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^RAS^

PYTHAGOREAN TRIANGLE;

THE SCIENCE OF NUMBERS,

G.O:

REV. ardLIVEE, D.D.

PaitM.P.S. Grand CommaHdefs.G.I.G. if for England a-ul Wales :

Pint D.G.M. of the Grand Lodge of Massachusetts;

Patl D.P.G.M./er Lincolnshire;

It onorary Member of numerous Ledges and Literary Societies

in every quarter of the Globe:

ll'TIIHH at "THE M VEXATIOUS OF < BQtJABE," "THE BOOK OF TBI LODOE,"
L1HDHAKEH," ETC. ETC.

'Apx% tuiv irdrrui 4 fterdt. — Hebktah.
WITH DIAGRAMS.

LONDON:
JOHN HOGG 4 CO., PATERNOSTER ROW.

\AU righto rtmitrt.}

042

t

sfl

blink—

PUBLISHERS' NOTE.

-*•-

The following posthumous work by the late Eev.
6. Oliver, D.D., so widely and deservedly known
by his numerous Masonic writings, is printed
verbatim et literatim from his hitherto unpub-
lished MS.

The opinion of several distinguished Free-
masons, competent to advise in such a matter,
was, that the work should not be revised, added
to, nor in any way altered. This opinion has
been the more confidently acted upon, as the
MS. bears evidence of having been very carefully
revised by the Doctor's own hand, and there is
xi his own statement to the effect, that both the
plan and treatment of the book had been well
matured.

^ London, Nwemher 1875.

*

TABLE OP CONTENTS.

-♦♦-

PUBLISHERS 7 NOTE
PREFACE .

PAGE
V

ix

INTRODUCTION.

THE PYTHAGOREAN TRIANGLE EXPLAINED, WITH A DISSER-
TATION ON THE PECULIARITIES OF MASONIC NUMBER 1

CHAPTER I.

THE MONAD OR POINT DISCUSSED AS THE ORIGIN OF ALL

CALCULATION.

(The Point, Monad, Unity, or the Number One) . 31

CHAPTER II.

THE DUAD OR LINE EXEMPLIFIED.

(The line, Duad, Duality, or the Number Two) . 53

CHAPTER III.

ILLUSTRATION OF THE TRIAD OR SUPERFICE.

(The Superfice, or Equilateral Triangle, Triad, Ternary, or

the Number Three) .77

CHAPTER IV.

PROGRESSIVE GENERATION OF THE TETRAD OR SOLID,

REPRESENTING FIRE.

(The Solid, Tetrad, Quaternary, or the Number Four) . 101

viii Contents.

CHAPTER V.

PAOE

GEOMETRICAL APPLICATION OF THE PENTAD OB PYRAMID,

REPRESENTING WATER.

(The Pyramid, Pentad, Quincunx, or the Number Five) 123

CHAPTER VI.

INFINITE DIVISIBILITY OF THE HEXAD OR DOUBLE
TRIANGLE, REPRESENTING EARTH.

(The Double Triangle, Hexagon, Hexad, or the Number
Six) 145

CHAPTER VII.

REMARKABLE PROPERTIES OF THE HEPTAD.

(The Heptagon, Heptad, Septenary, or the Number Seven) 167

CHAPTER VIII.

MYSTERIOUS REFERENCES OF THE OGDOAD OR CUBE,

REPRESENTING AIR.

(The Cube, Ogdoad, Octaedron, or the Number Eight) . 187

CHAPTER IX.

ANCIENT SUPERSTITIONS ATTACHED TO THE ENNEAD OR

TRIPLE TRIANGLE.

(The Ennead, Triple Triangle, Nonagon, or the Number

Nine) 199

CHAPTER X.

THE PERFECT NATURE OF THE DECAD OR CIRCLE, AND THE AP-
PLICATION OF THE DODECAEDRON AS A REPRESENTATION
OF THE SYSTEM OF THE UNIVERSE.

(The Circle, Decad, Panteleia, or the Number Ten) . 219

PREFACE.

-♦♦•

H

REEMASONEY is a science, as every
brother knows, whose Landmarks are
theoretically unalterable, and whose peculiar rites
and ordinances are pronounced to be the same
yesterday, to-day, and for ever. But, alas ! the
failure of these conditions proves that Masonry is
but a mere human institution after all. It would
be easy to produce a host of altered Landmarks
for the purpose of showing that no obsolete cere-
mony or antiquated observance has been able to
hold its own against the electric agency of modern
progress.

x Preface.

Accordingly, in tracing the science from the
earliest period of its existence, we must prepare
ourselves to meet with many changes which have
periodically occurred in consequence of improve-
ments and discoveries in the liberal arts, and the
amelioration of manners and customs, as science
progressed from ignorance to learning, and from
a comparatively savage condition to its present
palmy state of refinement and moral culture.

To look for a different result would be to ex- I

pect impossibilities. Improvements in art, sci-
ence, and civilisation, have a mutual dependence
on each other. A change in the one will neces-
sarily produce a modification of all. This is a
truism that will not admit of contradiction or
dispute. When we hear, therefore, of ancient,
quaint phrases, whether in general literature or
in Freemasonry, being swallowed up and lost in
the undeviating march of scientific and moral
improvement, and the substitution of others
which are more in accordance with the usages

Hie Inevitable Law of Mutation. xi

of a polished era, we are not to be surprised at
such occurrences, nor complain, as many worthy
Masons of the old school are apt to do, of modern
innovations ; as if the institution were expected
to stand still, and remain exempt from the inevi-
table law of mutation to which all human sci-
ences are exposed.

Thus, for instance, the present race of Masons
are ignorant of the reference to a Master Mason's
clothing, as the fraternity understood it a hun-
dred and fifty years ago, and would scarcely
refrain from an incredulous smile when they are
told that it consisted of " a yellow jacket and a
pair of blue breeches." But this was simply a
figurative expression to signify the Third Great
Light, which was appropriated to the Master, as
the instrument by the use of which he drew his
designs on the " Trasel Board " as a direction for
the workmen ; the upper part being of polished
brass, and its points blue steel. In like manner,
several other peculiar phrases have become obso-

xii Preface.

lete, and are now imperfectly understood ; as in
the instance of the " Broached Thurnel " for the
apprentices to learn their work upon, connected
with the Trasel Board and the Rough Ashlar —
the triad having been changed to the Tracing
Board, Rough Ashlar, and Perfect Ashlar.

Again, what Mason of the present day under-
stands the meaning of Irah, which our ancient
brethren were so proud of ? And indeed it has
puzzled many accomplished Masons of modern
times. Being associated with the second degree,
it is believed by some to have referred to a per-
son. But this exposition involves two hostile
interpretations, neither of which may be correct ;
one party holding the opinion that it signified
Hiram Abiff ; and another that it had a mysteri-
ous reference to King James III., as he was
designated by his followers ; and if the latter
interpretation be correct, it was probably one of
the symbolical words of the Order introduced
into Masonry by the Jesuits, to express Eediet

Peculiar and Obsolete Phra&es. xiii

(redeat, redibit) Ad Habenas (Hsereditatem) ;
according to the anagrammatic form of reading
by initials. This was the opinion of Schneider.
Some interpret Irah, PINT, to mean Fear, as the
fear of God ; while others take it to be m\ he
has taught; and lastly, it has been referred to
the Temple, as who should say, He has laid the
foundation. Utrum horum mavis accipe.

Who knows anything at the present day about
the obsolete degrees of the Link and Wrestle?
They were formerly connected with the Ark and
Mark, the latter having been recently revived ;
while the Ark, or, as the degree was denomi-
nated, the Royal Ark Mariners, is in abeyance,
and seldom practised amongst the English Masons,
although it bears a reference to a legitimate
Masonic event.

A cowan, or listener, was a character extremely
obnoxious to our predecessors, and is not in much
more favour amongst ourselves ; albeit their quaint
method of punishing him, when detected, is now

xiv Preface.

altogether unknown — e.g., to place him under the
eaves of a house in stormy weather until the
water ran in at his shoulders and out'at his knees.
Hence the appellation of eavesdropper, and the
origin of the cautionary exclamation, " It rains I"
The modern treatment of a cowan is simply —
contempt.

The three fixed lights, or windows, subsequently
exchanged for our lesser luminaries, were explained
one hundred and fifty years ago to signify " the
three Persons, Father, Son, Holy Ghost ; " and
were used to find out the meridian, " when the
sun leaves the south, and breaks in at the west
window of the Lodge." While the " mossy
bed," the ancient signs of disgust and recogni-
tion, as well as the primitive name of a Master
Mason, are equally obscure at the present day ;
having been swept away, along with the original
method of characterising chemical bodies by 1

symbols, as being no longer necessary to the ■

system. Even the Masonic cipher, of which our

i

Disused Landmarks. xv

brethren of the last century were justly proud,
is now in abeyance, if not obsolete, for it is con-
sidered by the English fraternity a useless appen-
dage that may be well dispensed with.

In the formula of opening the Lodge before
the union of ancient said modem Masons in 1813,
it was announced by the chair that " all swearing,
whispering, and unmannerly or profane conversa-
tion," were strictly prohibited during Lodge
hours, under such penalty as " the Bylaws shall
inflict or a majority think proper." And the
reason publicly assigned for this prudent course
was, " that the business of the Lodge being thus
happily begun might be conducted with decency,
and closed in harmony and brotherly love/'
This formula was discontinued at the above-
mentioned period, and a new form substituted,
which brought the Christian tendency of the
Order more prominently before the Lodge.

There are also some passages in the old lectures
which the brethren once took for genuine Land-

xvi Preface*

marks, that have long been disused. In the
Entered Apprentice's Lecture, the following
passage occurs : u What is the day for ? — To see
in. What is the night for ? — To hear in. How
blows the wind ? — Due east and west." Again :
" How long do you serve your master ? — From
Monday morning till Saturday night. How
do you serve him? — With chalk, charcoal,
and earthen pan, &c." When speaking in the
Fellow Craft's degree of the elevation of the
middle chamber, the door was technically said to
be " so high that a cowan could not reach to
stick a pin in." And the illuminated letter,
by which it was distinguished, was said to denote
"the Great Architect of the Universe, or Him
that was taken up to the topmost pinnacle of
the Holy Temple at Jerusalem."

As a counterpoise to the abandonment of this
group of trivial observances by modern practice,
many valuable additions were introduced in the
revised lectures during the eighteenth century as

k^ The Doctrine of Masonic Number, xvii

matters of detail, which our more ancient brethren
would have been proud to acknowledge as mani-
r fest improvements in the system. These were

at length collected and embellished by Bro. W.
Preston ; and his Ritual formed the solid basis
on which the Lodge of Reconciliation, in the year
1814, constructed the Union Lectures which are
now used in the English Lodges. During these
gradual improvements, the doctrine of Masonic
Number slowly but certainly progressed in every
successive formula, until it reached its acme, in
the above-named year, by the introduction of all
those scientific numeral phenomena which are
deduced from a philosophical consideration of the
Pythagorean Triangle.

In the earlier rituals, Number is but incidentally
alluded to. The degrees, steps, lights, ornaments,
furniture, and jewels, &c, were arranged on the
principle of the Triad ; the cardinal virtues, with
their appropriate signs and references, represented
the tetrad, which, together with the five points

xviii Preface.

of fellowship and the seven liberal sciences, ap-
pear to be all the numerical references which
they contain ; and they were not enlarged on or
explained until Preston promulgated his Lectures
under the sanction of the Grand Lodge. And
here the numbers 3, 5, 7, and 1 1 are illustrated
rather more in detail in his improved version of
the Winding Staircase.

In the following pages, the doctrines and re-
ferences which necessarily result from a minute
consideration of the Science of Numbers, as enun-
ciated in the Pythagorean Triangle, will be sub-
jected to a scientific analysation; for it is a
remarkable fact, that although the institution of
Freemasonry is based upon it, we have no autho-
rised lecture to illustrate its fundamental prin-
ciples, or display its mysterious properties. At
every step, we find a triad reference, but the
reasons why this occurs are not satisfactorily
explained. The monad, the duad, the triad, and
the tetrad, meet us at every turn ; and though

The Science of Numbers. xix

these numbers constitute the foundation of all
arithmetical calculations, the candidate is not
fully instructed how they operate, or in what
manner they ought to be applied.

A large portion of the Egyptian philosophy and
religion seems to have been constructed almost
wholly upon the science of numbers ; and we are
assured by Kircher (CEdip. Egypt., torn. ii. p. 2)
that everything in nature was explained on this
principle alone. The Pythagoreans had so high
an opinion of it, that they considered it to be the
origin of all things, and thought a knowledge of
numbers to be equivalent to a knowledge of God.
The founder of the sect received his instructions
in this science from the Egyptian priests; who
taught him that, while the monad possesses the
nature of the efficient cause, the duad is merely
a passive matter. A point corresponds with the
monad, both being indivisible ; and as the monad
is the principle of numbers, so is the point of
lines. A line corresponds with the duad, both

xx Preface.

being considered by transition. A line is length
without breadth, extending between two points.
A superfice corresponds with the triad, because
in addition to the duad, length, it possesses a
third property, viz., breadth ; which is effected by
setting down three points, two opposite, the third
at the juncture of the lines made by the other
two. A solid or cube represents the tetrad ; for
if we make three points in a triangular form, and
set a fourth over them, we have a solid body in
the form of a pyramid, which has three dimen-
sions — length, and breadth, and thickness.

In expressing their opinion of the Kegular or
Platonic bodies, the followers of Pythagoras
argued that the world was made by God "in
thought, and not in time ; " and that He com-
menced His work in fire and the fifth element ;
for there are five figures of solid bodies which
are termed mathematical. Earth was made of a
cube, Fire of a pyramid, Air of an octaedron,
Water of an icosaedron, the Sphere of the

A Subject of Surpassing Interest. xxi

Universe of a dodecaedron. And the combina-
tions of the monad, as the principle of all things,
are thus deduced. From the monad came the
indeterminate duad ; from them came numbers ;
from numbers, points ; from points, lines ; from
lines, superfices ; from superfices, solids ; from
these, solid bodies whose elements are four,
viz., fire, water, air, earth; of all of which,
under various transmutations, the world con-
sists.

Such dissertations, so far as they are appli-
cable to the Science of Number, have received
some attention in the revised Fellow Craft's
Lecture of Dr Hemming, by an elucidation of the
Pythagorean Triangle. The subject is one of sur-
passing interest to the Free and Accepted Mason,
particularly if he be a lover of general Science.
At my first initiation, I soon discovered the
numerical peculiarity by which the Order is
distinguished, and wondered that the Lectures
contained such a meagre explanation of this

xxii Preface.

extraordinary fact. Being somewhat addicted
to mathematical studies, I took an intense interest
in the pursuit, and, during a course of miscel-
laneous reading, made various collections on the
subject of numbers, simple and compound, which
•I found invaluable when I became the Master
of a Lodge.

True, I was sailing in the dark, without
either compass or pilot, for the philosophy of
Masonry was very imperfectly understood in
those days. My researches, however, still made
a gradual though slow progress, for what will
not perseverance effect? Whatever I read con-
tributed to my store, for there is no book so bad
but some benefit may be derived from it by
an industrious man,' as the bee extracts honey
from the poisonous flower; and even when I
made no notes, I was steadily amassing materials
for future use in the peculiar walk of Masonic
literature which I was destined to pursue. It
will readily be believed, that I had not the

The Origin of this Work. xriii

slightest intention of writing for the press at that
early period of my career ; for Masonic publica-
tions at the commencement of the present century
were by no means in favour with the English
Craft ; and therefore, I threw my acquisitions
together as they arose, simply for my own pri-
vate reference, and without suspecting that they
would ever appear in a printed form. But man
proposes, and God disposes.

From these collections the following Treatise
was drawn up. It has been several years in hand,
and was not originally intended for publication;
but in compliance with an urgent request which
has been recently made upon me, I have allowed
the manuscript to be put to press, in the hope
that it will afford amusement and instruction to
the assiduous Mason who consults its pages with
the sober intention of improving his knowledge,
by acquiring a store of additional facts which
may assist his investigations into the more
abstruse arcana of Masonic Numbers.

xxiv Preface.

It has been well observed, that such specula-
tions are by some considered as trifling and use-
less ; but perhaps they judge too hastily; fpr
few employments are more innocent, none more
ingenious, nor, to those who have a taste for
them, more amusing ; aud mathematical amuse-
ments sometimes lead to important and useful

discoveries,

GEO. OLIVER.

IN TR OD UC TION.

THE PYTHAGOREAN TRIANGLE EXPLAINED, WITH A
DISSERTATION ON THE PECULIARITIES OF

MASONIC NUMBER.

jRL^.j&4 3 >

/■

THE

PYTHAGOREAN TRIANGLE.

-M-

INTRODUCTION.

HAVE often wondered how it could
happen that our ancient brethren should
have omitted to work out the details of
Freemasonry in a more particular and perfect
manner than we find accomplished in the publica-
tions of the last century ; because it was generally
believed, even then, that such discussions would
be extremely advantageous, by dissipating the
mists and prejudices which biassed the minds of
men, and indisposed them for the reception of
truth. Numerous evidences of this fact are
scattered over the writings of the few masonic
authors which distinguished that period. "The
best way," says Lawrie in his preface, "of re-
futing the calumnies which have been brought
against the fraternity of Freemasons, is to lay
before the public a correct and rational account

4 The Pythagorean Triangle.

of the nature, origin, and progress of the insti-
tution, that they may be enabled to determine
whether or not its principles are in any shape
connected with the principles of revolutionary
anarchy, and whether or not the conduct of its
members has ever been similar to the conduct of
traitors." And from the publication of such
sentiments, it must be evident to every brother's
experience, that the feeling against Freemasonry,
which displayed itself so openly; only a few years
ago, has assumed a much milder form, if it be
not entirely removed.

It will not however be difficult to account
for the dearth, of masonic writers in a preced-
ing age. Before the eighteenth century, sym-
bolical masonry, being limited to the simple
ceremonial, needed few illustrations ; because, as
the science was chiefly operative, the most valu-
able secrets would be those which had a reference
to building — to the scientific ornaments and de-
corations of each particular style of architecture
as it flourished in its own exclusive period ; and
these mysteries were communicated gradually, as
the candidate rose through the different stages of
his order or profession. °

There appears to have been one general prin-
ciple, which extended itself over every style from
the early English to the florid, decorated, and
perpendicular, and constituted one of the most
ineffable secrets of the Masonic Lodges. It is
now known to have been the hieroglyphical device
styled Vesica Piscis; "which may be traced

Prevailing Secrets in Early Times. 5

from the Church of St John Lateran, and the old
St Peter's at Eome, to the Abbey Church at Bath,
which is one of the latest Gothic buildings of any
consequence in England. It was formed by two
equal circles cutting each other in the centres, and
was held in high veneration, having been invari-
ably adopted by master masons in all countries.
In bas-reliefs which are seen in the most ancient
churches, over doorways, it usually circumscribes
the figure of our Saviour. It was indeed a prin-
ciple which pervaded every building dedicated to
the Christian religion, and has been exclusively
attributed to the scientific acquirements of
Euclid." 1

The prevailing secrets of the Lodges in these
early times, were the profound dogmata of Geo-
metry and Arithmetic, by the use of which all
their complicated designs were wrought out and
perfected. These sciences are inseparable from
the system ; and accordingly have been faith-
fully transmitted to our own times. " The secret
meetings of master masons within any particular
district, were confined to consultations with each
other, which mainly tended to the communica-
tion of science, and of improvement in their art.
An evident result was seen in the general uni-
formity of their designs in architecture, with
respect both to plan and ornament, yet not
without deviations. We may conclude that the
craft or mystery of architects and operative
masons was involved in secrecy, by which a

1 Kerrich in Archaeol., voL xvi. p. 292.

6 The Pythagorean Triangle.

knowledge of their practice was carefully ex-
cluded from the acquirement of all who were
not enrolled in their fraternity. Still, it was
absolutely necessary that when they engaged in
contracts with bishops or patrons of ecclesiasti-
cal buildings, a specification should be made of
the component parts, and of the terms by which
either contracting party should be rendered con-
versant with them. A certain nomenclature was
then divulged by the master masons for such a
purpose, and became in general acceptation in
the middle ages." *

The abstruse calculations which accompanied
the sciences of geometry and arithmetic, are no
longer necessary to Freemasonry as an institution
purely speculative ; and they were accordingly
omitted in the revised system as it was recom :
mended to the notice of the fraternity by the
Grand Lodge in 1717, and we retain only the
beautiful theory of these sciences, with their
application to the practice of morality, founded
on the power and goodness of T.G^A.O.T.U.

It would be an injustice to our brethren of the
last century to believe that they did not enter-
tain a profound veneration for the principles of
the masonic order. But the customs and habits
of the people of England, living in that day,
differed materially from our own. They were
times when conviviality and a love of social
harmony prevailed over the more sedate pursuits
and investigations of science, in which such an

1 Dallaway, Archit., p. 410.

Tlie Organisation of Freemasonry. 7

astonishing progress distinguishes the present
times. In the seventeenth and eighteenth cen-
turies, London was an atmosphere of clubs, and
a society of this kind existed in every street for
the peculiar use of its inhabitants, besides those
which were exclusively frequented by persons
possessing similar tastes or habits of amusement.
And it will be no disparagement to masonry, if
we believe that its private Lodges did not sustain
a much higher rank than some of these celebrated
meetings ; for the Kit -Cat, the Beefsteak, and
other clubs, were frequented by the nobility
and most celebrated literary characters of that
polished era.

It was the organisation of Freemasonry that
gave it the distinctive character which elevated
its pretensions above the common routine of
club-life ; and although it is admitted that
the members of the latter entertained a strong
attachment to their several institutions, yet none
were so enthusiastic as those who had enlisted in
the cause of masonry, as we may learn from the
few testimonies which remain. A mason of high
standing, more than a century ago, thus expresses
his feelings respecting the order : « Masonry is
the daughter of heaven ; and happy are those
who embrace her. By it youth is passed over
without agitation, the middle age without anx-
iety, and old age without remorse. Masonry
teaches, the way to content, a thing almost un-
known to the greater part of mankind. In
short, its ultimate resort is to enjoy in security

8 The Pythagorean Triangle.

the things that are, to reject all meddlers in state
affairs or religion, or of a trifling nature ; to em-
brace those of real moment and worthy tendency,
with fervency and zeal unfeigned, as sure of
being unchangeable as ending in happiness.
They are rich without riches, intrinsically pos-
sessing all desirable good ; and have the less to
wish for by the enjoyment of what they have.
Liberty, peace, and tranquillity, are the only ob-
jects worthy of their diligence and trouble." *

But this, as well as almost all the testimonies
of that period to its superior excellence, is con-
fined exclusively to the practice and rewards of
Christian morality.

Modern revision has however extended the
limits of scientific investigation in the order of
Freemasonry beyond what was intended by those
who decreed that "the privileges of masonry
should no longer be restricted to operative
masons, but extend to men of various professions,
provided they were regiflarly approved and initi-
ated into the order." / And Dr Hemming and
his associates, in the year 1814, thought it expe-
dient to introduce some peculiar disquisitions
from the system of Pythagoras, on the combina-
tions of the point, the line, the superfice, and the
solid, to form rectangular, trilateral, quadrila-
teral, multilateral figures, and the regular bodies ;
the latter of which, on account of their singu-
larity, and the mysterious nature usually ascribed
to them, were formerly known by the name of the

1 Pocket Companion, p, 296.

Temperance and Early Hours. 9

five Platonic bodies ; and they were so highly re-
garded by the ancient Geometricians, that Euclid
is said to have composed his celebrated work on
the Elements, chiefly for the purpose of displaying
some of their most remarkable properties. These
disquisitions usually conclude with an explana-
tion of the forty-seventh problem of Euclid,
which is called the Eureka of Pythagoras.

Our transatlantic brethren have improved upon
this still further. Some of their Grand Lodges
have given a public sanction to the introduction
of literary and scientific subjects, not contained
in the usual lectures, and the open discussion of
them at the private meetings of the society. And
a committee of the Grand Lodge of New York,
in their report for the year 1842, decided that
"masonic periodicals, if judiciously conducted,
are calculated to accomplish a vast amount of
good, by diffusing more extensively those sound,
moral, and benevolent 'principles, which so emir
nently characterise this venerable institution;
your committee therefore recommend those publi-
cations to the liberal patronage of the fraternity."

To promote this laudable purpose, the Grand
Lodges have recommended temperance and early
hours ; a general observance of which, I am per-
suaded, would not only afford ample leisure for
scientific investigations, but would also operate
very favourably both for the welfare and credit of
the society; and it is much to be wished that
such a system of discipline could be established
by a similar authority in the English Lodges ; for

1 The Pythagorean Triangle.

a laxity of practice in these particulars is calcu-
lated to introduce loose and incorrect habits
which cannot fail to prove injurious to their
popularity. If a Lodge be opened beyond the
prescribed time, its labours may be protracted,
particularly if ite members are too much attached
to refreshment, to a late hour, which will be in-
consistent with domestic comfort, and may pro-
bably create dissatisfaction and hostility in their
families. There is a delicate sensibility in the
female mind which is easily excited, and an im-
pression may be made in a moment which will be
found difficult to eradicate. The members of a
Lodge, therefore, ought to be ever on their guard
lest an unfavourable prejudice against the craft
be thus created ; because, in such a case, every
little deviation, which, under extraordinary cir-
cumstances, may be unavoidable, will be magni-
fied into a serious fault. And when transgressions,
even though they be imaginary, are multiplied in
the opinions of those who ought to be most dear
to the fraternity, and whose happiness it is their
duty to promote by every attention in their
power, an estrangement of heart may be occa-
sioned, which will embitter domestic comfort,
and produce misunderstandings and disagree-
ments, for which the pleasures and enjoyments
of Freemasonry will be in vain expected to com-
pensate.

Nothing can supply the loss of domestic com-
fort, which is the one great source of happiness
that an all-wise Creator has provided for us on

Tlie Great Source of Happiness. 1 1

earth. If therefore a fear of injuring the inter-
ests of Freemasonry should fail to induce the
observance of decorous hours in the conduct of a
Lodge, let this consideration be superadded — let
an attention to the comforts, and a respect for
the prejudices of their families prompt the frater-
nity to avoid late sittings. It is a practice which
answers no one good purpose, secures no valu-
able end, conveys no true gratification in the
enjoyment, and embitters the reflections of the
ensuing day. And beyond all this, it places in
jeopardy those fireside comforts, those domestic
virtues, which the religion we profess, the
masonry we practise, and the reason with which
the Most High has endowed us, alike concur in
stimulating, us to cultivate and adorn.

To carry out all these points, and to bear
harmless the order during the process, much
depends on the knowledge and judgment of the
Master ; and it is of such importance to the pro-
sperity of Freemasonry that this officer be judici-
ously selected, that it behoves every candidate to
consider well his capabilities for the office before
his election. It is not enough that he is au fait
at the openings and closings of the several de-
grees, and well acquainted with all other routine
ceremonies ; he ought also to be conversant with
the history, the antiquities, and the philosophy
of the order, and the tendency of its mysteries
and pursuits to promote the practice of Christian
morality; for on this knowledge the success of
his administration will, in a great measure, de-

1 2 Tlie Pythagorean Triangle.

pend. In these clays, bodies of men meet together
for other purposes than to hear the repeated reci-
tation of a series of commonplace maxims, which
soon lose their interest and become as sounding
brass and a tinkling cymbal. Even an acquaint-
ance with the traditions of Freemasonry is not
without its utility. They lead to something of a
higher character, and are intimately connected
with its philosophy. The most minute legend,
although abstractedly it may be considered trifling
and unmeaning, is not without its use, and if
traced to its elements, will be found to bear a
relation to facts or doctrines connected with our
best and dearest interests.

It appears to me, that in the revision of the
English Eitual at the Union, a great omission
occurs which it would be well to supply ; and in
the present taste for scientific lectures and inves-
tigations, nothing would tend to elevate the cha-
racter of Freemasonry more than to afford an
opportunity for its indulgence by furnishing the
means of carrying out its references in the intro-
duction of a higher range of science. Free-
masonry, to be completely successful, should take
precedence in science as it does in morals and the
exercise of charity : for there are few institutions
which equal it in the walks of benevolence. Its
charities are unrivalled. It cherishes the orphan
— it supports the widow — it relieves the destitute
— and provides for the worthy aged brother an
asylum from the storms of penury and indigence,
at that helpless period of life when his strength

A Higher Range of Science. 13

fails him, and he is no longer able to wrestle suc-
cessfully with adversity and want.

It is true the seven liberal sciences are referred
to in the second degree ; but, with the exception
of Geometry, they occupy no important place in
the lecture. And for this reason, I suppose, that
in ancient times the order was denominated Geo-
metry. On this science, with its application to
architecture, our disquisitions are abundant and
powerfully interesting ; and why should not a lec-
ture on the elementary principles of other sciences
be equally gratifying to the members of a Lodge ?
Arithmetic, or the science of Number, is nearly
allied to Geometry ; we patronise Music in prac-
tice but hear nothing of it in theory ; and of As-
tronomy we are merely told that it is an art by
which we are taught to read the wonderful works
of God in those sacred pages the celestial hemi-
sphere, and that while we are employed in the
study of this science, we perceive unparalleled
instances of wisdom and goodness, and through
the whole of the creation trace the glorious Au-
thor by His works.

That great philosopher Pythagoras, who,by the
superiority of his mind, infused a new spirit into
the science and learning of Greece, and founded
the Italic sect, taught his disciples Geometry,
that they might be able to deduce a reason for all
their thoughts and actions, and to ascertain cor-
rectly the truth or falsehood of any proposition
by the unerring process of mathematical demon-
stration. Thus being enabled to contemplate the

1 4 The Pythagorean Triangle.

reality of things, and to detect imposture and
deceit, they were pronounced to be on the road to
perfect happiness. Such was the discipline and
teaching of the Pythagorean Lodges, It is related,
that when Justin Martyr applied to a learned
Pythagorean to be admitted as a candidate for the
mysterious dogmata of his philosophy, he was
asked whether, as a preliminary step, he had al-
ready studied the sciences of Arithmetic, Music,
Astronomy, and Geometry, which were esteemed
the four divisions of the mathematics; and he
was told that it was impossible to understand the
perfection of beatitude without them, because they
alone are able to abstract the soul from sensibles,
and to prepare it for intelligibles. He was further
told that in the absence of these sciences no man
is able to contemplate what is honest, or to deter-
mine what is good. And because the candidate
acknowledged his ignorance of them he was re-
fused admission into the society.

Above all other sciences or parts of the ma-
thematics, however, the followers of Pythagoras
esteemed the doctrine of Numbers, which they
believed to have been revealed to man by the
celestial deities. And they pronounced Arith-
metic to be the most ancient of all the sciences,
because, being naturally first generated, it takes
away the rest with itself, but is not taken away
with them. For instance, animal is first in nature
before man ; for by taking away animal we take
away man ; but by taking away man we do not
take away animal. They considered numbers ex-

The Doctrine of Numbers. 15

tending to the decad, to be the cause of the essence
of all other things; and therefore esteemed the
creation of the world as nothing more than the
harmonious effect of a pure arrangement of num-
ber. This idea has been adopted by Dryden —

From harmony, from heavenly harmony,
This universal frame began;

From harmony to harmony,
Through all the compass of the notes it ran,
The diapason closing full in man.

Pythagoras had another idea* as we are informed
by Censorinus, respecting the creation of the
world, and taught that it was fashioned according
to the principles of musical proportion ; that the
seven planets which govern the nativity of mortals
have a harmonious motion, and intervals corre-
sponding to musical diastemes, and render various
sounds according to their several distances, so
perfectly consonant that they make the sweetest
melody, but " inaudible to us by reason of the
greatness of the noise, which the narrow passage
of our ears is incapable of receiving."

And further, he esteemed the monad to repre-
sent the great and good Creator, under the name
of Dis, or Zeus, or Zau ; and the duad he re-
ferred to the evil and counteracting principle or
daemon, " surrounded," as Plutarch expresses it. 1
" with a mass of matter." And Porphyry adds, 3
that the monad and duad of Pythagoras seem to
have been the same with Plato's irepas and aireipov,
his finite and infinite in his Philebus ; the former

1 De Placitis Placitorum, 1. i c. 7. a Vit. Pyth., p. 47.

16 The Pythagorean Triangle.

of which two only is substantial, that first most
simple Being, the cause of all unity and the mea-
sure of all things.

According to the above doctrine, the monad was
esteemed the father of Number, and the duad its
mother : whence the universal prejudice in favour
of odd numbers, the father being had in greater
honour than the mother. Odd numbers being
masculine were considered perfect, and applicable
to the celestial gods, while even numbers, being
female, were considered imperfect, and given to the
terrestrial and infernal deities. Virgil has recorded
several instances of this predilection in favour of
odd numbers. In his eighth Eclogue, he says,

Terna tibi haeo primum triplici diversa colore
Licia circumdo; terque h»c altaria circum
Effigiem duco ; Numero deos impare gaudet.

Thus translated by Dryden —

Around his waxen image first I wind
Three woollen fillets of three colours join'd ;
Thrice bind about his thrice-devoted head,
Which round the sacred altar thrice is led.
Unequal numbers please the gods.

The Eastern nations of the present day appear
to reverse this principle. When two young per-
sons are betrothed, the number of letters in each
of their names is subtracted the one from the
other, and if the remainder be an even number, it
is considered a favourable omen, but if it be odd,
the inference is that the marriage will be unfor-
tunate.

Arithomancy. 17

Some curious superstitions of this character
were still in existence during the last century
amongst ourselves, and may not at the present
time be altogether obsolete. A Scottish minister,
who wrote a treatise on witchcraft in 1 705, says,
"Are there not some who cure diseases by the
charm of numbers, after the example of Balaam,
who used magiam geometricam, Build me here
seven altars, and prepare me seven oxen and
seven rams. There are some witches who enjoin
the sick to dip their shirts seven times in water
that runs towards the south." Sir Henry Ellis y
has collected many instances of the use of odd
numbers, in his notes on Brand's " Popular Anti-
quities," to which the curious reader is referred. 1

The superstition of divination by number,
called Arithomancy, was so firmly planted in the
mind of man by the observances of ancient times,
that it appears impossible entirely to eradicate it.
An old writer quaintly remarks, "I will not be
superstitiously opinionated of the misteries of
numbers, though it bee of longe standing amongst
many learned men ; neither will I positively affirm
that the number of six is fatall to weomen, and the
numbers of seaven and nine to men; or that those
numbers have (as many have written) magnum
in tota rerum natura potestatem, great power in
kingdoms and commonwealths, in families, ages,
of bodies, sickness, health, wealth, losse, &c. ; or

1 See also on this subject Censor, de die nat., e. xii. Philo de
leg., i. Bodin deRepub., 1. iv. c. 2. Varro in GelL, 1. iii. Jerom in
Amos, v. Practice of Piety, fol. 410, &c. &c.

B

1 8 The Pythagorean Triangle.

with Seneca and others, Septimus quisque annus,
&c. Each sea vent h yeare is remarkable with men,
as the sixth is with weomen. Or, as divines teach,
that in the number of seaven there is a misticall
perfection which our understandinge cannot at-
taine unto ; and that nature herself is observant
of this number."

Every tyro knows that odd numbers are mason-
ic ; and if he be ignorant of the reasons why 3,
5, 7, and 11, have been adopted as landmarks, let
him apply to the Master of his Lodge for infor-
mation, and he will then be satisfied of the
wisdom of the appropriation, because number
forms one of the pillars which contribute to
the support of scientific masonry, and constitutes
an elementary principle of Geometry. Thus, in
the celebrated Pythagorean triangle, consisting of
ten points, the upper single dot or
jod is monad or unity, and repre-
sents a point, for Pythagoras con-
sidered a point to correspond in
proportion to unity ; a line to 2 ; a
superfice to 3 ; a solid to 4 ; and he defined a point
as a monad having position, and the beginning
of all things ; a line was thought to correspond
with duality, because it was produced by the first
motion from indivisible nature, and formed the
junction of two points. A superfice was com-
pared to the number three, because it is the first
of all causes that are found in figures ; for a
circle, which is the principal of all round figures,
comprises a triads in centre — space — circumfer-

Application of Numbers to Physical Tilings. 19

ence. But a triangle, which is the first of all
rectilineal figures, is included in a ternary, and
receives its form according to that number ; and
was considered by the Pythagoreans to be the
^author of all sublunary things. The four points
at the base of the Pythagorean triangle correspond
with a solid or cube, which combines the princi-
ples of length, breadth, and thickness, for no
solid can have less than four extreme boundary
points.

Thus it appears that in applying number to
physical things, the system of Pythagoras termi-
nated in a tetrad, while that of Aristotle, by
omitting the point, limited the doctrine of mag-
nitude to a triad, viz., line— surface — body. In
divine things, however, the former philosopher pro-
fusely used the number three, because it represented
the three principal attributes of the Deity. The
first whereof, as we are informed by Cudworth,
is infinite with fecundity; the second infinite
knowledge and wisdom ; and the last active
and perceptive power. From which divine at-
tributes the Pythagoreans and Platonists seem
to have framed their trinity of archical hypostases,
such as have the nature of principles in the uni-
verse, and which, though they be apprehended as
several distinct substances gradually subordinate
to one another, yet they many times extend the
to Qhov so far as to comprehend them all within
it.

While employed in investigating the curious
and unique properties which distinguish many of

20 The Pythagorean Triangle.

the digits, we no longer wonder that the inhabi-
tants of the ancient world, in their ignorance of
the mysterious secrets of science, and the abstruse
doctrine of causes and effects, should have ascribed
to the immediate interposition of the Deity those
miraculous results which may be produced by an
artful combination of particular numbers. Even
philosophy was staggered ; and the most refined
theorists entertained singular fancies, which they
were unable to solve without having recourse to
supernatural agency. Hence the pseudo science
of Arithomancy, or divination by numbers, became
very prevalent in the ancient world; and was
used by Pythagoras as an actual emanation of
the Deity. By this means, according to Tzetzes,
he not only was able to foretel future events, but
reduced the doctrine to a science, governed by
specific rules, which he transmitted to posterity
in his "Book of Prognostics."

The ancients had°a kind of onomantic arith-
metic, the invention of which was in like manner
ascribed to Pythagoras, whether truly or not is
of no importance here, in which the letters of the
alphabet, the planets, the days of the week, and
the twelve zodiacal signs, were assimilated with
certain numbers; and thus, by the use of pre-
scribed tables, constructed astrologically accord-
ing to the aspects, qualities, dignities, and debili-
ties of the planets relatively towards the twelve
signs, &c, the adept would authoritatively pro-
nounce an opinion on questions affecting life and
death, good ai*d evil fortune, journeys, detection

The Jewish Cabalists. 21

of theft, or the success of an enterprise. It must
be confessed, however, that these predictions were
not always correct ; for the rules laid down in
different systems varied so essentially, that the
wisest magician was frequently puzzled to select
an appropriate interpretation. The numeral sys-
tem has been introduced into the modern practice
of astrology, and very important results appear
to depend on the trine, quartile, and sextile aspect
of the planets in the horoscope.

Something of this sort was used by the Jewish
cabalists ; and hence one of the rules of their
cabala was called gemetria, or numeration, which
was chiefly confined to the interpretation of their
sacred writings. The letters of the Hebrew lan-
guage being numerals, and the whole Bible being
composed of different combinations of those let-
ters, it was supposed that the correct meaning of
difficult passages could only be ascertained by
resorting to their numerical value. The Tal-
mudists entertained an opinion that the mystery
of numbers was actually taught in their scrip-
tures ; because, after the idolatrous priests of
Baal had accepted the challenge of Elijah, that
prophet constructed his altar of twelve stones,
corresponding with the twelve tribes of Israel ;
but they say that when he took this number for
the special purpose of conciliating the favour
of Jehovah, it was not merely because the sons of
Jacob were twelve in number, but because that
particular number was supposed to contain a pro-
found and unfathomable mystery.

22 The Pythagorean Triangle.

The system on which this doctrine was founded
appears to be, that every letter in the Hebrew
alphabet is in reality a distinct light or attribute ;
and hence the letters are symbols of everything
which the earth and heavens contain. The Rabbi
Barahiel taught that numbers proceed from Him
who was before all numbers, as they go not be-
yond ten. These lights are denominated rVTSD
in the singular, which is derived from n9D num-
bers ; each possessing the property of the number
which it represents. And hence the theologians
say that the Tetragrammaton represents the Ten
Sovereign Lights, in which all the divinity is in-
fused, because the words formed by these letters
are invariable ; and although they admit of
twelve transpositions and combinations, every
one of them means T.Gr.A.O.T.U. . Hence the
prophet Malachi says, "I am the Lord, and
change not ;" for the Tetragrammaton, or Sacred
Name, however it may be transposed, never
changes its meaning.

The Rabbi Manasseh, Ben Israel, in his expla-
nation of the cabala, says, "The fourth rule is
founded on the shape of the letters. If it be
asked, Why does the law begin with a 2 1 The
answer is, Because it is formed by three lines,
or Vs, which, being written at length, spell in%
numerically thirteen; this number being multi-
plied by three (the three lines), makes thirty-
nine, equal to in** HIT (the Lord is One), also
thirty-nine. The cabalists say that this letter 2
has a point above and another behind, signi-

The Magic Square.

23

fying that the Lord who is in heaven created the
world, which is represented by the antecedent
letter, that is the K, formed by two *'s and a i,
making together twenty-six, the same number as
the Tetragrammaton. Reason apparently sup-
ports the idea that profound mysteries are con-
tained in the characters of this holy language;
and who will contend that they do not all involve
many secrets and reasons for being used in the
law of God, from the perfect art with which they
are formed ? "

The same results were obtained by means of
the Magic Square, which is a figure made up of
numbers in arithmetical proportion, so disposed
in parallel and equal ranks that the sums of each
row, whether taken perpendicularly, horizontally,
or diagonally, are equal, as in the
adjoining diagram. Such squares
seem to have been so called be-
cause they were used in the con-
struction of talismans. It is pro-
bable they were so employed in
consequence of the ranks always making the same
sum, a circumstance extremely surprising in the
more ignorant ages, when mathematics passed for
magic. . The magic square was held in great
veneration among the Egyptians ; and the Py-
thagoreans, their disciples, in order to add more
efficacy and virtue to this square, dedicated it to
the then known seven planets divers ways, and
engraved it upon a plate of that particular metal
which was esteemed in sympathy with the planet.

2
9
4

7
5
3

6
1

8

24 The Pythagorean Triangle.

The square thus dedicated was enclosed within
a regular polygon inscribed in a circle, which was
divided into as many equal parts as there were
units in the side of the square, with the names of ***"
the angles of the planet; and the signs of the
zodiac written upon the void spaces between the
polygon and the circumference of the circum-
scribing circle. Such a talisman they vainly
imagined would befriend the person who carried
it about with him. 1

Divination by numbers was not confined to
Jewish or heathen nations, but occupied much
attention at different periods of Christianity ;
and superstitious properties, I am afraid, are still
attached to particular numbers, as forming cli-
macterics, or grand climacterics ; for the days of
a man's life are usually considered to be affected
by the septenary year, which, as it is frequently
believed, produces considerable changes in both
body and mind. But the most remarkable
change in a person's life is at the climacteric,
or 7 x 7 = 49 years ; or the grand climacteric,
7 x 9 = 63 ; or 9 x 9 = 81 years ; each of
which is conceived to be fraught with a peculiar
fatality. And there are numbers of persons, even
in the nineteenth century, who contemplate these
periods with some degree of terror, and esteem it
a relief when they have passed away.

Several other numbers have superstitious mean-
ings attached to them. Dr Brown, in his /

i See more of this in Chambers's Tracts, under the head of " Natural
Magic."

Superstitious Meanings of Numbers. 25

" Pseudodoxia Epidemica," says that "six have
found many leaves in its favour ; not only for
the daies of the creation, but its natural consider-
ation as being a perfect number, and the first that
is completed by its parts ; that is, the sixt, the
half, and the third, 1, 2, 3 ; which drawn into a
sum, makes six. The number ten hath been as
highly extolled, as containing even, odd, long,
plane, quadrate, and cubical numbers; and
Aristotle observed with admiration that barba-
rians as well as Greeks did use a numeration unto
ten ; which, being so general, was not to be judged
casual, but to have a foundation in nature. So
not only seven and nine, but all the rest have
had their elogies, as may be observed at large in
Rhodiginus, and in several writers ; since every
one extolling number according to his subject,
and as it advantaged the present discourse in
hand."

On the same subject, Smith, in his "Life of
William, Marquis of Berkeley/' who was born
in 1426, tells us that he " closeth the second
septenary number from Harding the Dane,
as much differing from his last ancestors, as
the Lord Thomas, the first septenary lord, did
from his six former forefathers." And he then
proceeds to say, " I will not be superstitiously
opinionated of the misteries of numbers, though
it bee of longe standing amongst many learned
men ; neither will I positively affirm that the
number of six is fatall to weomen, and the
numbers of seaven and nine to men ; or that

26 The Pythagorean Triangle.

those numbers have (as many have written)
magnum in tola rerum natura potestatem, great
power in kingdoms and commonwealths, in
families, ages, of bodies, sickness, health, wealth,
losse, &c. ; or with Seneca and others, Septimus
quisque annus, &c. Each seaventh yeare is re-
markable with men, as the sixth is with weomen.
Or, as divines teach, that in the number of seaven
there is a misticall perfection which our under-
standinge cannot attaine unto; and that nature
herself is observant of this number."

Numeral divination on some unimportant points
was at length reduced to an unerring system ; and
the memory of a few brief rules would enable even
a child to dive into another's thoughts, and thus
excite a high degree of astonishment, by a process
which cannot fail to produce a correct result.
For instance, if any person has an even number
of counters in one hand, and an odd number in
the other, it will be easy to determine in which
hand the odd or even number is by the following
certain rule. Desire the person to multiply the
number in his right hand by any odd figure,
and the number in his left by an even one;
and inform you whether the products when
added together are odd or even. If even, the
even number is in the right hand ; if odd, the
even number is in the left hand.

By a similar process, a number which any
person may think of will be easily ascertained.
Thus, request him to double the number with
the addition of four ; then let him multiply the

Numeral Divination. 27

whole by five, adding twelve to the product, and
placing a cipher after the amount. From the
number thus obtained let him deduct 320 and
tell you the remainder; from. which, if you reject
the two last figures, the number that remains will
be the one which he had fixed on in his mind. I
shall close these observations on the subject of
numeral divination with one other example. If
you would find the difference between two num-
bers, the greatest of which is unknown, it will
only be necessary to take as many nines as there
are figures in the smallest number, and subtract
that sum from the number of nines. Let another
add that difference to the largest number, and
taking away the first figure of the amount, add
it to the number that remains, and that sum will
be the difference required.

In these times of superior scientific knowledge,
when gas has superseded the use of oil, and steam
performs the labour of men and horses ; when
sage philosophers have discovered mushrooms in
potatoes, and sledge-hammers in the pollen of
wheat, these topics may be considered puerile
and useless ; but it was not so at that period —
of ignorance, as it may be esteemed by jnodern
presumption — when the standard of learning and
wit was borne by such men as Addison and
Steele, Pope, Swift, Johnson, and their coadjutors,
the jewels of the Augustan crown, when such
subjects were esteemed worthy the notice of a
Spectator, a Rambler \ a Guardian, or a World.

Dr Johnson, speaking in the Rambler of the

28 The Pythagorean Triangle.

climacteric periods, says, " The writers of medicine
and physiology have traced, with great appear-
ance of accuracy, the effects of time upon the
human body, by marking the various periods of
the constitution and the several stages by which
animal life makes its progress from infancy to
decrepitude. Though their observations have not
enabled theiji to discover how manhood may be
accelerated, or old age retarded, yet surely, if
they be considered only as the amusements of
curiosity, they are of equal importance with con-
jectures on those things more remote, with cata-
logues of the fixed stars and calculations of the
bulk of planets. It had been a task worthy of
the greatest philosophers to have considered with
equal care the climacterics of the mind ; to have
pointed out the time at which every passion
begins and ceases to predominate, and noted the
regular variations of desire, and the succession of
one appetite to another."

Amongst the ancients, number was divided
into two distinct parts, intellectual and sciential.
The former was considered the root and origin of
all things ; the cause of the existence of gods and
men; the principle of the universe and all that
it contains, by which matter was arranged into
form and order, and the systems perform their
accustomed revolutions with accuracy and pre-
cision. The sciential division was subdivided
into two portions, odd and even, the former
limited, the latter infinite. According to the
definition used by the Pythagoreans, "even num-

t

Odd and Even Numbers. 29

ber is that which at once admits division into
the greatest and the least ; into the greatest
magnitudes (for halves are the greatest parts) ;
the least in multitude (for two is the least
j number) according to the natural opposition of

these two kinds. Odd numbers cannot be thus
divided; for they are only capable of being
separated into two unequal parts." Pythagoras
called the monad the father, and the duad the
mother of number ; whence it was concluded
that those numbers which resembled the monad
were most propitious.

Hence, in all the heathen systems, odd num-
bers were esteemed the most perfect, and repre-
sented the celestial deities. In our own country
however, and under the influence of Christianity,
we find a predilection for even numbers in con-
nection with the mysteries of fairy mythology
so prevalent in the middle ages. In Morgans
" Phcenix Brittanicus " is a curious tract on this
subject, entitled "An account of Anne Jefleris,
now living in the county of Cornwall, who was
fed for six months by a small sort of airy people
called fairies ; and of the strange and wonderful
cures she performed with salves and medicines
she received from them, for which she never took
one penny of her patients." In this tract she
gives the following account of her commerce
with these creatures, which I quote so far as it
applies to my purpose. She says, "that in 1645,
as she was one day sitting knitting in an arbour
in the garden, there came over the hedge, of a

30 The Pythagorean Triangle.

sudden, six persons of a small stature, all clothed
in green, which frighted her so much as to throw
her into a great sickness. They continued their
appearance to her never less than two at a time,
and never more than eight, and always in even
numbers, 2, 4, 6, 8."

In order to a right understanding of the
application of the numeral system, it will be
necessary to give a detailed explanation of the
occult meaning of the several digits, as taught in
some of the ancient systems of the spurious Free-
masonry ; and this will show to what a beautiful
moral purpose it is capable of being applied.

THE MONAD, OR POINT, DISCUSSED AS
THE ORIGIN OF ALL CALCULATION.

THE POINT, MONAD, UNITY, OR THE
NUMBER ONE.

CHAPTER I.

THE POINT.

MONAD, UNITY, OR THE NUMBER ONE.

" A point is enough to put all the schools in the world in a combus-
tion. But what need has man to know that point, since the
creation of such a small being is beyond his power ? A fortiori, phi-
losophy acts against probability when, from that point which ab-
sorbs and disconcerts all her meditations, she presumes to pass on
to the generation of the world, or the ordering of God's decrees."
—La Pluche.

" The sciences may well compose
A noble structure, vast ;
A point, a line, a superfice,
But solid is the last."

Ancient Lectures of Masonry.

HE exalted ideas which were entertained
by the ancient poets and philosophers're-
spectingthe mysterious properties of num-
bers, may be estimated from the superstitious uses
to which they were made subservient in all coun-
tries, whether the inhabitants were savage or refined.
The former saw that the number of his fingers
ended at ten ; and this constituted the amount of

c

34 The Pythagorean Triangle.

his knowledge. It formed the standard of all his
computations. When a savage, on his war-path,
was asked the number of his enemies — if few, he
would hold up one or more of his fingers — if many,
them all. And in whatever manner his ideas of
units might be designated, the calculation would
always end in ten. Thus, in Homer, Proteus
counts his sea-calves by fives, or in other words
by the number of fingers on his hand. Several
nations in the wilds of America have to this day
no other instruments of calculation. It is an-
other strong presumption of the truth of what I
now advance, that all civilised nations count by
tens ; tens of tens, or hundreds ; tens of hun-
dreds, or thousands ; and so on, but always from
ten to ten. We can discover no reason why this
number should be chosen rather than any other
for the term of numeration, except the primitive
practice of counting by the fingers. 1

This was the general custom, although there
were some exceptions. For instance, M. de la
Condamine tells us of a certain tribe in South
America who had no particular word for any
number bevond three ; 2 while in Mexico and Cen-
tral America they added this three to their ten
fingers, and counted as far as thirteen ; beyond
which point they again commenced with the
unit. But the rule will hold good for the gene-
ral usage of antiquity ; and as such has been
delivered down to our own times.

1 Goguet, Origin of Laws, vol. i. p. 216.
9 Relat. de la rivi&re des Amazones, p. 67.

Ancient Methods of Expressing Numbers. 35

Arithmetical operations, says the Abbfi Pluche, 1
were facilitated and shortened first by the use of
counters, and afterwards by figures or chalked
letters. Thus the Romans, when they had a mind
to express unity, either held up one finger or
chalked the figure I. To express the succeeding
numbers they drew II, III, IIIL . For the num-
ber five they depressed the three middle fingers,
and extended the thumb and little finger only,
which formed the V. . They signified ten by
putting two V's, one upon the other, thus * or by
joining them together, which formed X. Then
they combined the X, the V, and the I, till they
came up to fifty, or five tens, which they ex-
pressed by laying the five upon its side, thus, ^.
The figure in this posture assumed the form of
an L. A hundred was marked with two L's put
one upon the other (£), which was subsequently
rounded into a C. Five hundred was expressed
by Lq, and a thousand by CLq. These figures
were afterwards changed, the one into D, and
the other into CIq, or M. The Greeks and
Hebrews employed the letters of the alphabet
ranged in order, to express all imaginable
numbers.

It was the belief of wise and learned men in all
ages that there was a secret virtue in particular
numbers, amongst whom Pythagoras occupies the
principal rank. He was followed by all the phi-
losophers of the Italic school ; and Plato trans-
mitted it, with many improvements, to his sue-

1 Spectacle de la Nature, vol. v. p. 141.

36 The Pythagorean Triangle.

cessors; until the superstition became so firmly
grafted in the human mind, that time and edu-
cation have failed entirely to extinguish it. An
examination into the mysterious properties of
numbers has constituted the serious occupation
of many a man of real talent in comparatively
modern times. But the old philosophers em-
bodied in their numeral system such excellent
doctrines, and beautiful lessons of morality as
have been deemed worthy of introduction into the
science of Freemasonry for the edification of the
brethren ; and the absurd superstitions in which
they were originally embodied may be forgiven,
as being incidental to their imperfect and spuri-
ous religion, for the sake of the genius with which
they were decorated and enriched.

Amongst these sages, the Monad represented
the throne of the Omnipotent Deity, placed in the
centre of the empyrean, to indicate T.G.A.O.T.U.,
by whom all things were made and are preserved.
This disposition was symbolised by the hierogram
of a Point within a circle or equilateral triangle,
to exemplify equally the unity of the divine
essence, and His eternity, having neither begin-
ning of years nor end of days. And this deduc-
tion appears perfectly reasonable, because the
Monad or Point is the original and cause of the
entire numeral system, as God is the cause of all
things, being the only and great Creator on whom
everything depends ; for, if there were more all-
powerful Beings than one, none would be inde-
pendent, nor would all perfections be centred in

The Mysterious Properties of Numbers. 37

one individual, " neither formally by reason of
their distinction, nor eminently and virtually,
for then one should have power to produce the
other, and that nature which is producible is
not divine. But all acknowledge God to be
absolutely and infinitely perfect, in whom all
perfections imaginable, which are simply such,
must be contained formally, and all others
which imply any mixture of perfection, vir-
tually." 1

And to the same effect, Sthenidas the Locrian
says, " The first god is conceived to be the father
both of gods and men, because he is mild to
everything which is in subjection to him, and
never ceases to govern with providential regard.
Nor is he alone satisfied with being the maker of
all things, but he is the nourisher, the preceptor
of everything beautiful, and the legislator to all
things equally." 2

The universal symbol by which this great Being
was designated, viz., the point within. a circle 9
it may be necessary to explain with some de-
gree of minuteness, because it constitutes one of
the most important emblems of masonry. One
of the earliest heathen philosophers of whom his-
tory gives any account was Hermes Trismegistus,
and he describes the Maker of the universe as
"an intelligible sphere whose centre is everywhere,
and whose circumference cannot be defined/' be-
cause the universe is boundless, and He existed

1 Pearson on the Creed, Art. 1.
* Taylor's Fragments, p. 27.

38 The Pythagorean Triangle.

from all eternity. David expressed a similar sen-
timent when he said, " Thou art the same, and
Thy years will, have no end." * We are told that
the Persians, when they wished to pay a high
respect to the Deity, ascended to the top of a
high mountain, and expanding both hands, they
prayed to Him in the name of "the circle
of heaven." In like manner, the Jews enter-
tained a belief that "the heaven of heavens
could not contain Him." The Komans placed
a circular target as a symbol of the Deity, be-
cause, as in the circumference there is but one
point at its centre, and can be no more, so in the
whole circumference of the universe there can
be only one perfect and powerful God; nor is
it possible there should be another.

I have received a suggestion from a very in-
telligent brother respecting this symbol, which
merits consideration. He says, When the W.M.
elect enters into the obligation of an Installed
Master, the brethren form a circle round him, he
being in the centre ; and in this situation he is
said to be the representative of Solomon, the son
of David. Now, as this is unquestionably a Chris-
tian degree, I understand this son of David to be
a figurative expression for the Redeemer of man-
kind. The W.M. is then specially intrusted with
the Holy Scriptures, and invested with a jewel
which is emblematical thereof, and it then be-
comes his duty to exhort his brethren to search
those Scriptures, because they contain the words

1 Psalm cii. 28.

The Point within a Circle. 39

of eternal life, and testify to the divinity of
Christ. Searching implies something lost ; and
our ancient brethren, the early Christians, after
they had lost, by an untimely death, their Lord
and Master, remembered that while assembled
together in Lodge here below, He had promised
that when two or three were gathered together
in His name, He would be in the midst of them ;
and cheered by the recollection, they were natur-
ally led to hope that He would always be found
in the centre of their circle, whenever regularly
assembled together in a just and perfect Lodge
dedicated to God and holy St John, In like man-
ner, we are reminded by that sacred symbol that
He is always in the midst of us — that His all-
seeing eye is always upon us, and therefore ex-
horted to discharge our duty towards Him and
our fellow-creatures with freedom, fervency, and
zeal.

The Monad, amongst the Grecian philosophers,
was a symbol of the hermaphrodite deity, or junc-
tion of the sexes, because it partakes of two
natures. 1 In a mysterious passage of the Yajur
Veda, Brahma is spoken of, after his emanation
from the golden egg, as experiencing fear at being
alone in the universe ; he therefore willed the
existence of another, and instantly became mas-
culo-feminine. The two sexes thus existing in
one god were immediately, by another act of voli-
tion, divided in twain, and became man and wife.
This tradition seems to have found its way into

1 Macrob. in somn. Scip., i. 6.

40 The Pythagorean Triangle.

Greece ; for the Androgyne of Plato is but an-
other version of this Oriental myth. 1 If the
Monad be added to an odd number, it makes it
even, and if to an even number, it makes it odd.
Hence it was called Jupiter, because it stands at
the head of numbers, as Jupiter is at the head of
gods and men ; and also Vesta or Fire, because,
like the point within a circle, it is seated in the
midst of the world. It was also called the Throne
of Jupiter, from the great power which the centre
has in the universe, being, able to restrain its
general circular motion, as if the custody of the
Maker of all things were constituted therein. 2

Plutarch tells us that Numa built a temple in
an orbicular form for the preservation of the sa-
cred fire ; intending by the fashion of the edifice
to shadow out, not so much the earth as the whole
universe ; in the centre of which the Pythagor-
eans placed Fire, which they called Vesta and
Unity. The Persians worshipped the circumfer-
ence, but it could only refer to the apparent course
of the sun in the firmament, which is the boun-
dary of common observation ; for the real circum-
ference is far beyond the comprehension of finite
man. And the sun, under the symbol of a point
within a circle, was the great object of worship
amongst the Dionysian artists who built the
Temple of Solomon.

On this interesting subject a learned and intel-
ligent brother offers the following opinion in a

1 The Hindoos, vol. i. p. 166.
* Procl. in Tirmenm, com. iv.

Sun - Worship. 4 1

letter to the author : The more I study the sub-
ject of masonry, the more I am convinced that
the mysteries were unknown at Jerusalem till
introduced by the Dionysian artificers ; * and that
[ the ceremonies were astronomical, mixed with

paganism and sun-worship. I believe also that
1 Solomon divested them of their evil tendency, and

* ' created a new legend ; but that the main object

was an astronomical emblem. The Jews did not
require masonry to keep them religious ; for their
religion was open to all, whereas that of the Dio-
nysians was known only to the initiated. Masonry
could not then be used for a religious purpose
among the Jews, although the ceremonial may
have been adapted at that time to both Jew and
Gentile ; so that the Dionysian artists thence-
forth transmitted the meaning of the point within
a circle, not as bearing any reference to sun-wor-
ship, but as regarding the sun merely as a great
work of the one uncreated God. Thus the em-
blems of the sun and moon became introduced
into masonry ; and however we may explain them
in our Lodges, they appear to me unquestionable
remains of the solar worship, or at least of astro-
nomy.

For some such reason Hierocles the Pythagor-
ean concluded that " the gods are immutable, and
firm in their decrees ; so that they never change
the conception of what appeared to them to be
fit from the beginning- Hence they were likened

1 See Joseph Hippolita'a D'Acosta's Sketch of the Dionysian
Artificers.

42 The Pythagorean Triangle.

to the Monad ; because there is one immutability
and firmness of the virtues, which it is reasonable
to suppose subsists transcendently with the gods,
and which imparts a never-failing stability to
their conceptions/' Under this description the
Monad represented Mind, because it is station-
ary; 1 and for a similar reason it was called
Good ; 3 and seminal power, because it is the root,
origin, and summary of all numbers. 8 It was
also considered the vehicle of number, as a ship at
sea or a chariot on land contains many persons
and things ; and hence it had the name of both
these vessels.

It was a symbol of love and friendship ; and
taught the mild Pythagoreans the doctrine of
forgiveness of injuries; for they argued — Will not
a man who is a brother, or even any casual person,
who deserves attention in a much greater degree
than a brute, be changed to milder manners by
proper treatment, though he should not entirely
forsake his rusticity ? In our behaviour, therefore,
towards every man, and in a much greater degree
towards a brother, we should imitate the reply of
Socrates to one who said to him, "May I die
unless I am revenged on you." For his answer
was, " May I die if I do not make you my
friend/'

The Monad further signified Chaos, the father
of life, substance, the cause of Truth, reason, and
the receptacle of all things. Also in greater and

1 Alex. AphrocL in metaph. * Porph. vit. Pyth.

* Mart. Capel., vii.

The Doctrine of Benevolence. 43

lesser it signified equal; in intention and remis-
sion, middle ; in multitude, mean ; in time, now,
the present, because it consists in one part of
time which is always present. 1 The cabalists
considered that the first eternal principle is magi-
cal, and like a hidden fire, is eternally known in
its colours, in the figure, in the wisdom of God,
as in a looking-glass. The magical centre of the
first principle is fire, which is as a spirit, without
palpable substance.

The number one symbolised the Platonic, or
rather the Pythagorean doctrine of Benevolence.
Thus Hierocles 3 says, " Each of us is, as it were,
circumscribed by many concentric circles ; some
of which are less, but others larger, and some
comprehend, but others are comprehended, ac-
cording to the different and unequal habitudes
with respect to each other. For the first and
most proximate circle is that which every one
describes about his own mind as a centre, in
which circle the body, and whatever is assumed
for the sake of the body, are comprehended. For
this is nearly the smallest circle, and almost
touches the. centre itself. The second from this,
and which is at a greater distance from the centre,
but comprehends the first circle, is that in which
parents, brothers, wife, and children are arranged.
The third circle from the centre is that which
contains uncles and aunts, grandfathers and grand-
mothers, and the children of brothers and sisters.

1 Macrob. in somn., L i. 8. 6.

* Ethical Fragments of Hierocles, by Taylor, p. 106.

44 The Pythagorean Triangle.

After this is the circle which comprehends the
remaining relatives. Next to this is that which
contains the common people, then that which
comprehends those of the same tribe, afterwards
that which contains the citizens ; and then two
other circles follow, one being the circle of those
that dwell in the vicinity of the city, and the
other of those of the same province. But the
outermost and greatest circle, and which compre-
hends all the other circles, is that of the whole
human race/' This admirable passage, says Tay-
lor, is so conformable to the following beautiful
lines in Pope's " Essay on Man," that it is most
probably the source from whence they were de-
rived —

Self-love but serves the virtuous mind to wake,
As the small pebble stirs the peaceful lake ;
The centre moved, a circle straight succeeds,
Another still, and still another spreads;
Friend, parent, neighbour, first it wttl embrace,
His country next, and next all human race;
Wide and more wide the overflowings of the mind,
Take every creature in of every kind.

The learned Aben Ezra, on the 11th chapter of
Daniel, says, that the number one is in a manner
the cause of all numbers, and is besides a com-
plete number; it causes multiplication and
remainder, but does not admit of either itself.
And in another place he says, "Numbers are
founded on the unit one." The sage Latif ob-
serves the same. According to Euclid, in his
second definition of the seventh book, numbers

Masonic Reference for the Monad. 45

are formed of many units ; but unity being indi-
visible, has no composition, nor is it a number,
but the fountain and mother of all numbers.
Being the cause of all numbers, they are formed
by a plurality of units. Thus 2 is twice 1 ; 3 is
three units, &c. ; so that all numbers require the
Monad, while it exists by itself without requiring
any other. All which is to be considered of the
First Cause ; for as one is no number, but the
cause and beginning of number, so the First
Cause has no affinity to creatures, but is the
cause and beginning of them ; they all stand in
need of Him, and He requires assistance from
none. He is all in all, and all are included in
Him in the most simple unity. The Jewish
Eabbins agree that He is One, and there is no
unity like His in the universe ; the nearest idea
that we can form of Him is symbolised by the
unit or the figure one. 1

The Pythagoreans say, " The Monad is the
principle of all things. From the Monad came
the indeterminate duad, as matters subjected to
the cause, Monad; from the Monad and inde-
terminate duad, Numbers ; from numbers, Points;
points, Lines; from lines, Superfces; from super -
fices, Solids; from these solid Bodies, whose
elements are four, Fire, Water, Air, Earth ; of
all which, transmutated, and totally changed,
the World consists." 2

But Freemasonry has a peculiar reference for

1 Manasseh ben Israel, Concil., vol. i. p. 105.
8 Laert. in vit. Pyth.

46 The Pythagorean Triangle.

the Monad, which produces some very striking
and remarkable coincidences in every nation
under the sun. In an old ritual of the Fellow
Craft's degree, used about the middle of the last
century, we find the following passage in refer-
ence equally to the first step of the winding
staircase, the Point, and the letter G : " God, the
great Architect of the Universe, whom it is at all
times our duty to worship and obey." In a ritual
still more ancient, the same meaning is rather
differently expressed, viz., " the Grand Architect
and Contriver of the Universe ; or He that was
taken up to the topmost pinnacle of the Holy
Temple."

This acknowledgment of the divine unity, or
point within either a circle or a triangle, was
common to all the systems of Spurious Free-
masonry that ever existed, from India and Japan
to the extremest west, including the Goths, the
Celts, and the aborigines of America. All ac-
knowledge the unity of T.G.A.O.T.U., whether
involved in the deepest ignorance, or refined by
civilisation and a knowledge of philosophy and
science. The sages of Greece, through a series of
wire-drawn reasoning, came to the same conclu-
sion as the uninformed savages of Britain, Scan-
dinavia, Mexico, or Peru.

It may be useful to examine a few of these
systems, all emanating from the Spurious Free-
masonry, to show the bearing of this universal
belief, which will prove the superiority of revela-
tion over the speculations of unassisted reason.

The Divine Unity. 47

The Divine Being was called by the Bomans Jove,
or Jah; by the Chaldeans, the Phoenicians, and
the Celtse, Bel or Bul; and by the Indians and
Egyptians, Aum (Om) or On. The first was
plainly Jehovah ; the second was a common name
of God ; and the last was used by the early
Christians to express the Being whom they wor-
shipped. c O /2N, teal 6 7jv 9 kcu 6 €pxpfjL€vo<; 9 God,
which is, and was, and is to come. 1 But it must
always be kept in mind that the heathen, in
acknowledging their chief god to be the Maker
or G.A.O.T.U., did not understand it in the ex-
act sense in which it is received by Jewvs and
Christians. They believed that God built the
world out of existing materials ; we are satisfied
that He created it out of nothing. The divine
unity was plainly revealed to the Jews at their
deliverance from the bondage of Egypt. Thus
when Moses promulgated the Law, he said,
" Hear, Israel : The Lord our God is one
Lord." 2 This declaration was so frequently
repeated, that the Jews, amidst all their rebel-
lious and religious defections, never doubted its
truth. In like manner, the Vedas of India, the
Zends of Persia, the Hermesian writings of
Egypt, the Eddas of the northern nations of
Europe, &c, all contained the same truth ; and
from these original sources, it was conveyed
through Thales and Pythagoras to the philoso-
phers of Greece and Kome.

The latter great philosopher styled the Supreme

1 Rev. i. 4. . • Dent. vi. 4.

48 The Pythagorean Triangle.

Deity to cv, the Unity, and /uwa?, the Monad ; a
term by which he doubtless intended to express
his conception of the simplicity as well as purity
of the divine nature. As the sole cause and first
principle of all that exists, Pythagoras esteemed
the Deity to be the centre of unity and source of
harmony. He likewise conferred on this Al-
mighty Sovereign the name by which Plato
afterwards distinguished the first hypostasis of
his triad, to ayaOov, the chief good. From this
eternal Monad, however, from this primeval
Unity, according to Pythagoras and all his dis-
ciples, there sprang an infinite duality. 1

The philosophers of most nations entertained
similar opinions respecting the undivided unity
of the Supreme God, which they learned through
the medium of the Spurious Freemasonry. Zoro-
aster is sublime in his description of the Deity;
but he had enjoyed the advantage of associating
with the learned Jews at Babylon, and from
them, doubtless, he had acquired his knowledge.
He taught that "God is the First ; incorruptible,
eternal, unmade, indivisible, not like anything,
the author of all good, the wisest of the wise,
the father of justice, self-taught, and absolutely
perfect." 3 Anaximenes, the follower of Thales,
like his master, was a bold and subtle reasoner,
and called everything by its proper name. He
denominated the one God Zeus, by which he
intended to intimate that, like the air we

1 Maur, Ind. Ant. cited from Diog. Laert., L viii. p. 507.
s Euseb. de Prop. Evan., 1. I c. ult.

Anecdote of the Emperor Trajan. 49

breathe, He is infinite, omnipresent, and eternal. 1
Xenophanes, the principal leader of the Eleatic
sect, entertained the same belief ; and described
that Great Being, whom they all admitted to be
incomprehensible, as " incorporeal, in substance,
and figure globular; and in no respect similar to
man. That He is all sight and hearing, but does
not breathe. That He is all things ; the mind and
wisdom ; not generate, but eternal, impassible,
and immutable." Parmenides held that "the
principle of all things is one ; but that it is
immovable. " Sophocles assures us that in his
time, the belief in one God, who made heaven
and earth, was prevalent amongst those who had
been initiated into the Greater mysteries.

Socrates and his pupil Plato maintained the
same opinion. " By the name of God," said they,
" we mean the parent of the world ; the builder
of the soul ; the maker of heaven and earth ;
whom it is difficult to know by reason of His in-
credible power ; and if known, it is impossible
to clothe our knowledge in words." Anaxagoras

1 The Emperor Trajan, in a conversation with the Rabbi Joshua,
hearing the latter say that " God is everywhere present ; " observed,
" I should like to see Him. " " God's presence is indeed everywhere,"
replied Joshua, " but He cannot be seen ; no mortal eye can behold His
glory." The Emperor insisted. " Well," said Joshua, " suppose we
try first to look at one of His ambassadors." The Emperor consented.
The Rabbi took him into the open air at noonday, and bid him look
at the sun in its meridian splendour. " I cannot — the light dazzles
me." " Thou art undble" said Joshua, " to endure the light of Bis
creatures, and canst thou expect to behold the resplendent glory of the
Creator ? Would not such a sight annihilate you?" — (Goodhugh's
Lectures on Bibliographical Literature).

J>

50 The Pythagorean Triangle.

contended for the supreme government of one
God, but acknowledged that he was unable to
comprehend His nature. His pupil Euripides,
however, was more fortunate, for he discovered
the omnipresence of the Deity ; and confesses it
by asking whether it is possible to confine Him
within the walls of a temple built with hands ?
Protagoras was banished by the Athenians for
impiety, in declaring that "he knew nothing of
the gods, because in so short a life it was impos-
sible to acquire a knowledge of them."

The revolution of ages did not efface this pro-
fession of the divine unity, though it shook the
credit of the Spurious Freemasonry, through whose
medium it was conveyed. The solemn obliga-
tions, under the seal of which this great secret
was communicated, proved but a slender tie upon
the more sceptical philosophers, who felt little in-
clination to be satisfied with the popular reasons
assigned for paying divine honours to a mixed
multitude of deceased mortals. Cicero argues
the being of a God from the regular structure of
the universe; and Virgil, in his description of
the process and end of initiation, winds up his
detail with a view of the divine unity.

In like manner, Zeno taught the unity and
eternity of the Deity. Plutarch, learned in all
the rites and doctrines of the Spurious Free-
masonry of Egypt and Greece, expresses himself
plainly on this point in his treatise of Isis and
Osiris. Aristides believed and taught his dis-
ciples that " Jove made all existing things, in the

The Doctrine of the Monad. 51

earth, the heavens, or the sea." Porphyry asserts
that the oracle of Apollo commanded men to
worship deum generatorem et regem ante omnia,
quern tremit ccelum et terra, atque mare, et infer-
norum abdita, et ipsa numina per horrescunt;
quorum lex est Pater, quern, valde sancti honor-
ant Hebrceis. Nor must I omit, in this brief
^numeration of testimonies in proof of the ad-
mission of the divine unity amongst heathen
nations, that remarkable expression which Lucian
puts into the mouth of Cato : " God makes him-
self known to all the world; He fills up the
whole circle of the universe, but makes His par-
ticidar abode in the centre, which is the soul of
the just,"

Thus was the doctrine of the Monad or unity,
the first Point in the Pythagorean Triangle, car-
ried out in these early ages, and amongst an
idolatrous people ; for however they might wor-
ship an indefinite number of intelligences, they
had discrimination enough to perceive that there
could be only one Being of unbounded power,
because a duplication of such beings would cir-
cumscribe the potency of each individual, and
destroy his omnipotence and immutability. " It
was idle," says Bryant, " in the ancients to make
a disquisition about the identity of any god, as
compared with another ; and to adjudge him to
Jupiter rather than to Mars, to Venus rather
than Diana. According to Diodorus, some think
that Osiris is Serapis; others that he is Dion-
usus ; others still that he is Pluto ; many take

52 The Pythagorean Triangle.

him for Zeus or Jupiter, and not a few for Pan.
This was an unnecessary embarrassment; for they
were all titles of the same god; there being
originally by no means that diversity which is
imagined, as Sir John Marsham has very justly
observed. Neque enim tanta irokvOeoTrp. Gen-
tium, quanta fuit deorum Trokvawfiia" 1

We shall see, however, in our examination of
the Duad, that this belief, correct as it was iu
principle, admitted of some modification,

1 Bryant, Anal., vol. i. p. 386.

THE DUAD OR LINE EXEMPLIFIED.

THE LINE, DUAD, DUALITY, OR THE
NUMBER TWO.

CHAPTER II.

THE LINE.

DUAD, DUALITY, OR THE NUMBER TWO.

" The next two points in the Pythagorean Triangle are denominated
Duad, representing the number two, and answers to the geomet-
rical Line, which, consisting of length without breadth, is bounded
by two extreme points." — Hjemmixo's Lectures.

" The emblematical objects characteristic of the second degree of
Masonry, are the two brazen pillars, the winding staircase, and the
blazing star with the letter G in the centre." — Ibid.

HE twofold reason of diversity and ine-
quality, and of everything that is divisi-
ble in mutation, and exists sometimes
oneway sometimes another, the Pythagoreans called
Duad, for the nature of the Duad in particular
things is such. These reasons were not confined
to the Italic sect, but other philosophers also have
left certain unitive powers which comprise all
things in the universe ; and amongst them there
are certain reasons of quality, dissimilitude, and
diversity. Now these reasons, that the way of
teaching might be more perspicuous, they called by

56 The Pythagorean Triangle.

the names of Monad and Duad ; but it is all one
amongst them if it be called biform, or equaliform,
or diversiform." 1 Pierius, in his thirty-seventh
book of Hieroglyphics, confirms this doctrine.
He says, "Ipse verb dualis numerus mystico
significato corpoream indicat naturam, et pro
imanundis accipitur in sacris, qubd is numerus
sociandis generandisque corporibus aptari solet.
De quo videndus Adamantius lib. tertio in epis-
tolam Pauli ad Eomanos, ubi de propitiatorio
loquitur. Summonet D. Hieron. in hanc sen-
tentiam ad versus Jovinianum, animadvertendum
esse juxta Hebraicam veritatem, in primo, et
tertio, et quarto, et quinto,et sexto die, expletis
operibus singulorum, subjectum esse, Et vidit
Deus qubd esset bonum. In secundo verb die
hoc omnino subtractum, ut admoneremur non
esse bonum duplicem numerum, qubd ab unione
dividat. Nam unitas tota Dei est, ducditas verb
signijicet hieroglyphic^ fcedera nuptiamim, qui-
bus ubique Hieronymus paulb se infensiorem
ostentat."

From such definitions and principles, it will not
be difficult to see that the Duad was sufficiently
comprehensive to admit of a vast number of refer-
ences ; and therefore the prolific fancy of poets and
philosophers assigned to it a variety of remarkable
qualities. Being even, it was esteemed an un-
lucky number, and dedicated to the malignant
genii and the infernal deities, because it conveyed
to the mind ideas of darkness, delusion, versa-

1 Porph. HUfc Phil., p. 82.

An Unlucky Number. 57

tility, and unsteady conduct. 1 For this reason,
the Pythagoreans spoke of two kinds of pleasure,
" whereof that which indulgeth to the belly and
to lasciviousness, by profusion of wealth, they
compared to the murderous songs of the Syrens ;
the other, which consists in things honest and
just, comprising all the necessary indulgences of
life, is quite as attractive as the former, and does
not bring repentance in its train." 2

The Duad was considered indefinite and inde-
terminate, because no perfect figure can be made
from two points only, which, if united, would
merely become a right line ; whence a notion
was originated that it is defective in its principles,
and superfluous in its application to the sciences.
It signified also misfortune, from a general belief
in its unpropitious qualities; and discord, because
in music that which renders dissonances grating,
is, that the sounds which form them, instead of
uniting to produce harmony, are heard each by
itself as two distinct sounds, though produced at
one and the same time. Brand tells us, 8 that
there is a little history extant of the unfortunate
reigns of William II., Henry II., Edward II.,
Richard II., Charles II., and J^mes II., entitled
" Numerus Infaustus;" in the preface to which
the author says, u Such of the kings of England
as were the Second of any name, proved very
unfortunate princes."

The number two was referred to several of the
female deities, and particularly to Juno, because

1 Porph. vit. Pyth., p. 84. * Ibid., p. 25. * Pop. Ant., vol. iii. p. 145.

58 The Pythagorean Triangle.

she was the sister and' wife of Jove ; x and hence
the Duad became a symbol of marriage. On this
subject Hierocles says, two things are necessary
to all men, in order to pass through life in a
becoming manner, viz., the aid of kindred, and
sympathetic benevolence. But we cannot find
anything more sympathetic than a wife, nor any-
thing more kindred than children, both of which
are afforded by marriage. And to produce these
two beDeficial effects, Callicratides gives the
following excellent advice : " Wedlock should be
coadapted to the peculiar tone of the soul, so that
the husband and wife may not only accord with
each other in prosperous, but also in adverse
fortune. It is requisite, therefore, that the
husband should be the regulator, master, and
preceptor of his wife. The regulator, indeed,
in paying diligent attention to her affairs; but
the master, in governing and exercising authority
over her; and the preceptor in teaching her such
things as it is fit for her to know/'

But how unfortunate soever the Duad may have
been esteemed as a general principle, it was not
devoid of its share of beneficent properties to
balance against those that were malignant or for-
bidding. " The two principles," said the Para-
celsic Lectures of Continental Masonry, " are not
always at strife, but sometimes in league with
each other, to produce good. Thus death and
anguish are the cause of Fire, but fire is the
cause of Life. To the abyss it gives sting and

1 Hart CapeL Eulog. in soma. Scip.

Beneficent Properties of the Duad. 59

fierceness, else there would be no mobility. To
the Light — world, essence, else there would be
no production but an eternal Arcanum. To
the world it gives both essence and springing,
whence it becomes the cause of all things."
The Duad was defined by the Pythagoreans,
" the only principle of purity ; yet not even,
nor evenly even, nor unevenly even, nor evenly
uneven." It was an emblem of fortitude
and courage, and taught that as a man ought
to do no wrong, neither ought he to suffer any,
without a due sense and modest resentment of it ;
and therefore, according to Plutarch, the " Ephori
laid a mulct upon Sciraphidas, because he tamely
submitted to many injuries and affronts, con-
cluding him perfectly insensible to his own
interest, as he did not boldly and honestly
vindicate his reputation from the wrongs and
aspersions which had been cast upon it ; under
the impression that he would be equally dull and
listless in the defence of his country, if it should
be attacked by a hostile invader."

I have already observed that the centre was a
representation of the Monad ; but according to
the doctrines promulgated by the Theosophical
Masons of the last century, it produced several
dualities ; for the centre was explained by them
as the Verbumjktt, the natural Word of God, the
maker of all creatures in the inward and outward
worlds. The same Word hath out of the Fire, the
Light, and the Darkness, made itself material,
moving, and perceptible, out of which existed the

60 The Pythagorean Triangle*

third principle, the visible world, thfc life and
substance whereof is come out of the eternal
nature the Fire, and out of the great mystery,
the Light, also out of the Darkness, which is
the separator of Fire and Light, Love and
Enmity, Good and Evil, Joy and Pain." And
they went on to say, that there are two sorts of
Fire, and two sorts of Light, which they explained
mystically.

The Duad was elevated by the ancient philoso-
phers of the Italic sect into a symbol of Justice,
because of its two equal parts. Hence Archytas,
who was a follower of Pythagoras, says, "The
manners and pursuits of the citizens should be
deeply tinctured with justice ; for this will cause
them to be sufficient to themselves, and will be
the means of distributing to each of them that
which is due to him according to his desert. For
thus also the sun, moving in a circle through the
zodiac, distributes to everything on the earth,
generation, nutriment, and an appropriate portion
of life ; administering, as if it were a just and
equitable legislation, the excellent temperature of
the seasons." 1

It signified also science, because the demonstra-
tion of an unknown number or fact is produced
from syllogistic reasonings on some other number
or fact which is known; and this is deducible by
the aid of science. It was further considered as
a symbol of the soul, which is said to be divided
into two parts, the rational and the irrational ;

1 Fragments of Archytas, p. 16. .

Symbols of the Duad. 61

the latter being subdivided into the irascible and
the appetitive. The rational part enables us to
arrive at the truth by contemplation and judg-
ment ; while the irrational uniformly impels the
soul to evil. And it signified Opinion, which must
be either true or false ; and Harmony, whence the
ancients introduced music at their banquets along
with wine ; that by its harmonious order and
soothing effect it might prove an antidote to the
latter, which being drank intemperately, renders
both mind and body imbecile.

In the science of astronomy there are two
jiodes, called the dragon's head and tail ; and in
astrology the aspects are of two kinds, dexter and
sinister, according as they are agreeable with, or
contrary to, the succession of the Signs ; and the
Duad referred particularly to the moon by reason
of her two horns when at the change. In the
first chapter of Genesis the Duad is applied to the
Sun and Moon ; which are there termed " the two
great Lights, the former to rule the day and the
latter to rule the night;" 1 and mystically signi-
fied the light of time. Freemasonry has added
a third. It will be observed, however, that the
sun and moon are called great lights, partly from
their nature and effects ; because they give more
light than other stars. The sun appeareth alone
in the day, not because he is alone, but because,
through his exceeding brightness, the other stars
cannot be seen. The moon also in her bright-
ness obscureth many stars; and being more

1 Gen. L 10,

62 The Pythagorean Triangle.

beautiful than any other, hath worthily the chief
pre-eminence in ruling the night. 1

The Pythagorean philosophy, says Reuchlin, 2
taught that the Monad and Duad were a symbol
of the principles of the universe ; " for when we
make inquiry into the causes and origin of all
things, what sooner occurs than one and two ? That
which we first behold with our eyes is the same,
and not another ; that which we first conceive in
our mind is' Identity and Alterity — one and two.
Alcmseon affirmed two to be many, which, he said,
were contrarieties, yet unconfined and indefinite, as
white and black, sweet and bitter, good and evil,
great and small. These multiplicitous diversities
the Pythagoreans designed by the number Ten, as
proceeding from the Duad; viz., finite and infinite,
even and odd, one and many, right and left, male
and female, steadfast and moved, straight and
crooked, light and darkness, square and oblong.
These pairs are two, and therefore contrary ; they
are reduced all into ten, that being the most
perfect number, as containing more kinds of
numeration than the rest : even, odd ; square,
cube ; long, plain ; the first uncompounded, and
first compounded, than which nothing is more
absolute, since in ten proportions four cubic
numbers are consummated, of which all things
consist.

u Categories, reducible to two, Substance and
Accident, both springing from one essence ; for
ten so loves two, that from one it proceeds to two,

1 Aquin. ex Chrys. Horn., vi. * A. Cabal., 1. ii.

Fancies about Colours. 63

and by two it reverts into one. The first Ternary
is of one and two, not compounded but consistent ;
one having no position, makes no composition;
an unit, whilst an unit, hath no position, nor a
point whilst a point. There being nothing before
one, we rightly say, one is first ; two is not com-
pounded of numbers, but a co-ordination of units
only. It is therefore the first number, being the
first multitude ; not commensurable by any
number, but by a unit, the common measure of
all number ; for one, two, is nothing but two ; so
that the multitude which is called Triad, arithme-
ticians term the first number uncompounded, the
Duad being not an uncompounded number, but
rather not compounded."

The Chinese philosophers entertained similar
fancies about the colour of blue, which is formed
by a mixture of red and black. This colour, they
say, " being the colour of heaven, represents the
active and passive principle reunited in one ; the
male and female, the obscure and brilliant. All
corporeal beings are produced by inapprehensible
nature, emanating from blue, which forms the
origin of all subtile natures." x In the science of
astrology, which was very prevalent half a century
ago, the signs were invested with significant
colours. Thus it was said that Taurus was
designated by white mixed with citron ; Aries
and Gemini, by white and red ; Cancer, green
and russet ; Leo, red and green ; Virgo, black
speckled with blue ; Libra, black or dark

1 Colebrook, Philosophy of the Hindus, p. 21.

64 The Pythagorean Triangle.

crimson ; Scorpio, brown ; Sagittarius, yellow or
green ; Capricorn, black or russet ; Aquarius, a
sky colour or blue ; and Pisces by a brilliant
white.

Nor were the Jews destitute of a respect for the
number two ; which was indeed inculcated in the
Mosaical writings. Thus while the clean beasts
-were admitted into the ark of Noah by sevens,
the unclean ones were allowed to enter only by
pairs. The angels that were deputed to destroy
Sodom were two ; Lot had two daughters ; the
sons of Isaac and the daughters of Laban were
each two in number, as were also the sons of
Joseph. Moses was directed to make two cheru-
bim; the Onyx-stones of remembrance on the
high priest's shoulders were two, to symbolise
the Sun and Moon, as Josephus says ; but Beda
thinks they were emblematical of the faith and
practice of the patriarch? and prophets, while
others suppose, with greater probability, that the
high priest bore them on his shoulders to pre-
figure the manner in which Christ was to bear
the sins of His people. The Jewish offerings
were frequently directed to be by pairs ; as two
lambs, two pigeons, two turtles, two kids, &c.
The waive loaves were two ; and the shewbread
was placed on the table in two rows ; the silver
trumpets to direct the march of the Israelites in
the wilderness were the same number.

Again, Joshua erected two monuments on pass-
ing the river Jordan, one in the bed of the river,
and the other on its banks ; the temples of Solo-

The Principle of Duality. 65

mon and of Gaza were each supported on two
pillars; Jeroboam made two golden calves, and
set them up at Dan and Bethel ; there were two
witnesses against Naboth, as the Mosaic law re-
quired in cases affecting human life; and two
bears were sent to vindicate the character of
Elisha. In the case of Naaman the Syrian, we
find the use of this number fully exemplified in
the two mules' burden of earth — two young men
of the sons of the prophets — two talents — two
changes of garments — two servants, &c. In the
visions of Daniel the ram had two horns ; and in
Zachariah we have two olive-trees, two anointed
ones, and two staves called Beauty and Bands, an
emblem of brotherhood. Similar coincidences
might be found in the Gospels, but the detail
would be tedious, and the result without utility,
as far as regards Freemasonry.

In our system, the principle of the duad is
plainly enunciated (although two is not esteemed
a masonic number) in the two Pillars of the
Porch of Solomon's Temple, which were placed
in that situation by the wise and judicious
monarch, to commemorate the remarkable pillar
of a cloud and of fire ; the former of which proved
a light and guide to the Israelites in their escape
from their Egyptian oppression; the other repre-
sents the cloud which proved the destruction of
Pharaoh and his host in their attempt to follow
them through the depths of the Red Sea. Our noble
and illustrious Grand Master placed them in this
conspicuous situation that the Jews might have

66 The Pythagorean Triangle.

that memorable event in their recollection,
both in going in and coming out from divine
worship.

These two famous pillars did not stand insu-
lated or detached from the building, but were
applied to the useful purpose of supporting the
entablature of the pronaos. They were of cast
brass, and their dimensions, use, and ornaments
are particularly described in the Fellow Craft's
Lecture. The chapiters represented the system
of the creation; and the balls by which they
were surmounted, the celestial and terrestrial
globes. The network denoting the strong and
beautiful texture of all created things ; the chain-
work, the different and complicated evolutions
of the several systems, moving with regularity
through the vast expanse, and revolving on their
own axes ; the opening flowers denote the mild
and genial influence of the fixed stars ; and the
pomegranate, the secret and unknown power
by which the universe is sustained. Their
height reminds us of the two Grand Master
Hirams ; while the sphere and cylinder are
sublime and significant emblems, which contain
the principles of the two higher branches of
Geometry.

In the spurious Freemasonry of some ancient
nations, this principle of- duality was extended to
support the doctrine of a good and evil power,
who possessed almost equal government in this
lower world ; and the prosperity or decadence of
a nation was supposed to be produced by the

The Principles of Light and Darkness. 6 7

superiority of one or other of these beings, which,
however, was esteemed, in most cases, accidental.
In Persia the doctrine attained its climax. Oro-
mases was Light, and Ahriman, Darkness. Hyde
says, " The first Magi did not look upon the two
principles as co-eternal, but believed that light
was eternal, and that darkness was produced in
time ; and the origin of this evil principle they
account for in this manner : Light can produce
nothing but light, and can never be the origin of
evil ; how then was evil produced ? Light, they
say, produced several beings, all of them spiri-
tual, luminous, and powerful ; but their chief,
whose name was Ahriman, had an evil thought
contrary to the light. He doubted, and by that
doubting he became dark. From hence proceeded
all evils, dissension, malice, and everything also
of a contrary nature to the light. These two prin-
ciples made war upon one another, till at last peace
was concluded, upon condition that the lower
world should be in subjection to Ahriman for
seven thousand years ; after which space of time,
he is to surrender back the world to the Light." *
In countries where the two principles were re-
presented by two serpents, the solstitial colures
were described under these symbols. Thus, in
the Egyptian hieroglyphics, two serpents inter-
secting each other at right angles, upon a globe,
denoted the earth. These rectangular intersec-
tions were at the solstitial points, 2 The Teutonic

1 Hyde, Rel. Ant. Pers., c. ix. p. 163.

* Jablonski, Panth. Eg., 1. i. c. 4, cited by Deane, p. 73*

68 The Pythagorean Triangle.

Masonry of the last century thus explained the
two principles of Light and Darkness. " From the
eternal centre is made the eternal substantiality
as a body or weakness, being a sinking down, and
the spirit is a springing up, whence ccmes motion,
penetration, and multiplication; and when the
spirit created the substantiality into an image,
breathing the spirit of the Trinity into it, the
whole essences, even all forms of nature, the
power of Light and Darkness, and the whole
eternity, it instantly blossomed and became the
paradise or angelical world. In the Darkness is
the genetrix, in the Light is the wisdom ; the first
imaged by devils, tlie other by angels, as a simi-
litude of the whole eternal being, to speak as a
creature. And Lucifer imaging beyond the meek-
ness of the Trinity, kindled in himself the matrix
of Fire, and that of nature becoming corporeal,
then was the second form of the matrix, viz., the
meekness of the substantiality enkindled, whence
water originated, out of which was made an hea-
ven to captivate the fire, and of that Fire and
Water came the Stars."

Other Oriental nations carry their belief of good
and evil genii (Jinns), who are for ever contending
against each other; the one to extend the do-
minion of vice, and the other that of virtue. The
beautiful fictions in the Arabian Nights Enter-
tainments are founded on this belief. The origin
of the Jinn is thus given by Lane from El-Kazi-
veenee. " It is related in histories, that a race of
Jinn in ancient times, before the creation of

Good and Evil Powers. 69

Adam, inhabited the earth, and covered it, the
land and the sea, and the plains and the moun-
tains ; and the favours of God were multiplied
upon them, and they had government, and pro-
phecy, and religion, and law ; but they trans-
gressed and offended, and opposed their prophets,
and made wickedness to abound in the earth;
whereupon God, whose name be exalted, sent
against them an army of angels, who took posses-
sion of the earth, and drove away the Jinn to the
regions of the islands, and made many of them
prisoners ; and of those who were made prisoners
was Azazeel, afterwards called Iblees, from his
despair." The Jinnee have fire circulating in
their veins in the place of blood ; and when
any of them receives a mortal wound this fire
generally consumes him to ashes. When they
appear to mankind it is usually in some hideous
form.

The legend of the Spurious Freemasonry is
founded on the above principle of duality. It
speaks of a good and evil power, the former being
destroyed by the machinations of the latter ; and
after a variety of adventures, the body is found
and restored to life. This gives vivacity to an-
other form of the duad. The aphanism and euresis
were both celebrated during the initiations ; lamen-
tation and sorrow marking the first, as a sacrifice
due to the immolated deity ; while the last was
a season of rejoicing at his recovery; and the
formula was — "Rejoice, ye Mystse, for your god
is found ! " And the legend was the same in all

70 The Pythagorean Triangle.

material points, whether the celebrations were in
honour of Osiris, Adonis, Bacchus, or the deity of
any other country ; and the duality was still fur-
ther extended by the supposition that the wife of
the dismembered god was the individual deputed
to search for the body. The reference was pre-
served as well in Osiris and Typhon as in Osiris
and Isis, and the corresponding deities in every
nation of the earth.

The superstition, which was so common through-
out all antiquity, of realising the duality by com-
bining the worship of the serpent with that of a
tree, or offering rites to the Ophite deity in a
sacred grove, originated with the paradisiacal
serpent and tree of knowledge. This united wor-
ship is depicted on the sepulchral monuments of
the Greeks and Romans, on the coins of Tyre, and
among the Fetiches of Whidah. We shall find
them, in the same union, pervading the religion
of the Hyperboreans of every description, the
superstition of the Scandinavians, and the wor-
ship of the Druids. 1

Pythagoras, in his system, enunciated the dual
principle in the exoteric and esoteric character of
the mysteries. The candidates for admission were
strictly examined respecting their moral character;
and if they bore the test, they were admitted as
exoterics, which continued five years, during which
period they were subjected to very serious trials,
both bodily and mental, and doomed to a per-
petual silence; and afterwards they were made

1 Dean., Serpent, p. 231.

Forms of Instruction. 71

esoterics, and permitted to see the Master, which
they had never yet been allowed to do, although
they had heard him deliver his lectures on the
outside of the screen. If they were rejected, they
were looked upon as dead, and a tomb was erected
to their memory.

Again, the form of instruction used by this
philosopher was twofold ; and his disciples passed
under the denomination of the Acousmatici and
the Mathematici. The former were instructed
only in the elements, and the latter in the more
elaborate and secret principles of science. And
Pythagoras taught, still adhering to the principle
of the duad, that every man was placed between
virtue and vice, like the lower part of the letter Y.
As there can be none happy before their death, so
none is to be esteemed unhappy whilst he lives.
But if at his death he is burdened with vice, his
misery then begins. This misery the philosopher
. divided into two kinds; some, he said, would
ultimately be delivered from punishment, others
would endure infinite pain everlastingly. Again,
he taught that there are two mansions in the
lower regions, one called Elysium, for those
who will ultimately ascend into heaven ; and
Tartarus, for those who are never to be delivered
from torment. On the other hand, those who
have chosen the path of virtue, who have lived
piously, and died in peace, shall ascend into the
transparent ether, and live with the blessed as
gods.

In Christian philosophy, the duad is equally

♦*

72 The Pythagorean Triangle.

esteemed, because it includes the entire essence
of the system, as expounded by its divine author,
who possessed two natures, and was comprehended
in two great moral precepts, the love of God and
our neighbour. For the same reason, Christianity
has two sacraments, and a divine symbol of two
united equilateral triangles, to figure the two
natures of Christ. It represents man in a twofold
state, as referring to time and eternity ; teaches
that the future will have two places of reward
and punishment, which are attained by two pre-
paratory steps, death and judgment. The two
great covenants or dispensations, represented by
Isaac and Ishmael, are symbolised in Freemasonry
by a most beautiful type. Thus, St Paul says, —
" Abraham had two sons, the one by a bondmaid,
the other by a free woman. But he who was
of the bond woman was born after the flesh ;
but he of the free woman was by promise.
Which things are an allegory ; for these are
the two covenants ; the one from Mount Sinai,
which gendereth to bondage, which is Hagar.
For this Hagar is Mount Sinai, in Arabia, and
answereth to Jerusalem which now is, and is
in bondage with her children; but Jerusalem
which is above is feee, which is the mother of
us all." 1 '

Here we have a plain exposition of the two
covenants, the Law and the Gospel, the first of
which was a shadow of the second. " Howbeit
that was not first which was spiritual, but that

1 Gal. iv. 22-26.

*♦

The Two Covenants. 73

which was natural, and afterward that which was
spiritual ; the first man is of the earth, earthy ;
the second man is the Lord from heaven/' 1 - Our
first estate is Time, our second Eternity. The
same beautiful allegory is kept up from the time
of the first prophecy relative to the two seeds ;
and as it was then with Cain and Abel, he that
was born after the flesh persecuted him that was
born after the Spirit. It appears, then, to have
been understood not only by Moses and Solomon,
but by all other holy men of old, that the two
colours of the Mosaic pavement, black and white,
were a figure of the divine and human nature of
Him who was in the pillar of a cloud and of fire,
the Kedeemer of His people from Egyptian bond-
age.

In like manner, there are two witnesses men-
tioned by St John in the Book of Kevelation
(Rev. xi. 3), which is in strict accordance with
customs of great antiquity ; as Moses and Aaron
in Egypt, Elijah and Elisha in the apostasy
of the ten tribes, and Zerubbabel and Jeshua
after the Babylonish captivity, to whom these
two witnesses are particularly compared. Our
Saviour sent forth His disciples by two and
two ; and Bishop Newton has observed, that
the principal Eeformers have usually appeared
as it were in pairs, as the Waldenses and
Albigenses, John Huss and Jerome of Prague,
Luther and Calvin, Cranmer and Ridley, and
their followers.

1 1 Cor. xv. 46, 47.

V4 The Pythagorean Triangle.

One great principle of the duality is in the for-
mation of the sexes, for the propagation of each
particular species of man and beast. The cabal-
istic Jews had some curious ideas respecting the
origin of male and female in the human subject.
The Eabbi Samuel bar Nachman held, with many
other of his brethren, that woman was jointly
created with man; being attached to his back;
so that the figure of Adam was double, one part
before being man, and the other part behind being
woman ; and he subsequently says that God
separated this back figure from man. This
opinion is adopted by Jarchi, Aben Ezra, R.
Bechayai, Eliezer Askenasi, and Isaac Caro, in
their commentaries, who all agree that by the
words "male and female created He them," is
to be understood literally that Adam and
Eve were created together in one form, which
was called Adam, and signifies both male and
female. 1

The lectures of the old German Rose Croix
contain a curious application of the duad, which
was adopted by M. Peuvret into his Paracelsic
degrees. It is as follows : — " Adam, seeing two
divine forms in himself, one paradisiacal, within
himself, the other without him, he thought to eat
of both, viz., the paradisiacal and the mixed of
good and evil, till he sunk into a sleep, which
signifies death, where the spirit of this world
formed him into such a man as we now are, and

1 See a great deal more on this subject in the " Conciliator of the
Rabbi Manassah ben Israel," vol. i. p. 17.

Curious Application of the Duad. 75

Eve into a woman ; and when they had eaten, the
spirit of this world captivated their souls ; their
essences were earthy, their flesh and blood bestial,
so that they begat children in two kingdoms,
viz., of Wrath and Love, the first a murderer,
the second holy ; for the word of grace and
covenant had, on their fall, set itself in the light
of their life."

ILLUSTRATION OF THE TRIAD,
OR SUPERFICE.

THE SUPERFICB, OR EQUILATERAL TRIANGLE, TRIAD,
TERNARY, OR THE NUMBER THREE.

*3§><5X§2? r

CHAPTER III.

THE SUPERFICE, OR EQUILATERAL

TRIANGLE.

TRIAD, TERNARY, OR THE NUMBER THREE.

*' Tres irabris torti radios, tres nubis aquo8»
Addiderant ; rutili tres ignis, et alitis Auatri ;
Fulgores nunc terrificos, sonitumque metumque
Miscebant open, flammisque sequacibus iras."

Virgil.

" The three Sojourners represent the three Stones on which the three
Grand Masters kneeled to offer up their prayers for the success of
the work ; and hereby we have a lesson that in everything we un-
dertake, we ought to offer up our prayers to the Almighty for a
blessing on our labours." — Old R.A. Lecture.

[HE Pythagoreans maintained the principle
of three worlds and pronounced the third
infinite ; for they thought that the triad
embraced all matter. These three worlds were
denominated the inferior, the superior, and the
supreme. The inferior contains bodies and mag-
nitudes, as the guardians of things generated and
consequently corruptible. Next above is the

80 The Pythagorean Triangle.

superior world, intended for superior powers,
called by Pythagoras in his Golden Verses, the
immortal gods, produced by the divine Mind.
The third world, called supreme, is the abode of
the One Great Deity, who existed from eternity,
and has the sole government of the world. These
three worlds were called receptacles ; the first of
quantity ; the second of intelligences ; the third
of principles ; the first circumscriptively, the
second definitively, and the third repletively.
But the ternary or triad was not only accounted
a sacred number amongst the Pythagoreans, but
also as containing some mystery in nature was
therefore made use of by other Greeks and
Pagans in their religious rites ; for Aristotle
says distinctly that the number three was taken
from nature as an observation of its laws, as
the most proper to be used in sacrificing to
the gods and other purifications. (De Cselo.,
LI, c. 5.)

The triad was esteemed the first perfect num-
ber, and hence oracles were delivered from a tri-
pod. It was denominated by way of eminence,
the mystical number ; and both Socrates and
Plato acknowledge three principles of things,
God, Idea, and Matter : which had been already
symbolised by Pythagoras in three secret figures,
viz., Infinite, One, and Two ; the former was the
way in which he designated the supreme Deity ;
by unity he meant form ; and by alterity, matter;
infinite, in the supreme world ; one, in the intel-
lectual ; and two, in the sensible. The peace and

The Three Blessings of a Married Stale. 81

concord which spring from happy marriages, was
represented by the triad ; whence probably it was
designated, in the notation of the Chinese, by the
figure of a point within a circle. The Pythago-
reans taught the duties which appertain to a man
and his wife, in order to secure the three bless-
ings of a married state. The things, say they,
" which are peculiar to a man are three, viz., to
lead an army, to govern, and to speak in public.
The offices peculiar to a woman are also three in
number ; i.e., to be the guardian of a house, to
stay at home, and to be attentive to the comforts
of her husband. And the virtues which make
the married state happy, appertain equally to
them both ; and these are Fortitude, Justice,
and Prudence. For it is fit that both the hus-
band and the wife should possess the virtues of
the body and the soul ; health, strength, and
beauty. Fortitude and Prudence pertain to the
man, while Temperance belongs peculiarly to
the woman."

Like the duad, this number was emblematical
of justice. Pierius affirms that "ut verb trini
prosequamur significata, ternarium veteres, ut
alibi etiam ostendimus, Justiti© dedicarunt, ut
de Pythagoricis disciplinis Plutarchus ait. In-
juria siquidem afficere, neque non affici, cum ex-
trema sint, et idcirco vitiosa, justum equaliter
utrinque reductum in medio residet. Sanfe Pytha-
gorici non numerus tantiim, vertim etiam figuras
deorum nominibus dedicarunt ; quippe qui tri-
angulum equilaterum Minervam appellabant.

82 The Pythagorean Triangle.

Verticigenam et Tritogeniam propterea, qubd tri-
bus perpendicularibus lineis ab angulis tribus
dissecetur." x To the above explanation Pierius
has subjoined these figures —

The triad was said to be a connective and col-
lective communion, as the symbol of justice,
because it is that disposition of the soul which
adapts itself to those that are near us. " For as
rhythm is to motion, and harmony to the voice, so
is justice to communion ; since it is the common
good of those that govern, and those that are
governed, because it co-harmonises political so-
ciety. But equity and benignity are certain
assessors of justice : the former softening the
severity of punishment, and the latter extending
pardon to less guilty offenders." 2 The same
number also inculcated the wisdom derivable from
prudence, because men, looking forward to the
future, conduct themselves at present by experi-
ence of the past. And prudence was defined
" the faculty of disposing all the accidents of life
so as to produce human happiness. Thus we
value medicine, not so much for the love of

1 Pier. Hier., fo. 292.

* Diotogenes in Taylor's Fragments, p. 25.

On Prudence and Temperance. 83

science, as for the promotion of health ; neither
would prudence be desirable, if it were not the
medium through which happiness may be obtained.
By prudence we provide against anything
which may afflict either the body or the mind.
Under its governance we are enabled to keep
within compass, to extinguish the ardour of
all unruly desires, and live in peace and tran-
quillity. The prudent person alone, being con-
tented to live within due bounds, avoids all
error, ignorance, and discontent, which produce
the troubles and afflictions that bear down other
men." l

Pythagoras entertained an idea that all human
virtues not only proceed from this number but
absolutely depend upon it ; and he particularly
mentions temperance. And for this reason, Soc-
rates advises us to beware of such meats as
persuade a man though he be not hungry to eat
them ; and of those drinks that would prevail with
him to swallow them when he is not thirsty.
Not that he absolutely forbade their use, but that
we might abstain from them, when they were not
necessary ; for that which is delightful to nature
as a matter of nourishment, is alone proper for
it. He that is hungry may eat things either ne-
cessary or pleasant ; but when he is freed from
his natural appetite, he ought not to raise up a
fresh one.

The Jewish cabalists had a curious opinion re-
specting the application of this number in the

1 Epicurus, in Stanley's. Philosophy, vol. iii. p. 3, c. 8.

84 The Pythagorean Triangle.

case of the three holy men mentioned by Ezekiel
(xiv. 14), each of whom they say was witness to
the creation, destruction, and restoration of the
world. Noah saw the earth reduced to chaos,
and after the flood restored to its primitive state.
Daniel saw his country, Jerusalem (a world in
miniature), entirely destroyed ; and in his days
flourish again by the rebuilding of the Temple.
In like manner Job saw • his house and family (a
small world to him) destroyed, and afterwards be-
come prosperous. The prophet, they add, names
these three for their constancy and firmness
when tried : Noah without fear of being killed,
building an ark in which he intended to save
only himself ; Job against Satan ; and Daniel in
the lions' den. He names them also from hav-
ing escaped the three evils — sword, famine, and
wild beasts. Thus Noah was preserved from
ferocious animals in the ark; from the famine
that happened in his time ; and from the sword
with which men tried to kill him when they
saw that he alone would escape at the deluge.
Job escaped famine ; the sword which, he
said, cleaveth my veins asunder; and from
the wild beasts of his country, Daniel es-
caped famine during the three years when
Nebuchadnezzar besieged Jerusalem; the sword
when he was taken prisoner, and lastly from the
lions. 1

The triad was said to be the cause of wisdom
and understanding, from its application to the

1 Concil., vol. ii.p. 211.

The Ineffable Secrets. 85

three sciences of Music, Geometry, and Astronomy.
Thus the harmonic triad in music is compounded
of three radical sounds consisting of a funda-
mental note, its third, and its fifth ; the latter of
which is divided into two thirds by different pro-
cesses. First harmonically ; as when the greater
third is lowest,' in which case the triad is said to
be perfect and natural. Secondly arithmetically ;
when the lesser third is lowest ; and then the
triad is called flat or imperfect. 1 In the two
latter sciences Pythagoras affirmed that the cube
of three has the power of the lunar circle, because
the moon goes round her orb in twenty-seven
days.

In the Hermesian system, the ineffable secrets
were reputed to have been transmitted through
three patriarchs only, viz., Adam, Seth, and
Enoch ; the latter of whom was identified with
Hermes himself, the founder of the spurious Free-
masonry of Egypt. Cudworth observes that
" since all these three, Orpheus, Pythagoras, and
Plato, travelling in Egypt, were there initiated
in that arcane theology of the Egyptians called
Hermaical, it seemeth probable that this doctrine
of a divine triad was also part of the arcane
theology of the Egyptians. It hath been also
noted that there were some footsteps of such a
trinity in the Mithraic mysteries amongst the
Persians, derived from Zoroaster ; as likewise
that it was expressly contained in the magic or
Chaldaic oracles, of whatsoever authority they

1 Busby, Diet. Mus. in voc.

86 The Pythagorean Triangle.

may be. Moreover, it hath been signified that
the Samothracians had very anciently a certain
trinity of gods, that were the highest of all their
gods, and that called by an Hebrew name too,
Cabbirim, or the mighty gods ; and that from
thence the Koman Capitoline trinity of gods was
derived."

The triad of master and wardens, which dis-
tinguishes our system of Freemasonry, are the
legitimate repository of its secrets, and bear a
reference to certain attributes of the Deity. This
triad is not peculiar to Freemasonry, but had
a corresponding application in the spurious sys-
tem of India. Wisdom was represented by the
symbol of a circle of heads ; Strength * by the
elephant ; and Beauty by horns, or a nimbus
formed by the solar rays. The great deity
of India, Siva or Maha Deo, is frequently de-
picted with three eyes, denoting the past, present,
and future, and thus constituting a symbol of
prudence. In general, his name is compounded
of the triad Cal-Agni-Eudra, or Time — Fire — Fate.

The French philosophers who contributed so
much to deteriorate genuine Freemasonry about
a century ago, affected to entertain a profound
respect for the mysterious institutions of anti-
quity, and comprehended the doctrine of the
Pagan cosmogonies, compared with that related by
Moses, under the form of two triads — viz., the
exoteric, consisting of Buddha — Revelation —
Church ; and the esoteric of intellect — Logos —
Great Union. And in their cabalistic jargon,

The Influence of the Number Three. 87

three was called " the mystical, number ;" and
the square of three " the number evolving itself."
The three mystical properties, they went on to
say in their theosophic lectures, "" which constitute
the essence of the world, consist of sulphur, mer-
cury, and salt. Sid is the free lubet of the eternal
abyss ; in the internal, sul is God, and phur is
nature — viz., the Eternal Nature — a hard attrac-
tion, the case of fire ; and sul the cause of the lustre
in the fire ; but the light riseth not in the sulphur
alone, but in mercury is the dividing made, and
its true real body is sal. The astringency makes
gross stones; mercury and the lubet metals. And
of the freeing from the wrath by the light
and meekness come the precious stones, gold,
&c, for all things consist in these three forms,
sulphur, mercury, and sal."

Sir Walter Scott, in his notes to the " Lay of
the Last Minstrel," has adduced a legend to show
the influence of the number three, even amongst
the aerial beings who were supposed to possess
superhuman powers. He said, " There were two
men, late in the evening, when it was growing
dark, employed in fastening their horses upon the
common, when they heard a voice, at some dis-
tance, crying tint, tint, tint, three times. One of
the men, named Moffat, called out, * What deil has
tint you ? Come here/ Immediately a creature
appeared, in something like the human form. It
was surprisingly little, distorted in features and
misshapen in limbs. As soon as the two men
could see it plainly, they ran home in a great

88 The Pythagorean Triangle.

fright, imagining they had met with some goblin.
By the way Moffat fell, and it ran over him, and
was at home at the house as soon as either of
them, and stayed there a long time. One evening,
when the women were milking the cows in the
loan, it was playing among the children near by
them, when suddenly they heard a loud, shrill
voice cry Gilpin Horner ! three times ; when it
started and said, * That is me, I must away,' and
instantly disappeared, and was never heard of
more." This being was an imp, and not a fairy,
which latter were somewhat obstinately attached
to even numbers.

The number three was incorporated into the
religious ceremonies of all nations. Among the
Eomans, says Borlase, 1 "Corineus went three
times round the assembly at Misenus's funeral to
purify them; three times was the effigy of a coy
lover to be drawn round the altar to inspire him
with love. In the festival called the Amburvalia,
the victim was to be led round the fields three
times. In the sacrifices of Bacchus, the priestesses
were to go three times round the altar with di-
shevelled hair. Among the Greeks, three times
did Medea, in imitation of the Bacchae, go round
the aged iEson with fire ; three times with water ;
and three times with sulphur; and when she was
about to invoke the three powers of the night,
her goddess Hecate, the moon, the stars, and all
the inferior deities resident in the elements of
nature, three times she turned herself about. The

1 Ant. Cor., p. 131.

Masonic Application of the Number Three. 89

description of her, the stillness of the night, the
propriety of the addresses, and parts of her prayer,
are all extremely poetical — -

Ter se convertit, ter sumptis flumine crinem
Irroravit aquis, ternis ululatibus ora
Solvit, et in dura" submisso poplite terr&,
Nox, ait, <fcc l

The names of the Pythagorean triad are legion.
I enumerate a few of them from Stanley : —
Saturnia, Latona, Cornucopia, Ophion, Thetis,
Harmonia, Hecate, Erana, Charitia, Polyhymnia,
Pluto, Arctus, Lichelice, Damatrame, Discordia,
Metis, Tridume, Triton, President of the Sea,
Tritogenia, Achelous, Nactis, Agyiopeza, Curetis,
Cratseis, Symbenia, Mariadge, Gorgonia, Phor-
cia, Trisamus, Lydius. From hence it will be
evident that the philosophers attached so much
veneration to the number three, as to extend
its supernatural influence to every object in
the creation. It was necessary to the success
of every undertaking, and without its aid, a
disgraceful failure was sure to be the inevitable
result.

The application of this number in our system
of Freemasonry is equally extensive, although the
reasons for it are inadequately explained in the
lectures. In one of the oldest known formulas, we
find three degrees, three chief officers, three mov-
able and three immovable jewels, three knocks,
three pillars, three working tools, &c, but no
reason is assigned why this peculiarity had been

1 Ovid, Met., lvil 182-190.

90 The Pythagorean Triangle.

adopted. In another ritual, used later in the cen-
tury, it is applied to the Holy Trinity, and the
three Grand Masters at the building of Solomon's
Temple. And in the lectures of Hemming and
Shadbolt, reference is given to the three great in-
terior senses or elements of human intellect ; the
first of which is perception, the cause of simple
ideas or impressions received from external ob-
jects, without any active exertions of the intellec-
tual powers. The second is judgment, or the
faculty of digesting, comparing, and reasoning upon
these simple ideas. The third is volition, or the
conclusion which results from the operations of
judgment, and concentrates the whole energy of
the mind in a fixed and certain point.

Freemasonry contains another beautiful illus-
tration of the number three, which ought not to
be overlooked. It alludes to an ancient and
venerable exhortation in the Sacred Scriptures
— " Ask, and you shall have — Seek, and you
shall find — Knock, and it shall be opened unto
you." These words were uttered by Him
who spake as never man spake ; and as He
has thus constituted a passport into an earthly
Lodge, so also must He be our passport into
a Lodge not made with hands, eternal in the
heavens.

M. Fustier, the inventor of a new system of
Masonry on the Continent, introduced into his
lectures, from the theories of Behmen and other
theosophical visionaries, a dissertation on three
principles of Light, all of which are eternal.

Legitimate Epochs in Masonry. 9 1

" The first was such a light as is produced by
darkness ; the second a meek and loving light,
but still majestic and potent ; the third resulting
from fire and light, brings perfect happiness, both
in this world and that which is to come. Thus
the stars figure God in His infinity and eternity,
according to the first principle ; in His majestic
kingdom of Light, according to the second ; and
in His gracious kingdom of Love, according to
the third. And they are, in the third principle,
the express word of what the devils are in the
dark abyss, and of what the holy angels are in
the heavenly world."

Des Etangs has promulgated an opinion which
requires to be seriously considered before it is
adopted as an undeniable truth — that the legiti-
mate epochs in Masonry are three; the first com-
prehending all antiquity from the establishment
of the famous Lodges in India, whence the science
passed to Egypt, and from thence to Italy and
Greece, and its secret mysteries were applied to
government and religion. The second period
commenced with the advent of Christ ; and its
principles inspired the first Christians with
brotherly love, and the theological and cardinal
virtues, and furnished them with equanimity
and resolution to undergo sufferings the most
excruciating, and deaths the most severe. The
third epoch was coeval, according to this theory,
with the revival of letters, and has continued to
the times in which we live.

It will be unnecessary to point out the numerous

92 The Pythagorean Triangle.

triad references 1 which occur in the mechanism
and lectures of our system of Freemasonry, be-
cause they have been already expatiated on at
large in Lecture ix. of the author's Historical
Landmarks of the Order.

The mysteries of heathenism imitated this
triple principle ; and in the religious services of
Delphi, when the priestess of Apollo delivered
her oracles, she sat upon a tripod, which
Athenseus calls "the tripod of truth." This
was a name commonly given to any sort of
vessel or table which was supported upon three
feet. The tripod of the Pythian priestess was
distinguished by a base emblematical of her god,
consisting of a triple-headed serpent of brass,
whose body, folded in circles growing wider
and wider towards the ground, formed a coni-
cal column ; and it is well known that the
cone was sacred to the solar deity. The three
heads were disposed triangularly, in order to
sustain the three feet of the tripod, which
was of gold. Herodotus tells us that it was
consecrated to Apollo by the Greeks, out of
the spoils of the Persians after the battle of
Plataea.

1 It may be remarked here as a note, that our British Solomon,
King James, broached a triad of what he esteemed detestable things,
unfit for human beings. " His Majesty professed that were he to
invite the devil to a dinner, he should provide these three dishes. 1.
A roasted pig. 2. A poll of ling and mustard. And 3. A pipe of
tobacco for digestion." — (Apophthegms of King James, p. 4.)

a See this subject more fully treated on in Dean's Worship of the
Serpent, p. 198.

Veneration for the Number Three. 93

The British Druids, some of whose rites and
institutions, according to the opinion of Hutchin-
son and other ancient brethren, " were probably
retained in forming the ceremonies of Masonry,"
had a peculiar veneration for this number ; and
arranged the classes both in their civil and
religious polity upon ternary principles. Nothing
could be transacted without a reference to this
number. On solemn occasions, the processions
were formed three times round the sacred en-
closure of Caer Sidi ; their invocations were
thrice repeated; and even their poetry was
composed in triads. The ternary deiscal, or
procession from east to west by the south, ac-
companied all their rites, whether civil or ecclesi-
astical ; and nothing was accounted sanctified
without the performance of this preliminary
ceremony. The tenets of their religion were
founded on three fundamental articles, viz., rever-
ence for the deity — abstaining from evil — and
behaving valiantly in battle ; and the triad rule
for the preservation of health was — cheerfulness
— temperance — exercise. 1 Indeed, the number
three was sacred throughout all antiquity. 2
And both Aristotle atid Plutarch could say,
equally with the British Druids, that it was
held mysterious, because it comprehended the

1 Smith, Gael. Ant., p. 80.

J Virg. Eel., viii. 73. Plato in Tim. Plut. de Isid. et Osir., p. 873.
Ovid, vii 189. Olaus Mag. Hist. Goth. Asiat. Res., vol i. p. 272,
voL iii. p. 369, &c. &c.

94 The Pythagorean Triangle.

beginning — middle — end. The jovial Horace
also exclaims : —

Tribus aut novem
Miscentur cyathis pocula commodis.

Qui musas ainat impares,

Ternos ter cyathos attonitus petet

Vates ; tres prohibet supra

Rixarum metuens taogere Gratia

Nudis juncta sororibus. 1

Very superstitious ideas were attached to bells
in the first ages of Christianity ; and the opposi-
tion to the Pelagian heresy, and the Druidical
triads united, probably produced that singular
exhibition of veneration for the Trinity which is
thus recorded. Three clergymen of St Telian's
three churches claimed his body when dead ; upon
which three several corpses appeared, and one was
buried in each of these churches. And Giraldus
Cambrensis records, that three persons usually
sat down to the table in honour of the Trinity
at the period when he flourished. 2 Nor are the
superstitions attached to this number yet extin-
guished. Scheffer tells us that the Laplanders
are in the habit of using a cord tied with three
magical knots for raising the wind. When they
untie the first knot, there blows a favourable gale
of wind ; which increases at the second, and be-
comes a perfect hurricane at the third. Most of
the northern nations were addicted to this super-
stition. Amongst the Mandingoes, in the interior
of Africa, according to Park, when a child is

1 Hor., L Hi. carm. 19. ' Fosbr, Monach., p. 16.

Superstitions attached to the Number Three. 95

named, the priest, after the blessing, whispers
something into the child's ear, and spits three
times in his face, after which the name is pro-
nounced, and the child placed in its mother's
arms. 1

To come a little nearer home. Martin, in his
book on the Isles of Scotland, gives several in-
stances of the superstitious use of the above num-
ber. "When the inhabitants," he says, "go a-
fowling, in order to prevent the transgression of
the least nicety, every novice is always joined
with another, who can instruct him in all the
punctilios observed on such occasions. When
arrived at their destination, after uncovering
their heads, turning round sun- ways, and thank-
ing God, they pray three times in three different
places ; the first prayer is made as they approach
the chapel ; the second in going round it, and the
third in the interior." Even some of our learned
Freemasons did not escape the taint of these
superstitious observances. Our learned brother
Elias Ashmole, when he had the. ague, used to
take a good dose of elixir early in the morning,
and to hang about his neck three spiders; and
this, he says, drove the ague away. 2 In the
" Life of a Satirical Puppy/' 3 the following pas-
sage occurs : " One of his guardians, being fortified
with an old charm, marches cross-legged, spitting
three times, east, west, and south ; and afterwards

1 Brand and Sir Henry Ellis, in the Popular Antiquities, have col-
lected many curious facts respecting the number three.
8 Diary, 11th April 1681. 8 Lond. 1657, p. 35.

96 The Pythagorean Triangle.

prefers his vallor to a catechising office. In the
name of God, quoth he, what art thou ? whence
dost thou come ? seeing something that he sup-
posed to be a ghost."

What a weak and unstable creature is man!
We all despise these idle fancies in others, and
yet, I am persuaded, there is scarcely an indivi-
dual at present in existence, notwithstanding the
improvements in science and philosophy which
distinguish our own times, who is not, in some
respect or other, under their influence. Is there
no young lady amongst us who will sit cross-legged
at the card -table as the harbinger of good-luck ?
Is no one alarmed at hearing the death-watch, or
the sight of a single magpie crossing his path ? I
knew a man — an educated man too — who always
removed his hat on such an occurrence. Which
of us is really and truly exempt from the dread
of apparitions and visions of the night ; or from
a belief in the efficacy of charms for ague, cramp,
or toothache ? Let every one answer to himself,
and not to the world, and his reply will be not far
from the truth.

Again. What opinion shall we pass upon the
pseudo-prophecies of Francis Moore, physician,
and his imitators, who have assumed the cabalistic
names of Raphael, Zadkiel, &c. ? Of what value
would their predictions be if their authors did not
place a greater dependence on the credulity of
mankind than on the stars and planets 1 Such
men fatten upon the weaknesses of their fellow-
creatures, and turn their superstitious feelings to

The Art of Transmuting Metals. 97

account. Southey, speaking of John Miiller, bet-
ter known under the name of Regiomontanus,
says, " He could talk of the fiery and earthy tri-
gons, the aerial and the watery, and of that pro-
perty of a triangle whereby Sol and Jupiter, Luna
and Venus, Saturn and Mercury, respectively be-
come joint trigonocrators, leaving Mars to rule
over the watery trigon alone." This is the kind
of jargon which won golden opinions from all
sorts of men a century or two back. It not only
advanced the science of astrology to eminence,
but excited such a general belief in the art of
transmuting metals, that an alarm was taken in
the highest quarters, and an Act of Parliament was
passed, 5 Henry IV., 1404, determining that "the
making of gold and silver shall be deemed felony."
" This law," says Watson, 1 "is said to have resulted
from the fear at that time entertained by the
Lords .and Commons, lest the executive power,
finding itself by these means enabled to increase
the revenue of the Crown to any degree it pleased,
should disdain to ask aid from the Legislature ;
and in consequence should degenerate into tyranny
and arbitrary power. "

The use of the number three is so firmly in-
corporated into many of our civil and religious
ceremonies, that its observance has become an
immovable item in the habits and customs of the
people. Thus public approbation of a toast or
sentiment is displayed at a banquet by the
honours of three or three times three acclamar

1 Chemical Essays, voL L

98 The Pythagorean Triangle.

tions. When a hostile British man-of-war meets
the enemy, the seamen salute him with three
hearty cheers. And the passing bell, at the de-
cease of any individual, commences and concludes
with three distinct knells for a man, and two for
a woman, each repeated three times for the follow-
ing reason, as is recorded in an old English homily
for Trinity Sunday : " The fourme of the Trinity
was founden in manne, that was Adam our fore-
fadir, of earth oon personne, and Eve of Adam
the secunde persone ; and of them both was the
third persone. At the deth of a manne three
bellis shulde be ronge, as his knyll, in worscheppe
of the Trinetee, and for a womanne, who was the
secunde persone of the Trinetee, two bellis should
be r ungen." l In a word, not only in reference to
the Trinity, and to the death and resurrection of
Christ at three days' distance from each other, but
from many ancient superstitions both Jewish and
heathen, the number three is likely to retain the
reputation of possessing mysterious properties as
long as man shall remain upon the earth.

In attempting to explain the arcane peculi-
arities of the number three we might be accused of
travelling out of the record. But there will be no
impropriety in remarking that numbers which in-
crease in arithmetical progression by threes, the
sum of the first and last terms will be equal to
that of the second and last but one, or the two
middle terms, if two, or twice the middle one if
an unit Thus, for instance, if we take a progres-

1 See Strutt's Manners and Customs, vol. iii p. 176.

Progression by Threes. 99

sion by threes consisting of six terms, it will stand
as follows, viz., 1, 4, 7, 10, 13, 16. And 16 + 1 =
17; 4+13=17; 10+7=17. Again, in 7 terms,
viz., 1, 4, 7, 10, 13, 16, 19, the same peculiarity
occurs, as 1 + 19=20 ; 4+16=20, &c., and twice
10=20. And here the seventh term is equal to
the first with the addition of 6 times 3, as 1 + 18
=19.

PROGRESSIVE GENERATION OF THE TETRAD
OR SOLID, REPRESENTING FIRE.

THE SOLID, TETRAD, QUATERNARY, OR THE

NUMBER FOUR.

CHAPTER IV.

THE SOLID.

TETRAD, QUATERNARY, OR THE NUMBER FOUR.

" By that pure, holy, Four-Letter Name on high,
Nature's eternal fountain and supply,
The parent of all souls that living be,
By Him, with faithful oath, I swear to thee. 1 *

Oath op Pythagoras.

" The Grand and Sacred Name ought to be saluted four times in four
peculiar positions, for the following reasons."— Old Lectures.

HE tetrad, though not essentially ma-
sonic, for the only instances in which it
is exemplified, viz., in the Sacred Name
and the Cherubim, are attached to the third de-
gree only, was esteemed the most perfect number,
and referred to the Author of nature,orT.G.A.O.
T.U. ; and his name was therefore composed of four
letters, nw, and was called Tetragrammaton by
the Jews, and Tetractys by the Gentiles; of
the latter of whom Hierocles, in his exposition of
the Golden Verses of Pythagoras, says, "He is
the Demiurgus, the architect and maker of all

104 The Pythagorean Triangle.

tilings. " These are his words : " The author of
these verses shows that the tetrad, which is the
fountain of the perpetual orderly distribution of
things, is the same with God who is the Demi-
urgus ; an intelligible god, the source of the
celestial and sensible good." The tetrad, as Mr
Taylor thinks, is, however, the animal itself of
Plato, who, as Syrianus justly observes, was the
best of the Pythagoreans ; subsists at the extrem-
ity of the intelligible triad, as is most satisfac-
torily shown by Proclus in the third book of his
treatise on the theology of Plato, And between
these two triads, the one intelligible, and the other
intellectual, another order of gods exists, which
partakes of both extremes.

This number forms the arithmetical mean be-
tween the monad and the heptad; and this
comprehends all powers, both of the produc-
tive and produced numbers ; for this, of all
numbers under ten, is made of a certain number ;
the duad doubled makes a tetrad, and the tetrad
doubled makes the hebdomad. Two multiplied
into itself produces four ; and retorted into itself
makes the first cube. This first cube is a fertile
number, the ground of multitude and variety,
constituted of two and four. Thus the two prin-
ciples of temporal things, the pyramis and cube,
foL and matter, flow* from Ze fountain, the
tetragon, whose idea is the Tetractys, the divine
exemplar. 1

Amongst the Hermesians, the number four, thus

1 Reuchlin & Cabala, L ii.

Symbols of the Number Four. 105

amplified into a cube, was the symbol of truth,
because in whatever point of view it may be
contemplated it is always the same ; and for this
reason Hermes or Mercury was esteemed the god
of eloquence ; l and the Greeks and Romans offered
to him in sacrifice the tongues of animals. The
gift of eloquence, however, according to Lucian,
was conferred by the Druids of Britain on a dif-
ferent deity. He was told by one of the Druids,
as he stood admiring a figure of Hercules, to
whose tongue were fastened chains of gold and
amber, which drew along a multitude of persons
whose ears appeared to be fixed to the other end
of those chains, that " they did not agree with the
Greeks in making Mercury the god of eloquence.
According to our system/' he continued, "this
honour is due only to Hercules, because he sur-
passes Mercury in power; we paint him advanced
in age, because eloquence does not exert her most
animated powers except in the mouths of aged
persons. The link, and the connection there is
between the tongue of the eloquent and the ears
of the audience, justify the rest of the representa-
tion. By understanding the history of Hercules
in this sense, we neither dishonour him nor depart
from truth; for we hold it indisputably true
that he succeeded in all his noble enterprises,
captivated every heart, and subdued every brutal
passion, not by the strength of his arms, but by
the power of wisdom and the sweetness of his
persuasion."

1 TertuL de coronis Featus.

106 The Pythagorean Triangle.

The most ancient Greeks 1 considered the tetrad
to be the root and principle of all things, because
it was the number of the elements. The fire was
considered to be Jupiter, the air Juno, the earth
Pluto, and water, taken from the womb, Nestis.
On this subject Pythagoras taught that when fire
resolves the dissolution of water into air, two
parts of air are generated, and one part of fire.
But when, on the contrary, water is generated
from air, three parts of air being resolved, the
four triangles which are mingled together from
the same cause, i.e., from condensation, together
with two parts of air, make one part of
water.

In the system of the Eose +, as propounded
by Fludd, Behmen, Meyer, and others, the four
elements were represented as being peopled and
governed by spirits, who possessed a decided in-
fluence over the destiny of man. These elementary
beings, which to grosser eyes were invisible, were
familiarly known to the initiated. To be admitted
to their acquaintance, it was previously necessary
that the organs of human sight should be purged
by the universal medicine, and that certain glass
globes should be chemically prepared with one or
other of the four elements/and for one month ex-
posed to the beams of the sun. These preliminary
steps being taken, the initiated immediately had
a sight of innumerable beings of a luminous sub-
stance, but of thin and evanescent structure, that
people the elements on all sides of us. Those who

1 See Plut. de Plac. Phil., p. 878.

The Number of the Elements. 107

inhabited the air were called sylphs ; and those
who dwelt in the earth bore the name of gnomes ;
such as peopled the fire were salamanders ; and
those who made their home in the waters were
called undines. Each class appears to have had
an extensive power in the element to which it be-
longed. They could raise tempests in the air, and
storms at sea, shake the earth, and alarm the in-
habitants of the globe with the sight of devouring
flames. They were, however, more formidable in
appearance than in reality. And the whole race
was subordinate to man, and particularly subject
to the initiated. The gnomes, inhabitants of the
earth and the mines, liberally supplied to the hu-
man beings with whom they conversed the hidden
treasures over which they presided. The four
classes were some of them male, and some female ;
but the female sex seems to have preponderated." 1
Thus Pope : —

For when the fair in aU their pride expire,
To their first elements their souls retire,
The sprites of fiery termagants in flame
Mount up, and take a Salamander's name.
Soft yielding minds to water glide away,
And sip, with Nymphs, their elemental tea.
The graver prude sinks downward to a Gnome,
In search of mischief still on earth to roam.
The light coquettes in Sylphs aloft repair,
And sport and flutter in the fields of air. 2

The figure of a cross, to symbolise the four ele-
ments, formed a disquisition in one of the Theo-

1 Godwin's Lives of Necromancers, p. 36.
* Rape of the Lock, Canto i. 57.

108 The Pythagorean Triangle.

sophic degrees of M. Peuvret, called the Rosy
Cross ; and was treated according to the funda-
mental principles of light and darkness, or good
and evil. Thus the element of air corresponded
with humility in the former class, and pride in
the latter. The earth, in like manner, was assimi-
lated with meekness on the one hand and covet-
ousness on the other ; water with patience and
envy; and fire with love and hatred. These
principles, arising out of the world's four elements,
when applied to the science of light, were denomi-
nated the four elements of God, and to darkness,
the four elements of the devil. The philosophy
of the subject was thus stated : "The fire preys
upon the water and air ; the air is breathed out
of the water by the incitement of the fire ; the
water is the contraction of the air by the vicinity
of the astringent cold earth, but the earth is one
body of no great intimacy with either of the
other, being only a sediment resulting from the
separating power of the other three elements.
Nor yet may it be wondered that the four were
once one, and proceeded from one ; seeing they
are still one, differing only in the degrees of rarity
and density ; for as the earth drives up the water,
so doth the water raise up the air, and the fire
being violently active surmounts 831/' The lec-
ture then goes on to explain how the one was
separated into four; but the exposition is too long
and too dry to be inserted here.

It should appear that the aboriginal savages of
America (if savages they were) had some attach-

Attachment to the Number Four. 109

ment to the number four; for the Mexican priests
were enjoined to burn incense before the image of
the deity four times a day. They had a public
celebration or general jubilee every four years ;
and forty days before the annual festival of
Quetzalcoatl, the Mexican Mercury, a slave was
purchased, and fattened as a victim to be sacri-
ficed at the solemnity; while the lives of four
children were offered to Tlaloc, the god of rain,
when the corn was bursting into spike, in order^
that he might be propitious, and by sending
genial showers, produce a good and plentiful
harvest.

These sacrifices were offered on the summit of
four square pyramids constructed for the purpose;
some of which remain in Central America to the
present day ; and one of them is thus described
by Stephens : * "It is sixty feet high, and one
hundred feet square at the base ; but it is now
. covered with earth, and though it retains the
symmetry of its original proportions, it is so
overgrown with trees, that it appears a mere
wooded hill, but peculiar in its regularity of
shape. Four grand staircases, each twenty-five
feet wide, ascended to an esplanade within six
feet of the top. This esplanade was six feet in
width, and on each side is a smaller staircase
leading to the top. The summit is a plain stoue
platform, fifteen feet square. Probably it was
the great mound of sacrifice, on which the
priests, in the sight of the assembled people,

1 Travels in Yucatan, vol L p. 131.

110 The Pythagorean Triangle.

cut out the hearts of human victims. At a short
distance from the base of the mound was an
opening in the earth, forming another of those
extraordinary caves which have been already-
mentioned. The entrance was by a broken,
yawning mouth, steep, and requiring some care
in the descent. At the first resting-place, the
mouth opened into an extensive subterraneous
chamber with a high roof, and passages branch-
ing off in every direction. In different places
were remains of fires and the bones of animals,
showing that it had probably been a place of
refuge, or residence of men ; and in the entrance
of one of these passages we found a sculptured
idol." 1

In Geometry, the tetrad combines within itself
all the materials of which the world and all things
therein are composed, viz., the point extended to
a line ; a line to a superficies ; and the superficies or
triad converted to a solid or tetrad by the point
beiug placed over it. Thus in the original lectures
of Masonry, which, like those of the Druids, were
constructed rhythmically, that they might be more
easily remembered, we have the following pas-
sage : —

The Science five [Geometry] may weU compose

A noble structure, vast ;
A point, a line, a supernce,

But solid is the last.

According to Philo Judaeus, the quadrate

1 See Hist. Init., p. 294, new ed., where the use of these caverns is
particularly described.

Perfections of the Quadrate. Ill

number not only comprehends all, point, line,
superficies, and body, but possesses other perfec-
tions, one of which is, that all the first numbers
of which it is formed make up the number ten,
which is so perfect, that in counting we can go no
farther ; for the parts of four added together, as
1+2+3 + 4=10. But Hierocles the Pythagorean
contends that before we make up ten by this pro-
cess, we must consider that there is an implicit
and complicate entireness of ten in the number
four, which is of itself amply sufficient to consti-
tute it a symbol of universality.

Another excellence is also found in the number
four, viz., that the principal consonances of music,
which are the diapente, diatessaron, and diapason,
are found to contain the same parts of this num-
ber. The diapente, which is the sesquialtera, as
from 9 to 6 ; the diatessaron is a sesquitertia,
as from 8 to 6 ; and the diapason, which is
a double, as 12 to 6. The quadrate number
was highly appreciated by the ancients on
account of the four liberal arts — Geometry,
Astronomy, Music, and Arithmetic, which are
highly important in the acquirement of all other
sciences. 1

From the above reasoning, the tetrad or tetrac-
tys was called Kosmos, the world, because it
numbered 36, the sum of the four odd numbers 1,
3, 5, 7, proceeding from a combination of the
digits, thus : —

• l Concil., yoL i. p. 106.

112 The Pythagorean Triangle.

1 + 2-3
3 + 4 = *7
5 + 6 = 11
7 + 8 = 15

36

r The Pythagorean world, according to Plutarch, 1
consisted of a double quaternary. The quater-
nary of the intellectual world is T'Agathon, Nous,
Psyche, Hyle ; while that of the sensible world,
which is properly what Pythagoras meant by the
word Kosmos, is Fire, Air, Water, and Earth.
The four elements are called by the name of
rizomata, the roots or principles of all mixed
bodies. In some ancient Greek verses to this
effect, Jupiter is the fire, Juno the air, Pluto the
earth, and Nestis the water, and these are the
four roots of all existing things.

"The intelligible world proceeds out of the
divine mind after this manner. The Tetractys,
reflecting upon its own essence, the first unit, pro-
ductrix of all things, and on its own beginning,
saith thus : Once one, twice two, immediately
ariseth a tetrad, having on its top the highest
unit, and becomes a Pyramis, whose base is a
plain tetrad, answerable to a superficies, upon
which the radiant light of the divine unity pro-
duceth the form of incorporeal fire, by reason of
the descent of Juno (matter) to inferior things.
Hence ariseth essential light, not burning but
illuminating. This is the creation of the middle

1 De anim. procr., 1027.

Analysis of Female Beauty. 113

world, which the Hebrews call the Supreme, the
world of the deity. It is termed Olympus, entirely
light, and replete with separate forms, where is
the seat of the immortal gods, deum domus alta,
whose top is unity, its wall trinity, and its super-
ficies quaternity." x

It forms a curious coincidence with this philo-
sophy, that the Arabian analysis of female beauty
should be founded on the same principles, and
thus made to consist of 4x9=36 excellences.
" Four things in a woman," says an anonymous
author quoted by Lane, 2 " should be black : the
hair of her head, the eyebrows, the eyelashes,
and the dark part of the eyes ; — four white : the
complexion of the skin, the white of the eyes, the
teeth, and the legs ; — four red : the tongue, the
lips, the middle of the cheeks, and the gums ; —
four round : the head, the neck, the forearms, and
the ankles ;— four long : the back, the fingers, the
arms, and the legs ; — four wide : the forehead, the
eyes, the bosom, and the hips ; — four fine : the
eyebrows, the nose, the lips, and the fingers ; —
four thick : the lower part of the back, the thighs,
the calves of the legs, and the knees ; — four small :
the ears, the breasts, the hands, and the feet ; —
in all, thirty-six."

The number four had a very significant reference
to masculine or manly performances ; and to body
and soul, because it consists of four properties,
mind, science, opinion, and sense ; 8 and also to

1 Reuchlin, ut sivpra, p. 689. * Arabian Nights, vol. i. p. 29.

8 Plut. Plac. Phil, i. 3.

H

114 The Pythagorean Triangle.

justice, because being quadrate, it is divided into
equals, and is itself equal. 1 It was a symbol of
Wisdom. Pierius says, 2 " Sapientiam in quadrato
statuebant ; ex hoc hieroglyphico volubilem illam,
uti paulo ante diximus, hujus verb sedem firmam
et inconcussam indicantes. Et nostri quadrata
ligna quae ad arcae Noes fabricam parari divinum
jussit numen, doctores et magistros in Ecclesia
significare dicunt, quorum sapientia inclusi intus
populi conservantur, et ab incursantibus haereti-
corum procellis muniuntur. Ex quadratis enin
lignis construere debere nos Bibliothecam admonet
Admantius, non ex agrestibus, rudibus, et im-
politis. Quippe ex Propheticis et Apostolicis
voluminibus, in quivus solis vera continentur
sapientia, utpote qui vitiis omnibus resectis
excisisque, quadratum vitae justioris tenorem."

The name of Harmony was given to the tetrad,
because it is a diatessaron in sesquitertia. The
Pythagoreans, however, were of opinion, according
to Theon in his " Mathematical that the division
of the canon of the monochord was made by the
tetractys in the duad, triad, and tetrad ; for it
comprehends a sesquitertia, a sesquialtera, a duple,
a triple, and a quadruple proportion, the section
of which is 27- In the ancient musical notation,
the tetrachord consisted of three degrees or inter-
vals, and four terms or sounds, called by the
Greeks diatessaron and by us a fourth. In the
ancient music, all the primitive or chief divisions
were confined to four chords, so that the great

1 Alex. Aphrod. metath., v. 2 Hieroglyphica, fo. 290.

The Key- Keeper of Nature. 115

scale consisted of replicates, and all the upper tet-
rachords were considered only as repetitions of
the first and lowest, called Hypate Hypaton ; the
third sound of which, answering to our D natural
on the third line of the bass, was called Hypate
diatonus ; while the Hypate meson was the
principal of the mean tetrachord, and equiva-
lent to our E natural on the third space in the bass.
The same number was called by the Pythago-
reans the key-keeper of nature, because the con-
stitution of the world cannot exist without it ;
and the square or cube being equivalent to truth
is considered equally applicable to nature. It
was denominated also Hercules, Impetuosity,
Strongest, Masculine, Inefieminate, Mercury, Vul-
can, Bacchus, Soritas, Maiades, Erynnis, Socus,
Dioscorus, Bassarius, Two-Mothered, of Feminine
Form, of Virile Performance, Bacchation, with a
variety of other names. 1 The Talmudists say
that four things are able to annul an evil decree
against any person, how guilty soever he may be,
which are Charity, Acquittal, Change of Name,
and Change of Conduct. From this belief some
of them superstitiously think that this tetrad will
cure the most severe sickness. And the number
four includes the winding up and result of every
man's probation ; for all things will terminate in
death, judgment, heaven, and hell. To avoid the
latter of which St Irenaeus says, that " four gospels
were given, and no more, from the four winds and
four corners of the earth."

1 Stanley, Pyth., p. 61.

116 The Pythagorean Triwngle.

A curious argument has been used by St
Augustine to prove that Christ could not pos-
sibly have added to the number of His apostles,
which is derived from the tetrad before us ; he
says, " The gospel was to be preached in the four
corners of the earth in the name of the Trinity,
and three times four make twelve " ! A modern
sect of Christians, perhaps in imitation of this
and the like mode of reasoning, assumed the
name of Mystics, and contended for the propriety
of allegorising Scripture by a quadruple process.
For instance, they put this construction- upon the
city of Jerusalem. Literally, they said, it is a city
of Judea; if understood allegorically, it is the
Church militant ; if morally, a sincere Christian ;
and if mystically, heaven, the Church triumphant.

The Tetragrammaton, or four-lettered Name of
the Most High, rfirp, appears to have been known
to the heathen. Archbishop Tenison says, 1 "This
Name was no mystery among the Greeks, as is
evident from the mention of Jerombaal, a priest
of the god Ieuo, in Sanchoniathon ; of Jaho in
St Hierom, and the Sibylline Oracles ; of Jaoth,
or Jaho in Irenseus ; of the Hebrew God called
Jaoia by the Gnostics ; of Jaou in Clemens Alex-
andrinus ; of Jao, the first principle of the first-
Gnostic heaven in Epiphanius ; the God of Moses
in Diodorus Siculus ; the god Bacchus in the or-
acle of Apollo Clarius ; and lastly, as was said, of
the Samaritan god Jabe, in Theodoret."

This Name is called by Josephus " the Sacred

1 Idolat.,p. 404.

The Tetragrammaton. 117

Letters — the shuddering Name of God ; " and
Caligula, in Philo, swears to him and the ambas-
sadors, by the God with the unpronounceable
Name. The Tetragrammaton, even down to the
seventeenth century of Christianity, was esteemed
a powerful amulet. ' Thus Stephens, speaking of a
witch, says, " Her prayers and Amen be a charm
and a curse ; her contemplations and soule's de-
light bee other men's mischiefe ; her portion and
sutors be her soule and a succubus ; her highest
adorations be yew-trees, dampish churchyards,
and a fayre moonlight ; her best 'preservatives be
odde numbers and mightie Tetragrammaton" 1

It was a doctrine taught by the Hebrew phil-
osophers that "the Tetragrammaton and PPJ1N
alike represent the substance of the Divinity ; the
latter being in the future tense and first person
singular, and the Tetragrammaton in the third
person, forming, between the two, these three

words, nvm mn «n\n Was, Is, Will be. R Judah

h, Levi in the Cuzari, and the learned Aben Ezra,
on the 33d chapter of Exodus, also explain that
the name TV is likewise the substance ; for the
Tetragrammaton is numerically 26, and the two
letters rP, written at full length RH D\ are also 26.
And this is what the Lord said to Moses, * Say
unto Israel, The Tetragrammaton and JVDN hath
sent me unto you ; ' for, on his inquiry what he
should say if they asked him the Name of the
divine Essence, He answered the two names it
signifies. Some learned Jews understand the

1 Characters, p. 375.

118 The Pythagorean Triangle.

words, What is His name ? to mean, What is His
Being or Essence ? " *

Marcellus Ficin observes on Plato, as we are
told by the Eabbi ben Israel, that the Name of
the Lord is written and pronounced by all nations
with four letters. The Egyptians called Him Teut;
the Arabs, Alia; the Persians, Sire; the Magi,
Or si; the Mahometans, Abdi ; the Greeks, Teos;
the ancient Turks, JEsar ; and the Latins, Deus ;
to which John Lorenzo Anania adds, the Germans
call him Gott; the Surmatas, Bouh and Istu;
the Tartars, Itga.

In the [Continental degree, called the Philoso-
phes Inconnus, the number four is thus noticed :
" Que signifie le nombre . Quatre adopts dans le
Grand Ecossisme de S. Andrd d'Ecosse, le comple-
ment des progressions magonniques? Outre le
parfait 6quilibre et le parfait 6galit6 des quatre
616mens dans le pierre physique, il signifie
quatre choses qu'il faut faire n^cessairement
pour Taccomplissement de Tceuvre, qui sont,
composition, alteration, mixtion, et union,
lesquelles, une fois faites dans les regies de Part,
donneront les fils legitimes du soleil, et pro-
duiront le ph&rix toujours renaissant de ses
cendres."

There is a curious anecdote told respecting this
number, of Pope Innocent III., who sent to our
King John a present of four rings set with four
different - coloured jewels; admonishing him at
the same time to consider seriously their four

1 ConciL, vol. i. p. 107.

Four Great Ciphers. 119

various properties of form, number, matter, and
colour. The form, being round, shadowed out
eternity, for which it was his duty to prepare ;
the number denoted the four cardinal virtues,
which it was his duty to practise ; the matter,
being gold, the most precious of metals, desig-
nated wisdom, the most precious of accomplish-
ments, which it was his duty to acquire ; and as
to the colour, the green of the emerald represented
faith ; the blue of the sapphire, hope ; the red-
ness of the ruby, charity ; and the splendid yel-
low of the topaz, good works." 1

The preceding observations on the philosophy of
the number four, will be received by the fraternity,
not as a perfect essay on the subject, but as a
series of collections towards such a dissertation ;
which, if it were to be fully developed and exem-
plified, would far exceed my limits. In 1636,
Beeton published a book on " The Figure of Foore,"
which I notice simply as a curious repository of
ingenious conjecture, although it contains nothing
to our purpose, being constructed on the plan of
the subjoined specimen. " There are foure great
cyphers in the world, hee that is lame among
dauncers, dumbe among lawyers, dull among
schollers, and rude among courtiers. Again —
there are foure things grievously empty : a head
without braines, a wit without judgment, a heart
. without honesty, and a purse without money."

If brevity be the soul of wit, it is also a bar to
the exercise of judgment, or the play of imagina-

1 Beckmann, Ancient Inventions, voL ii. p. 171.

120 The Pythagorean Triangle.

tion. A few dry facts strung together are not
favourable to the currente calamo, or pen of the
ready writer. If, however, there is no theory to
establish, or system to demonstrate, the writer
will escape the chances of offering contradictory
arguments, or of urging opinions which are at
variance with fact. This is something ; and may
serve as a set-off against the charge of dulness
and ultra-gravity, even where gravity is most
appositely used — in a dissertation on the subject
of Freemasonry. Now, as the composition of a
delicious beverage may be considered by some of
our brethren as connected, in a slight degree, with
the refreshments of the Lodge, I shall attempt to
relieve the dulness of these dissertations by tran-
scribing the opinion of a philosopher who illu-
minates the pages of Blackwood's Magazine, on
the ingredients of a liquor called punch, as it is
in some measure illustrative of the number under
our consideration. He pronounces, ex cathedra,
that it ought, like the fourth interval in music, to
be founded on the principles of the tetrad. These
are his words : " Punch is a liquor made by
mixing spirit and water, sugar and the juice of
lemon, and formerly with spice ; and is so called
from an Indian wood called five, that being the
number of the ingredients. The Greek equivalent
for punch, or more properly potinch, is But irevre ;
but the spice is now admissible only in bishop :
wherefore in the universities, and in convocations
of the clergy, and in other assemblies of learned
men, punch is more correctly called Sia reo-aapav,

^

The Ingredients of Punch. 121

signifying a combination of four" A small modi-
cum of the latter composition is not to be despised,
particularly if the three weaker ingredients be
well amalgamated and smoking hot, before it is
enlivened by the spirit. Can I conclude this
chapter more sweetly ? It is very doubtful ; and
therefore I shall leave it unat tempted.

GEOMETRICAL APPLICATION OF THE PENTAD
OR PYRAMID, REPRESENTING WATER,

THE PYRAMID, PENTAD, QUINCUNX, OR THE

NUMBER FIVE.

*z<£Sr2S&».

CHAPTEE V.

. THE PYRAMID.

PENTAD, QUINCUNX, OR THE NUMBER FIVE.

" The Blazing Star is depicted with five points or rays, to show, first,
that in the construction of the Temple, five orders of architec-
ture were made use of ; secondly, to represent the five points of
felicity ; ix. y to walk, to intercede for, to pray, to love, and to
assist your brethren, so as to be united with them right hear-
tily ; thirdly, to represent the five senses, which constitute the
dignity of man ; fourthly, to symbolise the five lights of Masonry ;
and fifthly, the five zones inhabited by the fraternity." — The
Ineffable Lectures.

T is remarkable that every number pre-
sents some charm, which may be applied
to a purpose not only peculiar to itself,
but also not transferable to any other subject
without impairing its efficiency. So thought our
forefathers ; and the question is, Do not we think
the same ? I have already mentioned our predi-
lection for the number three, and three times
three cheers ; would five, or five times five, answer
the same purpose ? It is not to be thought of.
There is not an assemblage of Englishmen, from
the highest to the lowest rank, but would resist

126 The Pythagorean Triangle.

the innovation. If any one be troubled with
that unsightly excrescence in the 1 eye, which is
called in some provinces a stye, it can only be
cured by drawing a lady's wedding-ring nine
times across the diseased part — no other number
would do. The charm would be profitless if it
were exceeded or diminished by a single unit. The
number thirteen is supposed to be unpropitious at
a dinner-party — one of the company is expected
to die within the year ; but no such belief is
attached to twelve or fourteen, or any larger or
smaller number.

Again, the seventh son of a seventh son, no
daughter intervening, is considered to be a physi-
cian by birth, and to be intuitively imbued with
a knowledge of the symptoms and treatment of
diseases ; but no such superstitious belief is at-
tached to any other son, who has hence no source
of knowledge but- what arises from incessant and
severe study. In an old Book of Knowledge, the
following paragraph occurs : " Astronomers and
astrologers say that in the beginning of March,
the seventh night, or the fourteenth day, let thee
bloud of the right arm ; and in the beginning of
April, the eleventh day, of the left arm ; and in
the end of May, third or fifth day, on whether
arm thou wilt ; and thus, of all that year, thou
shalt orderly be kept from the fever, the falling
gout, the sister gout, and losse of thy sight."
About the middle of the last century, or a little
later, there lived a curious character, well known
by the appellation of King Cole. He was a fish

The Efficacy of Particular Numbers. 127

salesman at Billingsgate, and on the day of the
liberation of the celebrated John Wilkes, he al-
ways invited 45 friends to dine; and he treated
them with a plum-pudding containing 45 pounds
of flour and 45 of fruit. It was boiled 45 hours,
and conveyed to the place, where the party were
at dinner, with flags and music, and 45 butchers
with marrow-bones and cleavers. There were
also upon the table 45 pigeon-pies and 45 apple-
dumplings. When this old man lost his son he
consoled himself by using the same mystical num-
ber. He had him buried 45 miles from town,
attended by 45 fishmongers ; he paid the sexton
45 shillings for 45 tolls of the bell; and mourned
45 days in deep, and 45 days in half mourning.

How is this attachment to certain numbers to
be accounted for ? Let the physiologist find it
out if he can ; if not, let him go to the Delphic
oracle, for I have no time for speculations on such
a mysterious subject. In the case of the old fish-
monger, however, the solution is easy. In most
other cases, if there were any truth in the facts —
which we are sure there is not — all that could be
said about the matter would be, that as they were
contrary to any demonstrable principle of science
or philosophy, they would constitute so many
vagaries of Nature, departing from her staid and
sober march, to display a series of hallucinations
which derogate from her dignity of demeanour,
as exceptions to her unerring rules.

The belief in the efficacy of particular numbers
is too firmly fixed in the mind to admit of being

128 The Pythagorean Triangle.

extinguished by the arguments of sober reason,
be they ever so specious and sound. It extends
through all ranks of society, and travels side by
side with other superstitions, the* existence of
which is a libel on the reason and understanding
of man. It preys upon his spirits, forces his in-
clinations out of their proper bias, compels him
to believe what, in his inward conscience, he
suspects to be delusive ; and induces his fears
to admit what his judgment pronounces to be
false.

It is a curious fact, that though we affect to
pity the ignorance of those rude barbarians of
antiquity, who could believe that when the sun
and moon disappeared beneath the horizon, they
became impure spirits, and wandered about the
world till break of day ; yet we admit, at least
inwardly, the doctrine of wraiths, ghosts, appari-
tions, and perhaps fairies ; and fancy that departed
spirits or fiends linger over a forgotten hoard of
gold till it be appropriated to the lawful owner.
Sir Walter Scott has accorded an illustration of
this kind of superstition, which was furnished
by his friend James Skene, Esq. 1 "Near the
little village of Franchemont, near Spaw, stands
an ancient castle, which is the subject of many
superstitious legends. It is firmly believed by
the neighbouring peasantry, that the last baron
deposited in one of the vaults of the castle a
ponderous chest, containing ah immense treasure
in gold and silver, which by some magic spell was

1 MarmioD, canto vi. note 7.

Popular Superstitions. 129

intrusted to the care of the devil, who constantly
sits on the chest in the shape of a huntsman.
Any one who is adventurous enough to touch the
chest is instantly seized with the palsy. On a
certain occasion, a priest of noted piety was
brought to the vault, who used all the arts of
exorcism to persuade his infernal majesty to
vacate his seat, but in vain ; for the huntsman
remained immovable. At last, moved by the
earnestness of the priest, he told him that he
would agree to resign the chest if he would sign
his name with blood. But the priest understood
his meaning, and refused, as by that act he would
have delivered over his soul to the devil. Yet it is
still believed, that if any one should discover the
mystical words used by the person who deposited
the treasure, and pronounce them over the chest,
the fiend would instantly decamp."

The reality of this superstition is undoubted ;
and it was so prevalent during the eighteenth cen-
tury, that directions were formally given to regulate
the conduct of a discovery of such a secret hoard,
by a German writer of the name of Stryck. He
says, " If the spirit stands by and remains neuter,
have nothing to do with the treasure ; it is a
temptation from Satan to burn your fingers —
there let it lie. But if the spectre offers it, and
presses it upon you, you may take it safely."

These superstitions are partly the effect of some
undefined principle in our nature, which suggests,
we know not how, that there are beings superior
to ourselves, by whom our actions are governed

130 The Pythagorean Triangle.

and directed ; and under this impression we sub-
mit to unforeseen calamities, without using any
means to prevent their approach. The supersti-
tionist, as Plutarch says when speaking on this
subject, " accounts every little distemper in his
body, or decay in his estate, the death of his
children, or other crosses or disappointments, as
the immediate effects of God's anger, and the in-
cursions of some vindictive demon. And therefore
he never attempts to use any remedy for his
relief, lest he should seem to fight against God, or
despise His correction." Amongst Christians, how-
ever, this feeling of despair ought never to be
indulged, because it has been revealed to us that
the prayer of a broken and a contrite heart will
neither be despised nor overlooked by a gracious
God, who willeth not the death of a sinner, but
had much rather he would repent and be saved.
The feeling, however, remains unsubdued at the
present day ; and, strange to tell, neither reason
nor revelation have been able to neutralise its in-
fluence over the human mind.

The pentad is a primary number, because it is
divisible by unity only. It is the Pyramis itself;
"the species of fire, of which a Pyramis, having
four bases and equal angles, is compounded, the
most immovable and penetrant form, without
matter, essential, separate light, next to God
sempiternal life. The work of the mind is life ;
the work of God is immortality — eternal life.
God himself is not this created Light, but the
author of it, whereof in the divine Trinity He

The Fifth Science. 131

containeth a most absolute pyramid, which im-
plieth the vigour of fire ; and is formed of the
tetrad with a point over the centre joined by
right lines to each angle ; and thus forming the
pentad ; but the pyramid is the fiery light of the
material world, of separate intelligences, beyond
the visible heaven, termed age, eternity, ether ;
which, being placed, like the uppermost point of
the pyramid, high above the tetrad, is free from
any disturbance by the other four." 1

This number completes both odd and even ;
and hence refers to Geometry, which, according
to an ancient masonic arrangement, is the fifth
science, and was thus expressed in the old lec-
tures : —

By letters four, and Science five,

This (G) aright doth stand
In art and due proportion.

You have your answer, friend.

And hence we refer the number five that are
competent to hold a Fellow Craft's Lodge, to the
five senses, the five orders of architecture, and the
five points of fellowship. In Geometry, however,
the pentad is more particularly represented by
the five regular bodies ; which, on account of their
singularity, and the mysterious nature usually
ascribed to them, were formerly known by the
name of " the five Platonic bodies." The ancients
regarded them with so much veneration, that it is
said our Grand Master Euclid composed his Ele-
ments for the express purpose of illustrating their

1 Reuchlin, ut supra, p. 68P.

132 The Pythagorean Triangle.

peculiar properties. These five bodies were called
— 1, the tetraedon, which has four equal triangular
faces ; 2, the hexaedron, or cube, which has six
equal square faces ; 3, the octaedron, which has
eight equal triangular faces ; 4, the dodecaedron,
which has twelve equal pentagonal faces ; and 5,
the icosaedron, which has twenty equal triangu-
lar faces. These are the only forms which it is
possible for regular bodies to assume. Kepler
was transported with joy when he made a discov-
ery which he conceived to be founded on these
principles. He exclaimed in rapture : " What I
prophesied two-and-twenty years ago, as soon as
I discovered the five solids among the heavenly
orbits, — what I firmly believed long before I had
seen Ptolemy's Harmonics, — what I had promised
to my friends in the title of this book, which I
named before I was sure of my discovery, — what
sixteen years ago I urged as a thing to be sought,
— that for which I joined Tycho Brahe and
settled in Prague, — for which I have devoted the
best part of my life to astronomical contempla-
tions ; at length I have brought to light, and
have recognised its truth beyond my most
sanguine expectations ! "

And what does the reader think the profound
discovery was which thus excited this great
astronomer % Why, it was — that as nature had
produced only five regular bodies, there could not
possibly be more than six planets attached to our
system ! And his theory was thus enunciated :
" It so happens that there are only five regular solids,

The P entangle of Solomon. 133

i.e., it is possible to make only five solids of diffe-
rent numbers of faces, so that all the faces of each
solid shall be equal to each other ; viz., thetetrae-
dron; the cube, or hexaedron ; the solid of eight
faces, or the octaedron ; the solid of twelve faces,
or the dodecaedron ; and the solid of twenty
faces, or the icosaedron. The orbit of the earth
is the ruler of all. Place within this orbit, touch-
ing it at all points, an icosaedron, and draw
within it a circle that will touch all its faces
internally, and we have the orbit of Venus.
Within the orbit of Venus place an octaedron,
and draw a circle as before — that is the orbit of
Mercury. Outside the orbit of the earth, place
a dodecaedron, and around this solid draw a
circle, which is the orbit of Mars. Outside of
the orbit of Mars describe a tetraedron, and
around this draw a circle, and you will have the
orbit of Jupiter ; and if you describe a hexaedron
outside of this orbit, you will have that of Saturn.
Now there are no more regular bodies, therefore
there can be no more planets ; and the observed
distances of the planets from each other corre-
spond exactly with the intervals between these
solids/'

Freemasons have another symbol referring to
this number in the star with five points, which
is sometimes called the seal, and at others the
pentangle of Solomon. It was thought that the
points corresp6nd with the five wounds of Christ
It was, however, used much earlier than the ad-
vent of our Saviour, both by Jews and heathens

134 The Pythagorean Triangle.

as an emblem of safety and health. Stukely has
the following remark on this figure : " One would
be apt to suspect that the Druids had a regard to
the sacred symbol and mystical character of medi-
cine, which in ancient times was thought of no
inconsiderable virtue ; this is a pentagonal figure
formed from a triple triangle, called by the name
of Hygeia, because it may be resolved into the
Greek letters which compose that word. The
Pythagoreans used it among their disciples as a
mystical symbol denoting health; and the cabal-
istic Jews and Arabians had the same fancy. It
is the pentalpha or pentagrammon among the
Egyptians, the mark of prosperity. Antiochus
Soter, going to fight against the Galatians, was
advised in a dream to bear this sign upon his
banner, whence he obtained a signal victory."

The attachment of the ancients to the number
five was so great that they mixed five or three,
but not four parts of water with their wine; and
in the cure of dysentery and other complaints,
Hippocrates mixed a fifth proportion of water
with milk. The astrologers used five principal
aspects, viz., the conjunct, the opposite, the
sextile, the trigonal, and the tetragonal; from
which they estimated the good or bad fortune of
the native whose horoscope was before them.

The peculiarities of this number were profusely
used in the science of architecture. Thus every
structure was composed of five parts, viz., the
foundation, the external walls, the openings of
the doors and windows, the apartments, and the

The Form oftlie Pentad. 135

roof. There are five orders, and five different
kinds of intercolumniations, which are deter-
mined by the proportions of height and diameter,
as the pienostyle, the systyle, the eustyle, the
diastyle, and the aerostyle. These are all men-
tioned by Vitruvius. Such a classification may
have originally arisen out of an imitation of Nature,
which, in many of her operations, has adopted the
form of the pentad. Thus Dr Brown says, in his
" Garden of Cyrus : " " Quincuncial forms and
ordinations are observable in animal figurations.
For to omit the hyoides or throat - bone of
animals : the furcula or merry-thoueht in birds
which supported the scapul*, affording a passage
for the windpipe and the gullet; the wings of
flies, and disposure of their legs in their first for-
mation from maggots, and the position of their
horns, wings, and legs, in their aurelian cases ;
the back of the Cimex arboreus, found often upon
trees and lesser plants, doth elegantly discover
the Burgundian decussation. Besides, a large
number of leaves have five divisions, and may be
circumscribed by a pentagon or figure of five
angles, made by right lines from the extremity
of their leaves ; as in the maple, vine, fig-tree.
But five-leaved flowers are commonly disposed
circularly about the stylus ; according to the higher
geometry of nature, dividing a circle by five radii,
which concur not to make diameters, as in quadri-
lateral and sexangular intersections.

"Now the number of fi,ve is remarkable in
every circle, not only as the first spherical num-

136 The Pythagorean Triangle.

ber, but the measure of spherical motion. For
spherical bodies move by fives ; and every globu-
lar figure, placed upon a plane, in direct voluta-
tion returns to the first point of contaction in the
first touch, accounting by the axes of the diame-
ters or cardinal points of the four quarters thereof ;
and before it arrives at the same point again, it
makes five circles equal unto itself, in each progress
from those quarters absolving an equal circle."

The ancients considered the pentad to be a
symbol of marriage and generation, because it
includes the first odd, or male, and the first even,
or female numbers, 3+2=5 ; and was hence ap-
plied to Venus, Cytherea, Lucina, Juga, Opigura,
and other deities who presided over nuptials and
parturition. At weddings, the Komans had con-
sequently a regard for this number ; and as a
practical display of its reference to the business
in hand, five wax tapers were lighted, and placed
in a conspicuous situation, as a symbol which
could not be misunderstood. And the same
people had a system of divination by the use of
this number, which determined the good or bad
fortune of the newly-married couple.

Vallancey tells us that in the " Memoirs of the
Etruscan Academy of Cortona" is a drawing of
a picture found in Herculaneum, representing a
marriage. In the front is a sorceress casting five
stones. The writer of the memoir justly thinks
she is divining. The figure exactly corresponds
with the first and principal cast of the Irish
purim ; all five are cast up, and the first catch is

The Five Virtues of a Wife. 137

on the back of the hand. He has copied the
drawing ; on the back of the hand stands one,
and the remaining four are on the ground. Op-
posite the sorceress is the matron, who appears to
be attentive to the success of the cast. No mar-
riage ceremony was performed without consulting
the Druidess and her purim. " Auspices solebant
nuptiis initeresse." 1 The ancients also reckoned up
five virtues of a wife, which are thus enumerated
by Phintys, the daughter of Callicrates. First,
in mental and bodily purity ; secondly, by ab-
staining from excessive ornaments in dress ;
thirdly, by staying at home ; fourthly, by refrain-
ing from the celebration of the public mysteries ;
and fifthly, by piety and temperance.

With a similar reference, Plato recommended
that a still more significant use should be made
of this number, by admitting the nuptial guests
by fives. 2 This custom did not escape the pene-
trative satire of Kabelais. In the prophecy, by
signs, of Goatnose, a deaf and dumb wizard, re-
specting the marriage of Panurge, 8 the following
passage occurs : " Then did he lift higher up than
before his said left hand, stretching out all the
five fingers thereof, and severing them as wide
from one another as he possibly could. Here, says
Pantagruel, doth he more amply and fully insin-
uate unto us, by that token which he showeth
forth of the quinary number, that you shall be
married. Yea, that you shall not only be affi-

1 Brand's Popular Antiquities, by Sir H. Ellis, vol. ii. p. 103.
1 In Leg. iv. 8 Book iii. c. 20.

138 The Pythagorean Triangle.

anced, betrothed, and married, but that you shall
live merrily with your wife; for Pythagoras
called five the nuptial number,, because it is com-
posed of a ternary, the first of the odd, and binary,
the first of the even numbers. In very deed it
was the fashion of old in the city of Home at
marriage festivals to light five wax tapers ; nor
was it permitted to kindle any more at the mag-
nificent nuptials of the most potent and wealthy;
nor yet any fewer at the penurious weddings of
the poorest and most abject in the world. More-
over, in times past, the heathen implored the
assistance of five deities, helpful in five several
good offices to those that were to be married.
First, to Jupiter, the chief deity ; to Juno, as
president of the feast ; to Venus, the fairest of
women ; to Pitho, the goddess of eloquence and
persuasion ; and to Diana, whose aid and suc-
cour were required in parturition."

And here the coincidence is too remarkable to
be overlooked, that our blessed Saviour, in His
parable of a marriage, classes the bride's attend-
ants by fives. 1 And hence it might probably be,
that the pentad was a symbol of equality and
justice, not only on account of the presumed
equality of the bridegroom and the bride, but
also because it divides the ineffable number ten
into two equal parts; and for this reason, amongst
the heathen, it had the name of a demi-goddess,
and was esteemed a twin.

Further, the pentad was a symbol of reconcilia-

1 Matt. xxv. 1.

The Triad Society. 139

tion ; the fifth element, ether, being considered
free from the disturbances of the other four. It
was also considered as an emblem of immortality,
because it implied the fifth essence ; and of sound,
because the perfect fifth in music was the first
diasteme. It was called providence, because it
makes unequals equal ; for any odd number being
added to it, becomes equal ; and it was identified
with nature, because if multiplied by itself it
returns into itself ; a peculiarity which is pos-
sessed only by it and the number six. It was
called justice, for justly dividing the digits, and
standing in the middle between one and nine ;
and Nemesis, who is the messenger of justice,
and the inspector of mens actions, because it
harmoniously compounds the three elements,
celestial, natural, and divine. Hence Plato, in
his fourth book of laws, speaking on the duty of
children to their parents, recommends the former
to be dutiful and obedient, lest Nemesis should
record their evil actions, and bring them to con-
dign punishment.

In China, a society has recently been discovered,
which boasts of great antiquity, under the name
of the Triad society, and bears a great resemblance
to Freemasonry. The seal, by which all the acts
of the society are authenticated, is of a quin-
quangular figure ; for five is the great mystical
number of the institution. The characters on
this seal are placed at the corners, and are thus
explained : x "1. T6o, the earth planet, or Saturn ;

1 P. Q. R., 1845, p. 165.

140 The Pythagorean Triangle.

which, according to the Chinese, especially re-
gards and influences the centre of the earth ; —
also one of the five elements. 2. Muh, the wood
planet, or Jupiter, or that which reigns in the
eastern part of the heavens. 3 . Sh wu y, the water
planet, or Mercury, to which the dominion of the
northern hemisphere is confided. 4. Kin, the
metal planet, or Venus, who has the care of the
west. 5. Ho, the fire planet, or Mars, to which
the southern hemisphere is assigned. The reasons
why these planets are placed at the corners of the
seal may be, because they form the basis of
Chinese astrological science, and because they
are considered the extreme points of all created
things."

In the Jewish system of religion, the gifts due
to the priests were regulated by this number :
(1) The heave-offering, or first-fruits; (2) the
heave - offering of the Levites' tithe; (3) the
cake ; (4) the first of the fleece ; (5) the field of
possession. Again, there were five things which
might not be eaten but in the camp, and after-
wards only in Jerusalem ; viz., (1) the breast
and shoulder of the peace - offerings ; (2) the
heave-offering of the sacrifice of thanksgiving ;

(3) the heave - offering of the Nazarites' ram;

(4) the firstling of the clean beast; (5) the
first-fruits." 1 The Jews were forbidden to eat of
their newly-planted fruit-trees till they were five
years old. The princes' peace-offering was five
rams, five he-goats, and five lambs ; the trespass

1 Pict. Bib., vol L p. 876, with authorities.

Peculiarities of the Number Five. 141

offering imposed on tha Philistines, when they
were desirous of returning the ark of alliance, was
five golden emerods, and five golden mice.

There was evidently, therefore, some peculiar
properties attached to the number five, even in
the earliest times, as appears from the fact that
Joseph gave Benjamin five changes of raiment,
and his mess was five times as much as those of
his brothers. And when Joseph was called on to
present his brethren to Pharaoh, he did not take
them all, but selected five only. And David,
with a like predilection for this number, selected
five pebbles from the brook as his weapons in
the encounter with Goliath.

Dr Brown * says, that the Israelites' being for-
bidden to use the fruit of trees under five years
old " was very agreeable unto the natural rules
of husbandry ; fruits being unwholesome and lask
before the fourth or fifth year. They did not
approve of the second day of the week, which is
the feminine part of five, but in the third or
masculine part ; they believed that a double
benediction enclosed both creations, whereof the
one in some part was but an accomplishment of
the other."

The articles of belief in the religion of Maho-
met were five ; viz., a belief in God — angels — the
Prophet — the day of judgment — and predestina-
tion. It had also five positive duties; viz., prayer,
fasting, purification, alms, and the pilgrimage to
Mecca,

1 Garden of Cyrus, p. 67.

1 42 The Pythagorean Triangle.

When Christianity was promulgated, the same
attachment to this number was transmitted by
our Saviour and His apostles. Five thousand
persons were fed in the wilderness with five
barley loaves ; and speaking of the probable effects
of Christianity under some of its phases — alas !
how accurately has the prophecy been accom-
plished ! — the Saviour said, " There shall be five
in one house divided — three against two, and two
against three." These were the male and female
numbers ; and therefore He goes on to say, " The
father shall be divided against the son, and the
son against the father ; the mother against the
daughter, and the daughter against the mother ;
the mother-in-law against her daughter-in-law,
and the daughter-in-law against her mother-in -
law." 1 St Paul affirmed that he had rather speak
five words in a language which was understood,
than ten thousand in an unknown tongue, which
is, as the commentators on the passage say, " as
little as could well be spoken ; i.e., a simple pro-
position consists only of three words, and a com-
plex one not ordinarily short of five." From
these examples, the Christian Church enjoined the
observance of five duties, viz., to keep holy the
festivals; to observe the fasts; to attend the
. public services of religion ; to receive the sacra-
ments ; and to adhere to the established customs
and usages of the Church.

The pentad was frequently used in the com-
position of charms, and thus produced some very

1 Luke xii. 52, 53.

Charms and Invocations by Five. 143

gross superstitions. Mr Douce, in his MS. Notes,
tells us of a curious custom used in Devonshire
by persons afflicted with the ague. He says,
" They visit at dead of night the nearest cross-
road five different times, and there bury so many
new-laid eggs. The visit is paid about an hour
before the cold fit is expected ; and they are per-
suaded that with the egg they shall bury the
ague. If the experiment fail (and the agitation
it occasions does often render it successful), they
attribute it to some unlucky accident that may
have befallen them in the way. In the execution
of this matter they observe the strictest silence,
taking care not to speak to any one whom they
may happen to meet/' The following curious
invocation to five saints for procuring sleep is
given in Bale's interlude concerning the three
laws of Nature, Moses, and Christ : —

" If ye cannot slepe, but slumber,
Geve Otes unto Saynt Uncumber,
And Beanes in a certen number

Unto Saynt Blase and Saynt Blythe.

" Give Onyons to Saynt Cutlake,
And Garlycke to Saynt Cyryake,
If ye wyll shurne Heade ake ;
Ye shaU have them at Quene hyth. w *

1 Brand, ut supra, vol. Hi. p. 149.

\
I

INFINITE DIVISIBILITY OF THE HEXAD
OR DOUBLE TRIANGLE, REPRESENTING
EARTH.

THE DOUBLE TRIANGLE, HEXAGON, HEXAD, OR THE

NUMBER SIX.

CHAPTER VL

THE DOUBLE TRIANGLE.

HEXAGON^ H.EXAD, OR THE NUMBER SIX.

" The second natural division of the circle is made by the radius, the
measure of which, being transferred upon the half circumference
with the compasses, always cuts it into three, or if transferred
upon the whole circle, divides it absolutely into six equal por-
tions, which is an introduction to a multitude of other no less
certain divisions, and innumerable proportions between great and
small figures." — La Pluchb.

" The Hexagon is composed of six equilateral triangles, is equal in all
its relations, and retains the quality of being infinitely divisible
into similar triangles, according to the geometrical projection ob-
served in the divisions of that trilateral figure, and may, there-
fore, be considered as the most perfect of all multilateral forms.
From a general inquiry it will result, that the three most perfect
of all geometrical diagrams are the equilateral triangle, the square,
and the equal hexagon." — Hemming' s Leotubes.

HAT Dr Wordsworth says about the re-
quisites to enable an author to describe
Athens, I would say, with a little altera-
tion, of a writer on the subject of Freemasonry.
"To describe Athens, a man should be an
Athenian, and speak an Athenian language. He
should have long looked upon its soil with a feeling

148 The Pythagorean Triangle.

of almost religious reverence. He should have
regarded it as ennobled by the deeds of illustri-
ous men, and have recognised in them his own
progenitors. The records of its early history
should not be to him a science ; they should not have
been the objects of laborious research, but should
have been familiar to him from his infancy, —
have sprung up, as it were, spontaneously in his
mind, and have grown up with his growth. Nor
should the period of its remote antiquity be to
him a land of shadows — a Platonic cave in which
unsubstantial forms move before his eyes as if he
were entranced in a dream. To him the language
of its mythology should have been the voice of
truth/'

The masonic writer, however, possesses some
advantages over the Athenian topographer. Dr
Wordsworth goes on to say: "This, we gladly
confess, is not our case. We commence our de-
scription of this city with avowing the fact, that
it is impossible, at this time, to convey, or enter-
tain an idea of Athens such as it appeared of old
to the eyes of one of its inhabitants. But there
is another point of view from which we love to
contemplate it, — one which supplies us with re-
flections of deeper interest, and raises in the heart
sublimer emotions than could have been ever sug-
gested in ancient days by the sight of Athens to
an Athenian. We see Athens in ruins/ 9 1

On the contrary, we rejoice because we live in
times when Masonry is in a palmy and prosper-

1 Wordsworth's Greece, p. 129.

Freemasonry not in Ruins. 149

ous state — flourishing like a green bay-tree — its
principles open to the inspection of every inquirer,
and its proud and lofty spirit animating every insti-
tution in existence, in every region of the globe.
There it stands — a tangible reality — and therefore
cannot be misrepresented by unsound theories, or
false hypotheses. It occupies a situation on which
the ideal cannot be permitted to set her foot ; be-
cause its ground is holy, and its footstool is truth.
And if Athens "issued intellectual colonies into
every quarter of the world," as the learned Doctor
assures us, Freemasonry has not been backward
in imitating so fructifying an example ; and has
accomplished the very same result which he
-assigns to the genius of the Athenians— it has
become immortal.

With what feelings Freemasonry in ruins might
be contemplated, it would be difficult to ascertain,
because it stands on too firm a basis ever to be
removed. It never will be in ruins, but will last
until our system shall be extinguished. If the
magnificent buildings of the Acropolis had been,
like Freemasonry, animated by the spirit of a true
faith, they might still have existed in all their
glory, and not have distributed their shattered
fragments to enrich the cabinets of modern na-
tions. Genius and intelligence may be transferred ;
but no people, how brave, rich, and powerful
soever they may be ; no monument of art, how-
ever massive, ponderous, and constructed for
durability — if not supported and animated by the
power of religion, and the purity of an unsophis-

150 The Pythagorean Triangle.

ticated worship — can escape the universal fiat of
annihilation which the lips of Wisdom have pro-
nounced against "all the works of darkness/'
And as Freemasonry is confessedly a system of
light, there is no fear that it will ever be extin-
guished.

Let us, then, as good and worthy Masons, orna-
ment our Order with deeds of virtue, truth, and
brotherly love, and remember the advice of one
who was inspired by wisdom, although not enlight-
ened by revelation —

Stat sua cuique dies ; breve et irreparabile tempus,

Omnibus est vitae ; sed fainam eztendere factis,

Hoc virtutis opus. Virgil.

The hexad was considered by all nations a
sacred number, because the world was created in
six # days ; and six of the properties of nature only
are said to belong to the active dominion, to good
and evil ; and the planetic orb is the figure of the
six properties of the spiritual world. It was re-
presented by the double triangle, because it has
six points which, amongst the Pythagoreans, de-
noted health, and was defined, " the consistence
of a form ; " while sickness was considered the
violation of it.

This figure was used by the heathen as a charm
against the influence of evil demons. The Arabs
believe that " communicable or contagious diseases
are six : smallpox, measles, itch, putridity, mel-
ancholy, and pestilential maladies ; and that dis-
eases engendered are also six : leprosy, hectic,

Perfection of Parts. 151

epilepsy, gout, elephantiasis, and phthisis. " The
double triangle constituted one form of the seal
of Solomon, which was so celebrated in the fic-
tions of Arabian romance ; and is used by Chris-
tians to express the two natures of Christ. With
this reference, it was introduced into the cathe-
drals and monastic edifices of the middle ages as
a conspicuous symbol ; and is still to be seen in
painted windows, altar screens, and other decora-
tive parts of these sacred buildings. 1 These two
intersecting triangles were also emblems of crea-
tion and redemption, fire and water, prayer and
remission, repentance and forgiveness, life and
death, resurrection and judgment.

The number six signified perfection of parts,
because it is the only number under ten which is
whole and equal in its divisions ; and produces a
hexagon by. extending the measure of the radius
of a circle six times round the circumference.
The above proposition is beautifully illustrated
"in the edificial palaces of bees, those monarchal
spirits, who make their combs six-cornered, de-
clining a circle, whereof many stand not close
together, and completely fill the area of the place ;
but rather affecting a six-sided figure, whereby
every cell affords a common side unto six more,
and also a fit receptacle for the bee itself, which,
gathering into a cylindrical figure, aptly enters
its sexangular house, more nearly approaching a

1 An engraving of the Dean's window in Lincoln Cathedral, in which
the above symbol occurs, will be found in the Historical Landmarks of
Masonry, vol. i. p. 356.

152 The Pythagorean Triangle.

circular figure than either doth the square or tri-
angle. And the combs themselves are so regu-
larly contrived, that their mutual intersections
make three lozenges at the bottom of every cell ;
which, severally regarded, make three rows of
neat rhomboidal figures, connected at the angles,
and so continue three several chains throughout
the whole comb." 1

Nature herself seems to affect a partiality for
the hexad, in the formation of crystals ; all of
which are hexangular or six-cornered ; for which
Pliny and other ancient naturalists endeavoured
in vain to assign a reason. There are three dif-
ferent forms, however, which crystals appear to
assume : 1. The perfect columnar crystal is com-
posed of eighteen planes, in an hexangular column,
terminated by an hexangular pyramid at each
end. 2. Crystals without a column are composed
of two hexangular pyramids, connected at the
base. 3. Imperfect crystals have usually an hex-
angular column, irregularly affixed to some solid
body, showing also an hexangular or pentangular
pyramid. "Which regular figuration," as Dr
Brown observes, "hath made some to opinion,
that it hath not its determination from circum-
scription, or as conforming unto contiguities,
but rather from a seminal root and formative
principle of its own, even as we observe in
several other concretions." 2

The sceptics used to amuse themselves by such
arguments as these : If something be detracted

1 Garden of Cyrus, p. 51. * Pseudodoxia, p. 53.

The Hexad, the Symbol of Harmony. 153

from another, either an equal is detracted from an
equal, a greater from a lesser, or a lesser from a
greater. But none of these — therefore detraction
is not possible. That detraction is not made by
any of these ways is manifest. That which is
detracted from another must be contained in it ;
but an equal is not contained in an equal, as six
in six ; for that which containeth ought to be
greater than that which is contained. Neither is
the greater contained in the lesser, as six in five ;
that were absurd. Neither is the lesser contained
in the greater ; for if five were contained in six,
by the same reason, in five will be contained four ;
in four, three ; in three, two ; and in two, one.
Thus six shall contain five, four, three, two, and
one, which being put together make fifteen,
which must be contained in six, if it be granted
that the lesser is contained in the greater. In
like manner, in the fifteen which is thus con-
tained in six, will be contained thirty-five ; and
so by progression, infinite numbers ; but it is
absurd to say that infinite numbers are contained
in the number six ; therefore it is absurd to say
that the lesser is contained in the greater.

From the harmonious movements of the
planets, the hexad was considered an apt
symbol of harmony ; although the Pythagoreans
ascribed it to a different cause. They explained
it in reference to musical proportions ; because 6
to 12 produced a diapason concord which con-
tains 1 2 semi-tones ; and 6 to 8 a diatessaron or
fourth ;. whence the hexad was sacred to Venus,

154 The Pythagorean Triangle.

as the patroness of harmony. Macrobius, Boethius,
and others, give a curious account of the accident
by which Pythagoras found out these proportions ;
which may class with his discovery of the 47th
proposition of Euclid, for which he is said to
have sacrificed a hecatomb. It is thus related by
Nicomachus : At one part of his life he was par-
ticularly anxious to discover some infallible in-
strument of music, by the use of which the entire
system might be enunciated. Accidentally pass-
ing by a blacksmith's shop, he took notice of the
hammers striking on the anvil ; and after listen-
ing attentively for some time, he observed that the
sound formed three perfect concords. Going into
the shop, he made various trials himself, and found
that the difference in the sounds was produced
by the weight of the hammers, and not according
to the force of those who struck. On this hint
he tied four strings across his private room of the
same substance, to each of which he hung a dif-
ferent weight. Then striking the strings he dis-
covered all the concords ; and that to which the
greatest weight was suspended, he found to be a
diapason. By the same process, he found out all
the intervals.

Aristotle has used some elaborate arguments
to prove that there are no figures capable of
filling a place about one point, except the
triangle, the square, and the hexagon ; viz., by
six equilateral triangles, four squares, and three
hexagons. But in solids, the pyramid and cube
will do the same. In this process, he shows that

A Famous Symbol. 155

for equilateral triangles to fill space, it is requisite
that some angles of such triangles composed
about one point should make four right angles.
But six equilateral triangles make four right
angles ; for one makes § of one right angle, and
therefore six make - 3 2 of one right, i.e., four right
angles. The four angles of a square, and the
three angles of a hexagon make each four rijght
angles. But no other figure can effect this, as
will clearly appear, if, its angles being found, it is
multiplied by any number ; for the angles will
always be less than, or exceed four right angles. 1

In ancient music, a sixth was Called hexachords,
of which Guido divided his scale into seven ;
three by B quardo, two by B natural, and two by
B flat. It was on this account that he disposed
his gamut in three columns. In these columns
were placed the three kinds of hexachords, ac-
cording to their order.

A famous symbol in the Egyptian mythology,
which has exercised the ingenuity of many com-
mentators, was the globe, serpent, and wings, of
which there were six various ways of disposing
the several parts : (1.) From the lower part of
an annulus surmounted by two wings rising per-
pendicularly, two serpents issue in opposite direc-
tions. The whole is enclosed within a circle. (2.)
The winged globe alone without the serpent.
The wings expanded. This figure might be in-
tended to represent the rays of the rising sun,
which are, poetically, his wings. From this

1 Taylor's Proclus, p. 17.

156 The Pythagorean Triangle.

sacred figure, which represented the deity of the
Gentiles, was probably borrowed the sublime
metaphor of Malachi — The Sun of Righteous-
ness shall arise with healing in His wings. (3.)
A simple globe without wings, from which issue
two serpents. (4.) A winged globe, through the
lower part of which passes a serpent. (5.) A plain
globe, over which passes the serpent. (6.) The
same as the first without the circumscribing
circle. 1

In the Theosophic or Rosicrucian systems of
Freemasonry, the number six was referred to the
rainbow, because it displays that number of
prismatic colours ; and from this principle they
deduced the following argument, which was used
in their lectures : " The rainbow is a token of
God's Covenant, a representation to man of all
the three principles out of which he was created
— viz., the red and dark brown betoken the first
principle, i.e., the dark, fire world, the kingdom
of God's anger. The white and yellow show the
second principle, the majestic colour, the holy
world, God's love. The green and blue is the
third principle's colour— the blue from chaos, the
green from saltpetre, where, in the flagrat, the
sulphur and mercury do sever, and produce
various colours, which betoken the inward worlds
hidden in the four elements. The rainbow is a
further symbol of Christ appearing in the three
principles, as the Judge of mankind. In the first,
or fiery, all evil things shall be swallowed up. In

1 Dean, Serpent, p. 53.

A Symbol of Marriage. 157

the second, or that of light, He will defend the
good, in love and meekness, from the flames of
fire. In the third, or kingdom of nature, the
humanity of -the Judge is typified, and shows His
impartiality in passing sentence on every man
according to his works."

In one of the degrees of ineffable Masonry, the
same number is denoted by the double equilateral
triangle, which is there said to refer to the six
peculiar branches of the noblest office in the
Temple — viz., (1) To survey the constitutional
rolls previous to their being deposited in the
archives of Masonry, or hollow pillars of the
temple ; (2) to see that the stones fitted into
each other with perfect exactness and geometrical
truth ; (3) to inspect the Holy Place, and (4)
the Sanctum Sanctorum ;. (5) the ark of the
covenant ; and (6) all the other utensils thus
emblematically pointed to by the double equi-
lateral triangle. ♦

Like the pentad, the number six was an ancient
symbol of marriage, being formed by the multipli-
cation of 3, the male, with 2, the female number ;
and from this cause it was named Conciliation,
because it links or conciliates, by such involution,
male and female into one body, husband and
wife. And the Pythagoreans extended the in-
fluence of this number to the periods of gestation.
They contended that "generally there are two
kinds of births ; one lesser, of seven months,
which comes into the world 207 days after con-
ception ; the other greater, of ten months, which

158 The Pythagorean Triangle.

is brought forth in the 274th day. The first and
lesser is chiefly contained in the number six ; for
the two first periods of 6 and 8 days make the
first concord, diatessaron ; the third period is of
9 days, in which time it is made flesh : these to
the first 6 are in sesquialtera proportion, and
make the second concord, diapente. Then follow
12 days more, in which the body is fully formed ;
these to the same 6 consist in duple proportion,
and make the diatessaron concord These four
numbers, 6, 8, 9, 12, added together, make 35
days. It is not without reason, therefore, that
the number six is the foundation of generation,
for the Greeks call it Teleion, or perfect, because
its three parts, J, J, and \ (i.e., 1, 2, 3), make it
perfect. The above 35 being multiplied by
6 make 210 days, in which the maturity is
fulfilled." 1

The cabalistic theologists say that this number
affect, the operation o! the aLea during sleep ;
because they consider sleep to be the sixtieth
part of death. "The soul," they say, "being
pure and holy, ascends in contemplation by
degrees to the communication with angels, by
which future events are often revealed to it ;
whence descending, after being perfectly purified,
it brings down, unmixed, the knowledge that has
been manifested to it — these are prophetic
dreams ; for, from imagination not entering into
them, they deviate in nothing from the truth. If
the soul be not perfectly pure, it meets with

i Stanley, Pyth., p. 103.

The Name of the Beast. 159

nothing but mixed and vain phantoms ; and if
impure, it does not ascend at all, but remains
confused by demons and unclean spirits."

The number 666, or the hexad thrice repeated,
has engaged the attention of cabalistical theo-
logians for 1800 years, as the mysterious Apoca-
lyptic number ; and many and various have been
its interpretations. "It has greatly perplexed
the curious," says Calmet, " to know whether the
name of the beast should be written in Hebrew,
Syriac, Greek, or Latin ; whether his name be
that of his person, or of his dignity, or that which
his followers should give him ; or , that which he
will deserve by his crimes. There are many con-
jectures in this matter ; and almost all commen-
tators have tried their skill, without being able
to say, positively, that any one has succeeded in
ascertaining the true mark of the beast, or the
number of his name." Calmet has enumerated
fourteen different interpretations, and concludes
by saying, " Since the number 666 is found in
names the most sacred, the wisest and safest way
is to be silent." I subjoin five instances of the
application of this number, to show how uncertain
it may be — viz., Diodesian, Julian the Apostate,
Luther, Abinu Kadescha Papa, our holy father
the Pope, and Elion Adonai Jehovah Kadosh, the
Most High, the Lord, the Holy God. And a
recent masonic writer (F. M. Mag., 1857, p .706)
says, that by means of a rational interpretation of
this number, the mysteries of the triangle and
square are united in one masonic symbol, typical

160 The Pythagorean Triangle.

of the chief essential attributes of the Great
Geometrician of the Universe.

" There was an ancient and almost immemo-
rial tradition among the Jews that the world was
to last only 6000 years. They divided the ages,
during which it was to continue, in the following
manner: Two thousand years were to elapse
before the law took place ; two thousand were
to be passed under the law ; and two thousand
under the Messiah. Indeed, this sexmillennial
duration of the world was, it is probable, too
much the belief of the ancient fathers, who con-
ceived that, as the creation was formed in six
days, reckoning according to that assertion in the
Psalms, that every day is with God as a thousand
years, and was concluded by a grand Sabbath, or
day of Almighty rest ; so the world was ordained
to last only during the revolution of six thousand
years." 1 Some visionaries, however, have been
bold enough to name the precise periods when
these six chiliads commence and terminate, and
have made each of them correspond with some
great historical epoch : 1. From the creation to
the flood. 2. To the promise made to Abraham.

3. To the commencement of David's kingdom.

4. To the Babylonish captivity. 5. To the
advent of Christ. 6. To the day of- judg-
ment.

But a reference to facts will prove this calcula-
tion erroneous. It is true the hypothesis that
the duration of the world will continue six ages

1 Maur. Ind. Ant., vol. v. p. 831.

The Duration of the World. 161

may be quite consistent with analogy and the re-
vealed will of God, but the length of the inter-
mediate periods vary considerably ; for the first
period, from the creation to the deluge, contains
1656 years; the second, from the flood to Abra-
ham, if it be considered to terminate at the com-
mencement of his peregrination, has only 427
years; the third, to the beginning of David's
kingdom at the death of Saul, has 866 years;
the fourth, to the Babylonish captivity, 448
years ; the fifth, to the advent of Christ, 602
years ; and the sixth is now incomplete.

On this subject, I remember reading a pamphlet
many years ago, which interested me by its in-
genuity ; and as the events which it commemo-
rates' are most of them comprised in the historical
lectures of Masonry, I will give a brief outline of
it, so far as my recollection will bear me out.
The author commenced by instituting a compari-
son between the days of the week and the mille-
naries of the world, in illustration of the text,
" One day is with the Lord as a thousand years,
and a thousand years as one day." 1 The first
day of the week, Sunday, or the first thousand
years, was, according to this author, opened by
the creation of the world, and closed with the
translation of Enoch ; an event, one would think,
which could scarcely fail to strike a wicked race
with wonder, awe, and reverence, and produce
the effect of turning them from their wicked-

1 2 Pet. iii. 8.

162 The Pythagorean Triangle.

ness to worship the living God. It failed
to do so; and the prevalence of fraud and
violence brought on its destruction by an uni-
versal deluge.

The next chiliad, or Monday, the second day
of the week, lie terminates with the mission of
Abraham ; and opens the third millennium, or
Tuesday, with a series of gracious revelations
which heralded the establishment of the Jewish
Church, a type of a more perfect dispensation
which would ultimately be revealed from on
high. During this period, the Mosaic dispensa-
tion was promulgated, and the law firmly estab-
lished for the civil and religious government of
the Hebrew nation, who were delivered from
their cruel bondage in Egypt, and received
possession of the Promised Land as an inherit-
ance.

The next millennial period, corresponding with
"Wednesday, commenced with the construction of
Solomon's Temple, and the attainment of that
exalted summit of prosperity and power which,
as had been promised to Abraham, his posterity
should attain. This period commenced gloriously
for the Jews ; but its progress was marked with
calamity. Their kingdom was taken from them,
and they were deprived of the power of govern-
ing their own people. At the period when their
sufferings were the most severe, and the sceptre
had for ever departed from Judah, a still more
refulgent era dawned upon the world. The day-
spring from on high called the bright Morning

The Millennial Periods. 163

Star — Orieus — the Sun of Righteousness — the
Messiah so long promised to the Jews — enlight-
ened the benighted atmosphere at the commence-
ment of the fifth millennium, or Thursday. Now
the fulness of time was come ; the prophecies of
the Messiah or Shiloh were fulfilled; the ever-
lasting gospel was preached ; and the work of
redemption completed by Him of whom Moses
and the prophets did write — Jesus of Nazareth,
the King of the Jews.

The sixth chiliad, corresponding with Friday,
opened in darkness. Literature and religion were
both at a low ebb. Emperors and potentates were
ignorant of letters, and the nobility of every Chris-
tian country were few of them able to read or
write their own names. Charlemagne and Bar-
barossa, famous for conquest, were neither of them
capable of writing their own despatches, or read-
ing them when written ; and some of the popes
were equally illiterate. Under such circum-
stances, religion would necessarily be exchanged
for superstition. The controlling spirits were
barbarous and ferocious ; for they had no mitigat-
ing principles to fall back upon. The yoke of
superstition was always burdensome; and by
its corrective policy — such as it was — the iron
chiefs of every Christian nation were overawed,
and subjected to the influence of an hierarchy
more ambitious and insatiable than them-
selves.

Such was the opening of the sixth millennial
period, in the year 1000 of the Christian era ;

164 The Pythagorean Triangle.

about which time vast improvements in ecclesi-
astical architecture were on the eve of being
accomplished; and the Freemasons spread over
the face of every country where the religion of
Jesus was professed, the proudest specimens of
human taste and genius which have distinguished
any age or nation since the world was made.
From the commencement of the period in which
we live, science and learning have rapidly in-
creased, and the day of perfect civilisation has
arrived. We are drawing near to the close of
this period, and the opening of a glorious mil-
lennium — prefigured by the Jewish Sabbath — the
day on which God rested from His labours at the
creation of the world. This period will also con-
tinue a thousand years, when Christ will reign in
glory over the whole society of the redeemed,
and Satan be cast, bound, into the bottomless
pit. .

Many of the primitive Christians, and par-
ticularly Barnabas, the companion of St Paul,
maintain this opinion. The latter writer, in his
Catholic Epistle, says : " God made in six days
the works of His hands, and He finished them on
the seventh day; and He rested on the seventh
day, and sanctified it. Consider then, my chil-
dren, what that signifies — He finished them in
six days. The meaning of it is this — that in
6000 years the Lord God will bring all things
to an end ; for with Him one day is a thousand
years, as Himself testifieth. Therefore in six
days shall all things be accomplished. And what

The Day of Best. 165

is this that He saith — and He rested on the
seventh day ? He meaneth this — that when His
Son shall come, and abolish the season of the
wicked one, and judge the ungodly, and change
the sun and the moon and the stars, then He
shall gloriously rest on that seventh day."

REMARKABLE PROPERTIES OF THE HEPTAD,
SEPTENARY, OR HEPTAGON.

THE HEPTAGON, SEPTENARY, OR THE NUMBER SEVEN.

CHAPTER VII. •

THE HEPTAGON.

SEPTENARY, OR THE NUMBER SEVEN.

" The number seven was held to be sacred by the Hebrews, and also
by the Mussulmans to this day, who reckon seven climates, seven
seas, seven heavens, and as many hells. According to Rabbis and
Mussulman authors, the body of Adam was made of seven hand-
fuls of mould, taken from the seven stages of the earth." —
Wilfobd.

" How old are you ?— Under seven." — Old Lectures of Masonry,

" There are seven mysterious voyages necessary for the reception of the
Master Mason's degree — 1. The candidate is instructed in Music,
Poetry, and Painting. 2 . He is made acquainted with the sciences
of Geology, Geography, and Natural History. 3. He is taught
Theology, Medicine, and Jurisprudence. The four other voyages
instruct him in the still higher sciences." — Rosenberg.

HILE engaged on the subject of numbers,
we cannot fail to be struck with its
illustration during the prevalence in this
country of the rage for lottery speculations, when
everything was supposed to depend on the choice
of a fortunate figure. There are some apposite
remarks on this fever of the mind in the Spec-

1 70 The Pythagorean Triangle.

tator, No. 191, which show its workings. The
writer says : " Caprice very often acts in the place
of reason, and forms to itself some groundless,
imaginary motive, where real and substantial ones
are wanting. I know a well-meaning man who
risked his good fortune upon the number of the
year of our Lord, whatever it might be. I am
acquainted with a tacker that would give a good
deal for the number 134. On the contrary, I
have been told of a certain zealous Dissenter who,
being a great enemy to Popery, and believing
that bad men are the most fortunate in this
world, will lay two to one on the number 666
against any other number ; because, says he, it is
the number of the beast. Several would prefer
the number 12,000 before any other, as it is the
number of pounds in the great prize ; and a
premium was publicly advertised for the ticket
numbered 132. In short, some are pleased to
find their own age in the number ; some that
they have got a number that makes a pretty
appearance in the ciphers ; and others because it
is the same number that succeeded in the last
lottery; while some are governed in the choice
of a number by dreams. Each of these, upon no
other grounds, thinks he stands the fairest for
the great lot, and that he is possessed of what
may not be improperly called the Golden
Number."

The Pythagoreans considered seven to be a
religious number and perfect, and consequently

The Stages of Life. 171

entitled to veneration ; although, strictly speak-
ing, no number can be perfect, unless it is capable
of being formed from the sum of its aliquot parts.
In the Continental system of Freemasonry, it is
termed a " nombre mystique et respectable."
We find in our own Scriptures such an abundant
use of it, as to convince the most inveterate
sceptic that it occupied no unimportant station in
the ordinances of divine worship, both amongst
the patriarchs and Jews ; and it appears to have
been held in equal estimation by the early Chris-
tian writers. 1

In the spurious Freemasonry of the Greeks and
Eomans, it represented good fortune ; and referred
to the periodical changes of the moon, which
alters its appearance every seven days. And with
this interpretation, and governed by lunary influ-
ence, the critical and climacterical points in the
life and fortunes of man were probably deter-
mined. Opinions appear to differ in the details,
although they agree in the principle. Thus, some
think that seven times seven is the most danger-
ous period of life ; others contend for seven times
nine, and some for nine times nine ; while others
conceive seven times nine to be the least danger-
ous. Varro divided the days of man into five
portions ; Hippocrates into seven ; and Solon into
ten; yet probably their divisions were to be re-
ceived with latitude, and their considerations not
strictly to be confined unto their last unities.

1 See the Hist. Landm. Mas., Lect. zs. vol. i. p. 512.

172 The Pythagorean Triangle.

When Hippocrates divided our life into seven
degrees or stages, he made the end of the first
period seven years ; of the second, fourteen ; of
the third, twenty-eight ; of the fourth, thirty-
five ; of the fifth, forty-seven ; of the sixth, fifty-
six ; and of the seventh, the last year, whenever
it happeneth. Herein we may observe, he maketh
not his divisions precisely by seven and nine,
and omits the great climacterical. Besides, there
is between every one at least the latitude of seven
years, in which space or interval, i.e., either in the
third or fourth, whatever falleth out is equally
verified in the whole degree, as though it had
happened in the seventh. 1 And hence this num-
ber was called Telesphoros, because by it all
mankind are led to their end. 2 This super-
stition was not confined to those ages and
nations, but has descended in all its force to our
own times.

The number seven was also a symbol of cus-
tody, because it was figured or believed (no mat-
ter which) that the government of the world was
in the custody of the seven planets. And from
this fiction Pythagoras formed his doctrine of
the spheres. He called that a tone which is the
distance of the moon from the earth; from the
moon to Mercury half a tone; from thence to
Venus the same ; from Venus to the sun, a tone
and a half ; from the sun to Mars a tone ; from
thence to Jupiter half a tone ; from Jupiter to

1 Brown, Pseudodoxia, p. 249. * Philo de mund. opif.

Doctrine of the Spheres. 1 73

Saturn half a tone ; and thence to the zodiac a
tone ; — thus making seven tones, which he called
a diapason harmony. Now it is well known that
there are in music seven original notes ; "but these
are capable of being transposed into situations
more acute or grave, still retaining their number
and order ; and though the octave contain twelve
semitonic intervals, and every interval may be
infinitely divided, still the eighth note of every
division, diatonically reckoning, will produce a
similar sound. From these seven sounds, taken %
in various successions, and different degrees of
time or measure, all melody is formed ; and
the sounds being fixed in themselves, nothing
is left to the choice of the composer, but the
order and time in which they shall succeed each
other." 1

Addison had some reference to the above sys-
tem when he wrote his celebrated paraphrase on
the nineteenth Psalm; which contains a repre-
sentation of the sun, moon, and stars continually
employed in announcing the wonderful works of
the Creator : —

For ever singing, as they shine,
The hand that made us is divine.

The heptad was considered to be the number
of a virgin, because it is unborn ; without a father
(the first odd number 3) or a mother (the first
even number 2), but proceeding directly from the

1 Busby, Diet. Mus., Introd., xii.

1 74 The Pythagorean Triangle.

monad, which is the origin and crown of all
things. On this principle the Arabs, and most
Eastern nations, usually name and circumcise
their children on the seventh day after their
birth ; and at the age of seven years teach them to
read and pray. The number seven being thus
introduced into the common offices of Arab life,
it is probable that the seven degrees of initiation
used by the Eastern order of Assassins, established
by the Sheik Hassan ben Sabah, originated.
These were — 1. The profane. 2. The aspirants.
3. The devoted. 4. The companions. 5. The
dais or ministers. 6. The rulers. 7. The grand
priors.

The same number was sacred to several male
and female deities, as, for instance, to Minerva,
because she was fatherless and motherless, being
hewn out of the skull of Jupiter with an axe. It
was consecrated to Mars, because he had seven
attendants, Bellona, Anger, Clamour, Fear, Terror,
Discord, and Fury. It was a symbol of Osiris,
because his body was said to have been divided
into seven parts, according to some accounts, and
twice seven according to others, by Typhon. It
was also sacred to Apollo or the sun, because be-
ing placed in the midst of the seven planets, they
proceed harmoniously together through the vast
expanse, whence the poets have feigned that the
instrument on which Apollo plays is a harp with
seven strings. Being thus made an emblem of
the chief deity, the Greek poet says : —

Veneration for the Number Seven. 175

Erra fie, &c.
Seven sounding letters sing the praise of me,
The immortal God, the Almighty Deity ;
Father of all that cannot weary be.
I am the eternal viol of all things,
Whereby the melody so sweetly rings
Of heavenly music.

Lightfoot, after quoting the above lines, adds,
"What these seven letters are that do express
God is easy to guess, that they be the letters of
the name of Jehovah."

The use of the number seven has not been con-
fined to any age or nation, as may be gathered
from the seven vases in the Temple of the Sun
near the ruins of Babian, in Upper Egypt ; the
seven altars which burned continually before the
god Mithras in many of his temples ; the seven
holy fanes of the Arabians ; the seven bobuns of
perfection exhibited in the religious code of the
Hindoos ; with the defective geographical know-
ledge of the same people, which circumscribed the
whole earth within the compass of seven penin-
sulas surrounded by seven seas ; the seven
planets; the Jewish Sephiroth of seven splen-
dours ; the seven Gothic deities ; the seven
worlds of the Indians and Chaldeans ; the seven
virtues, cardinal and theological ; the seven con-
stellations mentioned by Hesiod and Homer;
the seven wise men ; the seven wonders of the
world ; the seven cities which contended for the
birth of Homer ; the seven prismatic colours ; the
seven notes in music, and a host of other refer-

1 76 The Pythagorean Triangle.

ences to the same number, which it will be un-
necessary to adduce here, because they may be
found in the twentieth Lecture of the " Histori-
cal Landmarks of Masonry."

This universal veneration for the heptad might
probably derive its origin, even among the
heathen nations who were unacquainted with the
Mosaic writings, from the creation of the world ;
for the seventh day was looked upon as sacred
throughout the whole world. 1 Hesiod uses the
words, " The seventh is a sacred day ; " and
Linus says, " On the seventh day all things were
finished ; the seventh is beautiful; it is the origin
of all things ; it is perfect and complete." Theo-
philus, Bishop of Antioch, writing to Autolycus,
has this remarkable passage : " The greatest part
of the heathens are ignorant of the name of the
seventh day, nevertheless all men celebrate it."
Josephus against Apion affirms, that "there is
no Grecian city, nor barbarian, nor any nation
where the custom of observing the seventh day
has not reached."

The Jewish cabalists, as I have already
observed, believed in the existence of seven
Sephiroth, which they denominated Strength,
Mercy, Beauty, Victory, Glory, Foundation, and
Kingdom. The benefit of these divine splen-
dours were communicated by gradations, and

1 See Clem. Alex. Strom., viii. — Euseb. in the Fragments of Ariato-
bulus ; as -well as the passages out of Hesiod, Callimachus, and others
to the same purpose.

Seven Heavens and Seven Hells. 177

compared to ascending the steps of a ladder, on
the summit of which were the three hypostases
of the divine nature, surmounted by a crown of
glory and the throne of God, These were con-
sidered equivalent to seven heavens or divisions
of the celestial abodes. They had also seven
hells, because they say that Gehenna, the place
of abode for wicked spirits and sinful men, is
mentioned- in Scripture under so many different
appellations. They were called, Infernus, Perdi-
ticC Profundum, Taciturnitas, Umbra mortis,
Terra inferior, and Terra sitiens.

In like manner, the followers of Mahomet had
their seven heavens and seven hells. Of the
former, the first is described as formed of
emerald, the second of white silver, the third of
large white pearls, the fourth of ruby, the fifth
of red gold, the sixth of yellow jacinth, and the
seventh of shining light. Some assert Paradise
to be in the seventh heaven ; others contend
that next above the seventh heaven are seven
seas of light; then an undefinable number of
veils or separations of different substances,
seven of each kind ; and then Paradise, which
consists of seven stages one above another — the
first called the mansion of glory, the second
the mansion of peace, the third the garden
of rest, the fourth the garden of eternity, the
fifth the garden of delight, the sixth the
garden of Paradise, and the seventh the garden

of perpetual abode, or of Eden — this overlook-
Mi

1 78 The Pythagorean Triangle.

ing all the former, and canopied by the throne
of God.

In like manner, the seven hells are situated one
beneath the other. The first of these, according
to the general opinion, is destined for the re-
ception of wicked Mahometans, the second for
Christians, the third for Jews, the fourth for
Sabians, the fifth for the Magians, the sixth for
the idolaters, and the seventh for hypocrites.
To complete the system, the Mahometans believed
in the existence of seven earths, each forming a
story or gradation above the other ; the earth
which we inhabit being the next in succession
beneath the lowest heaven, and the first hell is
beneath the lowest earth. And hence the Ara-
bians assigned to the earth seven climates, and to
heaven seven spheres. "Each of these earths
is inhabited: the first by men, genii, brutes, &c. ;
the second by a suffocating wind; the third
by the stones of Jahennum or hell ; the fourth
by the sulphur of the infernal regions ; the
fifth by serpents ; the sixth by scorpions, in
colour and size like black mules, and with tails
like spears ; and the seventh by Iblees and his
troops." *

According to this system of belief the universe
was divided into three great portions, and sub-
divided into twenty-one steps or degrees, situated
at equal distances from each other; the lower
seven being places of punishment ; the interme-

1 Lane, Arabian Nights, vol. i. pp. 20-24.

Seven Properties in Man. 1 79

diate seven, places of probation ; and the upper
seyen, places of reward. Pythagoras and Plato
had some such system in their notion of seven
zones, which extended from the earth to the
supreme heavens, 1 and it is glanced at in the
writings of St Paul. 2

The Theosophic philosophy, which was copi-
ously introduced into the counterfeit Masonry
practised on the Continent during the last
century, counted seven properties in man — viz.,
1. The divine golden man. 2. The inward holy
body from fire and light, like pure silver. 3.
The elemental man. 4. The mercurial growing
paradisiacal man. 5. The martial soul-like man.

6. The venerine, according to the outward desire.

7. The solar man, an inspector of the wonders of
God. They had also seven fountain spirits, or
powers of nature^ called Binding, Attraction,
Anguish, Fire, Light, Sound, and Body. Ac-
cording to which the seven royal stars are like
vowels or spirits of letters ; and the innumerable
others are like consonants, forming an infinite
variety of syllables and words ; for as words are
the opening of the secret locked up in the mind,
so are the stars the opening of the dark mystery
or chaos shut up in the anguish chambers. And
as the various properties of the several principles
are couched in and expressed by the vowels and
spirits of the letters peculiar to them, so the seven,

1 Pliny, 1. ix. c. 21.

2 2 Cor. xii. 2.

180 The Pythagorean Triangle.

royal stars are suited in and qualified by tlie
three principles and seven properties of the
eternal nature.

The same philosophy, which formed the general
material from which Cagliostrd, Mesmer, Peuvret,
and other charlatans of the last century, con-
structed their several systems of Freemasonry,
professed also to believe that the gifts and graces
of the Holy Spirit were seven in number — viz.,
wisdom, understanding, counsel, grace, know-
ledge, piety, and the fear of God ; and that there
were the same number of works of mercy to
which a reward would be attached, i.e., to in-
struct the ignorant ; to correct offenders ; to
confirm the wavering ; to comfort the afflicted ;
to suffer patiently ; to forgive injuries ; and to
pray for enemies. In the same system, there
were accounted seven virtues — humility, liber-
ality, chastity, quietness, temperance, patience,
and devotion; and seven deadly sins — pride,
covetousness, luxury, envy, gluttony, anger, and
sloth.

In the French system of symbolical Masonry,
as it is now practised, the number seven in the
Fellow Craft's degree is explained by a reference
not only to the seven days of the creation, and
the seven years employed in building the Temple
of Solomon, but also to the seven virtues which
every good Mason ought to practise without
intermission. These differ slightly from the
former, and consist of wisdom, strength, beauty,

Masonic Reference of the Number Seven. 181

power, -humility, glory, and honour; and seven
vices which he ought to tread under his feet
—hatred, discord, pride, indiscretion, perfidy,
rashness, and calumny. The seven virtues
recommended by the same order are, friend-
ship, unity, submission, discretion, fidelity,
prudence, and temperance. They referred the
same number also, as we do, to the seven
liberal sciences. With respect to the latter,
a curious tale is told by M. d'Autun on
learned incredulity, where it is said that the
use of the Arabian numerals were imported
from Spain by Pope Silvester, to be used in
magical ceremonies ; for it should appear that
magic was publicly taught in the recesses of a
deep cavern at Salamanca. This Domdaniel is
said to have been founded by Hercules, and that
seven arts of enchantment were taught therein.
Sir Walter Scott, in his " Lay of the Last
Minstrel/' observes, that "if the classic reader
inquires where Hercules learned magic, he may
consult Les faicts et proesses da noble et
vaillant Hercules, where he will learn that
the fable of his aiding Atlas to support the
heavens arose from the said Atlas having
taught Hercules, the noble knight-errant, the
seven liberal sciences, and, in particular, that of
judicial astrology." x

. I shall here close my brief remarks upon this
number, because it is copiously explained in the

1 .Lay, canto iL note 12.

182 The Pythagorean Triangle.

" Historical Landmarks of Frefcmasonry." * There
is no other number which is so freely used by the
professors of every religion, both true and false.
It was uniformly considered to be worthy of
veneration, and there appears to have been ample
cause for it, in the profuse use of it which is
contained in the directions of the Almighty re-
specting the customs and ceremonies of the
Jewish Church. This people, however, had many
other superstitions besides a predilection for the
number seven as the harbingers of good-luck.
The following is to our purpose, because it em-
bodies a masonic custom : " Some of the modern
Jews are particularly careful, while dressing them-
selves in a morning, to put on the right stocking
and right shoe first, without tying them ; then
to put on the left, and so return to the right;
that so they may begin and end with the
right side, which they account to be the most
fortunate." 2

It may be observed here, in reference to the
above practice, that naked feet were a sign of
mourning, and also a mark of respect. Moses
had naked feet at the burning bush ; and it is
believed that the priests served both in the taber-
nacle and temple in the same manner. It is said
further that the Israelites were not permitted to
enter the holy place except they were divested of
their shoes. It was customary to loose the latchet

1 Lect. xx.
. * Lea Modena, p.. 17. '

. Remarkable Practices. 1 83

of the shoes when in the house, and fasten them
when going from home. Thus St Peter 1 was
commanded to gird himself, and bind on his
sandals, when he was miraculously delivered from
prison. With some nations, it was a custom when
they entered a temple to set the right foot upon
the first step. And the practice of takinig off the
shoes was ultimately converted to the purposes
of superstition. It was believed by the Romans
that if seven women walked barefoot round a gar-
den, it would be free from caterpillars and other
destructive insects. Sorceresses used to cast off
their shoes during their incantation* The abori-
gines of Peru were of opinion that it was sinful
to enter the Temple of the Sun without first
taking off their shoes ; which they considered to
be the greatest proof they could possibly give
of their unfeigned humility.

This remarkable practice, so extensive in its
operation, was most probably derived from the
Jewish law, in which it is directed, that if a hus-
band dies without issue, then his brother shall be
at liberty to marry his widow, or give her per-
mission to marry any other person. The latter is
called Caliga, and the sign is, " loosing the shoe."
A similar custom was used by the same people
in the conveyance of a title to an estate. The
person who sold or conveyed it pulled off one of
his shoes, and in open court delivered it to the
purchaser, thereby signifying that he had full

184 The Pythagorean Triangle.

right to walk, enter into, and tread upon the
land as his own proper and entire possession.
Sometimes the right-hand glove, and some-
times a handkerchief, is substituted for the
shoe.

Michaelis, 1 speaking on this subject, says, that
M in the age of David this usage had become anti-
quated; for the writer introduces it as an unknown
custom of former times, in the days of David's
great-grandfather. I have not been able to find
any farther trace of it in the East, nor yet has the
Danish travelling Emission to Arabia, as Captain
Niebuhr himself informs me. Bynseus, in his
4 Book de Calceis Hebrseorum,' treats of it at great
length ; but, excepting the mere conjectures of
modern literature, he gives no account of the
origin of this strange symbol of the transfer of
property. In the time of Moses, it was so familiar,
that barefooted was a term of reproach, and pro-
bably signified a man that had sold everything, a
spendthrift, and a bankrupt ; and in Deuteronomy
we find that Moses allowed it to be applied to the
person who would not marry his brother's widow.
Could it have been an Egyptian custom, as we
do not find it again in the East? The Egyptians,
when they adored the Deity, had no shoes on ;
and of this the Pythagoreans gave the following
explanation. The man who came naked from his
mother's womb should appear naked before his
Creator ; for God hears those alone who are not

1 VoL l p. 434*

"~l

Barefooted Symbols. 185

burdened with anything extrinsic. Among the
Egyptians, too, barefooted was equivalent to
naked, and naked synonymous with having no
property but one's self."

1

MYSTERIOUS REFERENCES OF THE OGDOAD
OR CUBE, REPRESENTING AIR.

THE CUBE, OGDOAD, OCTAEDRON, OR THE

NUMBER EIGHT.

^m^

CHAPTER VIII.

THE CUBE.

OGDOAD, OCTAEDRONy OR THE NUMBER EIGHT.

" When in his ark of gopher- wood
Noah rode buoyant on the flood,
Overwhelmed with sad despair and woe,
A guilt; race sunk down below.
With blest Omnipotence its guide,
The mastiess ark did safely ride,
And on the mount, from danger free,
Did rest the whole fraternity."

From an unpublished Masonic Ode.

" The double cubical figure hath always been a lively representation
of the chief attributes of the Divinity, as well as that which consti-
tutes the most capital problem in Masonry ; which is that of doub-
ling the cube, and was first proposed by the oracle at Delphus to
those who asked him what was necessary to be done to stop the
pestilence which then raged amongst them. He told them to
double his altar, and the plague should cease." — Old R. A.
Lectubes.

HEN the theory was once established
that names and numbers bore a mutual
relation to each other, it became a
favourite employment with the cabalists —
Jewish, Christian, and Mahometan — to trace by

190 The Pythagorean Triangle.

numbers the mysterious reference of certain
remarkable names. Thus the Egyptian Mercury
Thouth, the representative of wisdom, or moral
strength, was denoted by the number 1218, the
era A.A.C., in which Samson flourished, who was
the greatest example of physical strength the
world ever produced ; being 9 ; g>, 800; v, 400;
9 9. The monogram of Christ crucified, or L H. T.,

or more properly I.H. The former signifying the
two first letters of the Greek name of Christ, and
the latter His cross, was found in the number
318 ; i.e., I, 10 ; H, 8 ; and T, 300 ; being the
date of the abolition of that kind of death which
was inflicted on the Saviour of mankind. Again,
the Hebrew letters of the name Jabo-Shiloh, or
" Shiloh shall come," are numerically the same as
those of the word Messiah ; whence it was con-
cluded that Shiloh and Messiah were one and the
same person. By a sitnilar process the Creator
(H'Apxrj) was denoted by the number 737; and
Lateinos, according to Irenaeus, was found in the
number, 6 6 6. " Sed et Lateinos nomen habet
sexcentorum sexaginta sex numerum; et valde
verisimile est, quoniam novissimum regnum hoc
habet vocabulum. Latini enim sunt qui nunc
regnant; sed non in hoc nos gloriabimur" 1

The Arabs, according to Lane, have a method
of divination, used at marriages, to determine
whether the parties will be happy. This is done
by " adding together the numerical values of the

1 Iron., 1. v. c. 30.

Divination at Marriage. 191

letters composing his or her name, and that of
the mother, and subtracting from twelve the
whole sum, if it be less than twelve, or if larger,
dividing it by twelve. Thus is obtained the
number of the sign. The twelve signs, com-
mencing with Aries, correspond respectively with
the elements of fire, earth, air, and water, three
times repeated. If the signs of the two parties
indicate the same element, it is inferred that they
will agree ; but if they indicate different elements,
the inference is that the one will be affected by
the other, in the same manner as these elements
are ; thus if the element of the man is fire, and
that of the woman water, he will be subject to
her rule. Another method is to subtract the
numerical values of the two names one from the
other ; and if the remainder is an uneven number,
the inference is unfavourable ; but if even, the
reverse/'

The ogdoad, according to the philosophers, is
the first cube, consisting of six sides and eight
angles ; and, as was asserted by the Pythagoreans,
is the only number under ten which can be pro-
nounced evenly even. This, however, is not
strictly correct ; for evenly even means divisible
by any other even number without a remainder,
which will equally apply to the number four.
It does not appear to have been very highly
esteemed by the followers of Pythagoras, although
the deluge was commemorated in their mysterious
observances, and eight persons were believed to
have been saved in the ark from destruction

192 The Pythagorean Triangle.

during that terrible event. Amongst the Jews,
it appears to have been the number of circumci-
sion, because that ceremony took place on the
eighth day; and with the cabalists it was the
number of Jesod or Mercury, the dry water, or
water of immersion, in which lay the whole foun-
dation of the art of transmuting metals. They
observe eight orders of purification of the baser
metal, because the number of the word Zachu, or
purity, is equal to 33, which being multiplied by
8, the number of Jesod, produces 264, the num-
ber of the word Jordan. 1

The Pythagorean philosophers taught that the
cube proceeded from the tetractys. But they
conceived that some third principle was neces-
sary to unite the other two ; for matte?' and jforwi
do not flow one into K another spontaneously, be-
cause the matter of one substance does not receive
the form of the other without something to im-
press it. As, for instance, when the soul departs
out of a man, the body does not become brass or
iron ; neither is wool made out of a stone. There
must be some third principle to unite them ; and
that principle can be nothing else but the Deity.

The number eight had other references which
it may be useful to point out. It signified the
harmony produced by love and friendship, because
the perfect diapason constitutes the unison of two
notes in the same sound, which is termed an octo-
chord, and comprises eight notes and seven degrees.
This was a symbol of the intimate union which

i F. Q. R, 1838, p. 448.

Eight esteemed a Sacred Number. 193

subsists between two minds which are knit and
joined together by these two genial affections.
Pythagoras had a musical instrument which he
denominated an octochord, comprehending the
two disjunct tetrachords expressed by the letters
E, F, G, A, B, C, D, E. This number was in-
vested with the name of several heathen deities,
both male and female; as Neptune, Cybele,
Ehea, &c.

The Pythagoreans held that these are in man
eight organs of knowledge ; viz., sense, phantasy,
art, opinion, prudence, science, wisdom, and mind;
which constituted an inexhaustible source of dis-
quisition in the Pythagorean Lodges. In like
manner, the Christian system presents us with
eight beatitudes : poverty of spirit ; mourning ;
meekness ; desire of righteousness ; mercy ; purity
of heart ; the peacemaker ; and suffering for the
sake of righteousness. 1

This number was highly esteemed in Egypt ;
and in the sacred processions, a vessel or boat was
carried containing eight persons, in reference to
the Noetic ogdoad ; and Herodotus informs us
that the Egyptians had eight great gods. Now,
although this may not be strictly correct, yet it
shows that eight was esteemed a sacred number ;
for the tradition was universal, that the world
had been destroyed by a deluge of waters, and
eight persons preserved in a vessel which floated
on its surface.

The legend of initiation, or the account of the

1 Matt. y. 1-10.

N

194 The Pythagorean Triangle.

death of Osiris by the contrivance of Typhon, has
been variously interpreted. In one sense it is
sideral, and in another diluvian ; and their union
may approximate nearest to the truth. It is,
however, certain, that a knowledge of the uni-
versal deluge was preserved in the spurious Free-
masonry of ancient times; and the tradition is
not obscurely intimated or conveyed by symbols
of doubtful interpretation, but plainly declared
and explicitly proclaimed. The days of mourning
for the aphanism were usually 5 x 8 = 40 ; and
the rites of probation were forty days, in allusion
to the time which marked the increase of the
diluvian waters. This was accompanied amongst
the Eastern nations by a curious ceremony. They
held that sin being the pollution of man's soul,
regeneration could only be produced by bathing
in pure water, under the influence of a particular
planet. These ablutions were to be accompanied
by many trifling, and even ridiculous, observances,
the absence of any one of which would render the
whole ceremony inefficacious. According to Mr
Colebrooke, "the aspirant was taught to repeat
mentally the names of the seven worlds ; and
after sipping a little of the water, he was to cast
some of it eight times into the air, repeating the
prayer of ablution. If he chanced to spit or
sneeze during the performance of this ceremony,
he was obliged immediately to apply the fore-
finger of his right hand to his ear ; in compliance
with the maxim, — after sneezing, spitting, blow-
ing the nose, sleeping, putting on apparel, or other

Three Supplemental Degrees of Masonry. 195

unclean act, you must not perform your ablutions
till you have touched your right ear."

From this event, three supplemental degrees
of Masonry have been constructed, called respec-
tively the Koyal Ark Mariners, the Noachites, and
the Ark and the Dove. The former enters philo-
sophically in its ordinary lectures on the subject
of the salvation of Noah and his seven companions
in the ark, if they have undergone no alteration
of late years. The lectures of this degree, how-
ever, vary so considerably in different Lodges that
nothing certain can be pronounced respecting
them ; except that they relate to Noah and his
family — the construction of the ark — and the
planting of nations.

The degree of the Noachites includes circum-
stances which extended from the deluge to the dis-
persion of mankind ; the principal of which are, the
building of the tower of Babel, the confusion of
tongues, and the planting of nations ; together
with the death, and presumed sepulture, of the chief
architect in a cavern or vault on the continent of '
Europe. Respecting this degree, the following
account is given in Dr Mackey's "Freemason's
Lexicon;" the main facts of which correspond
with my own experience. " In this degree, the
Knights celebrate the destruction of the tower of
Babel, and for this purpose they meet on the night
of the full moon of each month. No other light
is permitted in the Lodge than what proceeds from
that satellite. The records of the order furnish
us with the following history. The Noachites,

196 The Pythagorean Tri&ngle.

at this day called Prussian Knights, are the
descendants of Peleg, chief architect of the tower
of Babel. Thus they trace the origin of their
order to a more ancient date than the descend-
ants of Hiram ; for the tower of Babel was built
many ages before the temple of Solomon. And
formerly, it was not necessary that candidates for
this degree should be Hiramites or Blue Masons.
But a different regulation was afterwards adopted,
and to receive the degree of Noachite, it is now
necessary that the candidate should have per-
formed the duties of a worthy office in a regularly-
constituted Lodge of Blue Masons. The order of
Noachites was established in Prussia in 1755, and
introduced into France by the Count St Gelaire
in 1757."

The degree of the Ark and Dove has also a refer-
ence to the deluge, and the eight persons saved
in the ark, as its name imports; and describes
the process by which Noah emerged from his con-
finement after the waters had subsided. There is
still another degree which partially includes the
same subject, only it confines its reference to the
building of the ark. It is called the Knight of
the Boyal Axe ; and by some the Grand Patriarch,
Prince of Libanus, because the timber for the ark
is feigned to have been felled in those extensive
forests.

As I am on this subject, into which I have been
insensibly led by its connection with the ogdoad,
I may as well mention a tradition which is pre-
served in one of these degrees. It is there said,

The Diluvian Grip. 197

that " when Noah and his family entered into the
ark, they assisted each other by means of a cer-
tain grip." There appears to be some doubt
about the correctness of this tradition, which in-
deed is given by others in a different form. They
say, that when the antediluvians underwent the
divine sentence, and were struggling with the
waves in the agony of death, they endeavoured to
escape by using the same grip to pull each other
up to the tops of mountains, or trees, or other
high places that presented a temporary refuge
from the justice of that irrevocable decree which
brought destruction on their heads.

ANCIENT SUPERSTITIONS ATTACHED TO
THE ENNEAD OR TRIPLE TRIANGLE.

THE TRIPLE TRIANGLE, ENNEAD, NONAGON, OR THE

NUMBER NINE.

iK»X'<C?Yi

CHAPTEE IX.

THE TRIPLE TRIANGLE.

ENNEAD y NONAGON, OR THE NUMBER NINE.

" The weird sisters hand in hand,
Posters of the sea and land,
Thus do go about, about,
Thrice to thine, and thrice to mine,
And thrice again to make up nine."

Shakespebe.

" The emblems used to explain the number of the Nine Elected Knights
were nine red roses, nine lights in the chapter, and nine strokes
to gain admittance. The colour was symbolical of the blood that
was shed in the temple, and ordered to remain there till revenge
was completed." — Leotube of the Nine Elected Knights.

HEEE can be no doubt but the system
of numerical cabalism, or divination by
numbers, commonly called Arithomancy,
may boast a very high antiquity. By which I
mean, a system of foretelling remarkable events
by the combinations of numbers according to the
rules of art ; and the results were sometimes
so extraordinary as to startle the uninitiated.

202 The Pythagorean Triangle.

Whether the sacred writings give any sanction to
the practice is doubtful. The Jews assert that
they do, and surely they ought to be the best
interpreters of their own holy books. The learned
critic and Hebraist, Dr Wootton, was of this
opinion ; and he thinks that we may safely receive
their exposition when there is no reason to sus-
pect any sectarian bias or prejudice in the mind
of the commentator. Let them therefore answer
the question about the cabalistic application of
numbers in the interpretation of scripture, if
they will — I shall not venture an opinion on the
subject.

We are quite sure, however, that divination by
numbers formed a part of the system of Pytha-
goras ; for Stanley has given an entire chapter on
the subject. He says, that Pythagoras derived
his knowledge of the properties of numbers from
Orpheus ; and Iamblichus asserts, that instead of
the art of divining by sacrifices, this philosopher
taught the art of prediction by numbers ; which
he conceived to be more sacred and divine, and
more agreeable to the celestial numbers of the
gods. Some authors have ascribed to Pythagoras
the invention of an onomantic kind of arithmetic,
in which particular numbers are assigned to the
letters of the alphabet, the planets, the signs of
the zodiac, and the days of the week ; thereby
resolving questions concerning nativities, victory,
journeys, thefts, prosperity or adversity, life or
death. Dr Fludd, in his " Microcosm," affirms,
that future events may be prognosticated by vir-

How to Foretel Remarkable Events. 203

tue of a wheel invented by Pythagoras, whereby
everything connected with the life of man may be
truly foretold. There are great doubts, however,
whether this wheel was not an invention of the
cabalists of an age long subsequent to the time
of Pythagoras, because it is not mentioned by any
ancient writer.

There is another method of using a combina-
tion of numbers to predicate or foretel remark-
able events; although, from the specimens before
us, they seem rather calculated, by an ingenious
adaptation of facts to figures, to speculate on the
past, rather than to vaticinate for the future.
Thus we are told, that by selecting any remark-
able year as the basis of the calculation, other
coincident circumstances will be pointed out by
adding the sum of the figures in them to the year
itself. And this may be carried out ad infini-
tum ; as in the following examples. The fall of
Eobespierre took place in the year 1794; now if
the sum of 1, 7, 9, and 4, viz., 21, be added to that
era, the result will give 1815, a year distinguished
by the fall of Bonaparte ; then add the sum of
1, 8, 1, and 5, viz., 15, to this latter year, and we
have 1830, which was marked by the fall of
Charles X. ; and proceeding still further to add
the sum of 1, 8, 3, and 0, viz., 12, to that year,
it gives 1842, remarkable for the death of the
Duke of Orleans. The same system has been
applied to the House of Brunswick on the throne
of England, with similar results. And it might
be made to bear with a corresponding facility on

204 The Pythagorean Triangle.

any individual in the universe, taking the day of
his birth for the era ; and some prominent event
will certainly mark every year which may be
produced by the above process.

The ancients were much addicted to these
puerilities, and considered every accidental co-
incidence as an extraordinary confirmation of a
mystical or magical system. And so it has de-
scended to our own times. Charms for curing
diseases are not entirely obliterated ; and a cen-
tury or two ago they were abundantly prevalent
amongst all ranks and descriptions of people ; and
every midwife was formally sworn before the civil
magistrate, that in the discharge of her duties she
will " use no kind of sorcery or incantation in the
time of the travail of any woman." The charms
which were in common use, most frequently com-
bined the numeral system in one shape or other.
For instance, the famous amulet, Abracadabra, con-
tains an odd number of letters, viz., 11, for which
number the Jews had a great veneration, because
it reminded them of the bondage of their fathers
in Egypt ; there being only eleven patriarchs re-
maining when Joseph was transported thither
and accounted dead ; but some of the cabalistic
Jews have given a more philosophical reason, by
supposing that the solar exceeded the lunar year
by so many days.

Again, the following charm " for woman that
traveylyth of chylde," which was directed to be
" byndyd to her thye," is founded on the numeral
system, for almost all the invocations run by

Ancient Charms. 205

threes. " In Nomine Patris ^ et Filii HE* et Spir-
itus Sancti ^ Amen. ^ Per Virtutem Domini
sint Medicina mei pia Crux et Passio Christi. ^
Vulmera quinque Domini sint Medicina mei. HE«
Sancta Maria peperit Christum. >k Sancta Anna
peperit Mariam. ^ Sancta Elizabet peperit Jo-
hannem. ^ Sancta Cecilia peperit Remigium.^
Arepo tenet opera rotas. >f« Christus vincit. >J«
Christus regnat. Hh Christus dixit Lazare veni
foras. ^ Christus imperat. ^ Christus te vocat.
►I* Mundus te gaudet. ^ Lex te desiderat. >{«
Deus ultionum Dominus. ^ Deus preliorum
Dominus libera famulum tuam N. *i* Dextra
Domini fecit virtutem. a. g. 1. a. ^ Alpha ^ et
fl. ^ Anna peperit Mariam. ^ Elizabet pre-
cursorem. ^ Maria Dominum nostrum Jesum
Christum, sine dolore et tristicia. Infans sive
vivus sive mortuus exi foras HE* Christus te vocat
ad lucem. ^ Agyos. ^ Agyos. ^ Agyos. ■*«
Christus vincit. ^ Christus imperat. HE* Chris-
tus regnat. 4« Sanctus ^ Sanctus ^ Sanctus
^ Dominus Deus. ^ Christus qui es, qui eras,
►P et qui venturus es. ^ Amen. Churnon ^
Clictaono ^ Christus Nazarenus ^ Rex Jude-
orum fili Dei *J* miserere mei. ^ Amen.*'

The Jewish purifications had an especial re-
ference to the numbers 3, 7, and 9. For instance,
a person who had been rendered unclean was
sprinkled on the third and seventh day by a
clean person with hyssop, dipped in water mixed
with the ashes of a red heifer ritually prepared.
Lightfoot informs us, that nine of these heifers

206 The Pythagorean Triangle.

were slain between the time of Moses and the
destruction of the second temple.

Many learned and wise men amongst the an-
cients were fully persuaded that divination was
a faculty which they themselves possessed, and it
would be too much to charge so virtuous a philo-
sopher as Pythagoras with the deliberate practice
of imposture in his assumption of the power of
foretelling future events. The truth is, he was
himself deceived ; and the fiction of having been
taught the art by Orpheus and Aglaophemus,
when he was initiated into the spurious Free-
masonry of Thrace, as Iamblichus informs us,
was as firmly implanted in his mind, as the
faith of Socrates, that he was attended by a
familiar demon, who, either openly or by the
mediation of dreams and omens, communicated
to him every important event of his life ; fore-
warning him of danger, and frequently preventing
him, by a timely admonition, from committing
actions which he would afterwards have repented

All this was rejected by Epicurus. He allowed
of no power either in oracles, dreams, or divina-
tion. He says, " They allege divination as an
argument to prove both Providence and the exis-
tence of demons ; but I am ashamed at human
imbecility, when it fetcheth divinations even out
of dreams ; as if God, walking from bed to bed,
did admonish supine persons, by indirect visions,
what shall come to pass ; and out of all kinds
of portents and prodigies ; as if chance were not

Curious Properties of the Ennead. 207

a sufficient agent for these effects, but we must
mix God, not only with the sun, the moon, and
living creatures, but also with brass and stone.
But to instance in oracles only. Many ways may
it be evinced that they are mere impostures of
priests, as may particularly be discovered, for
that the verses which proceed from them are
bad ; being for the most part maimed in the
beginning, imperfect in the middle, and lame
in the close; which could not be if they
came from divine inspiration ; since from God
nothing can proceed but • what is decent and
proper." l

The Ennead is the first square of an odd number,
and possesses many curious properties. Thus, if
we multiply 9 by itself, or by any other single
figure, if we add the two figures of the product
together, the sum in all cases will be 9. For
example ; 9 multiplied by 9 is 81 ; and 8 added
to 1, make 9, and so with every other digit.
Again, if all the nine digits be added together, the
amount will be 45 ; and 4 added to 5 make 9.
The amount of the several products of 9, viz.,
9, 18, 27, 36, 45, 54, 63, 72, 81=405, when
divided by 9 gives a quotient of 45, and the
figures forming either the dividend or the quo-
tient, added together, make 9. Again, if we mul-
tiply any row of figures either by 9, or by any of
the above products of 9, the sum of the figures
added together will be divisible by 9 without a
remainder. And if we multiply the nine digits in

1 Stanley, Hist. Phil., vol. iii. part 4, 8. 2, c. 6.

208 The Pythagorean Triangle.

their natural order by 9, or by any of the above
products of 9, the result will come out all in the
same figure except in the place of tens, which will
be a ; and that figure will be one, which, being
multiplied by 9, supplies the multiplier ; or in
other words, if 9 be the multiplier, the product
will be all ones ; if 18, all twos ; if 27, all threes ;
and if 8 be omitted from the multiplicand, the
will vanish, and leave the product all ones, twos,
threes, &c, as the case may be. Once more, if a
piece of square pasteboard be divided into nine
cells, it has often exercised the ingenuity of
curious persons to determine how the numbers
18, 20, 24, 28, 32, and 36 may be respectively
placed in the outer cells of the squares, so as
to form in every case the number 9, and no
more, in each of the rows. The result is as
follows : —

5

4

4

5

2

5

2

5

5

2

5

2

4 14

1 1

4 14

1 7 1

7 7

1 7 1

3

3

3

3

3
3

3

3

9

9

9

9

Another property of the number 9 is as fol-
lows: viz., take any number you choose, as, for

The Bridecake Charm. 209

instance, . . . 865374254

Invert their order and subtract them, 452473568

41S900686

then add together the figures in the last line,
viz., 4 + 1+2+9 + 6 + 8 + 6=36 ; and 3 + 6=9. If
the number in the uppermost line be smaller
than the lower line, and cannot be subtracted
from it, then take the top line from the bottom,
and the result will be the same ; as, for ex-
ample, .... 1579

9571

7992
and 7+9+9 + 2=27, or thrice 9.

Amongst the heathen, the purification of male
infants took place nine days after the birth ;
whence the goddess, who was supposed to pre-
side over this ceremony, was called Nundina,
from nonus, or the ninth ; and for the same rea-
son the Eoman market-days were termed Nun-
dinse, Novendinse, or Feriae nundinales, because
they were held every ninth day. The ennead had,
however, a variety of other references, some of
which are too curious to be passed over in silence.

It was called reXew, or perfect, in reference to
the time of gestation in the womb. And hence
it is a custom of very ancient standing at mar-
riages to put slices of bridecake through the
wedding-ring nine times, and being thus invested
with some supernatural power, the pieces are
distributed amongst the young friends of the

o

210 The Pythagorean Triangle.

bride, that being laid under their pillows, they
may have a dream or vision of the person who is
designed to be their partner for life.

With her own hand she charms the destin'd slice,
And through the ring repeats the trebled thrice.
The hallowed ring, infusing magic power,
Bids Hymen's visions wait the midnight hour ;
The mystic treasure placed beneath her head,
Will tell the fair if haply she may wed.

The number nine had the name of Likeness,
because it is the first odd triangle ; and Prome-
theus, because it is a perfect ternary; for he made
the first man and woman, and animated them with
fire from heaven. It was called Concord, because
it unites and knits together all other numbers. It
was considered to be unbounded, because, as we
have just seen, in all its combinations it returns
into itself ; and therefore was compared equally
with the horizon and the ocean ; whence it was
called E/caepyo? ; for the ocean flowing about the
habitable earth is believed by some to be so
immediately placed under the arch of heaven,
that the sun and stars rise from it, and set in
it. And the Epicureans demonstrated the fact
by this argument : " The universe consisting of
vacuum and body is infinite ; for that which is
finite hath a bound, that which hath a bound is
seen from some other thing ; or may be seen from
out of an interval beyond, or without it. But
the universe is not seen out of any other things
beyond it; for there is no interval or space which
it containeth not within itself, otherwise it could

Names of the Number Nine. 211

not be an universe if it did not contain all space ;
therefore neither hath it any extremity. Now,
that which hath no extremity hath no end, and
that which hath no end doubtless is not finite
but infinite. This is confirmed thus : If you
imagine an extremity, and suppose some man
placed in it who, with great force, throws a dart
towards its utmost surface ; the dart will either
go forward or not. If it go forward, there is
place beyond, wherefore the extremity was not
there, where we designed it ; if not, then there
is something beyond which hinders the motion ;
and so, again, the extremity was not in the fore-
designed place." x

The Pythagoreans gave the name of the num-
ber nine to several of the Grecian divinities, — as
Juno, because the sphere of the air has the ninth
place ; and, like the ennead in its conjunction
with unity, she was the sister and wife of Jupiter.
It was also called Vulcan, for a reason which I
do not well understand ; Proserpine, because she
presides over nine unpropitious deities ; the three
Fates, the three Furies, and Night, Sleep, and Death ;
Terpsichore, because the Muses are nine in num-
ber ; and also Curetis, Paean, Hyperion, Agelia,
and many others ; but I cannot ascertain any valid
reason for each particular appropriation.

The Mahometans had ninety-nine names for
the Deity ; and the Jews believed that God had
descended to the earth nine times ; and that He
shall come down oh the tenth in the person of

1 Stanley, Hist. PhiL, vol. iii. part 4, p. 145.

212 The Pythagorean Triangle.

the Messiah. His several appearances were — 1,
in the garden of Eden ; 2, at the confusion of
tongues ; 3, at the destruction of Sodom ; 4, to
Moses at Mount Horeb ; 5, at His appearance on
Mount Sinai ; 6 and 7, two other appearances to
Moses ; 8 and 9, in the Tabernacle.

There was at Cairo, during the dynasty of the
Fatimite Khalifs, a secret society, called the
Society of Wisdom. The members were clad in
white, and held their meetings twice a week
The institution consisted of nine degrees : 1.
Probation ; in which the candidate was perplexed
with abstruse questions, and taught to regard
his teacher with veneration. 2. The Oath ; and
acknowledgment of the divine authority of the
imams. 3. Instruction ; principally consisting in
a knowledge of mystical numbers ; and particu-
larly that seven was the noblest of God's creatures,
4. Illustrations of the number seven ; in which
he was taught, that as there were seven heavens,
seven earths, the same number of seas, planets,
metals, &c, so there were seven lawgivers, seven
helpers, seven imams, &c. 5. Illustration of the
number twelve. 6. The philosophy of religion.
7. Pantheism. 8. Scepticism. 9. This degree in-
culcated that nothing was to be believed, and that
anything may be done ; which, in point of fact,
is Deism at the least, if not absolute Atheism.

The critical period of human life, according to
a very ancient superstition, as we have already
seen under the number seven, had a reference
to this number. Thus 9 being multiplied by 7

-Remarkable Superstitions. 213

makes 63, the climacteric or dangerous year ;
and 9 multiplied by 9 make3 81, the grand cli-
macteric, or year of imminent danger. Jjevinus
Lemnius thus accounts for the existence of the
superstition. " Olde men/' he says, "seldome
passe their sixty-third year, but they are in con-
stant danger of their lives ; and I have observed
in the Low Countries almost infinite examples
thereof. Now there are two years, the seventh
and ninth, that commonly bring great changes in
a man's life, and great dangers ; wherefore sixty-
three, that containes both these numbers multi-
plied together, comes not without heapes of dan-
gers ; for nine times seven, or seven times nine,
are sixty-three. And, thereupon, that is called the
climactericall year; because, beginning from seven,
it doth, as it were, by steps, finish a man's life."
I shall conclude this chapter with the mention
of a few remarkable superstitions connected with
the ennead, which will show the honours that
were paid to it of olden time. It appears that in
the time when conjurers could profitably exercise
their art, they used to raise spirits within a circle
nine feet in diameter, which they consecrated by
sprinkling with a mixture of holy water, wine,
and salt ; that they might be protected from any
onslaught of the fiend. Brand informs us, that
it is unlucky to cut your nails upon a Friday or
a Sunday ; and that it ought to be done on the
ninth day, except it fell on either of the above
periods. This custom was used by the Eomans. 1

1 Pop. Ant., vol, iii. p. 92,

214 The Pythagorean Triangle,

Divination is sometimes practised by the use of
this number, even at the present day. Thus, the
female inquirer after a sight of the person to
whom she is to be married is directed to beg nine
keys of nine several persons ; fastening them
together by nine knots of a three-plaited braid of
her own hair. She is then to tie them to her
wrist at going to bed with one of her garters on
St Peter's Eve, repeating —

St Peter take it not amiss
To try your favour I've done this ;
You are the ruler of the keys,
Favour me then if you please ;
Let me then your influence prove,
And see my dear and wedded love.

In divination, or fortune-telling by cards, the nine
of spades is the most unfortunate in the whole
pack ; the nine of diamonds favourable to com-
mercial men ; the nine of clubs for married women ;
and the nine of hearts for lovers of either sex.

It would be easy to multiply instances of a
superstitious affection for the number nine, but it
is unnecessary, as the memory of every reader will
be sufficiently retentive to suggest cases without
end where it occurs. Our ancestors named nino
worthies in triads ; three being heathen, thres
Jewish, three Christian. The former were Hector,
Alexander the Great, and Julius Cesar ; the next,
Joshua, David, and Judas Maccabeus ; and the
last, King Arthur of Britain, Charlemagne of
France, and Godfrey de Bouillon, King of Jeru-
salem.

Astronomical Tendency of Freemasonry. 215

I am not aware of any reference to this number
in symbolical Masonry, unless, with the cabalists,
we consider it to be " the number evolving itself "
in the consecutive reports of the principal officers
of the Lodge, at opening, closing, and refreshment ;
but in the Royal Arch, and in the Ineffable De-
grees, it is abundantly used. As, for instance, in
the degree of Select Master, mention is made of
a secret vault underground leading from King
Solomon's most retired apartment westwardly,
and consisting of nine separate apartments or
arches, the latter being under the Sanctum Sanc-
torum. The method of giving and receiving the
sacred word is ninefold ; the arches of Enoch
were nine in number ; the Grand Masters of the
three original Lodges were nine ; and the sym-
bolical ages of the members of different degrees
were computed by the same number, as 27=3x9 ;
72=8X9; 81=9x9, &c.

These results are, I think, fatal to the theory
which gives to Freemasonry an astronomical ori-
gin ; because every rite and ceremony which may
be presumed to bear the authentic stamp of an-
tiquity is founded strictly on a reference to this
number. The advocates for the astronomical
tendency of Freemasonry thus state the grounds
of their opinion, as appears from a letter to the
author, written by a learned Scottish Mason. He
says, " My conviction is, that the whole of Free-
masonry is an astronomical allegory ; for we
cannot suppose that the wisest of men would
suffer the Dionysian artificers to practise either

216 The Pythagorean Triangle.

their own impurities, or worship their false gods,
in the Holy City. I think Faber has distinctly-
shown that the pagan mysteries refer to the Ark
of Noah — to some one who was dead or killed,
and again came to life — and that the rising and
setting of the sun so aptly represented this per-
son, that the type became subsequently wor-
shipped for the substance. Moreover, all the
ancient mysteries seem to have been celebrated
about the time of the vernal equinox ; and it is a
general belief that King Solomon laid the foun-
dation-stone of the Temple on the very same day.
Now Josephus informs us, that the Tabernacle was
a representation of the universe ; which inter-
pretation may also be applied to the Temple,
because it was merely a renewal of the Tabernacle
on a more magnificent scale. But the appearance
of the heavens is continually changing; and
therefore, if the above mean anything, the Temple
must have represented the universe at the exact
period of its erection. Although, then, the modern
symbols may be derived from astronomy in imi-
tation of the Egyptian Dionysiacs or Tsabaists,
still we need no more admit them to be inseparable
from the pagan idolatry, than that, as Solomon's
Temple was itself an astronomical or universal
emblem, Solomon had erected it for the rites of
the pagans, instead of the worship of the only
God. Why Solomon did permit such is not so
clear, as that they must be viewed in themselves
as having no tendency to idolatry, otherwise they
could not have been allowed to be used. That

Freemasonry Derived from Geometry. 217

afterwards Solomon and some of his successors
blended the symbolic with the gross ritual of the
Tsabaists is almost evident from several passages
of the Bible ; and it may have been after the
reign of Josiah, or at the rebuilding by Zerubbabel,
that the present tradition or legend of the Third
Degree was drawn up ; probably accidentally, from
some traditional account of a riot, by a few of the
workmen to obtain the secret of a superior degree ;
and in which they confounded H.A.B. with Urim,
literally Lights ; but being plural, this was used
for the great light, or the sun."

I have no room for a further statement of the
theory which ascribes an astronomical origin to
Freemasonry ; but this will be sufficient to show
the line of argument by which the hypothesis is
attempted to be supported. I am persuaded,
however, that the theory is erroneous, notwith-
standing the great names by which it is upheld;
amongst whom we find that of an eminent brother,
Sir W. Drummond, the erudite author of the
" Origin es," from the perusal of which I have de-
rived both amusement and instruction. It appears
more probable that Freemasonry is an emanation
from Geometry, which was indeed one of its
primitive names ; and the basis of Geometry is
the science of Numbers, whose elements are the
masonic point, line, superfice, and solid.

If, then, we turn our attention to Geometry, we
shall find that it is the foundation of architecture,
which we know was practised by the Tyrians and
Dionysiacs at the building of Solomon's Temple;

218 The Pythagorean Triangle.

and this is more than we can say for the know^
ledge of astronomy ; for though it may be per-
fectly correct that the Tabernacle and Temple were
emblems of the universe, yet this might be an alle-
gorical conceit of the later Jews after the inven-
tion of the cabala ; for Josephus lived at the very
latest period of the Jewish polity, and witnessed
the final destruction of the Temple by Titus. It
is reasonable, therefore, to conclude, that Numbers,
displayed in the science of geometry and applied
to architecture, the rules of which are all founded
on its principles, were the prototype and origin of
the masonic science.

i

THE PERFECT NATURE OF THE DEC AD OR
CIRCLE, AND THE APPLICATION OF THE
DODECAEDRON AS A REPRESENTATION OF
THE SYSTEM OF THE UNIVERSE.

THE CIRCLE, DECAD, PANTELE/A, OR THE

NUMBER TEN.

CHAPTER X.

THE CIRCLE.

DECADy FANTELEIA, OR THE NUMBER TEN.

" Qui venit hie fluctus, fluctus supereminet o nines,
Posterior nono est, undecimoque prior."

Ovid.

"A triangle with the Sun in the centre, its rays issuing forth to
every point, is an emblem of the Deity, represented by a Circle,
whose centre is everywhere, and circumference nowhere ; hereby
denoting His omnipresence, and that all His attributes are perfec-
tion." — Old R. A. Lectures.

HERE is little benefit to be derived from
Freemasonry in this Christian country,
if it be divorced from all connection
with the Christian religion ; although admitting
that it would be a violation of the true principles
of the Order to close our Lodges against the
sincere professors of any other faith which in-
cludes the belief of one only God, the creator and
governor of the world. And the framers of our
lectures entertained the same opinion. At the pre-
sent day, there are two classes amongst the fra-

222 The Pythagwean Triangle.

ternity who differ upon this point, although the
difference is not very essential, or difficult to be
reconciled. For this purpose a little discrimina-
tive arrangement is alone necessary. It is readily
admitted that ancient Masonry per se might be
intended as an universal institution, embracing
all mankind who acknowledge and worship the
Great Supreme. But the Lectures of Masonry,
as they are at present constituted in this country,
offer a modified view of the matter. They con-
sist almost exclusively of a series of typical
references to the Eedeemer of mankind. There-
fore, however the Christian Mason may be in-
clined to admit the application of Masonry to
all existing religions, he cannot deny the facts
contained in the lectures, without, at the same
time, denying the veracity of the New Testament.

If a Christian brother adihits that Freemasonry
is a system of Light, and I think there scarcely
exists a difference of opinion on the proposition,
he must also believe the truth of the words so
solemnly delivered by our venerable Grand Master
St John the Evangelist, who, speaking of Christ,
plainly says, " He is the true Light, which light-
eth every man that cometh into the world." * If,
therefore, Masonry be a system of Light, and the
Light be Christ, the unavoidable inference is, that
Masonry is a branch of that universal religion
which is destined, at some future period, to per-
vade the whole earth, as the waters cover the sea.

The great error of those who can find no

1 John i. 9.

Principles of Speculative Freemasonry. 223

Christianity in Freemasonry is, the very super-
ficial view which they take of our most holy
faith. They restrict its operation to the last
eighteen and a half centuries ; whereas, if they
believe the Scriptures, they would extend it
back to the beginning of time, as St Paul instructs
them to do. It is not to be wondered at that
this error should be committed by a layman ;
but it is surprising that any Christian minister
should exhibit such a total ignorance of the design
of that gospel which he preaches every week of
his life.

A talented American brother, the Rev. Salem
Town, asserts, that " the principles of Speculative
Freemasonry have the same co-eternal and un-
shaken foundation, contain and inculcate in
substance the same truths, and propose the same
ultimate end, as the doctrines of Christianity
taught by divine revelation." And to prove that
the Christian tendency of Freemasonry was an
admitted dogma with our brethren of the last
century, I subjoin an observation, which I have
found amongst the MS. papers of my father,
the late Eev. S. Oliver, under date of 1793 :
"Masonry, taken in any point of view, either
pagan or Christian, human or divine, is far supe-
rior to every other institution known amongst
men, and may, without impropriety, be termed
the Summum Bonum, inasmuch as it contains
the very essence of Christianity ; and when used
by the professors of any other faith, allures them
to the practice of the most sublime Christian

224 The Pythagorean Triangle.

virtues, whilst tliey do not suspect that almost
they have become Christians."

On the number ten the ancients were quite
ecstatic both in their feelings and their written
disquisitions. It represented Elysium, the abode
of happy spirits. Like the Deity, it is a circle
whose centre may be seen, but whose circum-^
ference is invisible. There is nothing beyond
it. It formed, in the opinion of the ancients,
the boundary and extent of every created thing.
Would you count a greater number than it con-
tains, you must recommence with unity, and go
on till you are again stopped by the decad, and
unity once more recurs.

What a sublime idea does this number present
to our minds, when it refers us to boundless
space ! Worlds piled upon worlds at immeasurable
distances from each other, all illuminated by their
own suns ; and myriads so farremoved, that their
light, though travelling for six thousand years, at
the rate of twelve millions of miles in every minute
of time, has not yet reached our globe. Her-
schel, with his forty-foot telescope, as Bro. Moran
tells us in the Freemason's Quarterly Review,
" could descry a cluster of stars consisting of 5000
individuals, 300,000 times deeper in space than
Sirius probably is ; or, to take a more distinct
standard of comparison, if it were at the remote-
ness of 11,765,475,948,678,678,679 miles; or,
in words, eleven millions seven hundred and sixty-
five thousand four hundred and seventy-five bil-
lions, nine hundred and forty-eight thousand six

-1

The Decad the Receptacle of all Things. 225

hundred and seventy-eight millions, six hundred
and seventy-eight thousand, six hundred and
seventy-nine miles/' 1

If this immense space be the centre, where is
the circumference? Bro. Moran advises, with great
judgment, in the above exquisite paper (would
that we had more of them !) : " Pause a moment,
and imagine, if you can, what it is that the
discoveries of Herschel have thus unfolded : a
distance between this earth and the remotest
visible system we behold with the unhelped eye,
nine hundred times greater than that of the
sun -from the earth. Then bear in mind that
such another system of stars is hung up in dis-
tant space, for no other object, at least as appa-
rent to terrestrial man, than to serve as a specular
resemblance of that which, until the other day,
he fancied was infinite. It is thus only that we
can conceive of the Great Architect of the Heavens,
until the purification of death shall quicken the
mortal conception."

Here, then, we have an apt illustration of the
decad as the receptacle of all things. Hence
it was called Universe and Sphere, because it
included the number ten, viz., the earth, the
seven planets, the heaven of fixed stars, and an-
tichthon. It was also called Kosmos, or world,
because the decad comprehends all numbers, as
the world comprehends all forms. Thus Ecphan-
tus, the Crotonian, who belonged to the school of
Pythagoras, affirmed, " that the nature of every

1 F. Q. R., 1837, p. 327, note.

226 The Pythagorean Triangle.

animal is adapted to the world, and to the things
contained in the world ; because every animal
thus conspiring, in union and consent, and hav-
ing such a colligation of its parts, it follows a
series which is most excellent, and at the same time
necessary, through the attractive flux of the uni-
verse about it, which is effective of the general
ornament of the world, and the peculiar perma-
nency of everything which it contains. Hence it
is called Kosmos, and is the most perfect of all
animals." l

The decad was the great number of the Pytha-
goreans, because it comprehends all arithmetical
and harmonical proportions. They deemed it to
proceed from the diffusive nature of the triad,
and its multiplying properties. Thus, if unity
and duality be multiplied in this form, once
twice 2 make 4, the sacred Tetractys, whence
1 + 2+3+4=10. Now the half of 10 being 5,
the middle number, if we take the next, superior
and the next inferior numbers 6 and 4, their sum
will be 10 ; the next two in a similar progression,
7 and 3, will also make 10; and so on throughout
the integers, i.e., 8 and 2, and 9 and 1, produce
the same result; and hence they called the num-
ber 10 the fountain of eternal nature, or God ;
His body Light, and His soul Truth. Numbers,
they said, fall all under the monad ; thus one
monad is a monad ; one duad is a duad, &c. ; but
the decad is the summary of number, which can-
not be increased without returning to the monad.

x Taylor's Fragments, p. 27.

Origin and Use of the Number Ten. 227

Goquet reduces the origin and use of this num-
ber to a very simple process. He says that it
proceeds simply from counting the fingers ; which
were the first instruments used by men to assist
them in the practice of numeration. Amongst
the cabalistic Jews, 5, 6, and 10, were called cir-
cular numbers, for they argue, that as a person
travelling on a circular road departs from a cer-
tain point, how often soever he goes round, he
still returns to the same point ; so is the property
of numbers. If 1 be multiplied by 1, the result
is one ; 5 multiplied by 5 also gives a 5 ; 6 times
6, the same, and so on to infinity. The number
10 may thus be said to be circular ; for, multi-
plied by itself, it is 100 ; and 10 times 100 are
1000, or 10 hundreds ; thus showing, that as a
circle has neither beginning nor end, so it is an
apt symbol of the First Cause, who is without
beginning and without end.

From this property of comprehending all num-
ber, the decad was called Power, for its command
over all numbers ; and also Atlas, because it sus-
tains all the ten spheres of heaven, as Atlas bore
the sphere of the universe upon his shoulders.
St Thomas Aquinas, in his definition of quality
or quantity compared with distance, has thus re-
corded his idea of the ten empyreal grades : " In
our universe the water is more than the earth ;
the air more than the water ; the fire more than
the air ; the first heaven is larger than the sphere
of fire ; the second larger than the first ; and so
on in regular gradation, until w r e arrive at the

228 The Pythagorean Triangle.

tenth sphere, which is inestimabilis et incompara-
bilis magnitudinis"

The decad was also called Fulness and Eter-
nity, by reason of its being the perfection of all
number, and comprehending all the nature of odd
and even, right and wrong, good and evil, light
and darkness. Hence it was used by the Jewish
prophets indefinitely for a great number. Thus,
at the building of the Temple of Zerubbabel,
Nehemiah interprets the ten generations men-
tioned in Deut. xxiii. 3, to mean " for ever ;" *
and speaking of Sanballat and his associates said,
" It came to pass, that when the Jews which dwelt
by them came, they said unto us ten times, from
all places whence ye shall return unto us they
will be upon you." 2 Meaning that they had
frequently told them so. Moses Lowman, in his
Commentary on the Book of Revelation, speaking
of the ten-horned beast, says, that " ten, in pro-
phetic language, does not always mean a precise
number, but is used as a certain number for an
uncertain, to express in general several or many;
so that there seems no necessity of finding a pre-
cise number of ten different kingdoms erected
on the ruins of the Eoman Empire." Several
interpreters, however, and amongst the rest
Sir Isaac Newton, have enumerated these ten
kingdoms.

The number ten had the further names of Sol,
Urania, Memory, Necessity, and Faith ; and was
esteemed the first square, because it is composed

1 Nehem, xiii. 1. * Ibid. iv. 12.

The Tenth Wave and Egg Ideas. 229

of the first four digits. Sir Isaac Newton, speak-
ing on this subject, says that the extent of
Solomon's Temple was 1460 cubits ; but if we
multiply this number by 4, and again by 365, the
days in a solar year, it will give the exact area of
the Temple, viz., the square of 1460 = 2,131,600
cubits ; thus practically illustrating the manner
in which the Jewish cabalists combined the
sciences of architecture and astronomy ; for 1460
was the old Egyptian canicular year.

Of the number ten, Dr Brown says, " that
fluctus decumanus, or the tenth wave, is greater
and more dangerous than any other ; some, no
doubt, will be offended if we deny ; which not-
withstanding is evidently false ; nor can it be
made out by observation, either upon the shore
or the ocean, as we have with diligence explored
them both. Of affinity hereto is that conceit of
Ovum decumanum — so called because the tenth
egg is bigger than any other. For the honour we
bear unto the clergy, we cannot but wish this were
true ; but herein will be found no more verity
than in the other ; and surely few will assent here-
to without an implicit credulity, or Pythagorical
submission unto every conception of number.
For surely the conceit is numeral, and, though
not in the sense apprehended, relateth unto the
number of ten, as Franciscus Sylvius hath most
probably declared. For whereas amongst simple
numbers or digits, the number of ten is the
greatest ; therefore whatsoever was the greatest

230 Hie Pythagorean Triangle.

in every kind, might be in some sense named
from this number." *

The foreign Masons of the last century, who
called themselves Theosophists, or followers of
Paracelsus, made use of this number in more than
one of their high degrees. They taught, that as
there were ten generations from Adam to Noah,
ten from Shem to Abraham, and ten spiritual
graces in Christianity, viz., love, joy, peace, long-
suffering, gentleness, goodness, faith, prudence,
meekness, and temperance; 2 so there are in
nature ten forms of fire, which they enumerated,
in imitation of the framers of the Koyal Order of
H.R.D.M., in doggrel rhyme : —

Of the ten forms of fire know the skill,
The Libert}/ both hath and is the will.
Next Strong desire. Third, sharp drawing Might
Makes an opposing will. Fourth, flash of Light
Brings Anguish. And in the fifth form doth lie
The Eternal nature, or Great Mystery.
Sixth, the two principles of Fire and Light,
The seventh Magia with reflecting sight.
The eighth with Turba ends the outward life.
Ninth Virgin tincture pacifying strife.
The tenth makes holy flesh and holy earth,
Of Angels and blest souls, the holy birth.

The theological ladder, which Masons make to
consist of three rounds, referring to Faith, Hope,
and Charity, the Jewish cabalists increased to
seven, and subsequently to ten principal steps,
called the seven divine splendours, which were

1 Pseudo. Epidem., p. 404, * See Gal. v. 22.

The Perfection of the Number Ten. 231

surmounted by the three great hypostases of the
Deity; which they made figuratively to penetrate
the heavens, which were represented by the num-
ber ten ; and, in consequence of the perfection of
that number, they crowned the symbol with a
nimbus to represent the throne of the Most High.
It has several times been remarked in the course
of these numeral dissertations, that the true
religion, under the Mosaic dispensation, had an
appointed reference to particular numbers. The
facts have been briefly stated under each several
head ; but they are too extensive to be wholly
included in my plan. This extraordinary fact still
forms a part of Jewish ceremony. A congrega-
tion with them consists of ten persons ; and a less
number would not make one. And we are told
that, formerly, wherever ten Jewish families were
resident in the same place; they were obliged to
build a synagogue. At marriages, the bridegroom
received seven blessings, which could not be pro-
nounced except in the presence of ten persons.
Again, the Jewish doctors hold that Abraham's
faith and obedience were ten times tried, viz., 1,
in quitting his native country ; 2, his flight to
Egypt from the famine of Canaan ; 3, the first
seizure of Sarah in Egypt ; 4, the war for the
rescue of Lot ; 5, his taking Hagar at the request
of Sarah ; 6, his circumcision ; 7, the second
seizure of Sarah in Gerar ; 8, the expulsion of
Ishmael ; 9, the expulsion of Hagar; 10, the
offering of Isaac.

232 The Pythagorean Triangle.

And again, with respect to the number 12.
The sons of Ishmael and Jacob were alike twelve
in number, the latter of whom formed the heads
of the house of Israel. The table of shewbread
was directed by God himself to be furnished with
twelve loaves ; and the offering of the princes at
the dedication of the altars, amongst other things,
was twelve golden spoons or censers for incense.
Joshua set up twelve stones in Jordan ; respecting
which an old masonic formula in my possession,
has the following illustration : " As Joshua was
conducting the Israelites towards the Promised
Land, a remarkable miracle was performed in be-
half of this people at the passing of the river
Jordan. When the priests who bore the ark
came near the narrow bridge, which would have
been extremely incommodious for so large a body
of people to pass, the waters of the river miracu-
lously separated, as they had done before at the
passage of the Red Sea, and left the bed of the
river for a considerable breadth perfectly dry, so
that the Israelites might pass over, with their
families and cattle, without the slightest obstruc-
tion. In commemoration of this extraordinary
interposition of the Most High in their behalf,
Joshua commanded that twelve of the largest
stones that could be found should be taken from
the foundation on the north side of the bridge,
and deposited in the adjoining field of corn, as
the basis of a pillar, which was intended to be a
memorial of this event; and that twelve similar

Application of the Number Twelve. 233

stones should be collected from the country on the
opposite side of the river, and placed in the situa-
tion from whence the other twelve were taken, to
form the basis of another pillar in the river.
These two pillars were solemnly dedicated by
Joshua to Elelohe Israel, or God of Israel ; and
together they formed a subject of disquisition
with our ancient brethren, which excited much
attention in the Lodges."

But to return to the application of the number
twelve in the Jewish scriptures. The chief officers
of Solomon's household were twelve ; the pillars
of the porch were twelve cubits in circumference ;
the molten sea was supported by twelve oxen;
and the steps of Solomon's throne were flanked by
twelve lions. In the temple described by Ezekiel,
the altar was directed to be twelve cubits square.

In Christian symbolism, the imagery was the
same, and had a particular allusion to this num-
ber, formed out of the two perfect numbers, the
triad and tetrad; thus 3X4=12. Jesus Christ
was taken by His parents to keep the Feast of the
Passover when He was twelve years old ; and He
chose for His companions twelve men whom He
taught His doctrines, and sent forth to preach the
everlasting gospel to mankind. In the Apoca-
lypse, we have a glorious figure which includes
this number : " There appeared a great wonder
in heaven ; a woman clothed with the Sun, and
the Moon under her feet, and upon her head a
crown of twelve Stars." This refers to the primi-

234 The Pythagorean Triangle.

tive Apostolic Church before the apostasy ; where
being clothed with the Sun, signifies her being
environed with the pure light of the gospel, or
the Sun of Righteousness communicated to her.
And her being crowned with twelve Stars de-
notes, that it was her glory, and her crown, that
she had not degenerated from the true Apostolic
faith and practice." l

The new Jerusalem is represented as being ac-
cessible by twelve gates, disposed in conformity
with the cardinal points of the compass ; and
those that were accounted worthy to be admitted
into the holy city, were sealed in their foreheads ;
viz., of each of the tribes twelve thousand ; which,
as Dr More observes, " is not numerally to be
understood, but symbolically, noting the condi-
tion of the sealed. And there were sealed an
hundred and forty-four thousand ; which chiliads
or thousands are cubical numbers, and signify
therefore stability or constancy. But it is said
there were 144,000, it being the square number
of these chiliads or companies, of which the root
is twelve, the Apostolical number. Of all the
tribes of the children of Israel, viz., the twelve
patriarchs typically or figuratively being put for
the twelve Apostles, and the children of Israel
for the Church of Christ, of which the Israelites
are a type, as they are in the Epistle to the
Church in Pergamus, in which Pergamenian in-
terval this sealing begins." 2

1 Mora, Apocalypsis, p. 114. * Ibid., p. 63.

The Mystical Ceremony of Sealing. 235

It is the opinion of Mr Faber, whose learning
and extensive researches into the hidden mysteries
of antiquity are entitled to universal respect,
that in the Book of Kevelation "an important
prophecy is most curiously and artfully veiled
under the very language and imagery of the
Orgies. To the sea-born Great Father was
ascribed a threefold state: he lived, he died, and*
he revived ; and these changes of condition were
duly exhibited in the mysteries. To the sea-
born wild beast is similarly ascribed a threefold
state : he lives, he dies, and he revives. While
dead, he lies floating on the mighty ocean, just
like Horus, or Osiris, Siva, or Vishnu ; when he re-
vives, again like those kindred deities, he emerges
from the waves ; and whether dead or alive, he
bears seven heads and ten horns, corresponding
in number with the seven art-preserved Rishis,
and the ten aboriginal patriarchs. Nor is this
all ; as the worshippers of the Great Father bore
his special mark or stigma, and were distinguished
by his name, so the worshippers of the maritime
beast equally bear his mark, and are equally
designated by his appellation." 1

If this be true, and the arguments adduced
in its support appear sound and conclusive, the
above mystical ceremony of sealing the redeemed
may be taken from the custom of marking the
aspirant with a permanent badge of initiation,
which may be an indelible token of his acceptance.

1 Fab. Pag. Idol., tqL iii. p. 643.