infinite, will not do. 

^ For the attributes great and small belong to the category of 
relation {Cat. 5^ lofif.). 

^ i.e. what is really asserted is a ratio, and ratio is independent 
of size. 

* Simplicius observes that the argument is justly called crude, since 

304^ DE CAELO 

ingeniously— the position may be supported by the follow- 
ing argument. As all bodies are composed of that which 

15 has the finest parts, so all solid figures are composed of 
pyramids : but the finest body is fire, while among figures 
the pyramid is primary and has the smallest parts ; ^ and 
the primary body must have the primary figure : therefore 
fire will be a pyramid.^ Others, again, express no opinion on 
the subject of its figure, but simply regard it as the body 

20 of the finest parts, which in combination will form other 
bodies, as the fusing of gold-dust produces solid gold. 
Both of these views involve the same difficulties. For (i) 
if, on the one hand, they make the primary body an atom, 
the view will be open to the objections already advanced 
against the atomic theory. And further the theory is incon- 

25 sistent with a regard for the facts of nature. For if all 
bodies are quantitatively commensurable, and the relative 
size of the various homoeomerous masses and of their 
several elements are in the same ratio, so that the total 
mass of water,^ for instance, is related to the total mass 
of air as the elements of each are to one another, and 

30 so on, and if there is more air than water and, generally, 
more of the finer body than of the coarser, obviously the 
element of water will be smaller than that of air.* But 
the lesser quantity is contained in the greater. Therefore 

it involves an undistributed middle : 'fire is piercing', 'the pyramid 
is piercing': they attempt to draw an affirmative conclusion in the 
second figure. 

^ Reading yuKpoixepicn-arov with FHMJ. The word is used as 
equivalent to XiiiTOfiepea-TaTov, which is the reading of EL and (prob- 
ably) of Simplicius. — The pyramid is presumably said to have the 
smallest parts because it contains fewer of the primary triangles than 
any other regular solid. But the assertion is not thereby justified. 
Given a certain size of triangle, the pyramid would be the smallest of 
the solids in cubic content ; thus the body composed of pyramids 
would be the body with the smallest parts. The epithet Xenrajxepes, 
in short, seems to be transferred from the whole to the part, just as 
ofxoioiJLcpes was (above, 302^31, note). 

^ To whom is this ' more ingenious ' version to be attributed ? 
* Heracleitus made fire the universal element but did not say it was 
a pyramid, and the Pythagoreans, who said that fire was composed 
of pyramids, did not make it the universal element ' (Simpl.). 

^ Perhaps olov t6 should be read for olov rd. 

* The ascertained fact on which this argument is based is that 
when (e.g.) water turns into air, the volume of the resultant air is 

BOOK III. 5 304'' 

the air element is divisible. And the same could be shown 304^ 
of fire and of all bodies whose parts are relatively fine. 
(2) If, on the other hand, the primary body is divisible, then 
(a) those who give fire a special shape will have to say 
that a part of fire is not fire, because a pyramid is not 
composed of pyramids,^ and also that not every body 5 
is either an element or composed of elements, since a 
part of fire will be neither fire nor any other element. 
And (l?) those whose ground of distinction is size will 
have to recognize an element prior to the element, a 
regress which continues infinitely, since every body is di- 
visible and that which has the smallest parts is the element.^ 
Further, they too will have to say that the same body is 
relatively to this fire and relatively to that air, to others 10 
again water and earth. 

The common error of all views which assume a single 
element is that they allow only one natural movement, 
which is the same for every body. For it is a matter 
of observation that a natural body possesses a principle 
of movement. If then all bodies are one, all will have 15 
one movement. With this motion the greater their quantity 
the more they will move, just as fire, in proportion as its 
quantity is greater, moves faster with the upward motion 
which belongs to it. But the fact is that increase of quantity 
makes many things move the faster downward. For these 
reasons, then, as well as from the distinction already 20 
established^ of a plurality of natural movements, it is 
impossible that there should be only one element. But 
if the elements are not an infinity and not reducible to 
one, they must be several and finite in number. 

greater than that of the original water. This increase of volume can 
only be accounted for (since the hypothesis of a void has been refuted) 
by supposing an increase in the volume of the atom proportionate to 
the observed increase in the volume of the total mass. But the 
enlarged atom would be divisible, and therefore no atom. 

' i. e. a pyramid cannot be divided so that every part is a pyramid. 

2 If every body is infinitely divisible, it is difficult to give a precise 
meaning to ' that which has the smallest parts '. Further, the phrase, 
as used, is somewhat illogical ; for the argument would point to the 
smallest part of any body, rather than the body with the smallest 
parts, as the element. But the use of XfTTTo/xfpes (and pxpo/xtpes) as 
an epithet of the part instead of the whole occurs elsewhere (cf. note 
on 304* 16). ^ Book I, c. ii. 

304'' DE CAELO 

First we must inquire whether the elements are eternal 6 
or subject to generation and destruction; for when this 

35 question has been answered their number and character will 
be manifest. In the first place, they cannot be eternal. 
It is a matter of observation that fire, water, and every 
simple body undergo a process of analysis, which must ^ 
either continue infinitely or stop somewhere, (i) Suppose 

. it infinite. Then the time occupied by the process will be 
infinite, and also that occupied by the reverse process of 

30 synthesis. For the processes of analysis and synthesis 
succeed one another in the various parts. It will follow 
that there are two infinite times which are mutually exclu- 
sive, the time occupied by the synthesis, which is infinite, 
being preceded by the period of analysis. There are thus 
305* two mutually exclusive infinites, which is impossible. 
(2) Suppose, on the other hand, that the analysis stops 
somewhere. Then the body at which it stops will be either 
atomic or, as Empedocles seems to have intended, a divisible 
body which will yet never be divided. The foregoing argu- 

5 ments ^ show that it cannot be an atom ; but neither can it 
be a divisible body which analysis will never reach. For 
a smaller body is more easily destroyed than a larger ; 
and a destructive process which succeeds in destroying, 
that is, in resolving into smaller bodies, a body of some 
size, cannot reasonably be expected to fail with the smaller 

10 body. Now in fire we observe a destruction of two kinds : 
it is destroyed by its contrary when it is quenched, and 
by itself when it dies out.^ But the efiect is produced by 
a greater quantity upon a lesser, and the more quickly the 
smaller it is. The elements of bodies must therefore be 
subject to destruction and generation. 

Since they are generated, they must be generated either 

15 from something incorporeal or from a body, and if from 
a body, either from one another or from something else. 
The theory which generates them from something in- 

^ Reading amyKrj de with the MSS. ^ c. iv. 

^ i.e. it may die out 'of itself . Aristotle does not develop this, but 
his point is only the simple one that the smaller the fire is, the sooner, 
by either process, it is destroyed. 

BOOK III. 6 305^ 

corporeal requires an extra-corporeal void.^ For every- 
thing that comes to be comes to be in something,^ and that 
in which the generation takes place must either be in- 
corporeal or possess body ; and if it has body, there will be 
two bodies in the same place at the same time, viz. that 
which is coming to be and that which was previously there, 20 
while if it is incorporeal, there must be an extra-corporeal 
void. But we have already shown ^ that this is impossible. 
But, on the other hand, it is equally impossible that the 
elements should be generated from some kind of body. 
That would involve a body distinct from the elements and 
prior to them. But if this body possesses weight or light- 
ness, it will be one of the elements ; and if it has no 25 
tendency to movement, it will be an immovable or mathe- 
matical entity, and therefore not in a place at all. A place 
in which a thing is at rest is a place in which it might move, 
either by constraint, i. e. unnaturally, or in the absence of 
constraint, i. e. naturally. If, then, it is in a place and 
somewhere,^ it will be one of the elements; and if it is 
not in a place, nothing can come from it, since that which 3° 
comes into being and that out of which it comes must 
needs be together. The elements therefore cannot be 
generated from something incorporeal nor from a body 
which is not an element, and the only remaining alternative 
is that they are generated from one another. 

7 We must, therefore, turn to the question, what is the 
manner of their generation from one another? Is it as 
Empedocles and Democritus say, or as those who resolve 35 
bodies into planes say, or is there yet another possibility ? 3^5 

* y€vvi>nevov is found only in EL, and the other four manuscripts 
offer no substitute. It was clearly not in Simplicius' text. Kexcopia-fxevov^ 
or another word of similar meaning, must be read. 

^ The words ev nvi yivfrni Kai are a conjectural addition suggested 
by Simplicius (after Alexander). They occur (without the Kal) in one 
of our manuscripts, M, whose original readings are mostly either 
errors or conjectures. Without these words it is almost impossible 
to make any sense of the passage; but they are not intrinsically 
a probable conjecture and are only accepted because a better remedy 
remains to be suggested. 

^ Phys. IV. 8. 

* Placing the comma after nov (1 29) instead of after totto) (1. 28). 
To be * somewhere ' is to be ' in a place '. 

305^ DE CAELO 

(i) What the followers of Empedocles do, though without 
observing it themselves, is to reduce the generation of 
elements out of one another to an illusion. They make it 
a process of excretion from a body of what was in it all the 
time — as though generation required a vessel rather than 
5 a material — so that it involves no change of anything. 
And even if this were accepted, there are other implications 
equally unsatisfactory. We do not expect a mass of matter 
to be made heavier by compression. But they will be 
bound to maintain this, if they say that water is a body 
present in air and excreted from air, since air becomes 

10 heavier when it turns into water.^ Again, when the mixed 
body is divided, they can show no reason why one of the 
constituents must by itself take up more room than the 
body did : but when water turns into air, the room occu- 
pied is increased. The fact is that the finer body takes 
up more room, as is obvious in any case of transforma- 

15 tion. As the liquid is converted into vapour or air the 
vessel which contains it is often burst because it does not 
contain room enough. Now, if there is no void at all, and 
if, as those who take this view say, there is no expansion of 
bodies,^ the impossibility of this is manifest : and if there 
is void and expansion, there is no accounting for the fact 
that the body which results from division occupies of 

20 necessity a greater space. It is inevitable, too, that genera- 
tion of one out of another should come to a stop, since a 
finite quantum cannot contain an infinity of finite quanta. 
When earth produces water something is taken away from 
the earth, for the process is one of excretion. The same 
thing happens again when the residue produces water. 

25 But this can only go on for ever, if the finite body con- 
tains an infinity, which is impossible. Therefore the 
generation of elements out of one another will not always 

^ More accurately, becomes heavy, since air rises and water falls. 
Lightness is treated here as a low degree of heaviness. 

^ The words KaOdnep (Paaiv oi t. X. must be taken to refer only to 
expansion, since Democritus of course believed in a void. 

^ In the end the elements will be sorted out, and there will remain 
several homogeneous masses between which no interchange is 

BOOK III. 7 305'' 

(a) We have now explained that the mutual transforma- 
tions of the elements cannot take place by means of ex- 
cretion. The remaining alternative is that they should be 
generated by changing into one another. And this in one of 
two ways, either by change of shape, as the same wax takes 30 
the shape both of a sphere and of a cube, or, as some assert, 
by resolution into planes, (a) Generation by change of 
shape would necessarily involve the assertion of atomic 
bodies. For if the particles were divisible there would be a 
part of fire which was not fire and a part of earth which 
was not earth, for the reason that not every part of a 35 
pyramid is a pyramid nor of a cube a cube. But if 306^ 
(d) the process is resolution into planes, the first difficulty 
is that the elements cannot all be generated out of one 
another. This they are obliged to assert, and do assert. It 
is absurd, because it is unreasonable that one element alone 
should have no part in the transformations, and also con- 
trary to the observed data of sense, according to which all 5 
alike change into one another. In fact their explanation of 
the observations is not consistent with the observations. 
And the reason is that their ultimate principles are wrongly 
assumed : they had certain predetermined views, and were 
resolved to bring everything into line with them. It seems 
that perceptible things require perceptible principles, 10 
eternal things eternal principles, corruptible things cor- 
ruptible principles ; and, in general, every subject matter 
principles homogeneous with itself. But they, owing to 
their love for their principles, fall into the attitude of men 
who undertake the defence of a position in argument. 
In the confidence that the principles are true they are 
ready to accept any consequence of their application. 
As though some principles did not require to be judged 15 
from their results, and particularly from their final issue ! 
And that issue, which in the case of productive knowledge ^ 
is the product, in the knowledge of nature is the unim- 
peachable evidence of the senses as to each fact. 

The result of their view is that earth has the best right to 
the name element, and is alone indestructible ; for that 

^ i. e. in the case of art. 

646.20 1 

3o6* DE CAELO 

3o which is indissoluble is indestructible and elementary, and 
earth alone cannot be dissolved into any body but itself. 
Again, in the case of those elements which do suffer 
dissolution, the * suspension ' of the triangles is unsatis- 
factory. But this takes place whenever one is dissolved 
into another, because of the numerical inequality of the 
triangles which compose them,^ Further, those who hold 
these views must needs suppose that generation does not 

25 start from a body. For what is generated out of planes 
cannot be said to have been generated from a body. And 
they must also assert that not all bodies are divisible, 
coming thus into conflict with our most accurate sciences, 
namely the mathematical, which assume that even the 
intelligible is divisible, while they, in their anxiety to save 

30 their hypothesis, cannot even admit this of every per- 
ceptible thing. For any one who gives each element a 
shape of its own, and makes this the ground of distinction 
between the substances, has to attribute to them indi- 
visibility ; since division of a pyramid or a sphere must 
leave somewhere at least a residue which is not a sphere or 
a pyramid. Either, then, a part of fire is not fire, so that 
306^ there is a body prior to the element — for every body is 
either an element or composed of elements — or not every 
body is divisible. 

In general, the attempt to give a shape to each of the 8 
simple bodies is unsound, for the reason, first, that they 

5 will not succeed in filling the whole. It is agreed that there 
are only three plane figures which can fill a space, the 
triangle, the square, and the hexagon, and only two solids, 
the pyramid and the cube.^ But the theory needs more 
than these because the elements which it recognizes are 
more in number. Secondly, it is manifest that the simple 

10 bodies are often given a shape by the place in which they 
are included, particularly water and air. In such a case 
the shape of the element cannot persist ; for, if it did, the 

^ e. g. the fiKoa-dedpov of water, with its twenty triangles, has to be 
converted into the oKvaedpov of air, with eight triangles. Four of the 
twenty component triangles of the water-particle will be ' suspended '. 

^ Only regular figures are included. 

BOOK III. 8 306* 

contained mass would not be in continuous contact with 
the containing body ; while, if its shape is changed, it will 
cease to be water, since the distinctive quality is shape. 
Clearly, then, their shapes are not fixed.^ Indeed, nature 15 
itself seems to offer corroboration of this theoretical con- 
clusion. Just as in other cases* the substratum must be 
formless and unshapen — for thus the * all-receptive ', as we 
read in the Timaetisl^ will be best for modelling — so the 
elements should be conceived as a material for composite 20 
things ; and that is why they can put off their qualitative 
distinctions and pass into one another. Further, how can 
they account for the generation of flesh and bone or any 
other continuous body ? The elements alone cannot produce 
them because their collocation cannot produce a continuum. 25 
Nor can the composition of planes ; for this produces the 
elements themselves, not bodies made up of them. Any one 
then who insists upon an exact statement of this kind 
of theory,^ instead of assenting after a passing glance at it, 
will see that it removes generation from the world. 

Further, the very properties, powers, and motions, to 30 
which they paid particular attention in allotting shapes, 
show the shapes not to be in accord with the bodies. 
Because fire is mobile and productive of heat* and com- 
bustion, some made it a sphere, others a pyramid. These 
shapes, they thought, were the most mobile because they 
offer the fewest points of contact and are the least stable of 307' 
any ; they were also the most apt to produce warmth and 
combustion, because the one is angular throughout ^ while 
the other has the most acute angles, and the angles, they 
say, produce warmth and combustion. Now, in the first 
place, with regard to movement both are in error. These 
may be the figures best adapted to movement ; they are 5 

^ Reading ahroiv for avrov, with LMJ. 

^ Plato, Tim. 51 A. At Mr. Ross's suggestion, I have altered the 
stopping of the sentence. Delete comma after aKXon (1. 17), and 
enclose the words /idXicrra yap . . . to rravbex^s (11. 18-19) within 

" Reading tovs toiovtovs with FHMJ. 

* Prantl's text (presumably by accident) omits the Kai before 


^ Cf. below, 307a 16. 

1 2 

307* DE CAELO 

not, however, well adapted to the movement of fire, which 
is an upward and rectilinear movement, but rather to that 
form of circular movement which we call rolling. Earth, 
again,^ they call a cube because it is stable and at rest. 
But it rests only in its own place, not anywhere ; from 

10 any other it moves if nothing hinders, and fire and the 
other bodies do the same. The obvious inference, there- 
fore, is that fire and each several element is in a foreign 
place a sphere or a pyramid, but in its own a cube. 
Again, if the possession of angles makes a body produce 

15 heat and combustion, every element produces heat, though 
one may do so more than another. For they all possess 
angles, the octahedron and dodecahedron as well as the 
pyramid ; and Democritus makes even the sphere a kind 
of angle, which cuts things because of its mobility .^ The 
difference, then, will be one of degree : and this is plainly 
false. They must also accept the inference that the mathe- 

2c matical solids produce heat and combustion, since they t( 
possess angles and contain atomic spheres ^ and pyramids^ 
especially if there are, as they allege, atomic figures.'* Any- 
how if these functions belong to some of these things an< 
not to others, they should explain the difference, instead" 
of speaking in quite general terms as they do. Again, 

25 combustion of a body produces fire, and fire is a sphere 
or a pyramid. The body, then, is turned into spheres or 
pyramids. Let us grant that these figures may reasonably 
be supposed to cut and break up bodies as fire does; still 
it remains quite inexplicable that a pyramid must needs 
produce pyramids or a sphere spheres. One might as well 

30 postulate that a knife or a saw divides things into knives 
or saws! It is also ridiculous to think only of division 
when allotting fire its shape. Fire is generally thought 
of as combining and connecting rather than as separating. 

" ^ Prantl has cirrfir' for encir by a misprint. 

^ Though it has a low degree of angularity, it is highly mobile and 
therefore extremely piercing. But the double cds is awkward, and 
perhaps the tradition is at fault. (J has rc/xi/fi ws emivrjTou, supporting 
E against the other MSS.) 

' Prantl's cr(pn'ipa is a misprint for (T<\)aipai. 

* i. e. indivisible units of line, of which the geometrical figures are 

BOOK III. 8 307^ 

For though it separates bodies different in kind, it combines 307*^ 
those which are the same ; and the combining is essential 
to it, the functions of connecting and uniting being a mark 
of fire, while the separating is incidental. For the expulsion 
of the foreign body is an incident in the compacting of the 
homogeneous. In choosing the shape, then, they should 
have thought either of both functions or preferably of the 5 
combining function. In addition, since hot and cold are 
contrary powers, it is impossible to allot any shape to 
the cold. For the shape given must be the contrary of that 
given to the hot, but there is no contrariety between 
figures. That is why they have all left the cold out, 
though properly either all or none should have their dis- 10 
tinguishing figures. Some of them, however, do attempt 
to explain this power, and they contradict themselves. 
A body of large particles, they say, is cold because instead 
of penetrating through the passages it crushes. Clearly, 
then, that which is hot is that which penetrates these 
passages, or in other words that which has fine particles. 
It results that hot and cold are distinguished not by the 15 
figure but by the size of the particles. Again, if the 
pyramids are. unequal in size, the large ones will not be 
fire, and that figure will produce not combustion but its 

From what has been said it is clear that the difference 
of the elements does not depend upon their shape. Now 
their most important differences are those of property, 20 
function, and power ; for every natural body has, we main- 
tain, its own functions, properties, and powers. Our first 
business, then, will be to speak of these, and that inquiry 
will enable us to explain the differences of each from each. 


307^ We have now to consider the terms ' heavy ' and * light \ I 
We must ask what the bodies so called are, how they are 
30 constituted, and what is the reason of their possessing these 
powers. The consideration of these questions is a proper 
part of the theory of movement, since we call things heavy 
and light because they have the power of being moved 
naturally in a certain way. The activities corresponding 
to these powers have not been given any name, unless 

308* it is thought that ' impetus ' is such a name. But because 
the inquiry into nature is concerned with movement,^ and 
these things have in themselves some spark (as it were) 
of movement, all inquirers avail themselves of these powers, 
though in all but a few cases without exact discrimination. 
5 We must then first look at whatever others have said, and 
formulate the questions which require settlement in the 
interests of this inquiry, before we go on to state our own 
view of the matter. 

Language recognizes (a) an absolute, (d) a relative heavy 
and light. Of two heavy things, such as wood and bronze, 
we say that the one is relatively light, the other relatively 
10 heavy. Our predecessors have not dealt at all with the 
absolute use of the terms, but only with the relative. I mean, 
they do not explain what the heavy is or what the light 
is, but only the relative heaviness and lightness of things 
possessing weight. This can be made clearer as follows. 
There are things whose constant nature it is to move away 
15 from the centre, while others move constantly towards the 
centre ; and of these movements that which is away from 
the centre I call upward movement and that which is 
towards it I call downward movement. (The view, urged 
by some,^ that there is no up and no down in the heaven, 
is absurd. There can be, they say, no up and no down, since 

* Read (f>vaiKfiv fxev flvai (E alone omits /xeV). 

2 The digression is directed against Plato, Twi. 62 E ; but the view 
was held by others besides Timaeus. 

BOOK IV. I 308^ 

the universe is similar every way, and from any point on 20 
the earth's surface a man by advancing far enough will 
come to stand foot to foot with himself. But the extremity 
of the whole, which we call ' above ', is in position above and 
in nature primary. And since the universe has an extremity 
and a centre, it must clearly have an up and down. Common 
usage is thus correct,^ though inadequate. And the reason 25 
of its inadequacy is that men think that the universe is not 
similar every way. They recognize only the hemisphere 
which is over us. But if they went on to think of the 
world as formed on this pattern all round, with a centre 
identically related to each point on the extremity, they 
would have to admit that the extremity was above and 
the centre below.) By absolutely light, then, we mean that 
which moves upward or to the extremity, and by absolutely 3° 
heavy that which moves downward or to the centre. By 
lighter or relatively light we mean that one, of two bodies 
endowed with weight and equal in bulk, which is exceeded 
by the other in the speed of its natural downward move- 

2 Those of our predecessors who have entered upon this 
inquiry have for the most part spoken of light and heavy 35 
things only in the sense in which one of two things both 308^ 
endowed with weight is said to be the lighter. And this 
treatment they consider a sufficient analysis also of the 
notions of absolute heaviness and absolute lightness, to 
which their account does not apply. This, however, will 
become clearer as we advance. One use of the terms 
' lighter ' and ' heavier ' is that which is set forth in writing 5 
in the Timaeus? that the body which is composed of the 
greater number of identical parts is relatively heavy, while 
that which is composed of a smaller number is relatively 

^ Read coo-Trep with FHMJ. 

^ Accepting Prantl's first correction, ol (for o), which seems to be 
necessary to the sense. His second correction, lorcoi/ (for "usov)^ is to 
be rejected as unnecessary. By water (/. of Phil, xxviii, p. 242) 
suggests Barepovy keeping o and taov; but the phrase, so emended, 
seems to be descriptive of the heavy rather than of the light. 

» 63 c. 

3o8^ DE CAELO 

light. As a larger quantity of lead or of bronze is heavier 
than a smaller — and this holds good of all homogeneous 
masses, the superior weight always depending upon a 

10 numerical superiority of equal parts — in precisely the same 
way, they assert, lead is heavier than wood.^ For all 
bodies, in spite of the general opinion to the contrary, are 
composed of identical parts and of a single material. But 
this analysis says nothing of the absolutely heavy and light. 
The facts are that fire is always light and moves upward, 
while earth and all earthy things move downwards or _ 

15 towards the centre. It cannot then be the fewness of the 
triangles (of which, in their view, all these bodies are com- 
posed) ^ which disposes fire to move upward. If it were, 
the greater the quantity of fire the slower it would move, 
owing to the increase of weight due to the increased 
number of triangles. But the palpable fact, on the contrary, 
is that the greater the quantity, the lighter the mass is and 

30 the quicker its upward movement : and, similarly, in the 3 
reverse movement from above downward, the small mass W 
will move quicker and the large slower. Further, since to 
be lighter is to have fewer of these homogeneous parts and 
to be heavier is to have more, and air, water, and fire are 
composed of the same triangles, the only difference being 

35 in the number of such parts, which must therefore explain ^ 
any distinction of relatively light and heavy between these '[ 
bodies, it follows that there must be a certain quantum of 
air which is heavier than water. But the facts are directly 
opposed to this. The larger the quantity of air the more 
readily it moves upward, and any portion of air without 
exception will rise up out of the water. 

So much for one view of the distinction between light 

30 and heavy. To others ^ the analysis seems insufficient ; and 
their views on the subject, though they belong to an older 
generation than ours, have an air of novelty. It is apparent 

^ I put a colon in 1. 6 after eXarTovutv and mark 11. 8-9, o/xot'ws Sc . . . 
eo-Tiv, as parenthetical. This leaves an asyndeton at coanep in 1. 7, 
but it seems to give the sequence of thought better than the stopping 
of Bekker and Prantl does. 

^ There should be a comma after rptytottov in 1. 15. 

^ The atomists, Democritus and Leucippus. 

BOOK IV. 2 308^ 

that there are bodies which, when smaller in bulk than 
others, yet exceed them in weight. It is therefore obviously 
insufficient to say that bodies of equal weight are composed 
of an equal number of primary parts : for that would give 35 
equality of bulk. Those who maintain that the primary or 
atomic parts, of which bodies endowed with weight are 
composed, are planes, cannot so speak without absurdity ; ^ 3^9^ 
but those who regard them as solids are in a better position 
to assert that of such bodies the larger is the heavier. But 
since in composite bodies the weight obviously does not 
correspond in this way. to the bulk, the lesser bulk being 
often superior in weight (as, for instance, if one be wool 5 
and the other bronze), there are some who think and say 
that the cause is to be found elsewhere. The void, they 
say, which is imprisoned in bodies, lightens them and 
sometimes makes the larger body the lighter. The reason 
is that there is more void. And this would also account for 
the fact that a body composed of a number of solid parts 
equal to, or even smaller than, that of another is sometimes 
larger in bulk than it. In short, generally and in every ^° 
case a body is relatively light when it contains a relatively 
large amount of void. This is the way they put it them- 
selves, but their account requires an addition. Relative 
lightness must depend not only on an excess of void, but 
also on a defect of solid : for if the ratio of solid to void 
exceeds a certain proportion, the relative lightness will ^5 
disappear. Thus fire, they say, is the lightest of things just 
for this reason that it has the most void. But it would 
follow that a large mass of gold, as containing more void 
than a small mass of fire, is lighter than it, unless it also 
contains many times as much solid. The addition is there- 
fore necessary. 

Of those who deny the existence of a void some, like 
Anaxagoras and Empedocles, have not tried to analyse the 
notions of light and heavy at all ; and those who, while still 20 
denying the existence of a void, have attempted this,^ have 

^ For, since the planes have no weight, their number cannot affect 
the weight of a body. 
^ Plato, in the Timaeus. 

309^ DE CAELO 

failed to explain why there are bodies which are absolutely 
heavy and light, or in other words why some move upward 
and others downward. The fact, again, that the body of 

25 greater bulk is sometimes lighter than smaller bodies is one 
which they have passed over in silence, and what they have 
said gives no obvious suggestion for reconciling their views 
with the observed facts. 

But those who attribute the lightness of fire to its con- 
taining so much void are necessarily involved in practically 
the same difficulties. For though fire be supposed to 

30 contain less solid than any other body, as well as more 
void, yet there will be a certain quantum of fire in which 
the amount of solid or plenum is in excess of the solids 
contained in some small quantity of earth. They may 
reply that there is an excess of void also. But the question 
is, how will they discriminate the absolutely heavy ? Pre- 
sumably, either by its excess of solid or by its defect 
309^ of void. On the former view there could be an amount of 
earth so small as to contain less solid than a large mass of 
fire. And similarly, if the distinction rests on the amount 
of void, there will be a body, lighter than the absolutely 
light, which nevertheless moves downward as constantly as 
5 the other moves upward. But that cannot be so, since the 
absolutely light is always lighter than bodies which have 
weight and move downward, while, on the other hand, that 
which is lighter need not be light, because in common 
speech we distinguish a lighter and a heavier (viz. water 
and earth) among bodies endowed with weight. Again, 
the suggestion of a certain ratio between the void and the 
solid in a body is no more equal to solving the problem 

10 before us. This manner of speaking will issue in a similar 
impossibility. For any two portions of fire, small or great, 
will exhibit the same ratio of solid to void ; but the upward 
movement of the greater is quicker than that of the less, 
just as the downward movement of a mass of gold or lead, 

15 or of any other body endowed with weight, is quicker in 
proportion to its size. This, however, should not be the 
case if the ratio is the ground of distinction between heavy 
things and light. There is also an absurdity in attributing 


BOOK IV. 2 309^ 

the upward movement of bodies to a void which does not 
itself move. If, however, it is the nature of a void to move 
upward and of a plenum to move downward, and therefore 
each causes a like movement in other things,^ there was 20 
no need to raise the question why composite bodies are 
some light and some heavy ; they had only to explain why 
these two things are themselves light and heavy respectively, 
and to give, further, the reason why the plenum and the 
void are not eternally separated. It is also unreasonable 
to imagine a place for the void, as if the void were not 25 
itself a kind of place.^ But if the void is to move, it must 
have a place out of which and into which the change carries 
it. Also what is the cause of its movement? Not, surely, 
its voidness : for it is not the void only which is moved, but 
also the solid.^ 

Similar difficulties are involved in all other methods of 
distinction, whether they account for the relative lightness 3° 
and heaviness of bodies by distinctions of size, or proceed 
on any other principle, so long as they attribute to each the 
same matter, or even if they recognize more than one 
matter, so long as that means only a pair of contraries. 
If there is a single matter, as with those who compose 
things of triangles, nothing can be absolutely heavy or light : 
and if there is one matter and its contrary — the void, for 3^0^ 
instance, and the plenum — no reason can be given for the 
relative lightness and heaviness of the bodies intermediate 
between the absolutely light and heavy when compared 
either with one another or with these themselves.* The 

^ Read (}}opas iKarepas. eKarepas is in all MSS. except E, and is 
implied in Simplicius' paraphrase. 

^ Read avro with FHMJ and the corrector of E. The construction 
is certainly loose, but the other reading {avrco) does not give the 
required sense. To give void a motion is to give it a ' place ', i. e. 
a natural place to which it moves. But it is itself nothing but a place 
where no body is (cf. PAys. IV. 7): and, as Simplicius punningly 
remarks, * it is out of place to give a place a place ' {rod de toitov tottov 
noielv Tcov droTrcorarcoi' eariv). 

^ If movement is natural to both void and solid, the cause of move- 
ment must lie in something common to both and not in the peculiar 
nature of either, i. e. not in voidness or solidity. 

* Aristotle's argument is that the observed diversity of movement 
necessarily involves a corresponding diversity of bodies : hence any 
view which makes the four elements one in substance fails to account 


view which bases the distinction upon differences of size is 
5 more like a mere fiction than those previously mentioned, 
but, in that it is able to make distinctions between the four 
elements, it is in a stronger position for meeting the fore- 
going difficulties. Since, however,^ it imagines that these 
bodies which differ in size are all made of one substance, 
it implies, equally with the view that there is but one 
matter, that there is nothing absolutely light and nothing 
lo which moves upward (except as being passed by other 
things or forced up by them) ; ^ and since a multitude of 
small atoms are heavier than a few large ones, it will follow 
that much air or fire is heavier than a little water or earth, 
which is impossible. 

These, then, are the views which have been advanced by 3 
15 others and the terms in which they state them. We may 
begin our own statement by settling a question which to 
some has been the main difficulty — the question why some ^ 
bodies move always and naturally upward and others down- ^ 
ward, while others again move both upward and downward. 
After that we will inquire into light and heavy and the 
20 explanation of the various phenomena connected with 
them.^ The local movement of each body into its own 
place must be regarded as similar to what happens in con- 
nexion with other forms of generation and change. There 

for the facts of movement. He here adds that it is not enough to 
recognize two kinds of substance or two contrary attributes. For 
there are four bodies to be accounted for. A single pair of opposites 
may yield an account of fire and earth, but they cannot account also 
for the * intermediate bodies ', water and air. Two pairs of opposites 
will be required, such as those which he uses himself (warm, cold : 
dry, moist). — In 1. 3 ratv cmXav must refer to the things also called tmv 
dn-Xcos ^aptoiv Ka\ Kov(f}a>v. Simplicius tells us that Alexander read 
tS)p ctTvKaiv, but found in some MSS. touv aiika>s. aiikois is tempting, 
but aivKSiv may be allowed to stand : for {a) the absolutely heavy and 
light are, on the theory criticized, pure solid and pure void respec- 
tively : thus TO. anXois are ra dnXa : [b) all other bodies whatever will 
be composed of these in combination, and may therefore be opposed 
to them as composite to simple. 

* Reading rw with HMLJ. Simplicius' paraphrase supports this. 

^ i. e. upward movement is either {a) illusory : as all things race 
downward, some, moving slower, are left behind, and thus appear to 
move up : or {b) unnatural : due to pressure applied from without by 
other bodies pushing downward. 

^ Prantl misprints yeverai. for yivfrai. 

BOOK IV. 3 310* 

are, in fact, three kinds of movement, affecting respectively 
the size, the form, and the place of a thing, c.nd in each it 
is observable that change proceeds from a contrary- to 35 
a contrary or to something intermediate : it is never the 
change of any chance subject in any chance direction, nor, 
similarly, is the relation of the mover to its object for- 
tuitous : the thing altered is different from the thing 
increased, and precisely the same difference holds between 
that which produces alteration and that which produces 
increase. In the same manner it must be thought that 30 
that which produces local motion and that which is so 
moved are not fortuitously related. Now/ that which pro- 
duces upward and downward movement is that which 
produces weight and lightness, and that which is moved 
is that which is potentially heavy or light, and the move- 
ment of each body to its own place is motion towards 
its own form. (It is best to interpret in this sense the 310^ 
common statement of the older writers that * like moves to 
like'. For the words are not in every sense true to fact. 
If one were to remove the earth to where the moon now is, 
the various fragments of earth would each move not towards 
it but to the place in which it now is. In general, when 5 
a number of similar and undifferentiated bodies are moved 
with the same motion this result is necessarily produced, 
viz. that the place which is the natural goal of the move- 
ment of each single part is also that of the whole.^ But 
since the place of a thing is the boundary of that which 
contains it, and the continent of all things that move 
upward or downward is the extremity and the centre, and 
this boundary comes to be, in a sense, the form of that 10 
which is contained, it is to its like that a body moves when 

^ Reading el ovu els with EL (Simplicius' MSS. had, some €i /leV ds, 
and some d /xcV. J has ds ovv). The apodosis does not begin till 
3Io^m6 TO 8e Crjrdv, the argument being interrupted by a long note on 
the meaning of the saying ojxowv npos ofioiov, which should be marked 
as a parenthesis. 

^ coa3^ oTTov . . . TO Trap is explanatory of tovto a-vfx^aiveip. Gram- 
matically the predicate to be supplied to to nau is necfivKe cfyepea-dai, 
though this in the context creates a slight illogicality. Aristotle's 
point is that a fragment of earth moves to the mass called the earth, 
not because it loves its like, but per accidens in the effort to reach the 
centre. It is the effort of numberless such fragments to reach 
the centre which has formed the mass, not the presence of the mass 
at the centre which causes the effort. 

3io^ DE CAELO 

it moves to its own place. For the successive members of 
the series ^ are like one another : water, I mean, is like air 
and air like fire, and between intermediates the relation 
may be converted, though not between them and the 
extremes ; thus air is like water, but water is like earth : ^ 
'5 for the relation of each outer body to that which is next 
within it is that of form to matter.^) Thus * to ask why fire 

^ €(fie^rjs should be read, with the other MSS. and Simplicius, rather 
than E's i$rjs. Cf. de Gen. et Corr. 331^4, 26, 34. 

^ i. e. though air is like fire, fire is not like air ; and though water is 
like earth, earth is not like water. See next note. Prantl proposes 
to take \ii(Toi^ and liKpoi^ in 1. 13 to mean inner and outer respectively, 
i. e. to make the former stand for earth and water, the latter for fire 
and air. His reason is grammatical : /ueVoty is in the dative and so 
are vhan and yfi. Thus a construction is provided for fxeirois. He 
omits to observe that toIs 6' aKpois ov becomes meaningless : which, 
with the admitted difficulty of taking the terms in this sense, is 
sufficient reason for rejecting the proposal. It is no doubt due to 
ofiota that fi^aois is in the dative : likeness to a [lidov is convertible, 
likeness to an aKpov not. 

^ The connexion is difficult, and may be explained as follows. 
Aristotle's argument is formally concluded at (f)ep€a6ai in 1. 11 (*to its 
own place '). The ' place ' (centre and extremity, as explained) gives 
form to the body, and the body in reaching its place attains its form, 
i. e. completes the transition from potentiality to actuality. In a sense, 
then, if the potential is like the actual, it moves * to its like '. The ydp 
in 1. II forestalls an objection. ' There remain the intermediate 
bodies : what of them ? ' These are given form or determined by 
the extreme bodies, and thus mediately determined by the 'place'. 
Instead of saying ' are given form ' or ' are determined ' Aristotle says 
* are like '; being entitled to do so by the meaning just given to ' like '. 
The like to which earth moves is that from which it receives its form, 
and the like to which water and air move is the extreme body — earth 
in the one case, fire in the other— from which each receives its form. 
Thus 'like' means 'receptive of form from'. In this sense water 
is like air vvhich is like fire, and air is like water which is like earth ; 
but the extremes themselves, earth and fire, are like nothing but their 
places. The relation of likeness is reciprocal (i. e. determination is 
mutual) only between the intermediates ; and the chain of resemblance 
breaks off in each direction short of the extreme. Starting from the 
centre, we find in the three terms, water, air, fire, a gradual approxima- 
tion {del TO dva)T€pov . . .) to the form realized in fire ; starting from the 
extremity, we find in the terms air, water, earth, a gradual approxima- 
tion to the form realized in earth. (Of these two complementary 
statements Aristotle gives only the first ; but the second is necessary 
to complete the argument.) Therefore the intermediate bodies, as 
well as the extremes, may be said in moving to their places to attain 
their form. — The above account agrees in principle with that of 
Simplicius, who, however, is not very clear. Alexander, he tells us, 
took another view, based on a different interpretation of del to 
dvciTepov kt\. As reported the view is not easy to fit into the 
context. — For the relation of upper to lower bodies, cf. 312*15 and 
Be Gen. et Corr. 335* 18. 

* Alexander's hi] for he here, like his tSv aXAwi^ for Tommv in 1. 22, 

BOOK IV. 3 310 

moves upward and earth downward is the same as to ask 
why the healable, when moved and changed qua healable, 
attains health and not whiteness ; and similar questions 
might be asked concerning any other subject of alteration. 
Of course the subject of increase, when changed qua in- 20 
creasable, attains not health but a superior size. The same 
applies in the other cases. One thing changes in quality, 
another in quantity : and so in place, a light thing goes 
upward, a heavy thing downward. The only difference is 
that in the last case, viz. that of the heavy and the light, 
the bodies are thought to have a spring of change within 25 
themselves, while the subjects of healing and increase are 
thought to be moved purely from without. Sometimes, 
however, even they change of themselves, i.e. in response 
to a slight external movement reach health or increase, as 
the case may be. And since the same thing which is heal- 
able is also receptive of disease, it depends on whether it is 3° 
moved qua healable or qua liable to disease whether the 
motion is towards health or towards disease. But the 
reason why the heavy and the light appear more than 
these things to contain within themselves the source of 
their movements is that their matter is nearest to being. 
This is indicated by the fact that locomotion belongs to 
bodies only when isolated from other bodies,^ and is generated 
last of the several kinds of movement; in order of being 
then it will be first. Now whenever air comes into being 311^ 
out of water, light out of heavy, it goes to the upper place. 
It is forthwith light : becoming is at an end, and in that 
place it has being.^ Obviously, then, it is a potentiality, 

was advanced as a conjecture unsupported by MSS. None of our 
MSS. have either. The apodosis to the protasis introduced by et in 
310* 31 begins here, hi] is therefore attractive, but 5e in apodosi 
is easily excused in view of the long intervening parenthesis. 

^ The use of cmo\i\v[kkv<>iv ('isolated') is interesting, as Prantl 
points out, because of its later technical use (= absolutus, absolute). 
Simplicius here takes it to stand for complete substances (oXoxXiypo)!/ 
Kar ovcr'iav outcov) not involved in any process of yeuea-i^^ av^rjais, or 
aXXoi'axrts-. Prantl says dn-oXeXvfXiva means ' independent beings ' 
(unabhangige Wesen). Bonitz, 7nd. 84* 26, says ' idem fere ac otto- 
K€KpifjL€vov, x<'>pi-(^t6v '. The ' independence ' intended is rather physical 
than metaphysical. 

^ Read €K(1 icrnv. 

311^ DE CAELO 

5 which, in its passage to actuality, comes into that place and 
quantity and quality which belong to its actuality.^ And 
the same fact explains why what is already actually fire 
or earth moves, when nothing obstructs it, towards its own 
place. For motion is equally immediate in the case of 
nutriment, when nothing hinders, and in the case of the 
thing healed, when nothing stays the healing. But the 
lo movement is also due to the original creative force and to 
that which removes the hindrance or off which the moving 
thing rebounded, as was explained in our opening discus- 
sions, where we tried to show how none of these things 
moves itself^ The /eason of the various motions of the 
various bodies, and the meaning of the motion of a body to 
its own place, have now been explained. 

15 We have now to speak of the distinctive properties of 4 
these bodies and of the various phenomena connected with ^ 
them. In accordance with general conviction we may dis- 
tinguish the absolutely heavy, as that which sinks to th< 
bottom of all things, from the absolutely light, which is that 
which rises to the surface of all things. I use the term! 
' absolutely \ in view of the generic character of * light ' andj 
' heavy \^ in order to confine the application to bodies 
which do not combine lightness and heaviness. It is 

30 apparent, I mean, that fire, in whatever quantity, so long 
as there is no external obstacle, moves upward, and earth 
downward ; and, if the quantity is increased, the movement 
is the same, though swifter. But the heaviness and light- 
ness of bodies which combine these qualities is different 
from this, since while they rise to the surface of some bodies 
they sink to the bottom of others. Such are air and water. 
Neither of them is absolutely either light or heavy. Both 

25 are lighter than earth — for any portion of either rises to the 
surface of it — but heavier than fire, since a portion of either, 
whatever its quantity, sinks to the bottom of fire ; compared 
together, however, the one has absolute weight, the other 

^ Omitting, with F, the words Kai onov, which I assume to have 
been inserted by some one who mistook ov = ubi for the genitive of 
the relative. 

2 Phys. VII. I, 241b 24; VIII. 4, 254^7. 

' i. e. because there are distinct species of light and heavy. 

BOOK IV. 4 3"* 

absolute lightness, since air in any quantity rises to the sur- 
face of water, while water in any quantity sinks to the 
bottom of air. Now other bodies are severally light and 3° 
heavy, and evidently in them the attributes are due to the 
difference of their uncompounded parts : that is to say, 
according as the one or the other happens to preponderate 
the bodies will be heavy and light respectively. Therefore 
we need only speak of these parts, since they are primary 
and all else consequential : and in so doing we shall be 35 
following the advice which we gave ^ to those who attribute 
heaviness to the presence of plenum and lightness to that of 3^^ 
void. It is due to the properties of the elementary bodies 
that a body which is regarded as light in one place is 
regarded as heavy in another, and vice versa. In air, for 
instance, a talent's weight of wood is heavier than a mina 
of lead, but in water the wood is the lighter. The reason 
is that all the elements except fire have weight and all but 5 
earth lightness. Earth, then, and bodies in which earth 
preponderates, must needs have weight everywhere, while 
water is heavy anywhere but in earth, and air is heavy 
when not in water or earth. In its own place each of these 
bodies has weight except fire, even air. Of this we have 
evidence in the fact that a bladder when inflated weighs lo 
more than when empty. A body, then, in which air pre- 
ponderates over earth and water, may well be lighter than 
something in water and yet heavier than it in air, since such 
a body does not rise in air but rises to the surface in water. 

The following account will make it plain that there is an 15 
absolutely light and an absolutely heavy body. And by 
absolutely light I mean one which of its own nature always 
moves upward, by absolutely heavy one which of its own^ 
nature always moves downward, if no obstacle is in the 
way. There are, I say, these two kinds of body,^ and it is 
not the case, as some ^ maintain, that all bodies have weight. 

^ Above, 309^ 20 : if they would only give an account of the simple 
bodies, their questions as to the composite would answer themselves. 

' Read eVW nva (E and Simpl. omit nva). 

* This view is maintained in its most unqualified form by those 
(atomists, probably) who distinguish the four elements by the size of 
their particles (cf. c. ii. 310*9). 

645.20 K 

311^ DE CAELO 

Different views are in fact agreed that there is a heavy- 
body, which moves uniformly towards the centre. But 

20 there is also similarly a light body.^ For we see with our 
eyes, as we said before,^ that earthy things sink to the 
bottom of all things and move towards the centre. But 
the centre is a fixed point. If therefore there is some body 
which rises to the surface of all things — and we observe 
fire to move upward even in air itself, while the air remains 
at rest ^ — clearly this body is moving towards the extremity. 
It cannot then have any weight. If it had, there would be 

35 another body in which it sank : and if that had weight, 
there would be yet another which moved to the extremity 
and thus rose to the surface of all moving things.* In fact, 
however, we have no evidence of such a body. ' Fire, then, 
has no weight. Neither has earth any lightness, since it 
sinks to the bottom of all things, and that which sinks 
moves to the centre. That there is a centre ^ towards which 

30 the motion of heavy things, and away from which that 
of light things is directed, is manifest in many ways. First, 
because no movement can continue to infinity. For what 
cannot be can no more come-to-be than be, and movement 
is a coming-to-be in one place from another. Secondly, 
like the upward movement of fire, the downward movement 

35 of earth and all heavy things makes equal angles on every 

side with the earth's surface ^ : it must therefore be directed 

312* towards the centre. Whether it is really the centre of the 

earth and not rather that of the whole to which it moves, 

may be left to another inquiry, since these are coincident.' 

^ It cannot be right to print II. 14-19, \iyco d' . . . Kovcfiov, as a 
parenthesis, with Prantl. The sentences are not sufficiently self- 
contained nor closely enough inter-connected to justify such treatment. 
The argument which begins in 1. 19 with opSoixev yap is a justification 
of the statement last preceding : as there is, by general admission 
and by the evidence of observation, a heavy body, so there is a light 

2 Above, 311^20. 

^ Since the air is at rest, the explanation that the fire is 'forced up * 
{eKOh^ofjievov, 310*10) is inadmissible. 

* Reading o with the MSS. Prand's conjecture, ov, is unnecessary. 

* Read eVn for eVn'. 

^ i. e. the line of movement is at right angles to any tangent. 
Cf. above, 296^20, 297^ 19. 

■^ The question is discussed in II. xiv, 296^9. 

BOOK IV. 4 3ia^ 

But since that which sinks to the bottom of all things moves 
to the centre, necessarily that which rises to the surface 
moves to the extremity of the region in which the move- 5 
ment of these bodies takes place. For the centre is opposed 
as contrary to the extremity, as that which sinks is opposed 
to that which rises to the surface. This also gives a reason- 
able ground for the duality of heavy and light in the spatial 
duality centre and extremity. Now there is also the inter- 
mediate region to which each name is given in opposition 
to the other extreme. F'or that which is intermediate 10 
between the two is in a sense both extremity and centre.^ 
For this reason there is another heavy and light ; namely, 
water and air. But in our view the continent pertains to 
form and the contained to matter : and this distinction is 
present in every genus.^ Alike in the sphere of quality 
and in that of quantity there is that which corresponds 15 
rather to form and that which corresponds to matter. In 
the same way, among spatial distinctions, the above belongs 
to the determinate, the below to matter. The same holds, 
consequently, also of the matter itself of that which is 
heavy and light : as potentially possessing the one character, 
it is matter for the heavy, and as potentially possessing the 
other, for the light. It is the same matter, but its being is 
different, as that which is receptive of disease is the same as 20 
that which is receptive of health, though in being different 
from it, and therefore diseasedness is different from 

5 A thing then which has the one kind of matter is light 
and always moves upward, while a thing which has the 

^ Read eo-Ti yap COS, omit f o-rt after afxcfiorepoov, and put a colon after 
pera^v. (J has an erasure in the position of the second eo-rl.) 

^ i.e. in every category. For this use of yevos see Bonitz, Ind. 
152^ 16. 

' The doctrine here expressed is the same as that expressed in the 
last chapter (310^ 15, note). A single matter is receptive of two 
opposed forms, weight and lightness or health and disease. But 
Aristotle here adds the new point that of two such alternative forms 
one is always more formal and the other more material. Weight and 
lightness, disease and health, are not true coordinates. A form, we 
may say, is realized in disease, in weight, in the female ; but if/ie form 
is realized in health, in lightness, and in the male. The principle 
is stated in the Metaphysics in the form roiv evapTicov 17 hepa (xvaToixia 
(TTeprjais (1004^27). 

K 2 

312^ DE CAELO 

opposite matter is heavy and always moves downward. 
Bodies composed of kinds of matter different from these 
but having relatively to each other the character which 
25 these have absolutely, possess both the upward and the 
downward motion.^ Hence air and water each have both 
lightness and weight, and water sinks to the bottom of 
all things except earth, while air rises to the surface of all 
things except fire. But since there is one body only Avhich 
rises to the surface of all things and one only which sinks 
to the bottom of all things, there must needs be two other 
3*^ bodies which sink in some bodies and rise to the surface of 
others. The kinds of matter, thegujuust beas-munerQU^ as 
these bodies, i. e. four, but though they are four there must 
be a common matter of all — particularly if they pass into 
orie another — which in each is in being different. There 
3^2^ is no reason why ^ there should not be one or more inter- 
mediates between the contraries, as in the case of colour ; 
for * intermediate ' and ' mean ' are capable of more than 
one application.^ 

Now in its own place every body endowed with both 
weight and hghtness has weight — whereas earth has weight 
5 everywhere — but they only have lightness among bodies to 
whose surface they rise. Hence when a support is with- 
drawn such a body moves downward until it reaches the 
body next below it, air to the place of water and water to 
that of earth. But if the fire above air is removed, it will 
not move upward to the place of fire, except by constraint ; 
and in that way water also may be drawn up, when the up- 
10 ward movement of air which has had a common surface with 
it is swift enough to overpower the downward impulse of 
the water. Nor does water move upward to the place of 
air, except in the manner just described. Earth is not so 
affected at all, because a common surface is not possible to 

^ In 1. 24 put the comma aftei', not before, dnXas. (The correction 
is due to Mr. Ross.) The intermediates, air and water, are only 
relatively light and heavy. In the absolute sense these characters 
belong only to fire and water. 

^ ovde in Bekker and Prantl must surely be a misprint for ov8h 
(so J). 

^ 'Intermediate' stands for a region, not a point, and includes as 
a rule a variety of things. 

BOOK IV. 5 312 

it.^ Hence water is drawn up into the vessel to which fire 
is applied, but not earth. As earth fails to move up- 
ward, so fire fails to move downward when air is withdrawn 15 
from beneath it : for fire has no weight even in its own 
place, as earth has no lightness. The other two move 
downward when the body beneath is withdrawn because, 
while the absolutely heavy is that which sinks to the 
bottom of all things,^ the relatively heavy sinks to its own 
place or to the surface of the body in which it rises, since it 
is similar in matter to it.^ 

It is plain that one must suppose as many distinct species 20 
of matter as there are bodies. For {{, first, there is a single 
matter of all things, as, for instance, the void or the plenum 
or extension or the triangles, either all things will move up- 
ward or all things will move downward, and the second 
motion will be abolished. And so, either there will be no 
absolutely light body, if superiority of weight is due to 
superior size or number of the constituent bodies or to the 25 
fullness of the body : but the contrary is a matter of obser- 
vation, and it has been shown that the downward and 
upward movements are equally constant and universal : or, 
if the matter in question is the void or something similar, 
which moves uniformly upward, there will be nothing to 
move uniformly downward.'^ Further, it will follow that 

^ The surface of earth is too rough to allow of the necessary a-vfKfivcris 
(Simpl.), or continuity of surface, with another body. 

^ Read eanv o (not eanu, o with Bekker). Prantl's ingenious 
conjecture, fls rt]u vnu, is not quite convincing. 

^ The downward movement of earth (absolute weight) is quite 
determinate, having its limit at the centre. But the downward move- 
ment of air and water (relative weight) is not equally determinate: 
it is limited only by the surface of the body next beneath, air by that 
of water, water by that of earth, the upper body being attracted to the 
lower by similarity of matter. This admission inflicts some damage 
on the doctrine of ' places ' — for where a body has weight it cannot be 
said to ' rest naturally ' or to ' be in its place ' — and also on the 
symmetry of the elements— for if the fire above air were removed 
the air would not move upward, but if the earth below water were 
removed the water would move downward. — In 1. 18 els must be 
construed with (peperai, and in 1. 19 fj ols, more fully expressed, would 
be ^ els T)]v eKeivoiv ols. The construction is difficult*, and the passage 
may be corrupt. 

* The stopping of this sentence requires alteration, e'av 8e in I. 27 
is an irregular second limb to the disjunction introduced by ?) kov<j>ov 
in 1. 23. Put a colon at 'n\i]pr) (1. 25) and at livoi (1. 27), and delete the 
comma after likeiovonv (1. 25). 

312^ DE CAELO 

the intermediate bodies move downward in some cases 
quicker than earth : for air in sufficiently large quantity 
30 will contain a larger number of triangles or solids or 
particles. It is, however, manifest that no portion of air 
whatever moves downward.^ And the same reasoning 
applies to lightness, if that is supposed to depend on 
superiority of quantity of matter.^ But if, secondly, the 
kinds of matter are two, it will be difficult to make the 
intermediate bodies behave as air and water behave. 
313^ Suppose, for example, that the two asserted are void and 
plenum. Fire, then, as moving upward, will be void, earth, 
as moving downward, plenum ; and in air, it wilt be said, 
fire preponderates, in water, earth.^ There will then be 
a quantity of water containing more fire than a little air. 
and a large amount of air will contain more earth than 
5 a little water : consequently we shall have to say that air 
in a certain quantity moves downward more quickly than 
a little water. But such a thing has never been observed 
anywhere. Necessarily, then, as fire goes up because it has 
something, e. g. void, which other things do not have, and 
earth goes downward because it has plenum, so air goes to 
10 its own place above water because it has something else, 
and water goes downward because of some special kind 
of body. But if the two bodies'* are one matter, or two 
matters both present in each,^ there will be a certain quantity 
of each at which water will excel a little air in the upward 
movement and air excel water in the downward move- 
ment, as we have already often said. 

The shape of bodies will not account for their moving 5 
15 upward or downward in general, though it will account 
for their moving faster or slower. The reasons for this 

"^ sc. in earth. 

^ On the somewhat absurd theory that the universal 'matter' is 
void or absolute lightness. 

' 312*^33—313=13, oiov . . . >?)f, is a parenthesis and should be so 
printed, with a colon, instead of a full-stop, at nXripfs and at kcitw. 
This is proved by the infinitive ex^iv (after jxur]) in 1. 3, as well as by 
the yap which follows. 

* viz. air and water. 

^ Prantl's eKarepco is a misprint for cKarepco. 

BOOK IV. 6 313* 

are not difficult to see. For the problem thus raised is 
why a flat piece of iron or lead floats upon water, 
while smaller and less heavy things, so long as they are 
round or long — a needle, for instance — sink down ; and 
sometimes a thing floats because it is small, as with gold 20 
dust and the various earthy and dusty materials which 
throng the air. With regard to these questions, it is 
wrong to accept the explanation ofl"ered by Democritus. 
He says that the warm bodies moving up^ out of the 
water hold up heavy bodies which are broad, while the 313** 
narrow ones fall through, because the bodies which offer 
this resistance are not numerous. But this would be 
even more likely to happen in air — an objection which 
he himself raises. His reply to the objection is feeble. In 
the air, he says, the * drive ' (meaning by drive the move- 5 
ment of the upward moving bodies) is not uniform in 
direction. But since some continua are easily divided and 
others less easily, and things which produce division differ 
similarly in the ease with which they produce it, the ex- 
planation must be found in this fact. It is the easily 
bounded,^ in proportion as it is easily bounded, which is 
easily divided ; and air is more so than water, water than 10 , 
earth. Further, the smaller the quantity in each kind, 
the more easily it is divided and disrupted. Thus the 
reason why broad things keep their place is because they 
cover so wide a surface and the greater quantity is less 
easily disrupted. Bodies of the opposite shape sink down 
because they occupy so little of the surface, which is there- 15 
fore easily parted. And these considerations apply with 
far greater force to air, since it is so much more easily 
divided than water. But since there are two factors, the 
force responsible for the downward motion of the heavy 
body and the disruption-resisting force of the continuous 
surface, there must be some ratio between the two. For 
in proportion as the force applied by the heavy thing 

^ dva(f)€p6fji€pa is the better-attested reading (ELMJ Simpl.) and 
should be preferred to ava (f)€p6fx€ua. The word is elsewhere used 
of upward movement by Aristotle. 
/^ i. e. the fluid or moist. Cp. de Gen. et Corr. 329'*' 30. 

313*' DE CAELO 

20 towards disruption and division exceeds that which resides 
in the continuum, the quicker will it force its way down; 
only if the force of the heavy thing is the weaker, will it 
ride upon the surface. 

We have now finished our examination of the heavy and 
the light and of the phenomena connected with them. 


INDEX I. English 

[The sign + following a reference means that many other references 
could be given.] 

68-13 = 268-313. 

Above-below (up-down) — (i) in 
ref. to motion of elements = ex- 
tremity and centre 68^ 22, 08* 

18 + ; (2) applied to universe 
by analogy from animals : upper 
and lower hemispheres 85*^ i ; 
above prior to below 84^ 25, 
'more divine' 88^ 5. 

Action— attributed to stars 92* 14 ; 
most varied in man 92^ 2. 

Air — one of the two elements 
which move upward 69* 18 + ; 
one of the two intermediates 
{g.v.) ; ignited by movement of 
stars 89* 20 ; thought to sup- 
port the earth 94^ 14 ; assists 
movement of bodies 01^ 23. 
See also Intermediate. 

Ait her — special name for the 
highest place, meaning ' what 
runs always ' 70^ 21 ; Anaxa- 
goras interprets otherwise 70^ 
24, 02^ 4. 

All— connexion of, with number 
three 68* 11. 

Alteration — def. movement in re- 
spect of quality 70* 27, 10* 23 ; 
not applicable to fifth element 
70* 13 ; nor to any infinite 75* 
I ; comparison with local move- 
ment, 'j']^ 14, lo^ 16. 

Anaxagoras — makes aither = fire 
70^ 24, 02^ 4 ; explains immo- 
bility of earth by flatness 94^ 
14 ; his cosmogony 01* 11 ; his 
homoeomeries = elements 02* 
29 ; denies existence of void 09* 

19 ; referred to by implication 
69^ II, 74^ 19,89* 17, 97** 13- 

Anaximander — explains immobi- 
lity of earth by indifference 95^ 
10 ; referred to by implication 
98^ 33 ; reference doubted 03^ 

Anaximenes — explains immobility 
of earth by flatness 94^ 14; re- 

ferred to by implication 98^ 33, 
03^ 12. 

Animals — growth of, 70* 31 ; spa- 
tial oppositions in, 84^^ 11 ; phy- 
sical composition 8& 1 5 ; organs 
for movement 90* 30 ; compari- 
son with stars 90* 30, 92*^ i, 

Astronomy — A.'s conception of, 
91*30^ 21, 97* 4 ; astronomical 
records of Egypt and Babylon 
70^ 14, 92* 7. 

Atlas — not required 84* 20. 

Atoms — (of Democritus and Leu- 
cippus) dififer only in shape 75^ 
30, 03* 10 ; in perpetual move- 
ment 00^ 9 ; infinite in number 
03* 5 ; in conflict with fact 04* 
25, with matheniatics 03* 25. 
See also Democritus, Leucippus. 

Babylonians — their astronomical 

records 92^ 7, 70^ 14. 
Below — see Above. 

Category — 81* 32, 12* 14. 

Centre — of earth )( of universe 96^ 
10, 12* I ; goal of movement 
of heavy bodies 68^ 21, 69^ 23, 
76^ I, 97^ 5, 11^ 29; Pythago- 
rean view of 93* 20. See also 

Chance — 83* 32, 87^ 25, 89^ 23. 

Circles (or spheres)— solid revolv- 
ing bodies, composed of the 
primary body, in which the stars 
are fixed 89^ i, 92^ 26; also 
called ' heavens ' and * motions ' 

Coan (? Chian) throw — 92* 30. 
Coincidenceof predicates— 82* 30. 
Commensurability — of weights 

73^* 10 ; of bodies 04* 25 ; of 

diagonal 81* 5, ^7. 
Complete— defined 86^ 20 (cf. 71** 

31,. 68^). 


Continuum— 68^ 7, So* 20, 06^ 
24, 13^6. 

Contrary — c.s exist together and 
have same matter 86* 22 ; c.s 
essential to generation 70* 13 • 
c.s admit of intermediates 12" 
I ; examples, unnatural) (natu- 
ral movement 69* 9 + , upward )( 
downward movement 73* 7 + , 
hot )( cold 07^ 6, spatial 71* 26, 
87^ 6 ; c. relations between any 
two elements 86* 30 ; no c. to 
circular movement 70^ 31, to 
any figure 07^ 7. 

Counter-earth— supposed by Py- 
thagoreans 93* 25. 

Cyprus — 98* 4. 

Dfecay — see Generation. 

Democritus — supposes the uni- 
verse not continuous 75^ 30; 
explains immobility of earth by 
flatness 94^ 14 ; views in regard 
to movement 00^ 8, to elements 
03* 4, to generation 05* 35 ; 
makes the sphere a kind of 
angle 07* 17 ; his explanation 
of floating 13* 21 ; associated 
with Leucippus 75^ 30, 00^ 8, 
03* 4 ; referred to by implica- 
tion 77^' I (extrusion), 79^ 13 
(destructible world), 08^ 30 
(void). See also Atoms, Drive, 
Extrusion, Void. 

Dense-rare— 99^ 8, 03* 12, ^ 23. 

Differences— importance of study- 
ing 94^ 12 ; number limited 
03a I. 

Diminution— j-^f? Increase. 

Divination — = inspired guess 84^ 
5 ; uses opposition right )( left 

Divisibility — conditions of 68* 25, 
13^ 6 ; consequences of denial 
of 99* 17. 

Drive — term used by Democritus 

Duration — special name for the 
life of the universe, implying 
eternal existence 79* 23. 

Earth — (i) the element : moves 
naturally to the centre and rests 
there 69* 27, 86* 20, 95^ 20 + ; 
absolutely, not merely rela- 
tively, heavy li* 15; ace. to 
the theory of planes the only 

true element 06* 18.— (2) the 
central mass : its central posi- 
tion 93* 17 ; its immobility 93^ 
16, 94* 12, 96* 24; its spheri- 
cal shape 93^ 33, 97* 9, con- 
firmed by shadow on the moon 
97^ 25 ; its size 97^ 31 ; view of 
Pythagoreans (in motion about 
the centre) 93* 20 ; of Plato, 
Thnaeus (similar) 93^ 31, 96* 
24 ; of Xenophanes (infinite 
deeps) 94* 22 ; of Thales (floats 
on water) 94* 28 ; of Anaxime- 
nes, Anaxagoras, Democritus 
(immobile because of its flat- 
ness) 94^ 14 ; of Empedocles 
(immobile because of the vor- 
tex) 95* 15 ; of Anaximander 
(immobile because of its indif- 
ference) 95^ 10. 

Eclipse — of moon more frequent 
than of sun (Pythagoreans) 94^ 
23 ; of moon by earth gives 
curved outline 97"^ 25 ; of Mars 
(or Mercury ?) by moon 92* 4. 

Egypt — astronomical records of 
92* 7, 70^ 14 ; stars seen in 
98* 4. 

Elements — normally called ' sim- 
ple bodies ' 98* 30, 02^ 7, 06^ 
4 + ; specifically distinct parts 
68^ 5, 14; possess a principle 
of movement 68^ 28 ; three in 
number, 77^ 14, 98^ 8 ; their 
distinction depends on natural 
movements 76^ 8, 04^ 20, and 
places 77^ 14 (cf. 1 2^5 19). — 
(i) the primary body, substance 
of the outer heavens (Bks. I, 
II) : moves naturally in a circle 
69* 5, a sign of its perfection 
69* 16 ; neither light nor heavy 


not subject to genera- 

tion, increase, or alteration 70* 
12, 88* 34 ; not infinite 71^ i ff. ; 
its several movements 86* 3, 
89^ I, 91^ 30; why spherical 
86^ 10; direction of movement 
87^ 22 ; regularity of movement 
88* 14 ; substance of the stars 
89* 13 ; its movement the mea- 
sure of all movement 84* 2, 87* 
23. — (2) below the moon (Bks. 
Ill, IV): primary constituents 
of bodies 02* 1 1 ; four in num- 
ber (earth and fire, with two 
intermediates, water and air), 


but treated as two, 'jf' 14, 98*^ 
8 ; based on opposition light )( 
heavy 01^ 22, 07^ 28 ; their 
natural movement 00* 20, 10^ 
14; a passage to form, being, 
or actuality 10^ i, ii^^ 4; their 
serial character 10^ 11 ; dis- 
tinctive properties ii'^ 15 ; in- 
volve generation 70* 33, qS'^ 10, 
02* 10, 04^ 23 ; pass into one 
another 05^ 14; not infinite in 
number 02^ 10 ; nor reducible 
to one 03^ 14; not distinguish- 
able by size 04^ i ; nor by shape 
06^ 3. — Views of others : early 
thinkers 03^ 13 ; Anaxagoras 
02* 29; Empedocles 95^ 31, 
02* 30, 05^ I ; Leucippus and 
Democritus 03=^ 3 ; Plato, Ti- 
maeus 06^ i . 

Elephants— found in India and in 
N. Africa 98'^ 12. 

Empedocles— his views on the 
destructibility of the world 79^ 
15 ; on the immobility of the 
earth 84^ 24, 94^ 25, 95a 8, 30, 
00^ 2 ; on the elements 02* 29, 
^ 23, 05* 35 ; ignores opposition 
light ){ heavy 09^ 19 ; his prin- 
ciples 'Love' and 'Hate' 80^ 
16, 95a 31, oQb 29, oi* 16; 
quoted 94* 25 , 00^ 30. See also 
Vortex, Excretion. 

Excretion— process by which Em- 
pedocles accounts for the gene- 
ration of the elements 05^ I. 

Extrusion — forced motion of a 
body due to action of other 
bodies, a term used by ' some 
writers ' (Leucippus and Demo- 
critus ?) 'j']^ I. 

Form— opp. matter ']^^ i, 10^ 15, 
12* 12 ; Platonic 78* 16. 

P'ront-back- applied to universe 
84b 21, 88* 6. 

Generation— depends on inter- 
action of contraries 70* 15; 
hence excluded from sphere of 
the primary body 70* 19, 79^ 4, 
88* 34 ; necessity of, below the 
moon 70* 33, 98^ 10, 02^ 10; 
g. of elements from one another 
04^ 24, 05* 34 ; not absolute 
01^ 2 ; not admitted by Melis- 
sus and Parmenides 98^ 1 5. 

Geometry — construction in 79^ 35. 

God — as creative 71* 33 ; his ac- 
tivity eternal life 86* 9 ; popu- 
larly connected with the hea- 
vens 70^ 7, 84* 12 ; use of 
number 3 in worship of 68* 15. 

* Harmony of the spheres '—a Py- 
thagorean view, refuted 90^ 12. 

Hate — (in Empedocles) j^^ Love. 

Heaven — three senses distin- 
guished 78^ 10 ; sense {a) ' first * 
or 'outermost' h. 70^ 15, 88* 

5, 92" 22, 

24 (cp. 91* 35, 

91^2); 'fixed' h. 72^31;— sense 
{b) (including the planets) ani- 
mate 85* 29, Divine 86* 10, 
spherical ^10, eternal, 87^ 26 ; 
— sense {c) (=world, universe) 
90* 6, 98* 31, GO* 15, 01* 17, 
03^ 13, 08* 17; hemispheres 
85^ 10, 08* 26 ; includes all 
body, place, time, 76* 18, 'j^^ 
26,79^12. 5<?<?«/j<? Elements (17. 

Heavy-light — applied to bodies 
which move naturally towards 
and away from the centre 69^ 
20; imply a finite system 'j'^^^ 
22 ; not applicable to primary 
body 69^ 19, 76* 16; not ac- 
counted for by Empedocles 95* 
30 ; nor by the theory of planes 
99* 24 ; dist. absolute-relative 
08* 7 ; heavy the privative, 
light the positive term 86* 26. 

Heraclitus— on generation 79^ 15, 
98^ 30 ; referred to by implica- 
tion 03b 12 (cf. 04* 18). 

Hercules, Pillars of — 98* 11. 

Hesiod — on generation 98^28(cf. 
79^ 13). 

Hippasus— 03^ 12. 

Hippon— 03^ II. 

Homoeomeries — of Anaxagoras 
02* 31, 04* 26. 

Hydrarpax — name for water- 
clock in Simpl.'s day 94^ 21. 

Hypothesis— dist. false-impossi- 
ble 81^ 4. 

Waios — of Himera 03^ 13. 
Increase-diminution — 70* 23, 84^ 

28, 88^ 15, 10*27, 10^ 20. 
India — 98* 11. 

Indivisible lines — 99* 10, 07* 22. 
Infinite — not predicable of body 

71^ 2 ff. ; of weight 73* 22 ; of 


elements 03* 5 ; of process of 
analysis 04^ 28 ; not to be tra- 
versed co^ 4 ; as applied to line 
69* 22, 72^ 17 ; i. shapes, ace. 
to Democritus 03* 12. 

Intermediate — bodies (viz. air and 
water) 76^ i, 86* 29, 10^ 12, 
12^ 28 ; places (i.e. where these 
bodies rest) Ti^ 23, 12* 9; i. 
body cannot be primary 03^ 22 ; 
between contraries 12^ i. 

Ixion — 84* 35. 

Klepsydra— 94^* 22. 

Leucippus— conjoined with Demo- 
critus 75^ 30, 00^ 8, 03* 4 (cf. 
'j']^ 1 , 08^ 30). See also Demo- 

Light— i-^^ Heavy. 

'Like to like' — means matter to 
form 10^ I. 

Love-hate— opposed causal prin- 
ciples in cosmology of Empedo- 
cles 80* 16, 95* 31, 00^ 29, 01* 

Magnitude— complete in three 
dimensions 68* 9 ; simple, two 
only, viz. straight and circular 
line 68^ 19; minimum, impos- 
sible 71^ 10. 

Mars — (or Mercury?) eclipse of, 
by moon, observed by A. 92* 5. 

Mathematics — contributions of, to 
astronomy 91^ 9, 97* 4, 98* 16 ; 
admits no minimum 71^ 10 ; 
its principles finite 02^ 30; in 
conflict with the atomic theory 
03* 21 ; with the theory of 
planes 06* 28 ; the mathemati- 
cal the most accurate sciences 
06'^ 28. 

Melissus — and Parmenides de- 
nied generation 98^ 17. 

Minimum— no m. magnitude 71^ 
10 ; no m. time 74* 9 ; m. move- 
ment the measure ^'j^ 23 (cf. 


Missiles — movement of 88* 23, 
89* 23. 

Moon— phases 91^ 20; move- 
ments 91^ 35 ; so-called face 
90* 26. 

Motion— = circle {q.v.) to which 
stars are attached 79* 20, 92* ! 
14. I 

Movement — physics concerned 
with 68* 2, 08* I ; not present 
in all things 98^ 19; of three 
kinds, qualitative, quantitative, 
local 10* 23. 

— (i) local: belongs naturally to 
all bodies 68^ 15 ; finite in 
character 77* 17 ; dist. natural- 
constrained 76* 22, 94^ 32, GO* 
20 -f ; dist. simple-compound 
68^ 30, <X)* 20 -f ; kinds of 
simple m. 68^ 17; (i) circular 
70b 31, 77a 3^ 84a 4, 86^2 -h ; 
(ii) rectilinear 10* 14 + ; down- 
ward, goal of 96^ 7 ; * makes 
equal angles ' 96^ 20, 97^^ 19. 

— of heavens : variety 86* 3, 91^ 
29; direction 87^ 22; regu- 
larity 88* 14; w. ref. to stars 
89b I. 

—of animate things 84^ 32, 85* 
29 ; of spherical bodies 90* 9, 
91^ 15 ; as cause of fire 89*21. 

— (2) qualitative — see Alteration; 
* sense-m.' 84^ 29. 

— (3) quantitative — see Increase. 

— ' discussion of m.' = P/^ji-. V- 
VIII 73* 20, 75^ 23, 99* 10; 
' of time and m. ' 03* 23. 

Nature — as agent 68* 20, 71* 33, 
%^^ 3, 90* 30, 91* 25, b 14, 93a 
2 ; as form 86* 18, 01* 8 ; as 
source of movement 68'' 16, 01^ 
17 -f ; perfection of 88* 9 ; order 
of 03b 19; inquiry into 68* I, 
98^ I. 

Numbers— allotted to geometrical 
figures 86'' 34; compose the 
world, ace. to Pythagoreans co* 
15 ; the n. three 68* 15. 

Ocean— unity of 98* 10. 
Orpheus— cosmogony of 79*^ 13, 
98^ 27. 

Parmenides — and Melissus de- 
nied generation 98^ 17. 

Philosophy — first 'j'j^ 10 ; popular 

Physics of Aristotle — cited as 
' opening discussions ' 70* 17, 
11*12; Bks.I-IV cited as 'dis- 
cussion of principles ' 72* 30 n., 
74* 21; Bks. V-VIII as Mis- 
cussion of movement ' 72* 30, 
75^ 23, 99* 10; as * d. of time 


and m.' 03* 23 ; treated gener- 
ally as continuous vv. De Caelo 
73* 18, 85a 28, 86^ 20, 05a 22 + . 

Place — belongs to the perceptible 
75^ II ; contrarieties of 71* 5, 
26, 73* 12 ; proper or natural 
76* 12, 10^ 7 ; intermediate 'j'j^ 
23, 12* 9; w. ref. to void 09^ 
26 ; none outside the heaven 
79* 12. 

Planes, theory of— 86^ 27, 98^ 33, 

Planets — secondary revolution of 
85^ 29, 91^ I ; absence of twink- 
ling 90* 19. See also Heaven, 

Plato— (not mentioned by name) 
his Timaetcs cited 80* 30, 93^ 
32, 00* 1,^17, 06^ 19, 08^ 4. 

Poles— 85^ 10, 93^ 32, 96^ 27. 

Possibility — notion of, examined 
81* I, 83^ 8; no unrealized p. 
83^ 25. 

Principle— m logical sense 71^ 12, 
02^ 27,03a 18, 06* 7 ; structur- 
al, in animals 84^ 11, 85^ 20; 
in geometrical figures 03^2 ; of 
movement 68^ 16, 84^ 32, 85* 
29, ^7; 'discussion of p.s' = 
Phys. I-IV 74* 21 (cf. 72* 30 n.). 

Privation— 86* 26. 

Pyramid — 03* 32, 04* 12, ^4, 06^ 

Pythagoreans — on the number 
three 68* 11 ; on right and left 
in the heaven 84^ 7 ; on the 
hemispheres 85^ 26; on the 
motion of the earth 93* 20 ; 
their 'counter-earth' 93* 25, 
^ 20 ; ' Guard-house of Zeus ' 
93^ 4 ; compose the world of 
numbers 00* 15 ; cf. also 90^ 15 
(' harmony of the spheres '). 

Right-left— applied to universe 
84^ 6; motion of first heaven 
starts from right and moves to 
right 85^ 17; right prior to left 
88* 6. 

Rolling — a motion appropriate to 
a sphere 90* 10 

Sense-movement — 84^ 29. 

Sound — said to be unheard if con- 
tinuous 90^ 27 ; has physical . 
effects 90^ 34. 

Spheres — the primary shape 86^ 

10; suited only to movement 
in one place 90*^ 2 ; its proper 
movements 90* 10 ; spherical 
I shape of universe 87^ 15, 90^ i ; 
j of stars 90* 8, ^i, 91^ 10; of 
j the earth 97'' 21 ; of surface of 
water 87^ i ; (supposed) of par- 
ticles of fire 06'' 33 ; ' harmony 
of the s.s' 90^ 12. See also 
I Circles. 

Spinning — a motion appropriate 

j to a sphere 90* 10. 

I Stars — composition, 89* 15 ; car- 

i ried on moving spheres 89* 29, 

j ^ 31 ; distances 91* 30 ; speed 

I of motion 91* 33 ; shape 91^ 10; 

distribution 92* 10 ; number of 

\ movements 91^ 30 ; unchang- 

I ing intervals 88*^ 10, 96^ 4; 

j twinkl ing (dist. planets ) 90* 1 8 ; 

seen differently in. different 

couiTtries 97^ 31 ; comparison 

with animals 90* 30, 92^ i, 93*^ 6. 

! Substrate— 70* 16,06* 17. 

i Sun— its heat 89* 32 ; apparent 

spinning motion 90* 1 5 ; eclipses 

I of, by moon 91^ 23 ; number of 

' movements 92* i ; distance 


Suspension — of triangles 06* 22. 

Text — (basis Prantl, 1881) (i) con- 
jectures adopted or suggested 
72** 17, 80^ 18, 81* I, 7, 83* 29, 
92^ II, 95* 22, 99^ 19, 01^ 19, 
04* 28, 12* 10. 

— (2) alterations of punctuation 
68*24,73^25,74*5, II, 76^17, 
T]"" 16, 18, 78'' 15, 79^ 22, 26, 
80*30, ^28, 81^ 29, 82* 12, 26, 
83* 14, 24, 29,^9,21,89*2,23, 
92^3, 13, 93^ 18, 95* 10, ^33, 
01* 19, ^ 23, 05* 28, 06^ 17, 08'' 
6, 15, 10^ I, 11^ 14, 12* 24 ^25, 

— (3) misprints corrected 76* 5, 
18, ^^^ 32, ^27, 78b 16, 79^ 6, 
80* 29, 81* 16, 83*^ 21, 84b 20, 
86^ 28, 91* 22, 29, 95^ 15, 06^ 
32, 07* 8, 21, 10* 20, 12* 33, 

13* II- 
— (4) other alterations 68* 22, 
^ 25, 69* 7, 23, 28, ^ 21, 26, 70* 
23,71*29,^5, 19,30,33,72^ I, 
73* 16, 74* 22, ^5, 32, 75* 10, 
81^ 18, 21, 33, 83» 17, ^5, 7, 


84V, 30,86^1, 19, 87^27, ^34, 
88^ 10, 26, 89^ 28, 92^ 4, 93b 

28, 94^ 20, 95b 4, 991^ 22, 28, 32, 

01^ 9, ^ 15, 20, 02» 2, 12, 03* 2, 
04a 16,^ 27, 06^ 15, 28, 08* I, 

24, 32, o9'> 20, 25, lo^ 7, 31, 
^12, 16, iia 3, 6, bi6, 26, 29, 

12^ 17, 13* 23. 

— (5) other comments 68* 19, 70* 
26, 71* 24, 72^ 14, *M8, 28, 76* 
30, 77* 2,29, 31,78* 20, 80^20, 

29, 83* 26, 85* 7, 88* 6, 92* 26, 
29, 93*24. ^31,96*26,97* 34, 
99* 19, 01^ 17, 31, 05* 17, 07* 
17, 08^ 31, 10* 3, ^22. 

Thales — said earth rests upon 

water 94* 28 ; referred to by 

implication 03*^ II. 
Three— mystical significance of 

the number 68* 15. 
Thunder — spHts rocks by its noise 

90b 35. 
Time — inconceivable outside the 

heaven 79* 14 ; no minimum t. 

74* 9 ; every performance has 

its minimum t. 88^ 32. 
Transverse — in the universe, def. 

85^ 12. 
Triangle — constituent of bodies, 

in the Timaeus 08^ 15, 09^ 34 ; 

its Pythagorean number 87* i. 

Vegetables — liable to increase 70* 
33 : compared with lower stars 
92^ 2. .^.^^tyoa 

Visual ray— 90* 17. 

Void — supposed by Leucippus and 
Democritus to account for 
movement 00'^ 10; cannot be 
the matter of things, either alone 
12^ 21, or with plenum 13* i : 
extra-corporeal, impossible 02* 
1,05* 17; intra-corporeal, as 
cause of lightness 09* 6, 11^ i ; 
as explaining expansion, 05^ 1 7 ; 
no V. outside the heaven 79* 12 
(cf. Z']^ 15) ; has no natural 
movement 09^ 18 (cf. 13* i). 

Vortex (or Whirl) — supposed by 
Empedocles 84* 24, 95* 8, 00^ 3. 

Water — moves downward 69* 1 8 ; 
proof that its surface is spheri- 
cal 87^ I ; supposed by Thales 
to support the earth 94* 28 ; to 
be the one element 03*5 1 1. See 
also Intermediate. 

Water-clock -94^ 22. 

Xenocrates- possibly referred to 

79^ 33, 98^' 33- 
Xenophanes — cited 94* 22. 

INDEX II. Greek 

[The reference is to the foot-note in which the word is cited.] 

avTaKokovfln 82* 30. 
dTroXeXrfieVo? lO^ 33. 
d1daTr1iJ.11 71^ 31. 
8iopi(€iv 01^ 17. 
dCpaixis 81* 7. 
eyKVKkios 86* 12. 
€K(TTaaLS 86* 20. 
e^(OT€piKo\ }.6yoL 79* 31 

tWeadtu 93b 31. 

KC!VI(T19 92* 26. 
KOfffiOS 72'* 20. 

oiJLOiOTrjs 95'^ II. 
oyj/'LS 90* 17. 
TrXrjyii 89* 28. 
crii'y;Ccopfii/ 97* 12. 
(fiopa 92* 14. 




'• ( 










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This translation has been made from a revised text, 
which is now being published for me by the Delegates of 
the Clarendon Press as part of an edition of Aristotle's 
Trept yevia^oas Kai cf)dopas. I have indicated in a few brief 
footnotes the chief passages in which the readings I have 
adopted differ from those of Bekker ; a full explanation, 
and a defence of my interpretation in detail, will be found 
in my edition. 

To Mr. W. D. Ross, Fellow of Oriel College, I am 
greatly indebted for many most valuable criticisms and 
suggestions. The references in the footnotes to Burnet are 
to the third edition of that author's Early Greek Philosophy 
(London, 19:^0) ; and the references to Diels are to the 
second edition oi Die Fragmente der Vorsokratiker (Berlin, 

H. H. J. 



cc. 1-5. Coming-to-be and passing-away are distinguished fro7n 
' alteration ' and from growth and diminution. 


1. Are coming-to-be and passing-away distinct from 'alteration*? 

It is clear that, amongst the ancient philosophers, the monists 
are logically bound to identify, and the pluralists to distinguish, 
these changes. Hence both Anaxagoras and Empedokles (who 
are pluralists) are inconsistent in their statements on this subject. 
Empedokles, it must be added, is inconsistent and obscure in 
many other respects as well. 

2. There are no indivisible magnitudes. Nevertheless, coming-to-be 

and passing-away may well occur and be distinct from * altera- 
tion *. For coming-to-be is not effected by the ' association ' of 
discrete constituents, nor passing-away by their ' dissociation ' ; 
and ' change in what is continuous ' is not always ' alteration '. 

3. Coming-to-be and passing-away (in the strict or ' unqualified ' 

sense of the terms) are in fact always occurring in Nature. Their 
ceaseless occurrence is made possible by the character of 
Matter [materia prima), 

4. ' Alteration ' is change of quality. It is thus essentially distinct 

from coming-to-be and passing-away, which are changes of 

5. Definition and explanation of growth and diminution. 

cc. 6-10. What comes-to-be is formed out of certain material con- 
stituents, by their Uo7nbination\ Combination implies * action 
and passion ', which in turn imply * contact \ 

6. Definition and explanation of 'contact'. 

7. Agent and patient are neither absolutely identical with, nor sheerly 

other than, one another. They must be contrasted species of 
the same genus, opposed formations of the same matter. 

8. Bodies do not consist of indivisible solids with void interspaces, 

as the Atomists maintain : nor are there ' pores ' or empty 
channels running through them, as Empedokles supposes. 
Neither of these theories could account for 'action-passion'. 

9. The true explanation of ' action-passion ' depends (a) upon the 

distinction between a body's actual and potential possession of 
a quality, and {b) upon the fact that potential possession (i.e. 
'susceptibility') may vary in intensity or degree in different 
parts of the body. 
10. What ' combination ' is, and how it can take place. 



cc- 1-8. The tnaterial constituents of all that comes-to-be and 
passes-away are the so-called ' elements \ i. e, the * simple ' bodies. 
What these are, how they are transformed into one another, and 
how they ^combine \ 


1. Earth, Air, Fire, and Water are not really * elements ' of body, but 

* simple ' bodies. The ' elements ' of body are ' primary matter ' 
and certain * contrarieties '. 

2. The * contrarieties' in question are 'the hot and the cold' and 

' the dry and the moist '. 

3. These four ' elementary qualities ' (hot, cold, dry, moist) are 

diversely coupled so as to constitute four ' simple ' bodies 
analogous to, but purer than, Earth, Air, Fire, and Water. 

4. The four ' simple ' bodies undergo reciprocal transformation in 

various manners. 

5. Restatement and confirmation of the preceding doctrine. 

6. Empedokles maintains that his four * elements ' cannot be trans- 

formed into one another. How then can they "be 'equal' 
(i.e. comparable) as he asserts? His whole theory, indeed, is 
thoroughly unsatisfactory. In particular, he entirely fails to 
explain how compounds (e. g. bone or flesh) come-to-be out of 
his ' elements '. 

7. How the ' simple ' bodies combine to form compounds. 

8. Every compound body requires all four 'simple' bodies as its 


cc. 9-10. The causes of coming-to-be and passing-away. 

9. Material, formal, and final causes of coming-to-be and passing- 
away. The failure of earlier theories — e. g. of the * materialist ' 
theory and of the theory advanced by Sokrates in the Phaedo — 
must be ascribed to inadequate recognition of the efficient cause. 

10. The sun's annual movement in the echptic or zodiac circle is the 

efficient cause of coming-to-be and passing-away. It explains 
the occurrence of these changes and their ceaseless alternation. 


11. In what sense, and under what conditions, the things which 

come-to-be are ' necessary '. Absolute necessity characterizes 
every sequence of transformations which is cyclical. 



I Our next task is to study coming-to-be and passing- 314^ 
away. We are to distinguish the causes, and to state the 
definitions, of these processes considered in general — as 
changes predicable uniformly of all the things that come-to- 
be and pass-away by nature. Further, we are to study 
growth and 'alteration'. We must inquire what each of 
them is ; and whether * alteration ' is to be identified with 5 
coming-to-be, or whether to these different names there 
correspond two separate processes with distinct natures. 

. On this question, indeed, the early philosophers are 
divided. Some of them assert that the so-called ' unqualified 
coming-to-be ' is ' alteration ', while others maintain that 
* alteration ' and coming-to-be are distinct. For those who 
say that the universe is one something (i. e. those who 
generate all things out of one thing) are bound to assert 
that coming-to-be is ' alteration ', and that whatever ' comes- 10 
to-be ' in the proper sense of the term is ' being altered ' : 
but those who make the matter of things more than one 
must distinguish coming-to-be from ' alteration '. To this 
latter class belong Empedokles, Anaxagoras, and Leukippos. 
And yet Anaxagoras himself failed to understand his own 
utterance. He says^ at all events, that coming-to-be and 
passing-away are the same as ' being altered ' : ^ yet, in 15 
common with other thinkers, he affirms that the elements 
are many. Thus Empedokles holds that the corporeal 
elements are four, while all the elements — including those 
which initiate movement— are six in number; whereas 

^ Cf. fr. 17 (Diels, pp. 320-1). 

645.18 B 


Anaxagoras agrees with Leukippos and Demokritos that 
the elements are infinite. 

(Anaxagoras posits as elements the * homoeomeries ', viz. 

ao bone, flesh, marrow, and everything else which is such that 
part and whole are the same in name and nature ; while 
Demokritos and Leukippos say that there are indivisible 
bodies, infinite both in number and in the varieties of their 
shapes, of which everything else is composed — the com- 
pounds differing one from another according to the shapes, 
' positions ', and * groupings ' of their constituents.) 

25 For the views of the school of Anaxagoras seem diamet- 
rically opposed to those of the followers of Empedokles. 
Empedokles says that Fire, Water, Air, and Earth are four 
elements, and are thus * simple ' rather than flesh, bone, and 
bodies which, like these, are ' homoeomeries '. But the 
followers of Anaxagoras regard the ' homoeomeries ' as 
* simple ' and elements, whilst they affirm that Earth, Fire, 
Water, and Air are composite ; for each of these is (accord- 
314* ing to them) a * common seminary ' of all the ' homoeo- 
meries '.^ 

Those, then, who construct all things out of a single 
element, must maintain that coming-to-be and passing- 
away are 'alteration '. For they must affirm that the under- 
lying something always remains identical and one ; and 
change of gnrVi ^ s^z/jc/f-f^/^/pf i<; wY^ ^t w^ r^ll ^alterinor *. 
Those, on the other hand, who make the ultimate kinds of 
5 things more than one, must maintain that ' alteration ' is 
distinct from coming-to-be : for coming-to-be and passing- 
away result from the consilience and the dissolution of the 
many kinds. That is why Empedokles too ^ uses language 
to this effect, when he says ' There is no coming-to-be of 
anything, but only a mingling and a divorce of what has 
been mingled '.^ Thus it is clear (i) that to describe coming- 

^ Aristotle's point (from 314*11 to 314^1) is that Anaxagoras, 
Empedokles, Leukippos, and Demokritos are all pluralists, and there- 
fore logically bound (whatever they may say) to distinguish coming-to- 
be and 'alteration'. They are all pluralists, though their theories 
differ, and though the theory of Anaxagoras is actually ' contrary ' to 
that of Empedokles. ^m- 

^ i. e. as well as Anaxagoras : cf. above, 314* 13-15- ^^^ 

^ Cf. fr. 8 (Diels, p. 175), and the paraphrase in MXG 975*36-^1! 


BOOK I. I 314* 

to-be and passing-away in these terms is in accordance 
with their fundamental assumption, and (ii) that they do in 10 
fact so describe them : nevertheless, they too ^ must recog- 
nize * alteration ' as a fact distinj;^i_Jmm ^^mi"g-^^-^^i 

though it is impossible for them to do so consistently with 
what they say. 

That we are right in this criticism is easy to perceive. 
For ' alteration ' is a fact of observation. While the sub- ' 

stance of the thing remains unchanged, we see it ' altering ' 
just as we see in it the changes of magnitude called ' growth ' 15 
and ' diminution '. Nevertheless, the statements of those 
who posit more ' original reals ' than one make ' alteration ' 
impossible. For ' alteration ', as we assert, takes place in 
respect to certain qualities ; and these qualities (I mean, 
e. g., hot-cold, white-black, dry-moist, soft-hard, and so 
forth) are, all of them, differences characterizing the 20 
' elements \ The actual words of Empedokles may be 
quoted in illustration — 

The sun everywhere bright to see, and hot ; 
The rain everywhere dark and cold ; ^ 

and he distinctively characterizes his remaining elements in 

a similar manner. Since, therefore, it is not possible ^ for 

Fire to become Water, or Water to become Earth, neither 

will it be possible for anything white to become black, or 

anything soft to become hard ; and the same argument 25 

applies to all the other qualities. Yet this is what 'alteration' 

essentially is. 

It follows, as an obvious corollary, that a jingi£_iiiaitej* 

must always be assumed as iinHpi-jying ^^^ /^^ntrary < pojfg ' 

of any change — whether change of place, or growth and 

diminution, or * alteration ' ; further, that the being of this 

matter and the being of ' alteration ' stand and fall together. 

For if the change is ' alteration ', then the substratiim is 315^ 

a single element,: i. e. all things which admit of change 

i nto one another have a single matter . And, conversely, if 

the substratum of the changing things is one, there is 

' alteration '. 

* i.e. as well as ordinary people : cf. ^ 13 ff. 
2 Cf. fr. 21, 11. 3 and 5 (Dials, p. 180). 
' i. e. according to Empedokles. 

B 2 


Empedokles, indeed, seems to contradict his own state- 
5 ments as well as the observed facts. For he denies that any 
one of his elements comes-to-be out of any other, insisting 
on the contrary that they are the things out of which every- 
thing else comes-to-be ; and yet (having brought the 
entirety of existing things, except Strife, together into one) 
he maintains, simultaneously with this denial, that each 
thing once more comes-to-be out of the One. Hence it was 
clearly out of a One that this came-to-be Water, and that 

ro Fire, various portions of it being separated off by certain 
characteristic differences or qualities — as indeed he calls the 
sun * white and hot ', and the earth * heavy and hard *. If, 
therefore, these characteristic differences be taken away (for 
they can be taken away, since they came-to-be), it will 
clearly be inevitable for PZarth to come-to-be out of Water 
and Water out of Earth, and for each of the other elements 
to undergo a similar transformation — not only then^ but 

15 also now — if, and because, they change their qualities. And, 
to judge by what he says, the qualities are such that they 
can be ' attached ' to things and can again be ' separated ' 
from them, especially since Strife and Love are still fighting 
with one another for the mastery. It was owing to this 
same conflict that the elements were generated from a One 
at the former period. I say * generated \ for presumably 
Fire, Earth, and Water had no distinctive existence at all 
while merged in one. 

There is another obscurity in the theory of Empedokles. 

20 Are we to regard the One as his ' original real ' ? Or is it 
the Many — i. e. Fire and Earth, and the bodies co-ordinate 
with these ? For the One is an ' element ' in so far as it 
underlies the process as matter — as that out of which Earth 
and Fire come-to-be through a change of qualities due to 
' the motion '.^ On the other hand, in so far as the One 
results from composition (by a consilience of the Many), 
whereas they result from disintegration ^ the Many are more 

25 * elementary ' than the One, and prior to it in their nature. 

^ i. e. at the period when Empedokles himself appears to recognize 
that his ' elements ' come-to-be. 

M. e, the motion of dissociation initiated by Strife. 

BOOK I. 2 . 315* 

2 We have therefore to discuss the whole subject of ' un- 
qualified ' coming-to-be and passing-avvay ; we have to 
inquire whether these changes do or do not occur and, if 
they occur, to explain the precise conditions of their occur- 
rence. We must also discuss the remaining forms of change, 
viz. growth and 'alteration '. For though, no doubt, Plato 
investigated the conditions under which things come-to-be 
and pass-away, he confined his inquiry to these changes ; 30 
and he discussed notW/ coming-to-be, but only that of the 
elements. He asked no questions as to how flesh or bones, 
or any of the other similar compound things, come-to-be ; 
nor again did he examine the conditions under which 
* alteration ' or growth are attributable to things. 

A similar criticism applies to all our predecessors with 
the single exception of Demokritos. Not one of them pene- 35 
trated below the surface or made a thorough examination 
of a single one of the problems. Demokritos, however, 
does seem not only to have thought carefully about all the 
problems, but also to be distinguished from the outset by 3^5 
his method. For, as we are saying, none of the other philo- 
sophers made any definite statement about growth, except 
such as any amateur might have made. They said that 
things grow 'by the accession of like to like', but they did 
not proceed to explain the manner of this accession. Nor 
did they give any account of * combination ' : and they neg- 
lected almost every single one of the remaining problems, 
offering no explanation, e. g., of ' action ' or ' passion ' — how 5 
in physical actions one thing acts and the other undergoes 
action. Demokritos and Leukippos, however, postulate the 
'figures', and make 'alteration' and coming-to-be result 
from them. They explain coming-to-be and passing-avvay 
by their ' dissociation ' and ' association ', but ' alteration ' 
by their ' grouping ' and ' position '. And since they thought 
that the truth lay in the appearance, and the appearances 10 
are conflicting and infinitely many, they made the ' figures ' 
infinite ^n number.^ Hence — owing to the changes of the 
compound — the same thing seems different and conflicting 
to different people : it is ' transposed ' by a small additional 
^ And in variety of shape also: cf. above, 3i4'*22-3. 



ingredient, and appears utterly other by the * transposition ' 
15 of a single constituent. For Tragedy and Comedy are both 
composed of tAe same letters. 

Since almost all our predecessors think (i) that coming- 
■"^^^ to-be is distinct from 'alteration', and (ii) that, whereas 
things ' alter * by change of their qualities, it is by * asso- 1 
elation ' and ' dissociation ' that they come-to-be and pass- 
away, we must concentrate our attention on these theses. 
For they lead to many perplexing and well-grounded 
20 dilemmas. If, on the one hand, coming-to-be is * association ', 
many impossible consequences result : and yet there are 
other arguments, not easy to unravel, which force the con- 
clusion upon us that coming-to-be cannot possibly be any- 
thing else. If, on the other hand, coming-to-be is not 
' association ', either there is no such thing as coming-to-be 
at all or it is ' alteration ' : or else ^ we must endeavour to 
unravel this dilemma too — and a stubborn one we shall 
find it. 

The fundamental question, in dealing with all these difii- 
culties, is this: 'Do things come-to-be and "alter 'J and 


nitude indivisible ? ' For the answer we give to this question 
makes the greatest difference. And again, if the primary 
' reals ' are indivisible magnitudes, are these bodies^ as Demo- 
kritos and Leukippos maintain ? Or are they plmtes, as is 
asserted in the Timaeus} 

To resolve bodies into planes and no further — this, as 
we have also remarked elsewhere,^ is in itself a paradox. 
Hence there is more to be said for the view that there are 
indivisible bodies. Yet even these inVolve much of paradox. 
Still, as we have said, it is possible to construct ' alteration ' 
35 and coming-to-be with them, if one ' transj^oses ' the same 
315a by ' turning ' and ' intercontact ', and by ' the varieties of the 
figures ', as Demokritos does. (His denial of the reality of 
colour is a corollary from this position : for, according to 

^ i.e. if we still wish to maintain that coming-to-be (though it 
actually occurs and is distinct from ' alteration ') is not * association '. 
^ Cf. e. g. de Caelo 299^ 6- 1 1 . 

niies, IS rnis : uo mmgs come-to-oe ana * alter ana 
•ow, and undergo the contrary changes, vbecause )the 
'imary 'Vf^j^'^aTpJn(^ jvi.qih]e m^ j pr nfiides ? , Or is no mag- 



BOOK I. 2 316* 

him, things get coloured by ' turning ' of the ' figures '.) But 
the possibility of such a construction no longer exists for 
those who divide bodies into planes. For nothing except 
solids results from putting planes together: they do not 
even attempt to generate any quality from them. 

Lack of experience diminishes our power of taking 5 
a comprehensive view of the admitted facts. Hence those 
who dwell in intimate association with nature and its 
phenomena grow more and more able to formulate, as the 
foundations of their theories, principles such as to admit of 
a wide and coherent development : while those whom 
devotion to abstract discussions has rendered unobservant 
of the facts are too ready to dogmatize on the basis of a few 10 
observations. The rival treatments of the subject now 
before us will serve to illustrate how great is the difference 
between a ' scientific ' and a ' dialectical ' method of in- 
quiry. For, whereas the Platonists argue that there must 
be atomic magnitudes * because otherwise " The Triangle *' 
will be more than one ', Demokritos would appear to have 
been convinced by arguments appropriate to the subject, 
i.e. drawn from the science of nature. Our meaning will 
become clear as we proceed. 

For to suppose that a body (i. e. a magnitude) is divisible 15 
through and through, and that this division is possible, 
involves a difficulty. What will there be in the body which 
escapes the division ? 

If it is divisible through and through, and if this division 
is possible, then it might be^ at one and the same moment, 
divided through and through, even though the dividings 
had not been effected simultaneously : and the actual 
occurrence of this result would involve no impossibility. 
Hence the same principle will apply whenever a body is 20 
by nature divisible through and through, whether by 
bisection,^ or generally by any method whatever : nothing 
impossible will have resulted if it has actually been divided — 
not even if it has been divided into innumerable parts, 
themselves divided innumerable times. Nothing impossible 

^ i. e. by progressive bisection ad infinitum. 


will have resulted, though perhaps nobody in fact could so 
divide it. 

Since, therefore, the body is divisible through and 
through, let it have been divided. What, then, will remain ? 
A magnitude ? No : that is impossible, since then there 

25 will be something not divided, whereas ex hypothesi the 
body was divisible through and through. But if it be 
admitted that neither a body nor a magnitude will remain, 
and yet division ^ is to take place, the constituents of the 
body will either be points (i.e. without magnitude) or 
absolutely nothing. If its constituents are nothings, then 
it might both come-to-be out of nothings and exist as 
a composite of nothings : and thus presumably the whole 
body will be nothing but an appearance. But if it consists 

30 of points, a similar absurdity will result : it will not possess 
any magnitude. For when the points were in contact and 
coincided to form a, single magnitude, they did not make 
the whole any bigger (since, when the body was divided 
into two or more parts, the whole ^ was not a bit smaller or 
bigger than it was before the division) : hence, even if all 
the points^ be put together, they will not make any 

But suppose that, as the body is being divided, a minute 
316^ section — a piece of sawdust, as it were — is extracted, and 
that in this sense a body * comes away' from the magnitude, 
evading the division. Even then the same ^ argument 
applies. For in what sense is that sectief^ divisible ? But if 
what ' came away ' was not a body but a separable form or 
quality, and if the magnitude is ' points or contacts thus 
5 qualified ' : it is paradoxical that a magnitude should 
consist of elements which are not magnitudes. Moreover, 
where will the points be ? And are they motionless or 
moving? And every contact is always a contact of two 
somethings, i. e. there is always something besides the 
contact or the division or the point. 

^ i.e.* through and through ' division. 
^ i. e. the sum of the now separated parts. 

' i. e. all the points into which the body has been dissolved by the 
* through and through ' division. 
* Cf. above, 316*24-5. 

BOOK I. 2 316^ 

These, then, are the difficulties resulting from the 
supposition that any and every body, whatever its size, 
is divisible through and through. There is, besides, this 
further consideration. If, having divided a piece of wood 10 
or anything else, I put it together, it is again equal to what 
it was, and is one. Clearly this is so, whatever the point 
at which I cut the wood. The wood, therefore, has been 
divided potentially through and through. What, then, is 
there in the wood besides the division? For even if we 
suppose there is some quality, yet how is the wood 
dissolved into such constituents ^ and how does it come-to- 
be out of them ? Or how are such constituents separated so 
as to exist apart from one another ? 

Since, therefore, it is impossible for magnitudes to 15 
consist of contacts or points, there must be indivisible 
bodies and magnitudes. Yet, if we do po^s^iilate the latter, 
we are confronted with equally impossible consequences, 
which we have examined in other works.^ But we must try 
to disentangle these perplexities, and must therefore formu- 
late the whole problem over again. 

On the one hand, then, it is in no way paradoxical that 20 
every perceptible body should be indivisible as well as . 
divisible at any and every point. For the second predicate 
will attach to it potentially ^ but the first actually. On the 
other hand, it would seem to be impossible for a body to 
be, even potentially, divisible at all points simultaneously. 
For if it were possible, then it might actually occur, with 
the result, not that the body would simultaneously be 
actually both (indivisible and divided), but that it would 
be simultaneously divided at any and every point. Con- 25 
sequently, nothing will remain and the body will have 
passed-away into what is incorporeal : and so it might 
come-to-be again either out of points or absolutely out of 
nothing. And how is that possible ? 

But now it is obvious that a body is in fact divided into 
sepa rable ip agfnitudes which are smaller at each division — 
into magnitudes which fall apart from one another and are 

* i. e. points-of-division and quality. 

^ Cf. Physics 231^ 21 ff. ; de Caelo 3038' 3 ff. ; de Lin, Insec. 969^ 29 ff. 


actually separated. Hence (it is urged) the process of 
30 dividing a body part by part is not a ' breaking up ' which 
could continue ad infinitum ; nor can a body be simul- 
taneously divided at every point, for that is not possible ; 
but there is a Jimit, beyond which the ' breaking up ' can- 
not proceed. The necessary consequence — especially if 
coming-to-be and passing-away are to take place by 
' association ' and ' dissociation ' respectively — is that a 
body ^ must contain atomic magnitudes which are invisible. 
317* Such is the argument which is believed to establish the 
necessity of atomic magnitudes : we must now show that it 
conceals a faulty inference, and exactly where it conceals it. 
For, since point is not ' immediately-next ' to point, 
magnitudes are ' divisible through and through ' in one 
sense, and yet not in another. When, however, it is ad- 
5 mitted that a magnitude is ' divisible through and through ', 
it is thought there is a point not only anywhere, but also 
everywhere, in it : hence it is supposed to follow, from the 
admission, that the magnitude must be divided away into 
nothing. For — it is supposed — there is a point everywhere 
within it, so that it consists either of contacts or of points. 
But it is only in one sense that the magnitude is ' divisible 
through and through', viz. in so far as there is one point 
anywhere within it and all its points are everywhere within it 
if you take them singly one by one. But there are not 
more points than one anywhere within it, for the points are 
not * consecutive ' : hence it is not simultaneously * divisible 
10 through and through '. For if it were, then, if it be 
divisible at its centre, it will be divisible also at a point 
* immediately-next' to its centre. But it is not so divisible: 
for position is not 'immediately-next' to position, nor point 
to point — in other words, division is not ' immediately- 
next ' to division, nor composition to composition. 

Hence there are both ' association ' and * dissociation ', 

though neither (a) into, and out of, atomic magnitudes (for 

15 that involves many impossibilities), nor {b) so that division 

takes place through and through — for tlys would have 

resulted only if point had been ' immediately-next ' to 

* i.e. every perceptible body : cf. above, 316^21. 

BOOK I. 2 317 

point : but * dissociation ' takes place into small (i. e. re- 
latively small) parts, and ' association ' takes place out of 
relatively small parts. 

It is wrong, however, to suppose, as some assert, that 
coming-to-be and passing-away in the unqualified and 
complete sense are distinctively defined by ' association ' 
and ' dissociation ', while the change that takes place in 
what is continuous is ' alteration '. On the contrary, this is 
where the whole error lies. For unqualified coming-to-be 20 
and passing-away are not effected by * association ' and 
'dissociation'. They take place when a thing changes, \ 
from tjiis to that, as a whole. But the philosophers we I 
are criticizing suppose that all such change ^ is ' alteration ' : 
whereas in fact there is a difference. For in that which 
underlies the c hange there is a fftc^nr ror^f^spnndin ^ to the 
de finit ion - and there is a material factor. When, then, the 25 
change is in thes qf constitutive factors Ahere will be coming- 
to-be or passing-away : but when it is in the thing's 
qualities, i. e. a change of the thing per accidens^ there will 
be ' alteration '. 

' Dissociation ' and ' association ' affect the thing's sus- 
ceptibility to passing-away. For if water has first been 
' dissociated ' into smallish drops, air comes-to-be out of it 
more quickly : while, if drops of water have first been 
' associated ', air comes-to-be more slowly. Our doctrine 
will become clearer in the sequel.^ Meantime, so much 30 
may be taken as established — viz. that coming-to-be 
cannot be * association ', at least not the kind of * associa- 
tion ' some philosophers assert it to be. 

3 Now that we have established the preceding distinctions, 
we must first* consider whether there is anything which 
comes-to-be and passes-away in the unqualified sense : or 
whether nothing comes-to-be in this strict sense, but 
everything always comes-to-be something and oiit of some- 
thing — I mean, e. g., comes-to-be-healthy out of being-ill 35 

* i. e. all change ' in what is continuous '. 
"^ i.e. a * formal' factor. 

» Cf. 328*23 ff. 

* The second main topic of investigation is formulated below, 


and ill out of being-healthy, comes-to-be-small out of being- 

317^ big and big out of being-small, and so on in every other 

instance. For if there is to be coming-to-be without 

. qualification, 'something' must — without qualification — 

* come-to-be out of not-being ', so that it would be true to 
say that * not-being is an attribute of some things '. For 
gtmli/ied com'mg-to-he is a process out of qualified not-being 

5 (e. g. out of not-white or not-beautiful), but unqicalified 
coming-to-be is a process out of unqualified not-being. 

Now ' unqualified' means either (i) the primary predica- 
tion within each Category, or (ii) the universal, i. e. the all- 
comprehensive, predication. Hence, if ' unqualified not- 
being ' means the negation of ' being ' in the sense of the 
primary term of the Category in question, we shall have, in 

* unqualified coming-to-be ', a coming-to-be of a substance 
out of not-substance. But that which is not a substance or 
a * this ' clearly cannot possess predicates drawn from any 

10 of the other Categories either — e.g. we cannot attribute to 
it any quality, quantity, or position. Otherwise, properties 
would admit of existence in separation from substances. 
If, on the other hand, ' unqualified not-being' means 'what 
is not in any sense at all ', it will be a universal negation of 
all forms of being, so that what comes-to-be will have to 
come-to-be out of nothing. 

Although we have dealt with these problems at greater 

length in another work,^ where we have set forth the 

difficulties and established the distinguishing definitions, the 

15 following concise restatement of our results must here be 

offered : — 

In one sense things come-to-be out of that which has no 
' h^ing ' without qualification : yet in another sense they 
come-to-be always o ut of 'what is'. For coming-to-be 
necessarily implies the pre-existence of soinething which 
potentially ' is ', but actually ' is not ' ; and this something is 
spoken of both as ' being ' and as ' not-being '. 

These distinctions may be taken as established : but even 
then it is extraordinarily difficult to see how there can be 
' unqualified coming-to-be ' (whether we suppose it to occur 
* Physics A. 6-9. 

BOOK I. 3 317 

out of what potentially ' is \ or in some other way), and we 20 
must recall this problem for further examination. For the 
question might be raised whether suii^tance (i.e. the 'this') 
comes-to-be at all. Is it not rather the 'such', the 'so great', 
or the * somewhere ', which comes-to-be ? And the same 
question might be raised about ' passing-away ' also. For 
if a substantial thing comes-to-be, it is clear that there will 
* be ' (not actually, but potentially) a substance, out of 
which its coming-to-be will proceed and into which the 
thing that is passing-away will necessarily change. Then will 25 
any predicate belonging to the remaining Categories attach 
acUially to this presupposed substance ? In other words, 
will that which is only potentially a ' this ' (which only 
potentially is)^ while without the qualification ' potentially ' 
it is not a ' this ' (i. e. is not), possess, e. g., any determinate 
size or quality 01; position ? For (i) if it possesses none of 
these determinations actually, but all of them only 
potentially, the result is first that a being, which is not 
a determinate being, is capable of separate existence; and 
171 addition that coming-to-be proceeds out of nothing pre- 
existing — a thesis which, more than any other, preoccupied 30 
and alarmed the earliest philosophers. On the other 
hand (ii) if, although it is not a ' this somewhat ' or a sub- 
stance, it is to possess some of the remaining determinations 
quoted above, then (as we said) ^ properties will be 
separable from substances. 

We must therefore concentrate all our powers on the 
discussion of these difficulties and on the solution of a 
further question — viz. What is the cause of the pe rpetuity 35 
of coming-to-be? Why is there always unqualified.^ as _ 
well as partial,^ cominp^-to-be ? 

* Cause ' in this connexion has two senses. It means 318^ 
(i) the qn^^rnp, from which, as we say, the process 'originates', 
and (ii) the matte r. It is the material cause that we have 
here to state. For, as to the other cause, we have already 

' Cf. above, 317^10-11. 

^ * Unqualified coming-to-be' = substantial change. 
^ ' Partial ' = ' qualified ' coming-to-be, i. e. change of quality, 
quantity, or place. 


explained (in our treatise on Motion^) that it involves 
(a) something immovable through all time and (d) some- 

5 thing always being moved. And the accurate treatment of 
the first of these — of the immovable * originative source ' — 
belongs to the province of the other, or * prior ', philo- 
sophy : ^ while as regards * that which sets everything else 
in motion by being itself continuously moved ', we shall 
have to explain later ^ which amongst the so-called * specific' 
causes exhibits this character. But at present we are to | 
state the ma^aaLcause — the cause classed under the head 

lo of matter — to which it is due that passing-away and com- 
ing-to-be never fail to occur in Nature. For perhaps, if we 
succeed in clearing up this question, it will simultaneously 
become clear what account we ought to give of that which 
perplexed us just now, i. e. of unqualified passing-away and 

Our new question too — viz. ' what iq the cause of j he 
unbrpJkeii-CQnlimiit y of com ing-to-be ? ' — is sufficiently per- 
plexing, if in fact what passes-away vanishes into ' what is 

15 not ' and ' what is not ' is nothing (since ' what is not ' is 
neither a thing, nor possessed of a quality or quantity, nor 
in any place). If, then, some one of the things ' which are ' 
is constantly disappearing, why has not the whole of ' what 
is ' been used up Jong ago and vanished away — assuming of 
course that the material of all the seyeral coonings-to-be 
was finite? For, presumably, the unfailing continuity of 
coming-to-be cannot be attributed to the infinity of the 

20 material. That is impossible, for not hing is^actually infinite. 
A thing is infinite only potentially, i. e. the dividing of it 
can continue indefinitely : so that we should have to sup- 
pose there is only one kind of coming-to-be in the world — 
viz. one which never fails, because it is such that what 
comes-to-be is on each successive occasion smaller than 
before. But in fact this is not what we see occurring. 

25 Why, then^ is this form of change necessarily ceaseless ? 
Is it because the passing-away of this is a coming-to-be of 

1 Physics e. 3 if., especially 258^ 10 ff. 
^ i. e. npMTT] (j)iXocro(f)ia or deoXoyiKTj. 
^ Cf. below, II. 10. 

BOOK I. 3 318^ 

something else, and the coming-to-be of this a passing-away 
of something else ? 

The cause imph'ed in this solution^ must no doubt 
be considered adequate to account for coming-to-be and 
passing-away in their general character as they occur in all 
existing things alike. Yet, if the same process is a coming- 30 
to-be of this but a passing-away of that, and a passing-away 
of this but a coming-to-be of that, why are some things said 
to come-to-be and pass-away without qualification, but 
others only with a qualification ? 

This distinction must be investigated once more,^ for it 
demands some explanation. (It is applied in a twofold 
manner.) ^ For (i) we say ' it is now passing-away ' without 
qualification, and not merely ' this is passing-away ' : * and 
we call this change ' coming-to-be ', and that ' passing- 
away \ without qualification. And (ii) so-and-so * comes-to- 
be-something ', but does not 'come-to-be' without quali- 
fication; for we say that the student * comes-to-be-learned', 35 
not * comes-to-be ' without qualification. 

(i) Now we often divide terms into those which signify 318*^ 
a ' this somewhat ' and those which do not. And (the first 
form of) ^ the distinction, which we are investigating, results 
from a similar division of terms : for it makes a difference 
into what the changing thing changes. Perhaps, e.g., the 
passage into Fire is 'coming-to-be' unqualified^ but 'passing- 
away-of-something ' (e. g. of Earth) : whilst the coming-to- 
be of Earth is qualified (not unqtcalified) ' coming-to-be ', 5 
though unqualified ' passing-away ' (e. g. of Fire). This 
would be the case on the theory set forth in Parmenides : ^ 
for he says that the things into which change takes place 
are two, and he asserts that these two, viz. what is and 
what is not, are Fire and Earth. Whether we postulate 

^ i.e. the material cause, in the sense of Trpwr?? vkx]-. cf. 319^* 18-22. 

- ' Once more ' : for it was from this same peculiarity of linguistic 
usage that Aristotle started (317*321?.) to establish the being of cniKx] 

' I have inserted this sentence in view of what follows : cf. 319* 3-11. 

* i.e. not merely ^ this is passing-away and that is coming-to-be*. 

^ See note 3. 

^ The theory is put forward by Parmenides (fr. 8, 11. 5 iff.; Diels, 
pp. 1 21-2) as the prevalent, but erroneous, view. See Burnet, 


these/ or other things of a similar kind, makes no difference. 
For we are trying to discover not what undergoes these 
changes, but what is their characteristic manner. The 
lo passage, then^ into what ' is ' not except with a qualification 
is unqualified passing-away, while the passage into what 
*is' without qualification is unqualified coming-to-be. 
Hence whatever the contrasted ' poles ' of the changes may 
be — whether Fire and Earth, or some other couple — the 
one of them will be ' a being ' and the other * a not-being '.^ 
We have thus stated one characteristic manner in which 
unqualified will be distinguished from ^//^/^}?^^ coming-to-be 
and passing-away: but they are also distinguished according 
to the special nature of the material of the changing thing. 

15 For a material, whose constitutive differences signify more 
a 'this somewhat', is itself more 'substantial' or 'real': 
while a material, whose constitutive differences signify pri- 
vation, is 'not real'. (Suppose, e.g., that 'the hot' is a 
positive predication, i.e. a 'form', whereas 'cold' is a priva- 
tion, and that Earth and Fire differ from one another by 
these constitutive differences.) 

The opinion, however, which most people are inclined to 
prefer, is that the distinction ^ depends upon the difference 
between ' the perceptible ' and ' the imperceptible '. Thus, 

20 when there is a change into perceptible material, people say 
there is 'coming-to-be'; but when there is a change into 
invisible material, they call it ' passing-away '. For they 
distinguish ' what is ' and ' what is not ' by their perceiving 
and not-perceiving, just as what is knowable 'is' and what 
is unknowable ' is not ' — perception on their view having 

25 the force of knowledge. Hence, just as they deem them- 
selves to live and to ' be ' in virtue of their perceiving or 
their capacity to perceive, so too they deem the things to 
' be ' gi/a perceived or perceptible— and in this they are in a 
sense on the track of the truth, though what they actually 
say is not true. 

* sc. as the things into which the unquahfied changes take place — 
as the contrasted ' poles ' of unqualified yepeais and (pdopd. 

^ i. e, one will be ' a positive real 
something '. 

^ sc. between the unqualified and the qualified changes. 

BOOK I. 3 318^ 

Thus unqualified coming-to-be and passing-away turn out 
to be different according to common opinion from what 
they are in truth.^ For Wind and Air are in truth more 
real — more a * this somewhat' or a ' form ' — than Earth. 
But theY _gLre less real to perception — which explains why 
things are commonly said to ' pass-away ' without qualifica- 30 
tion when they change into Wind and Air, and to ' come-to- 
be*^ when they change into what is tangible, i.e. into Earth. 

We have now explained why there is 'unqualified coming- 
to-be ' (though it is a passing-away-of-something) and ' un- 
qualified passing-away' (though, it is a coming-to-be-of- 
something). For this distinction of appellation depends upon 35 
a difference in the material out of which, and into which, 
the changes are effected. It depends either upon whether 
the material is or is not ' substantial ', or upon whether it is 3^9^ 
more or less ' substantial ', or upon whether it is more or 
less perceptible. 

(ii) But why are some things said to ' come-to-be ' with- 
out qualification, and others only to *come-to-be-so-and-so', 
in cases different from the one we have been considering 
where two things come-to-be reciprocally out of one another? 
For at present we have explained no more than this: — why, 5 
when two things change reciprocally into one another, we 
do not attribute coming-to-be and passing-away uniformly 
to them both, although every coming-to-be is a passing- 
away of something else and every passing-away some other 
thing's coming-to-be. But the question subsequently formu- 
lated involves a different problem — viz. why, although the 
learning thing is said to ' come-to-be-learned ' but not to"" 10 
'come-to-be' without qualification, yet the growing thing 
is said to ' come-to-be '. 

The distinction here turns upon the difference of the 
C ateg ofjes. For som^ things signify a t^is some^iuhat^ others 
a such^ and o thers a so-much. Those things, then, which 
do not signify substance, are not said to * come-to-be ' with- 
out qualification, but only to ' come-to-be-so-and-so '. 

^ *Jn truth', i.e. according to Aristotle's own view which he has 
just stated (above, 318^ 14-18). 
* sc. without qualification. 

645-18 C 


Nevertheless, in all changing things alike, we speak of 

15 'coming-to-be'^ when the thing comes-to-be something in 
one'^ of the two Columns — e.g. in Substance, if it comes-to- 
be Fire but not if it comes-to-be Earth ; and in Quality, if 
it comes-torbe learned but not when it comes-to-be ignorant. 
We have explained why some things come-to-be without 
qualification, but not others — both in general, and also 
when the changing things are substances and nothing else ; 
and we have gtaf^H \\'^\ thr snh^tratw" ^'^ ^hf m aterial cause 
of th£ _continuous occu rr ence of coming-to-be. because it is 

20 s uch as to change from contrary to contrary an d because, 
in_substances , the coming-to-be of one t hing is always 
a passin£- away of another, and the passing-awav of on e 
thing is always another's coming-to-he. But there is no 
need even to discuss the other question we raised — viz. 
why coming-to-be continues though things are constantly 
being destroyed.^ For just as people speak of ' a passing- 
away ' without qualification when a thing has passed into 
what is imperceptible and what in that sense ' is not ', so 

25 also they speak of 'a coming-to-be out of a not-being ' when 
a thing emerges from an imperceptible. Whether, there- 
fore, the substratum is or is not something, what comes-to- 
be emerges out of a ' not -being ' : ^ so that a thing ' comes- 
to-be out of a not-being' just as much as it 'passes-away 
into what is not'. Hence it is reasonable enough that 
coming-to-be should never fail. For coming-to-be is a 
passing-away of ' what is not ' and passing-away is a coming- 
to-be of ' what is not '.^ 

But what about that which ' is ' not except with a quali- 

30 fi cation ? ^ Is it one of the two contrary poles of the change 
— e. g. is Earth (i. e. the heavy) a ' not-being ', but Fire (i. e. 

* i. e. without qualification. 

^ i. e. in the Column containing the positive terms : cf. above, 

^ Cf. above, 318* 13-23. 

* A * not-being ' in the popular sense of the term, i. e. an * imper- 
ceptible'. The imperceptibility of the material is irrelevant to the 
question of its reality. 

•^ ' what is not ' = what is imperceptible. 

^ The matter of substantial change, according to Aristotle's own 
theory, is \ir] ov dn\a)s — i. e. it is not, unless you qualify * is' and say it 
' is-potentially '. Cf. above, 317^15-18. 

BOOK I. 3 319* 

the light) a * being ' ? Or, on the contrary, does * what is ' 
include Earth as well as Fire, whereas * what is not ' is matter 
— the matter of Earth and Fire alike ? And again, is the 
matter of each different ? Or is it the same, since otherwise 
they would not come-to-be reciprocally out of one another, 319^ 
i. e. contraries out of contraries ? For these things — Fire, 
Earth, Water, Air — are characterized by ' the contraries \^ 

Perhaps the solution is that their matter is in one sense 
the same, but in another sense different. For that which 
underlies them, whatever its nature may be qi^a underlying 
them, is the same : but its actual being is not the same. So 
4 much, then, on these topics. Next we must state what the 5 
difference is between coming-to-be and 'alteration' — for 
we maintain that these changes are distinct from one 

Since, then, we must distinguish (a) the mbstratum^ 
and [h) the property whose nature it is to be predi- 
cated of the substratum ; and since (;hange of each of 10 
these occurs ; t here is ' alteration ' when the substratum A s 
perceptibl e and persists , but changes in its own properties, 
the properties in question being opposed to one another 
either as contraries or as intermediates. The body, e. g., 
although persisting as the same body, is now healthy and 
now ill ; and the bronze is now spherical and at another 
time angular, and yet remains the same bronze. But 
when nothing perceptible persists in its identity as a sub- 15 
stratum, and the thing changes as a whole (when e.g. the 
seed as a whole is converted into blood, or water into air, 
or air as a whole into water), such an o ccurrence is no longer 
'alteration '. It is a coming -to-be of one substance and 
a p assing-away of the other^^ especially if the change pro- 
ceeds from an imperceptible something to something 
perceptible (either to touch or to all the senses), as when 
water comes-to-be out of, or passes-away into, air : for air 20 
is pretty well imperceptible. If, however, in such cases, any 
property (being one of a pair of contraries) persists, in the 
thing that has come-to-be, the same as it was in the thing 

1 Cf. below, II. 1-3. 
C 2 


which has passed-away — if, e.g., when water comes- to-be 
out of air, both are transparent or cold ^ — the second thing, 
into which the Jirst changes, must not be a property of this 
persistent identical something. Otherwise the change will 
be * alteration \ 

25 Suppose, e.g., that tke 7nusical man passed-away and an 
unmnsical man came-to-be, and that the maji persists as 
something identical. Now, if * musicalness and unmusical- 
ness ' had not been a property^essentially inhering in man, 
these changes would have been a coming-to-be of un- 
musicalness and a passing-away of musicalness : but in fact 
* musicalness and unmusicalness ' are a property of the 
persistent_Jdentityj_yiz. man.^ (Hence, as regards man, 
these changes are 'modifications'; though, as regards 

30 musical man and unmusical ma7i, they are a passing-away 
and a coming-to-be.) Consequently such changes are 
' alteration \^ 

"When the change from contrary to contrary is in quantity ^ 
it is ' growth and diminution ' ; when it is in place, it is 
•motion'; when it is in property, i.e. in quality, it is 
320^ * alteration ': but when nothing persists, of which the re- 
sultant is a property (or an ' accident ' in any sense of the 
term), it is 'coming-to-be', and the converse change is 
' passing-away '. 

' Matter ', in the most proper sense of the term, is to be 
identified with the substratum which is receptive of coming- 
to-be and passing-away : but the substratum of the remain- 
ing kinds of change is also, in a certain sense, ' matter ', 
5 because all these substrata are receptive of * contrarieties ' 
of some kind. So much, then, as an answer to the ques- 

* Aristotle is not saying that water and air are in fact 'cold ', but is 
only quoting a common view in illustration. 

^ I follow Philoponos in transposing vvv . . . v-n-o^ivovros (which the 
manuscripts read after (fyOopd in 1. 30) to 1. 28 after tov Se (f>6opd. 

^ Aristotle's doctrine is: (i) If 'musicalness and unmusicalness' 
were not a property of man, the change in which ' a musical man 
becomes unmusical ' would be a (pdopd of musicalness and a yevfo-is 
of unmusicalness. But (ii) since ' musicalness and unmusicalness ' are 
a property of man, the change is in fact an 'alteration' of man from 
a state of musicalness to a state of unmusicalness. At the same time, 
(iii) the change is a (f)dnpd of musical man and a yeveais of unmusical 

BOOK I. 4 320* 

tions (i) whether coming-to-be * is ' or * is not ' — i. e. what 
are the precise conditions of its occurrence — and (ii) what 
5 ' alteration ' is : but we have still to treat of growth.^ We 
must explain (i) wherein growth differs from coming-to-be 
and from ' alteration '/and (ii) what is the process of grow- 
ing and the process of diminishing in each and all of the 10 
things that grow and diminish. 

Hence our first question is this : Do these changes differ 
from one another solely because of a difference in their 
respective ' spheres ' ? In other words, do they differ 
because, while a change from this to that (viz. from poten- 
tial to actual substance) is coming-to-be, a change in the 
sphere of magnitude is growth and one in the sphere of 
quality is ' alteration ' — both growth and * alteration ' being 15 ^ 
changes from what is-potentially to what is-actually 
magnitude and quality respectively? Or is there also 
a difference in the manner of the change, since it is evident 
that, whereas neither what is ' altering ' nor what is coming- 
to-be necessarily changes its place, what is growing or 
diminishing changes its spatial position of necessity , though 
in a different manner from that in which the moving thing 
does so ? For that which is being moved changes its place 20 
as a whole : but the growing thing changes its place hke 
a metal that is being beaten, retaining its position as a whole 
while its parts change their places. They change their 
places, but not in the same way as the parts of a revolving- 
globe. For the parts of the globe change their places 
while the whole continues to occupy an equal place: but 
the parts of the growing thing expand over an ever-increas- 
ing place and the parts of the diminishing thing contract 25 
within an ever-diminishing area. 

It is clear, then, that these changes — the changes of that 
which is coming-to-be, of that which is ' altering ', and of 
that which is growing — differ in manner as well as in sphere. 
But how are we to conceive the ' sphere ' of the change 
which is growth and diminution ? The * sphere ' of growing 
and diminishing is believed to be magnitude. Are we to 

^ Cf. above, 315*26-28. 


suppose that body and magnitude come-to-be out of some- 
30 thing which, though potentially magnitude and body, is 
actually incorporeal and devoid of magnitude? And since 
this description may be understood in two different ways, 
in which of these two ways are we to apply it to the process 
of growth ? Is the matter,^ out of which growth takes 
place, (i) ' separate ' and existing alone by itself, or (ii) 
' separate ' but contained in another body ? ^ 

Perhaps it is impossible for growth to take place in either 
320^ of these ways. For since the matter ^ is * separate ', either 
(a) it will occupy no place (as if it were a point), or (d) it 
will be a ' void ', i. e. a non-perceptible body. But the first 
of these alternatives is impossible. For since what comes- 
to-be out of this incorporeal and sizeless something will 
always be ' somewhere ', it too must be * somewhere * — 
5 either intrinsically or indirectly.* And the second alterna- 
tive necessarily implies that the matter is contained in some 
other body. But if it is to be ' in ' another body and yet 
remains ' separate ' in such a way that it is in no sense 
a part of that body (neither a part of its substantial being 
nor an ' accident ' of it), many impossibilities will result. 
It is as if we were to suppose that when, e.g., air comes-to- 
be out of water the process were due not to a change of the 
10 water, but to the matter of the air being * contained in ' the 
water as in a vessel. This is impossible. For (i) there is 
nothing to prevent an indeterminate number of matters 
being thus ' contained in ' the water, so that they might 
come-to-be actually an indeterminate quantity of air ; * and 
(ii) we do not in fact see air coming-to-be out of water in 
this fashion, viz. withdrawing out of it and leaving it 

It is therefore better to suppose that in all instances of 

' i.e. the supposed incorporeal and sizeless matter. 

'^ It is clear from what follows that the incorporeal and sizeless 
matter is assumed to be * separate ' — to be real independently of body — 
under both alternatives. 

^ i. e. the supposed incorporeal and sizeless matter. 

* i.e. either as itself occupying a place, or as contained within 
a body which itself occupies a place. 

^ The original is obscure owing to its extreme compression : I have 
expanded it in accordance with Zabarella's interpretation. 

BOOK I. 5 320^ 

coming-to-be the matter is inseparable/ being numerically- 
identical and one with the ' containing ' body, though isol- 
able from it by definition. But the same reasons also forbid 
us to regard the matter, out of which the body comes-to-be, 15 
as points or lines. The matter is that of which points and 
lines are limits, and it is something that can never exist 
without quality and without form. 

Now it is no doubt true, as we have also established else- 
where,2 ^^^^ q^q thing 'comes-to-be' (in the unqualified 
sense) out of another thing : and further it is true that the 
efficient cause of its coming-to-be is either (i) an actual 
thing (which is the same as the effect either generically 
— for the efficient cause of the coming-to-be of a hard thing 
is not a hard thing ^ — or specifically^ as e. g. fire is the ao 
efficient cause of the coming-to-be of fire or one man of the 
birth of another), or (ii) an actuality.* Nevertheless, since 
there is also a matter out of which corporeal substance 
itself comes-to-be (corporeal substance, however, already 
characterized as such-and-such a determinate body, for 
there is no such thing as body in general), this same matter 
is also the matter of magnitude and quality — being separ- 
able from these matters by definition, but not separable in 
place unless Qualities are, in their turn, separable.^ 25 

It is evident, from the preceding^ development and dis- 
cussion of difficulties, that growth is not a change out of 
something which, though potentially a magnitude, actually 
possesses no magnitude. For, if it were, * the void ' would 
exist in separation ; but we have explained in a former work "^ 
that this is impossible. Moreover, a change of that kind 
is not peculiarly distinctive of growth, but characterizes 

* * inseparable ' from the actual body in which it is contained. 
2 Cf. Physics A. 7 ; Metaph. 1032* 12 ff. 

^ The efficient cause of the coming-to-be of a hard thing (e. g. of ice 
or terra-cotta) is something cold or hot (a freezing wind or a baking 
fire) ; cf. Meteor. 382* 22 ff. Such efficient causes are only generically, 
not specifically, identical with their effects. I have transposed the 
words (TKXrjpov yap ovx vtto a-Kkrjpov -yiWrai SO as to read them as 
a parenthesis after ofjLoyevoiis in 320^ 19. 

* An * actuality ' or * form ' : cf. Metaph. 1032* 25 ff. 

" i. e. unless Qualities or Adjectivals are separable from Substances. 
^ Cf. above, 320*27-^ 12. 
' Cf. Physics A. 6-9. 


30 coming-to-be as such or in general. For growth is an in- 
crease, and diminution is a lessening, of the magnitude which 
is there already — that, indeed, is why the growing thing 
must possess some magnitude. Hence growth must not 
be regarded as a process from a matter without magnitude 
to an actuality of magnitude : for this would be a body's 
coming-to-be rather than its growth. 

We must therefore come to closer quarters with the 
321^ subject of our inquiry. We must * grapple ' with it (as it 
were) from its beginning, and determine the precise character 
of the growing and diminishing whose causes we are in- 

It is evident (i) that any and every part of the growing 
thing has increased, and that similarly in diminution every 
part has become smaller : also (ii) that a thing grows by 

5 the accession, and diminishes by the departure, of some- 
thing. Hence it must grow by the accession either 
(a) of something incorporeal or (d) of a body. Now, if 
(a) it grows by the accession of something incorporeal, 
there will exist separate a void : but (as we have stated 
before) ^ it is impossible for a matter of magnitude to exist 
' separate '. If, on the other hand, {b) it grows by the 
accession of a body, there will be two bodies — that which 
grows and that which increases it — in the same place: 
and this too is impossible. 

10 But neither is it open to us to say that growth or 
diminution occurs in the way in which e. g. air is generated 
from water. For, although the volume has then become 
greater, the change will not be growth, but a coming-to-be 
of the one — viz. of that into which the change is taking 
place — and a passing-away of the contrasted body. It is 
not a growth of either. Nothing grows in the process ; 
unless indeed there be something common to both things 

15 (to that which is coming-to-be and to that which passed- 
away), e.g. 'body', and this grows. The water has not 
grown, nor has the air: but the former has passed- 
away and the latter has come-to-be, and — if anything has 
grown — there has been a growth of ' body '. Yet this too 
^ Cf. above, 320^27 - ^25. 

BOOK I. 5 321^ 

IS impossible. For our account of growth must preserve 
the characteristics of that which is growing and diminishing. 
And these characteristics are three : (i) any and every 
part of the growing magnitude is made bigger (e. g. if flesh 20 
grows, every particle of the .flesh gets bigger), (ii) by the 
accession of something, and (iii) in such a way that the 
growing thing is preserved and persists. For whereas a 
thing does not persist in the processes of unqualified 
coming-to-be or passing-away, that which grows or ' alters ' 
persists in its identity through the ' altering ' and through 
the growing or diminishing, though the quality (in ' altera- 25 
tion') and the size (in growth) do not remain the same. 
Now if the generation of air from water is to be regarded 
as growth, a thing might grow without the accession (and 
without the persistence) of anything, and diminish without 
the departure of anything — and that which grows need not 
persist. But this characteristic ^ must be preserved : for the 
growth we are discussing has been assumed to be thus 

One might raise a further difficulty. What is ' that which 30 
grows ' ? Is it that to which something is added ? If, e. g., 
a man grows in his shin, is it the shin which is greater ^ — 
but not that * whereby ' he grows, viz. not the food ? Then 
why have not both ' grown ' ? For when A is added to B, 
both A and B are greater, as when you mix wine with 
water ; for each ingredient is alike increased in volume. 
Perhaps the explanation is that the substance of the one ^ 
remains unchanged, but*the substance of the other (viz. of 35 
the food) does not. For indeed, even in the mixture of wine 321^ 
and water, it is the prevailing ingredient which is said to 
have increased in volume. We say, e. g., that the wine has 
increased, because the whole mixture acts as wine but not 
as water. A similar principle applies also to * alteration '. 
Flesh is said to have been ' altered ' if, while its character 
and substance remain, some one of its essential properties, 
which was not there before, now qualifies it : on the other 5 

* viz. the third characteristic — that the growing thing * persists '. 

^ i. e. has ' grown '. 

^ i. e. the substance of the shin. 


hand, that ' whereby ' it has been ' altered * may have under- 
gone no change, though sometimes it too has been affected. 
The altering agent, however, and the originative source of 
the process are in the growing thing and in that which is 
being ' altered ' : for the efficient cause is in these.^ No doubt 
the food, which has come in, may sometimes expand as well 
as the body that has consumed it (that is so, e. g., if, after 
having come in, a food is converted into wind^), but when 
lo it has undergone this change it has passed-away : and the 
efficient cause is not in the food. 

We have now developed the difficulties sufficiently and 
must therefore try to find a solution of the problem. Our 
solution must preserve intact the three characteristics of 
growth — that the growing thing persists, that it grows by 
the accession (and diminishes by the departure) of some- 
thing, and further that every perceptible particle of it has 
15 become either larger or smaller. We must recognize also 
(a) that the growing body is not ' void ' and that yet there 
are not two magnitudes in the same place, and (d) that it 
does not grow by the accession of something incorporeal. 

Two preliminary distinctions will prepare us to grasp 
*"• the cause of growth. We must note (i) that the organic 
parts ^ grow by the growth of the tissues * (for every organ 
is composed of these as its constituents) ; and (ii) that flesh, 
20 bone, and every such part ^ — like every other thing which 
has its form immersed in matter — has a twofold nature : for 
the form as well as the matter is called ' flesh ' or * bone *. 

Now, that any and every part 'of the tissue qua form 
should grow — and grow by the accession of something — is 
possible, but not that any and every part of the tissue qua 
matter should do so. For we must think of the tissue after 

' And therefore it is these which are said to grow or to be ' altered '. 

^ Aristotle may be thinking of the conversion of a flatulent food into 
wind. But more probably he has in mind the maintenance and growth 
of the c^(l)VTov (or o-v/x0utoi^) nvevfxa : cf. tfe Spiritu 481* llf. 

' The Greek is rh dvonoiofxeprj, i. e. those parts (of the living thing) 
whose texture is not uniform throughout. 

* The Greek is ra oiioLoneprj, i. e. those parts whose texture is uniform 
throughout : cf. above, 314* 19-20. In living things such parts corre- 
spond roughly to 'the tissues'. 

'^ i. e. every ' homoeomerous ' part (or every ' tissue '). 

BOOK I. 5 321^ 

the image of flowing water that is measured by one and 25 
the same measure : particle after particle comes-to-be, and 
each successive particle is different.^ And it is in this 
sense that the matter of the flesh grows, some flowing 
out and some flowing in fresh ; not in the sense that fresh 
matter accedes to every particle of it. There is, however, 
an accession to every part of its figure or ' form '. 

That growth has taken place proportionally,^ is more 
manifest in the organic parts — e. g. in the hand. For there 
the fact that the matter is distinct from the form is 30 
more manifest than in flesh, i. e. than in the tissues. That 
is why there is a greater tendency to suppose that a 
corpse still possesses flesh and bone than that it still has 
a hand or an arm. 

Hence in one sense it is true that any and every part 
of the flesh has grown ; but in another sense it is false. 
For there has been an accession to every part of the flesh 
in respect to its form, but not in respect to its matter. 
The whole, however, has become larger. And this increase 35 
is due {a) on the one hand to the accession of something, 
which is called * food ' and is said to be ' contrary ' to flesh, 322^ 
but {b) on the other hand to the transformation of this food 
into the same form as that of flesh — as if, e.g., 'moist' 
were to accede to ' dry ' and, having acceded, were to be 
transformed and to become ' dry '. For in one sense ' Like 
grows by Like ', but in another sense ' Unlike grows by 

One might discuss what must be the character of that 
' whereby ' a thing grows. Clearly it must be potentially 5 
that which is growing — potentially flesh, e. g., if it is flesh 
that is growing. Actually, therefore, it must be * other ' 
than the growing thing. This ' actual other ', then, has 
passed-away and come-to-be flesh. But it has not been 
transformed into flesh alone by itself (for that would have 

* I think this clause refers to the matter of the tissue, not to the 
water. In Aristotle's simile, the ' measure ' corresponds to the tissue's 
form, and the ' water ' to its matter. The matter is a flux of different 
particles always coming-to-be and passing-away, always ' flowing in 
and out ' of the structural plan which is the ' form '. 

^ i. e. by an expansion of all parts of the * form '. 


been a coming-to-be, not a growth) : on the contrary, it 
is the growing thing which has come-to-be flesh (and grown)^ 
by the food. In what way, then, has the food been modi- 
fied by the growing thing ? ^ Perhaps we should say that 
it has been ' mixed ' with it, as if one were to pour water 

10 into wine and the wine were able to convert the new 
ingredient into wine. And as fire lays hold of the in- 
flammable,^ so the active principle of growth, dwelling 
in the growing thing (i.e. in that which is actually flesh), 
lays hold of an acceding food which is potentially flesh and 
converts it into actual flesh. The acceding food, therefore, 
must be together with the growing thing : ^ for if it were 
apart from it, the change would be a coming-to-be.® For 

15 it is possible to produce fire by piling logs on to the already 
burning fire. That is 'growth '. But when the logs them- 
selves are set on fire, that is ' coming-to-be '. 

* Quantum-in-general ' does not come-to-be any more 
than ' animal ' which is neither man nor any other of the 
specific forms of animal : what * animal-in-general ' is in 
coming-to-be, that ' quantum-in-general ' is in growth. 
But what does come-to-be in growth is flesh or bone — 
or a hand or arm (i. e. the tissues of these organic parts).® 

20 Such things come-to-be, then, by the accession not of 
quantified-flesh but of a quantified-something. In so far 
as this acceding food is potentially the double result — 
e.g. is potentially so-much-flesh^it produces growth: for 
it is bound to become actually both so-much and flesh. 
But in so far as it is potentially flesh only, it nourishes: 
for it is thus that * nutrition ' and ' growth ' differ by their 
definition. That is why a body's * nutrition ' continues so 

^ All the manuscripts read rjv^TjOrj after tovtov in 322* 9. We must 
either delete it, or correct it into rjv^rja-ev (cf. Philoponos, ed. Vitelli, 
p. 117, 1. 12), or transpose it so as to read it after tovtco in * 8. I have 
adopted the last alternative in my translation. J 

^ i. e. ' been modified ' so as to be transformed into flesh. ^ 

' i.e.* lays hold ' of it and converts it into fire. 

* i. e. ' must be together with ' it when this conversion takes place. 

* i.e. an independent coming-to-be of flesh, not a growth of the 
already existing tissue. 

^ i.e. what comes-to-be in growth is so-much flesh or bone, or 
a hand or arm of such and such a size : not ' quantum-in-general ', 
but a ' quantified-something *. 


BOOK I. 5 322' 

long as it is kept alive (even when it is diminishing), though 
not its ' growth ' ; and why nutrition, though ' the same ' 25 
as growth, is yet different from it in its actual being. For in 
so far as that which accedes is potentially ' so-much-flesh ' it 
tends to increase flesh : whereas, in so far as it is potentially 
' flesh ' only, it is nourishment. 

The form of which we have spoken ^ is a kind of power 
immersed in matter — a duct, as it were. If, then, a matter 
accedes — a matter, which is potentially a duct and also 30 
potentially possesses determinate quantity — the ducts to 
which it accedes will become bigger. But if it ^ is no 
longer able to act — if it has been weakened by the con- 
tinued influx of matter, just as water, continually mixed 
in greater and greater quantity with wine, in the end makes 
the wine watery and converts it into water — then it will cause 
a diminution of the quantum ; ^ though still the form per- 

6 (In discussing the causes of coming-to-be) ^ we must first 322^ 
investigate the matter, i. e. the so-called * elements '. We 
must ask whether they really are elements or not, i. e. whether 
each of them is eternal or whether there is a sense in which 
they come-to-be: and, if they do come-to-be, whether all 
of them come-to-be in the same manner, reciprocally out 
of one another, or whether one amongst them is something 

' i.e. the form which grows in every part of itself: cf. above, 

"^ i. e. this form or power immersed in matter. 

' i. e. a diminution of the size of the tissue whose form it is. 

* For the reading and interpretation of 322*28-33 see my text 
and commentary. 

^ I have added these words to explain ' first ' : cf. Zabarella, whose 
interpretation I have followed. 


5 primary. Hence we must begin by explaining certain 
preliminary matters, about which the statements now 
current are vague. 

For all (the pluralist philosophers) — those who generate 
the ' elements ' as well as those who generate the bodies 
that are compounded of the elements — make use of ' dis- 
sociation ' and * association ', and of ' action ' and ' passion '. 
Now ' association ' is ' combination ' ; but the precise mean- 
ing of the process we call ' combining ' has not been ex- 
plained. Again, (all the monists make use of ' alteration ' : 

lo but) without an agent and a patient there cannot be ' alter- 
ing ' any more than there can be ' dissociating ' and ' asso- 
ciating '. For not only those who postulate a plurality of 
elements employ their reciprocal action and passion to 
generate the compounds: those who derive things from 
a single element are equally compelled to introduce ' acting'.^ 
And in this respect Diogenes is right when he argues that 
. 15 ' unless all things were derived from one, reciprocal action 
and passion could not have occurred '.^ The hot thing, 
e. g., would not be cooled and the cold thing in turn be 
warmed : for heat and cold do not change reciprocally into 
one another, but what changes (it is clear) is the substratum. 
Hence, whenever there is action and passion between two 
things, that which underlies them must be a single some- 
thing. No doubt, it is not true to say that all things are of 

20 this character : ^ but it is true of all things between which 
there is reciprocal action and passion. 

But if we must investigate ' action-passion ' and * com- 
bination ', we must also investigate ' contact *. For action 
and passion (in the proper sense of the terms) can only 
occur between things which are such as to touch one 

25 another; nor can things enter into combination at all un- 
less they have come into a certain kind of contact. Hence 

^ I have added the explicit reference to ' the pliiralists' at ^6 and to 
'the monists' at ^9, because Aristotle's argument in the present 
passage presupposes this classification and the consequences that were 
drawn from it in the first chapter. 

"^ Cf. Diogenes, fr. 2 (Diels, p. 334). 

^ i. e. are transformations of a single substratum^ or * derived from 
one thing ' as Diogenes maintained. 


BOOK I. 6 322^ 

we must give a definite account of these three things — of 
' contact ', * combination ', and * acting '. 

Let us start as follows. All things which admit of 

* combination ' must be capable of reciprocal contact : and 
the same is true of any two things, of which one 'acts' and 
the other ' suffers action ' in the proper sense of the terms. 
For this reason we must treat of ' contact ' first. 

Now every term which possesses a variety of meanings 30 
includes those various meanings either owing to a mere 
coincidence of language, or owing to a real order of deriva- 
tion in the different things to which it is applied : but, 
though this may be taken to hold of 'contact' as of all such 
terms, it is nevertheless true that * contact ' in the proper 
sense applies only to things which have ' position '. And 

* position ' belongs only to those things which also have 

a ' place ' : for in so far as we attribute ' contact ' to the 323* 
mathematical things, we must also attribute * place' to them, 
whether they exist in separation or in some other fashion.^ 
Assuming, therefore, that ' to touch ' is — as we have defined 
it in a previous work ^ — ' to have the extremes together ', 
only those things will touch one another which, being 5 
separate magnitudes and possessing position, have their 
extremes ' together '. And since position belongs only to 
those things which also have a ' place ', while the primary 
differentiation of ' place ' is ' the above ' and ' the below ' 
(and the similar pairs of opposites), all things which touch 
one another will have ' weight ' or ' lightness ' — either both 
these qualities or one or the other of them.^ But bodies 
which are heavy or light are such as to 'act' and 'suffer 10 
action '. Hence it is clear that those things are by nature 
such as to touch one another, which (being separate magni- 
tudes) have their extremes 'together' and are able to move, 
and be moved by, one another. 

The manner in which the ' mover ' moves the ' moved ' is 

* i. e. whether they exist in separation from the perceptible things, 
or whether they 'are' e.g. as inseparable adjectives of the (fyvo-iKu 
aa>naTa or as abstracted objects of thought. 

^ Cf. Physics 226^21-23. 

^ i. e. if A and B are in reciprocal contact, either A must be heavy 
and B light, or A light and B heavy : or A and B must both be heavy, 
or both be light. 


not always the same: on the contrary, whereas one kind 
of ' mover ' can only impart motion by being itself moved, 
another kind can do so though remaining itself unmoved. 

15 Clearly therefore we must recognize a corresponding variety 
in speaking of the ' acting ' thing too : for the ' mover' is said 
to ' act ' (in a sense) and the ' acting ' thing to 'impart motion'. 
Nevertheless there is a difference and we must draw a dis- 
tinction. For not every ' mover ' can ' act ', if (a) the term 
'agent' is to be used in contrast to 'patient' and (d) 'patient' 
is to be applied only to those things whose motion is a 'quali- 

20 tative affection ' — i. e. a quality, like * white ' or ' hot ', in 
respect to which they are ' moved ' only in the sense that 
they are ' altered ' : on the contrary, to ' impart motion ' is 
a wider term than to ' act '.^ Still, so much, at any rate, is 
clear: the things which are 'such as to impart motion', if 
that description be interpreted in one sense, will touch the 
things which are ' such as to be moved by them ' — while 
they will not touch them, if the description be interpreted 
in a different sense. But the disjunctive definition of 
' touching ' must include and distinguish (a) ' contact in 
general ' as the relation between two things which, having 
position, are such that one is able to impart motion and the 
other to be moved, and (3) 'reciprocal contact' as the rela- 
tion between two things, one able to impart motion and 
the other able to be moved in such a way that * action and 

35 passion ' are predicable of them. 

As a rule, no doubt, if A touches B, B touches A. For 
indeed practically all the 'movers' within our ordinary 
experience impart motion by being moved : in their case, 
what touches inevitably must, and also evidently does, 
touch something which reciprocally touches it. Yet, if A 
moves B, it is possible — as we sometimes express it — for 
A ' merely to touch ' B, and that which touches need not 

30 touch a something which touches it. Nevertheless it is 
commonly supposed that * touching ' must be reciprocal. 
The reason of this belief is that ' movers ' which belong to 
the same kind as the ' moved ' impart motion by being 
moved. Hence if anything imparts motion without itself 
^ i. e. if to ' act ' be understood in the narrow sense just explained. 


BOOK I. 6 323^ 

being moved, it may touch the ' moved ' and yet itself be 
touched by nothing — for we say sometimes that the man 
who grieves us ' touches ' us, but not that we * touch ' him. 

The account just given may serve to distinguish and 
define the ' contact ' which occurs in the things of Nature. 
7 Next