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MATHEMATICAL TABLES :
COVTAINIHO THB
COMMON. HYPERBOLIC, AND LOGISTIC
LOGARITHMS,
ALSO
SINES, TANGENTS, SECANTS, AND VERSED SINES,
BOTH NATURAL AND LOGARITHMJl^X^ ^ '' /. .
TOQETHER WITH f^ ""^ V, _,. \
SEVERAL OTHER TABLES { -' }
USKFUI. IK \ v-.'/, ^\ »^' •
MATHEMATICAL CALCULATIOlfer^
s AI£0
THE COMPLETE DESCRIPTION AND USE OF THE TABLES.
CHARLES HUTTON, LL.D. F.R.S. &c.,
VOKHKBLT PROFESSOR OF MATHEKATIOS m THE ROTAL MIUTART ACADEirY.
WITH SEVEN ADDITIONAL TABLES OF TRIOONOHETRICAL FORHULiE.
OLINTHUS GREGORY, LL.D.
frofnaor of Uathematict m the Boyal Military Academy ; Vice Pretident of the Atironomioat
Society of Loncbm ; Honorary Member of the Cambridge PhUotophical Society,
the InsHtution of Civil Engineertf ^c.
THE TWELFTH EDITION.
LONDON:
AHD 00.; HAMILTON AMD CO.; fllMPKlM AlCD CO.; WHITTAKCB IHD 00 ; OOWTE
AVD 00. ; HOUt^rON AMD 8T0NEMAN ; F. AND J. BIVINOTON ; SMITH, KLDEB, AND CO. ,
i; Bourns ; H. O. BOHN ; J. COftNUII ; ALLEN AND CO. ; C. H. LAW • AND J. OREEN. CAHURIOOE,
^, DEMHTON.
1855
CONTENTS.
I— INTRODUCTION.
Pngn
Detcription and iise of logarithmic tables ik
Definition and notation «>,
Ph)perties of logarithms t
Construction of logarithms si
Description and use of these tables xiii
Of the large table •&.
IjOgarithmical arithmetic .... xvii
or the table to 20 places xxi
Of llie hyperbolic logarithms xxvi
Of the logistic log-irilhnis xxvii
Of the lug. sines and tangents to ever; second xxriii
Of the general table of log. sines, tangents, ftc xxx
Tbeorems for the construction of tablei, and surd expressions for the
sines xxxvii
Trigunumetrical rules xU
Tlie cases of'plane triangles resolved by logarilhins . . *. . > xlvi
The same by natural sines, &c. xlviit
The cases of spherical triangles resolved by logarithms • . . . xlix
Use of the versed sines Ix
Of the traverse table Ixiii
Of Mercator's sailing ...Ixv
or the lengths of circular arcs -Ixvii
Of comparing the common and hyp, 1<^ ..•■••• Ixviii
II^TABLBS.
Tablfl
1 —I/>earirhma from 1 to 108000 1
2.— U.giinthms, &c. to 20 placet 202
3.— Id. vith differences 213
4. — Numbers to logarithms to 20 places 216
5 g[ 6. — Hyperbolic logarithms 219
7. — Logi»^tic logarithms 230
8. — Sines and tangents to seconds 237
9. — Natural and loganthmic uoes, tangents, secants, and versed sines 268
I 10.— Traverse table 355
[ 11.— Length of arcs 360
|- 12. — Tabto to change common and hyperbolic logarithnu from one to
[ the other 361
13. — Points of the compass ib.
14. — Equivalent expressions for sin. A, cos. A, tan. A . . . . 362
15. — Formulat fur two arcs • 363
16. — Formulse Tor the solution of a plane triangle , . ... 364
17. — Analytical expressions, spherical triangle . •«.... 36S
18. — Formulee for quadratics and cubics 367
19. — FormulB useful in astronomy .....••.•■ t A.
29.— -Useful numbers and their logsrithm* . 368
I.
^^^^^H CORRBCTION OF ERRORS IN THE
^^^^^r [As many pt^rsons in Public Iiistilutio
^^^^H seventh edition wilt be inimflticed, ha
^^^^H to vise the sixth edition ; they are rec
^^^^^ with tlie Logarithms, Sines, Tnugenl
^^^^^^ LogATtlhini : —
1 Log. of G47 should br S109043
1 lu070 0030295
B- 10989 . . 0409&S2
SIXTH GOmON OP THB5K TABLES. ^^H
IS and Privnte Seminaries, where ttiis ^M
ve pnrchaicd und will prubahly continue H
ueslpd to correct iheir copies, to ag^rce ^M
S &c. Rpecitied below.] ^H
Nat, aad Log. Smcs, Taftg. Ac.:— ^M
Ug.aio. 0°23' 19" should be 78313803 H
Log lan. 47 4S 81431820 H
^^^^^^^^ iinni
A ta 7HM110J H
^^^^^^^^^m 11'?3ff f>'Tin7ffft
i-p -.^,^^ 1^ ^ \n.7'.nn\ta ^M
^^^^^^H
Log. ver4. 12 59 8-4076:180 H
Nat.cnAec. 13 4 44231224 ^t
r 67999 8325025
NaL«in. 14 6 •24)61.'>0 ■
^^^^^^K 77649
^^^^^^^ 77918 8917493
r a3290 9205929
Nat. eorei«. 19 51 •6604<1 1 ■
Nat versiii. 20 7 ■O6100'>7 ^M
NtL COS. 20 7 -9389943 ^|
I In the »xnic \>t^^, No. 3330 should be 8330.
^^ Log. of8339J should be 9:ill244
Nat. f>in. 22 42 •38.59060 ^M
Nat coven. 24 6 ■5910695 H
T..J -„f ac ^ in.'infio-.TD ^M
^^B ^612 9222686
Log. coven. 26 42 9-7409001 ^M
^^H 84071 9246462
Nil nrrrn 'i7 Ifl •^l''U"'f ^U
93542 9710067
V,. ««*-. OT or. O.^Tn^Tll ^M
94688 9762949
94750 9765792
95339 9792706
104891 02O7JS23
105879 02480983
^^^^^^ In the Logarithms to 20 places: — •
^^^^^^^ Log. or 554 ^liould be 9 tri the 19th place.
^^^^^^H 627 6 & 7ih
^^^^^^1 644
^^^^^^H 20
^^^^^H 762
v-i ,«.»« 1^ }7 .A^}Oitaa ^H
Nat.iaii 35 35 7154898 ^M
Nil. COS. 37 2 -799JS53 ^M
Nat. COS. 37 35 -79.'4671 ^M
L4>g.5ec. 38 3 101037643 ^1
Nal.cniec.39 7 1-5650334 ^M
Nat. cove. 39 19 1-5782680 ^M
Nal. cnL 39 45 1 2023693 ^M
NaLTcrs 39 57 *23339J9 ^K
Nal coL 40 40 1-16.39763 ^H
Nat. un. 40 56 -867-2460 ^H
^^^^^^^^H Tn the DilTerrnces of Lo]:^. to 20 places ; —
Nal. col. 40 56 11530754 ^|
^^^^^^ Log.of l0102S,thrUtdi(r.«hould be42987,&c.
Los. ro«. 41 44 9-8728849 H
Nat sec 42 9 I-348SI68 ^M
^^^^^K 00021, ihir 2d
^^^^^V Hyp. Lo;; of 837 ehould be 6-7298241.
^^^^V LogUiic lx>g. utuler 17 npp. 57 thould be 5241
^^^^^H ...53.. 8703
^^^^^B 8547
^^^^^^^^ 8387
Nat.Lin. 42 45 -92J3905 ^M
Nit. vermin 42 59 -268417) ^|
Table OitT. (aI. and Departure:— ^H
Diit. ."^ deg. 14 ahould be 2-9169. ^H
Tab. 12. Cornmun and Hyp. Log«:— ^^H
A*al>»lo.L.09shouldbeHyp.Log -20723266. ^H
PREFACE.
The very ample introduction, prefixed to the following collection of
Mathematical Tables, supersedes the necessity of using rauiiy wonis
here by way of preface, and leaves little more to be mentioned than
the necessity and occ&sion of this work, with some accouttt of the
contents and mode of execution.
The undertaking was occasioned by the great incorrectness of all
the editions of Sherwin*s or Gardiner's Tables, and more especially
by the bad arrangement in the 6flh or lust edition. Finding, as
well from the report of others, as from my own experience, that those
editions (to say nothing of the very improper alteration in the form
of the table of sines, tangents, and secants in the last of ihein) were
so very incorrectly printed, the errors being multiplied t)eyond all
tolerable bounds, and no dependence to be placed on them for any
thing of real practice, I was led to undertake the painful office of
preparing a correct edition of another similar work. And I was
lucky enough to meet with a bookseller of sufficient spirit to be at
the great expense of printing the book, as well as to allow me what
I demanded for my trouble in preparing it; which demand, however,
was nothing adequate to the great labour attending it, as I was well
aware that the protiti of the book would not enable him fully (o
reward my pains.
1 have, in the first place, therefore, used all the means in my
power to render the work correct. I began by collating the third or
best edition of Sherwin*'s tables, with some othi-rs of the most perfect
works of the same kind, as Brifjgs's. Vlacq's, Gardiner's quarto book,
&c. ; by which means I detected many errors in each of them, which
had not before been discovered ; ami of these, between twenty and
thirty were in the iwo editions of Gafliner's quarto work, printed at
London in 1742, and at Avignon in 1770. But, besides detecting
many previously unknown errors in the said third ediuon of Sherwin,
which was no more than wa-s expected, I discovereil, witti no small
surprise, that the last figures in the table of logarithms were not
uniformly true to the nearest unit, except in a very few pages at the
VI
PRKKACr,
beginning and end ofllic lablc; though Mr. Gardiner, the editor
that edition, had made the tuble currect in thnt respect in his own
ijnarto work before mentioned, which was also printed in the same
year, 1742. with the said third edition of Sherwin ! Thii errors from
this cause, in that third edition, amounted to several thuiisimds ; and
they have continued to rnn through all the editions of Sherwin ever
since that time ! But they are here corrected. Nor has less atlentioa
been employed in correcting the press, than in previously correcting
the copy ; every proof having been several times read over, and
compared with the best of the books hitherto printed, by several
persons attending to the reading of everv* proof-sheet.
But in giving this edition to the world, I was not satisfied with
barely making it correct. I was aware thnt the materials iheniselves
might be much improved ; and I have accordin^^Iy enlarged, or
Otherwise greatly amended them, in various res|iects. Among the
improvements of the old materials maybe reckoned the following: —
namely, in the large table of logarithms, the [Toportional parts, near
the beginnings are more conveniently arranged, being now all plHce<l
in the same opening of the book where their corresponding differences
occur ; the logarithms to sixty-one figures are brought to their
proper place in the book, and more conveni<:ntly dis|)0!>ed all in one
page ; the large table of sines, tangents, and secants, »s more com-
rnodiously arranged, and rendered more distinct and convenient for
use; the natural smes. tangents, secants, and versed sines, being all
separated from the others, and placed all together on the left-hand
pages, and the logarithmic ones facing them on the right-hand pages;
the common diflerences, in both, set between the two columns to
which each of thera answers; and the versed sines here introduced
into their proper place in the same pages with ihe sines, tangents,
and secants. Besides these, there are some other alterations in the
new tables here given, and the reader will find a number of very
im|>ortant improvements in the description and use of the whole;
especially in the arithmetic of logarithms, and in the resolution of
plane and spherical triangles, according to the present improved
methods of calculation used by the Astronomer Royal, and other
|)ersons the most experienced in these matters.
The improvements in the tables, by the introduction of new
matter, are both great and numerous. The tables numberei' 2, 3,
and 4, are here added, being an entire new set, with their differences,
for finding numbers and logarithms to twenty places. The columns
of common diflerences, in the pages of natural sines, &c., are now
PREPACK.
VII
first introduced : as are also ihe tables of h\'perbotic and logistic
logarithms; ilie Iogari[hmic sines and tangents for every second, in
ihe first two degrees of the quadrant ; together with a table of the
length of arcs, a table to change common and hyperbolic logarithms
from the one to the other, &c., — tlie uses and exempliiLCations of
the whole being very amply detailed.
Royal Mil Acad, ifodwich^
Febmaryy 1765.
*p* Ix the large table of common logarithms, when the first of
the last four figures in any logarithm changes from a 9 to a 0, in
any line, in which case the first three or constant figures are pre-
fixed to the next following line, instead of these three, it often
happens that young beginners by mitit^tlce take out tlie three constant
figures next above the said tine. To guard against this error, the
figures in this edition are so contrived, that where the said change
happens, a bar is placed over the cipher, thus o, through the re-
maining part of the line, in order to catch the eye, and remind the
learner that the change there takes place. In this edition, too, the
black rules formerly drawn across the pages, at the intervals of every
five, or six, or ten lines, have been taken out, leaving thin white
spaces across the pages instead of them. Tliese improvements,
besides that of new and better forme<l figures now introduced, and
other attentions, contribute to render this edition of the ta.bles more
convenient and correct than either of Ihe former ones.
December^ 1800.
C. H,
In \\\\s fifth edition several of the tables have been much en^larged
and improve<l, and some new ones introiluced. Thus, the first large
table of logarithms, which heretofore extended only to 100,000 num-
bers, is now enlarged by one whole sheet more, being continued to
108.000 numbers. Other tables are also extended to more numbers
than formerly : and a new and extensive fable of Hyperbolic Loga-
rithms is introduced after the old one.
London^ May^ 1811.
The seventh edition is now presented to the public with still farther
improvements. In order to reduce the price, the Historical Intro-
duction, which occupicxi 124 pages, is omitted. The impartial,
interesting, and valuable information, contained in that Introduction*
1
VI u
PREFACE.
is now to be found in Dr. Hniion^s Mathematical Tracts, a work
possessed by many purchasers of these Tables : so that the necessity
for continuing its insertion in this volume no longer exists. lliC
tables of logarithms to (>l places^ with their tlifTerences, are also
omitted, as of little, if any, use, to the ordinary purchasers of loga-
rithm tables.
Seven tables of trigonometrical formulae, relative to arcs and
angles, their sums and differences, the differentials of trigonometrical
lines, the sides and angles of plane and spherical triangles, and the
solution of quadratic and cubic equations, are now added ; as well as
the logarithms of many numbers often employed in mathematical
computations. These are known and appreciatetl by the readers- of
Cagnoli, Callet, Borda, Ursin, &c.: but are, as yet, by no means
so well known to English computers as they ought to be, notwith-
standing the exhibition of tables nearly similar, by Mr. F, Baity, in
his elegant and valuable collection for the use of astronomers.
The description and use of the tables have been, in some places,
enlarged and improved. A few pailiculars have been transferred
into this part from the Historical Introduction just mentioned ; and
B page, exhibiting the surd values of the sines of arcs to e\ery thiid
degree in the quadrant. These, with the decimal values of the prin-
cipal surds, as ^3, ^5, ^(5 + \/5), &c,, arranged in immediate
connection with them, will ofteu serve to facilitate the labour of men
of science.
Great care has been taken to render this edition as free from
errata as possible ; and the editor cannot but hope that the im-
provements now introduced, will preserve to Button's Mathematical
Tables the reputation, for accuracy and extensive utihty, which they
have maintained for nearly half a century*.
OLINTHUS GREGOaY,
Roy at Mil. Acad, ff^oolwich,
Manh, 1S30.
DESCRIPTION AND USE
OF
LOGARITHMIC TABLES,
The Dtfinition and Notation of Logarithm»,
LoojLBiTKMS may be considered the indices or arithmetical series of
numbers, adapted tu t[it> terms of a rreumetrical series in such sort that
corresponds to I, or is the index of It, in the geomelricaLs.
Itms
or
or
u
1
2
3
4
I
2
4
8
10
1
2
S
4
1
3
9
27
81
1
2
3
4
I.
10.
100,
1000,
10000
5, &c. indices or lo^rithms.
32, &c. peomelric prog;resston.
5, &e. indices or logarithms.
243, Ac. p^eometric series.
5, &c. indices or logarithms.
100000, &c. geometric series.
Where the same indices serve equally for «ny geometric scries ; and from
which it is evident, that there may be an endless variety of systems of loga-
rithms to the same common numbers, by varying the 2d term. 2, ur 3, or 10.
&c. of the geometric series ; as this will change the original series of terms,
whose indices are the integer numbers, 1, 2, 3, &c. ; then by interpolation
the whole system of numbers may be made to enter the geometricul series,
and receive their proportional logarithms, whether integers or decimals.
Or, the logarithm of any number is the index of that i)ower of some other
number, which is equal to the given number. So, if n be = r", then ihe
logarithm of n is n, which may he either positive or negative, and r any
number whatever, according to the different systems of logarithms. When
N is 1, then » = 0, whatever the value of r is; and consequently the logarithm
of I is always in every system of logarithms. When n is = 1, then N is
= r: consequently r is always the number whose logarithm isl.inevciy
system. When r is = 2-718281828459, Ac. the indices are the h>perholic
logarilhmB. such as in our 5th table : so that n is the hyperbolic logarithm uf
(2'7I8, &c.)*. fine in the common logarithms, i* is := 10 ; so that Ihe
common logarithm of any number (10") is (n) the index of that power of 10
which is equul to the said nuniber. So 1000, being the 3d power of 10,
has 3 for its Kigarithm ; and if 50 be = 10 . Dien is I. G9S97 the common
logarithm of 50. And hence it follows, (hat (Itis decuple series of terms
10* . l(f , 10*, 10^ 10\ 10~\ lO"*, lO"". lO"*,
or 10000, 1000, 100, 10 , 1 , 1 ,01 , -001 , '0001 ,
have 4 . 3,2,1,0 ,—1 . — 2 , — 3 , — 4 ,
respectively for their logarithms.
The logarithm of a number comprehended between any two terms of the
first series, is included between the two corresponding terms of the latter
and therefore that logarithm will consist of the same index (whether positive
or negative) as the less of those two terms, together with a decimal fraction.
which will always be positive. So the number 50, falling between 10 and
100, its logarithm will fall between 1 and 2, and is = 1-69897, the index of
the less term, together with the same decimal *69897 as before : also the
number 05, falling between the terms I and *01, its logarithm will
DESCRIPTION AND USE
fall between — 1 and — 2. and is indeed = - 2 + -69897. The index i9
also called the charaeteriBtic of the logarithms, and i.s alwiiys an inle<rer
either positive nr Tiep"ulivp, op else = ; and it shows what pliu:e is ocsMijiied
by the first sicruificunt lii^ure of the ifiven number, either above or below ihc
place of units, being; in llie former cas*^ -|" "i" positive, in the latter — or
ne!i;aiive.
When the characteristic of a losrarithm isnei^tive, the si^n — is commonly
set nv«*r it. to distinp^iiish it from the decimal part, which beinuT the logarithm
found in the tables is always positive : bo — *2 -f- '69897, or the lo^ritlun of
•05» is written thus 5'69697. But on some occasions it is convenient to
reduce the whole expression to a nejfative forrp ; which is done by making
the characteristic tii^ure less by l»and taking the arithmetical complement nf
ihe decimal, that is, he^inninpf at the left hand, subtract each ti^urc from 9,
except the last sitrnificunl liirure, which subtruct from 10; so shall the re-
mainders furm the log-nrith in entirely ne<7ative. Thus the Io<rarithm of *U3,
which is S-69897, or - 2 -f- '69897, is also ex[)resse<I by — 130103. which
is whtvlly negative. It is also sonietimes thou3;ht more convenient to express
such lo^rarithms wholly as positive, namely, by only jninin^ to the tabidar
decimal the complement of the index to 10: in which way the at)o\e too^a-
riilim is expressed by 8*69897 ; which is only increasing; the indices in the
scale by 10 ; and is now commonly done in the tables of lo^^aritiiin sines,
tangents, &c. It is also convenient, in many operations with logarithms, to
take their arithmetical complements, which is done, by beginning at the left
hand, and subtracting every figure from 9, but the last figure from 10 . bo ihc
arithmetical complement
of 1-69897 f and of ^-69997") where the index - 2, being negative, ia added
is 8-30103 (^ is 11-30103 Jto 9, and makes Ih
Tks Propertiet of Losarithmt,
From the definition of logarithms, cither as being the indices of a series of
geomctricals, or as the imiices of the powers of the same root, it follows, ihot
the multiplication of the numbers will answer to the addition of their loga-
rithms ; ttic division uf numbers, to the subtraction of their logarithms; the
raising of powers* to the multiplying the logarithm of the root by the index
uf the power; and the extracting of roots, to the dividing the logarithm of
the given number by the index of the root required to be extracted. So,
using L. to denote the logarithm of the quantity which follows it: —
Ut. L. a6 or a X 6 is =r l.
L. 18 or 3 X 6 is =: l.
L. 5 X 9 X 73 is = L.
2d. L. rt -J- 6 is = L,
L. 18 -5- 6 Is = I..
L. 79 X 3-r9 is = L.
L. ^ or 1 -f- ^ is ^ L.
L, — or I -r '< IS = —
n
3 + I. 6
5 + L. 9 + L
a — L. 6
18 - L. 6
79 -f. L. 5 - I. 9
1 - L. 2 = -
73
L 2 :^ - I.. 2
L. n,
3<l. t. r*is = n L.
L. r'
or L. V '' is = — L. r
/i
L. r'
m
IS = —
n
L. r.
L. 2* is = 6 L. 2; L. 2» or L. V 2 is = i t. 2 ; L. 2' is = ^ i. 2.
Thus, any number and its reciprocal have the same logarithm, but with
aintrury signs; and the sum of the logarithms of any number ond its com-
plement, ifl equal to 0.
OF LOGARITHMIC TADLE3.
XI
To conttntct Losat'Uhmt,
[t is shown in my Hiaiory of LogarUhmt^ llial ttie logarithm uP — in =
2 J y y a7
— X : - -i i + — i + — = &c , where z is the sum and x ihe difference
m Z 32" i::* 72'
of a and 6; also m = 2-302585092994, &c., ihe hyp. logarithm of 10.
1*herefore if a and 6 be any two numbers diHering only by unity, bo Ihot x or
2
6 •— a may be = 1 ; then shall the logarithm oi h be = l. a + — X :
m
- + — i -f~ j~i ^- VVhich 'gives this rule in word» at length : call z the
sum of any number (whose loi^arithm is souf^ht) and the number next less
by unity ; divide -SSBhSSOGSS, &c. (or 2 -h 2'3025, &c.) by 3. Jind reserve
the quotient: divide tlie reserved quotient by the square of z, and re-
ser\'e this quotient: divide this last quotient al»o by tlie square of «, and
agnin reserve this quotient: and thus proceed continiiutly, dividing tlic hist
quotient by the square of 2, as long as division can be made. Then write
these quotients orderly under one another, the first uppermost, and divide
them respectively by the uneven numbers I, 3, h, 7, 9, 11. &c., as long as
division can l>e made: thut is, divide tlie first reserved quotient by I, the 2d
by 3, Ihe 3d by 5, the 4lh by 7, &c. Add all these last quotients together,
then the sum will be the logarithm of 6 -f- fl ; and therefore to this logarithm
adding also the logarithm of a the next less number, the sum will be the re>
quired logarithm of b the number proposed.
Eiamplc I. To Jind the Log, of 2.
Here the next less number is 1
3) -668598964
9) -289529654
9) 32169962
9) 3574440
9) 397160
9) 44129
9) 4903
9) 545
9) 61
and 2 + I = 3 =z. whose square is 9. Tlien
1)
3)
5)
7)
9)
H)
13)
15)
•289529654
32169962
3574440
397160
44139
4903
545
61
289529654
10723321
714888
56737
4903
446
42
4
Log, \ -31.1029995
Add Log. I .. -000000000
Log. of 2 -301029995
KxampU 2. To find (he Log. ofS.
Here the tiext less number is 2, and 2 + 3 = 5 =
divide by which always multiply by *04. Then
whose square i) 25, lo
5 )
25)
25)
25)
25>
25)
868588964
1737 17793
6948712
277948
11118
445
18
1) 173717793 (173717793
3) 6948712 ( 2316237
5) 277948 ( 55590
7) 11118 ( 1588
9) 448 ( 50
11) 1 8 ( ^ 2
Log. I -176091260
Log. 2 add -301029995
Log. 3 -477121255
nil DESCRIPTION ANP USE
Then, because the sum of the logarithms ofnumtrers gives the Ingiinthin
of their prmiuct, aiul the difference of the lug^rithtns gives the logarithm of
the quotient of the numbers, from the above two logarithms, and the toga*
rithm of 10 which is I, we may raise a great many other logarithms, thus :
Example 3.
Because 2X2 = 4. therefore lo L. 2. . . -3010299951
addL.? •3010299951-
sum is L. 4 "602059991^^
• — ^— —
Example 4.
H4*c&u8« 2X3=6. therefore to L. 2 '301029995
odd L. 3 -477121255
sum is L. 6 -778151250
Example 5.
Because 2» = 8. therefore L. 2 -301029995}
mult, by 3 3
gives L. 8 '903089987
Example 6.
Because 3< = 9, therefore L. 3 ■47712l2547„
mult, by 2 2
gives L. 9 "954242509
Example 7.
Because i* = 5, tlierefore from L. lU.. I'OOOOOOOOO
lake K 2 '301029995|
leaves L. 5 ^698970004 J
Example 8.
Because 12 = 3 x 4, therefore to L. 3 -477121255
add L. 4 -602059991
gives L. 12 1-079181246
And thus, computing by the general rule, the logarithms of the other
prime numbers, 7. 11, 13, 17, 19, 23. Ac. ; and then using composition and
division, we may easily lind as many logarithms aa we please, or may speedily
examine any logarithm in the table.
See, farther, the History of Logarithms, In my Tracts, vol. i. 8to.
»u
THE DKSCRIPTION AND USE OF THE TABLES.
Thf following collection consists of various tables, in the following orcer,
viz. 1. A large laMe of logarithms to 7 places of 6g-ure8 ; 2. A table for find-
ing: iogarithins and numbers to 20 places ; 3. Logarithms to 20 places, with
Uieir 1st, 2d, and 3il ditferences ; 4. Another table of lo^rilhms to 20
places, with tlieir Isl, 2il, and 3d dilFercnces ; 5. Hyperbolic loj^arithms ;
6. Logistic logarithms; 7. Logarithmic bines and tangents to every second
of the first 2 degrees; 8. Natural and logarithmic sines, tangents, secants,
und versed sines, with their ditferences to every minute of the quadrant.
After which follow several smaller tables : as, a table of the lengths of cir-
cular arcs ; a traverse table, or table of difference of latitude and departure,
to every degree und (piarier point of the compass ; a table for changing the
common logarithms into hyperbolic logarithms; and a table of the names
and number of degrees, &c.. in every point of the compass ; tables of ubei'ul
trigonometrical formulas &c. Of each of which in their order.
Of ihe large Table of Logarithms,
The first is the large table of logarithms, to all numbers from 1 to 108000 ;
by which may be found the logarithm to any number, and the number lo any
logarithm, to 7 places of fig^ures. This table consists of two parts; the first
contains, in 4 pages, the first 1000 numbers, with tlieir corresponding loga-
rithms in adjacent columns; the second contains all the lObOOO numbers ond
their logarithms, with the ditferences and proportional parts, disposed as
follows: in the first colututi of euch page are the first 4 figures of the num-
bers, and along the top and bottom r)f the columns is the 5tli figure, in which
columns are placed all the logarithms, the lirsl 3 fi.;ures of each logarithm
being at the beginning of the lines in the fir^l column of logarithms, signed
at the top and bottom, and the oiher 4 figures in the remaining columns.
Sometimes the first three figures of the loguritlims are tbund in the tine next
below tlie number, viz. when the fourth figures have changed from S's lo 0*s,
in which case, a bur is pbiced over the first ciphers in the whole of tlial line
to catch the eye, thus O. Afier the 10 columns of logaritluns stands their
column of diiierences. signed D ; and lastly, after that, the column of pro-
portional parts, signed Pro. Pts., showing what proportional part uf each
ditferoncc corresponds to 1, :2, 3, &c., ilie whole dilfcrence answering lo lU ;
orshowmg the -j^j, -j'^, -ff^, &c., of the dilierences.
NoU, The logarithms in these columns ure all supposed to be decimals,
and their corresponding natural numbers may be either integers or decimals
or mixt numbers ; for the same figures, whatever be their dennniination,
have the same decimal logarithm, and these differ oidy in the index or
characteristic, which is the integer number to be prefixed to the decimal part
of the logarithm ; and this is always the number which expresses the distance
of the highest denominution. or left-hand figure, of the natural number, from
the units place. So that, if ihe natural nuinbt;r consist of only one place of
integers, the index of its log. wilt be U : if of 2, 3. 4, 5, &c., the index of its
logarithm will be respectively I, 2, 3, 4, &c., being I less than the number
of integer places : and the same figures made negative will give the index
of the logarithm of a decimal, viz. if the natural number be u decimal, and
its first significant figure be in the place of primes, 2d5, Sds, 4ths, &c., the
index of its logarithm will be respectively 1, 2, 3, 4. &c. ; or the figure which
expresses the distance of the first place of the natural number from the
XlV
DESCRIPTION AND USK
Number
US4r. !
'Jg:^i
3 423409-
265- 1
2 423409:
2C-51
1-4234097
2*651
0-4234097
•2651
T-4a34oy7
■02651
2 4234097 ;
002G51
3 4234097
units place, but with a nef^ative sign, as the number is below the place o(
units, the s);;n being written abovt; the index instead of before it, as that part
only of iJie logarithms is to be considt'red as ncf^ntivc, the decimal part of it
being alwayj; affirmative. And in the uritlimetical operations of addition
and subtraction with logarithms, the iici^ative indexes will have llie contrary
effect to that of the decimal pari of the Ion;arilhm, viz. when the hij^ritlim is
to be addcti, the figure of the negative index must be subtracli'd, et rice vtr»a
Hence, if 4234097 l^ the tabular or decimal part
of the logarithm belonging to the figures 2651,
without any regard to iheir particular denomi-
nations ; then according as they arc varied with
respect to the number of decimals, as in the 1st
annexed column, the index of their logarithm,
and the complete logarithm, will vary as in the
2d column here annexed. And hence, like as
when the natural number is given, we find the
index of its logarithm by counting bow far il.^
first figure on the left hand is from the units
place; so when a lo^^arithm is given the denominations of the figures in its
natural number will be found by placing the decimal point so, that the num-
ber of integer places may be 1 mure than that of the index when positive^ or
by setting the firist significant figure in that decimal placCf which is expressed
by the number of the index when negative.
Of finding the Logarithm of a given Number^ or the number to a given
Logarithm,
1. To find the Logarithm of a Number eonsi$ling of S figures.
Find the nnmber in the column of numbern in one of the first 4 pag«s of
the table, auil immediately on the right of it is its logarithm »tught. So the
Logarithm of 7*2 is I •8573325, and the logarithm of 3*33 is 0*5224442. when
the proper index is supplied.
2. To find the Logarithm of a Number comitUng ofi Places.
In llie first column (signed N) in some one of the pages of the table after
the first four, find the given number, then against it in the 2d column (signed
0) is the logarithm sought. So the logarithm of 22bA is 33529539, and
that of 31 32 is 1-4958218.
3. To find the Logarithm of a Number consisting of 5 Places,
Find the first 4 figures of the given number in the first column as before,
and the 5lli figure at the lop or bottom ; then the 7 figures of the logarithm
are found in two columns on the line of the first 4 figures of the given num-
ber, viz. the first 3 figures of the lugurithm are tlie firtit 3 common figures of
the 2d column (signed 0), ami the last 4 figures are on the same line, but in
the column signed wJlh the 5th figure of the given number. So the loga-
rithm of 232U4 is 4 3655029, uiid that of 746 40 is 2-8729716, and that of
■083178 is ii-9200095.
Noie^ When the last four figures of the logarithm begin with a cipher, or
any figure less than the lust four in the 2d column begins with, then the first
3 common figures are those in the next lower line : so, in the lust example,
the first 3 common figures are 920. and not 919. This is indicated by the
bar over llif tirst cipher in 0095, as already exj)iained
OF THE TABLES.
sv
4. Tojind the Logarithm of a Nnmher of 6 Places.
Find the locrarithm of ilie first five fig-ures hy the last Hrlicle and take llie
ditl'erence between that logarithm and the next (ollowino; loj;anthm, or (which
is the same thin^) find the dilFerence nearest opposite in tjie last column but
one, signed D; then under that difference in the last colnnm (of proportional
parts) and ajrainst the 6th figure of the given number, is tlie part to be added
to the logarithm before found for the first 5 figures, the Bum being the loga-
rithm sought. So to find the logarithm of 3-109-26 : the logarithm of 34092
the first 5 figures, being 5326525, and the common difference 127, under
which and against 6 in the loist column is 76, which being added to the
former lognrithm, and the proper index prefixed, i. e. 3 for 4 places of
whole numbers, we have 3*5326601 for the whole logarithm required.
Numb,
114092
6
5. Tojind the Loi^arUhm of a Number of 7 Places.
Find the logarithm of the first 5 figures by the 3d article, and of the sixth
figure by the 4th article; then for the higarithm of the 7ih figure, divide its
proportional part by 10, that is, set it one place farther to the right hand
than the last figure of the logarithm reaches ; add all the three together, and
their sum will be the logarithm required.
Tims, to find the logarithm of 3-409264. The
several parts being taken out according to the
rule, and placed as in the margin, the sum gives
the whole logarithm sought.
Noie^ In the same way we might take out the
proportional part of an 6ih figure, divrdiug its
tabular part by lOO, or setting it two places farther
to the right hand than the first logarithm. Or the whole proportional part
for any number of figures above five, may be found at once, by multiplying
the common tabular ditference of the logarithms, found as
before, by all the figures after the 5th, cutting off from the
product as many figures as we multiply by, and adding the
rest to the logarithm of the first 5 figures before found.
So in the last example above, having found the common
difference 127, multiplying it by 64 the last two figures,
cutting off two, add the rest to the logarithm of the first 5,
as in the margin.
For another example, suppose we wanted the logarithm of the following
8 figures, 34092648. The operation by both methods will be as below.
■ 127
Logar.
5326525
76
4 . 5J
3-409264 . U -5326606
127
64
608
762
61. 2S
r>326525
0:i3 26606
34092 5326525
6 76
4 5,1
8 1.02
34092648 7 • 5326607
643
1016
508
762
82,296
5326525
7 * 5326607 the same as the oilier.
6. To find the Logarithm of a Fulmar Fraelion^ or of a Mixt Number,
Kilhcr reduce the vulgar fraction to a dtcimdl, and find its logarithm ai?
above. Or else (having reduced the mixt number to an improper fraction).
xvi DESCRIPTION AND USE
subtract ihe log-arithm of the denominator Irom the logat ilUm of the uume
rator, aiid the remainder will be Ihe logarithm of the fraction sought.
Example 1.
To find the loff. ot -/^ or 0'I675.
From log of 3 0-4771213
Tuke log. of 16 1*2041200
Rem. loer- of -^^ or • 1875 1-2730013
Exampfe 2.
To find the log. of ISjorS.
From log. of 55 1-7403627
Take log, of 4 06020600
Leaves log. of ¥ or 13 '75 I ' 1383027
7. Tojitid the Natural Ntwther anncerin^ to any gictn Logarithni.
Find the firsl 3 figures, next after the inder of Uie given logarithm, in the
tec<nid column, signed 0, und the other 4 figures on the same lirie in one of
ihe nine following columns; if the figures of the logarithm l>e thus found
exactly, then on the same line in the first column are llie first four figures of
the natural numl>er, and the 5th \s at the top or bottom of that column
in which the last four fiin'res of the log. were found. So to find tlie number
answering to the logarithm 2*dS9010S. In p. 63 I find the first three
figures 5&9, and in column 6 of the line above ure found the other four -0109
(becaust* the first three common figures are supposed to begin at that part of
the line above where they are placed) : then on the same line in the column
of numbers stand ihe first four figures 389" I, and 6 at the lop of the column,
making in alt 333*16 for the numl>er sought; having placed the decimal
point so as to make three integers, being 1 more than 2 the index of the
given logarithm.
Bui if the given logarithm he not found exactly in the table, subtruci the
next less tabular logarithm from it, and look for the remainder in the pro-
portional parts under the dilference between the two tabular logarithms next
less and greater than the given logarithm, and against it, or the part next
less, is a 6lh figure to be annexed to the five figures before found. And if
the reniaiudiT lie not found exactly in the proportional parts, subtract the
next less part from it, and annex a ci]>hei to this 2d remainder, then against
the nearest proportional part (either greater or less) is a 7th figure to be
annexed lu the six before tbund. And that figure will be the nearest lo the
truth in that place, eillier too much or too little.
ExainpU.
To find the number answering to the logaritlim 1*2335678
The next less tab. log. is the log. of 17122, viz. 2335545
1st rem. 133
The dtfierence is 254 J ^
and the Ubie of pro. pU. givesl „ ^ ^d rem. 60
*^ *^ ** L . 2 for Oie part 51
So that the number sought is 17*12252, making two integers for Iheitidea 1
OF THE TABLES.
3IV|{
254^ 133,00 (53
' i27.0
Or the 6lh and 7th As^res may be tbiind without the table of proportional
paru, by dividing the first remainder by the labtilar dif-
ference, annexing one cipher to the dividend tor each
figure to be found. So, in the last example, the re-
muinder 133, with two ciphers annexed, being; divided e^^
by the tabular diltereiice 254, an in the uiar^u, the
quotient gives 52 fur the 6th and 7th fi<i:ures, the same as before. In like
manner may be found the numbers to the followinj^f io^nrilhm^.
Logar. 1-2345678 13-7343003
Numb. 17-10200 5-423758
T'0921406| 5-3720468
1236348 -02355303
4-6123004
40954*39
3-2946809
1970974
OF LOGARITHMICAL ARITHMETIC.
I. Multiplication hy Logarithms.
Add together the logarithms of all the factors ; then the sum U a logarithm,
the natural number corresponding to which, being found in the table, will be
the product required.
Observing to add, to the sum of the affirmative indices, what is carried
from the sum of the decimal parts of the loyarilhms.
And thai the di^'crcncc between the affirmative and negative indices, ia tu
oe taken for the index to the logarithm of tlic product.
Example 1.
To multiply 23 14 by 5 062.
23-14 its tog. is i-3613634
5 062 lis log. is 0-7013221
Product 1171347 2 0686855
Example 2.
To multiply 2'58I926 by 3-457291.
2-581926 its log. i» 0*4119438
3-457291 0-5387359
Product 8-92647 09506797
Example 3.
To multiply 3 902, and 597*16, and 0314728 all together.
3 902 its log. is 0'59I2S73
597 16 2-7760907
•0314728 2-4979353
Product 73-33533 1 •8653 133
The £ cancels the 2, and the I to carry from (he decimals is set down.
Example 4.
To iDdUiply 3-586 and 21046, and 0'8372, and 00294, all together.
3-586 its log. is 5546103
2-1046 3231696
0-8372 1-92*28292
0294 2-4683473
Product -1857618 I 2699564
Here the 2 to carry cancels the S, and there remains the T to set down
miM
xvin
DESCRIPTION AND USE
II. Division by Logarithma,
Frnm the lo^rithm of the dividend, subtract the lo^rithm of ihe divisor;
the remainder is a togarithm, wliose corresponding number will be the
qunlienl required.
. But first observe to chang^e the si{^ of the index of the lofraritbro of the
divisor, viz. from neg^ative to affirmative, or from affirmative to nejjaiive ;
then take the sum of the indices if they be of the same kind, or their difference
when of diflerent kinds, with the siga of the greater* for the index to the
logarithm of the quotient.
When 1 is borrowed in the left-hand place of the decimal part of the
lop^arithm, add it to the index of the logarithm of llie divisor when thai index
is affirmative, but subtract it when neg;auvc ; then let the index thus found
be changed, and worked with as before.
Example 1.
To divide 24163 by 4567.
Dividend 24163 its log. 4 3S31509
Divisor 4&67. .. 3-6596310
Quotient 5*290782 U-7235199
Ej-ample 3
To divide 37-149 1^ 523 76.
Divid. 37- 149 its log I -559947
Divis. 523 76 2 719132S
Quot. 07092752 £'8508148
Example 3.
To divide 06314 by '007241.
Divid. -06314 its log. 2-8003046
Divis. -007241 3*8597985
Quot. 8-719792 09405061
Here 1 carried from the decimals to the 9 makes it become 2, which taken
from the other Sj leaves remaining.
Example 4.
To divide -7438 by 129476.
DiTid. -7438 its log. T-8714562
Divis. 12-9476 11121893
Quot, -05744694 37592669
Here the S taken from the 1 makes it become & to set down.
III. The Rule of Three, or Proportion,
Add '.hii logarithms of the 2d and 3d terms together, and from their sum
subtract the logarithm of the 1st, bv llie foregoing niles; the remainder will
be the logarithm of the 4th term required.
Or in any compound proportion whatever, add together the logarithms of
OK TliE TABLES.
XIX
&1I the t«rms that are to be multiplied, and from that sum lake the sum of the
others; the remainder will be the logarithm of the term sought.
But instead of subtractings any logarithm, wc may add its complement, and
the result will be the same. By the complement is meant the logtirithm of
the leciprocal of the jyiven number, or the remainder by takings the g;iven
logaritJini from or from 10, changing: l^'c radix fniiii to 10; the eaitiest
method of doing which, is to begin at the lefl-hand, and subtract each figure
from 9, except the last significant figure on the right hand, which mtist be
subtracted from 10. But when the index is negative, add it to 9, and subtract
the rest as before. And for every complement that is added, subtract 10 from
the last sum of the indices.
Example I.
To find a 4th proportional to 72 34. and 2.519, and 357*4862.
As 72-34 . comp. log, . . . 81406215
To 2 519 0-1012282
So357"4862 2 5532592
To 12-44827
1-0961089
Example 2
Tn find a 3d proportional to 12-796 and 324718.
As 12-796 . comp log. . 8*8929258
To 3 24718 0-5115064
So 3 24718 0-5115064
To '3240216 1-9159386
Example S.
To find a number in proportion to '379145 as -65132 is to 0649.
As 0649 . comp. log 111877553
To -85132 .. 19300928
So '379145 . T-579S054
To 4*973401 6966535
Example 4.
If the interest of 100/. for a year or 365 days be 4-5/., what will be the in-
terest of 279*25/. for 274 days ?
._/100-i fS'OOOOOOO
^"l365r°"'P '°ff 17-4377071
,p J 279-25 2-4459932
t274 2 4377506
So 4-5 6532125
To 9-433296 9746634
IV. Involution, or RaUin^ of l^owen.
Multiply the logarithm of the number given by the proposed index of the
power, and the prr)d(ict will be the logarithm of the power sought
Note, In multiplying a logarithm with a negative index by ai{y nflirmative
number, the product will be negative. — But what is to be carried from the
b 2
•XX DESCRIPTION AND USE
decimal part of ihe lofrarilhm will be affirmalivc-Thepefore the diirerenee
will be the index of the product; and it is to be accounted of the same kind
with the greater
To find the 2d power of 2-5791.
Root 2-5791 iulo^ 04 II 4682
index 2
Power G-6j1756 "^8229364
•
Example 2.
To find the cube of 307146.
Root 307146 its log 0-4673449
index S
Power 2S-97575 r4620347
Erampte 3.
To find the 4 th power of '09 163.
Root 09163 its log 2*9620377
index 4
Power 0000704938 5 8481508
Here 4 limes the negative index being 8, and 3 carried on, the difference
5 is the index of the product.
Example 4.
To find the 365th power of 10045.
Root 1*0045 il9 log 0019499
index 365
97495
116994
58497
Power 5*148888 0-7117135
V, Etoluliofi, or Extradion of Roott.
Divide tne ogarilhm of the power, or given number, by its index, and the
quotient will be the logarithm of the root required.
Sole, When the index of the logarithm is negative, and the divisor is not
exactly contained in it without a remainder, increase it by such a number as
will make it exactly divisible; and carry tlie units borrowed, an so mnny
tens, (o the left-hand place nf the decimal part of Ihe logarithm ; then divide
the results by the index uf Uie root
Example 1
To find the square root of 365.
Power 365 2 ) 2 5622929
Root 1910498 12811465
OF THE TABLES.
Example 2.
To find the cube root of 12345.
Power 1-2345 3) 4 0914911
Root 231U62 1-363S304
Example 3.
To find the lOlh root of 2.
Power 2 10)0 3010300
Root 1U71773 0301030
Example 4.
To Hnd the 365th root of 1 045.
Powerl045 865)00191163
Root I000i21 O*OU0U524
1X1
Example 5.
To find the square root of -093.
Power 093 2 ) 8 9G84S29
Root -304969 1*48 124 15
Here the divisor 2 is contained exactly once in % the ne^tive index, there-
fore the index of the quotient is I.
Exumpin 6.
To find the cube root of 00049.
Power00048 3)4 6812412
Roiil 07829735 g-893747 1
Here the divisor 3 not brinsf exactly contained in 4, aii^nent it by 2, to
make it become 6. in which the divisor is conlaiiied just 2 times ; »nd the 2
borrowed heU\^ carried to the other figures 6, &c, makes 2"6912412, which
divided by 3 gives '8937471.
OF THE TABLKS FOR LOGARITHMS TO TWENTY PLACES-
TiiEsB nre tables 2d, 3d, and 4lh. Of these, table 2 contains a1! numbers
from 1 to 1000. and nil uneven numbers from 1000 to 1 161 ; with their
lograrithiiis to Iwenly places; table 3 oonluins all numbers from lUlOOO to
101139, wi(h their log-arithuis to twenty jilaces and the Ul, 2d, and 3d dif-
ferences of those logarithms : and table 4 euntains all logarithms re^rularly
from 00001 lo 00139, wilh their (orrcspondin^ natural numbers to twenty
places, as also the 1st, 2d, and 3d differences of those numbers. And by
means of them may be found the lu<ritrithm to any other number, and the
number to any other logarithm, to twenty places of figures.
(I.) Tojind the Logaritlimx lo given Numbat.
Cask 1. If the given number 6 be found in any of these three tables;
then it^ logarithm b is in the line even with it.
toAi DESCRIPTION AND USE
Case S. If 6 is known to be llie product or quotient of numbers found
in these tables ; then B is the sum or difference of the logarithms of those
numbers.
Case 3. If a\ the first six significant fibres of a given number b\ be
found in table 3 ; let a' be an integer, a' its logarithm ; c the remaining
figures of 6* ; x the compltmenl of i to d' or 1 ; d', d", d'", the Ui. 2d. 3d
dilferencea of the log-arilhms in the same line with a' ; / = ^ d"' X
^+ 1 + d" : Then b' the logarithm of the number 6' will be
(d' X J) + a' to la"!
( J J u' _|_ o' X S) 4- a' to 1 7 > places of figures nearly.
(ix/ + o' X 5) + a' to 20)
EsampU I.
Given the number 1/ = 001010,26227,6351. to find o' its logarithm nearly
to twelve places.
Here a'=r 101026 a' = 00443,31579.747
J = 2276351 J d'. . .. -f 9785.618-
1/=: 429881746 b' = £'00443»4 1365,365-
Example 2.
Given 6' = 001010.26227.63509,626, lo find a' iu log. nearly (o 17
places. Here a' = 101026.
5 = 0-22763.509626 ; j = 0'772365 ; d' = 42988,174579 ; d" =: 425510.
Nowi*D" 16432,45
d' 42988.17457,80
jxp" -\- o' 42988.33s90T3n'
J X 0" -f d' X > , , . 9785.6ii46G.42
a' ■ 00443,31579.74695.33
And (4 X d" + d' X J) + A', or b' . 200443,4 1365,40 161,75
Example 3.
Given i/ = 001010.26227,63500.62573, 17345. lo find b' its log. nearly
to 20 places. a' = 101026.
S = 0*22763.50962,573173; x =: 772363490374; x + 1 = 1'772365 ;
o' = 42938,17457.86301 ; d" = 42550,96343 ; d'" = 84236.
Now i d"* X X + 1 49766
of* ,,.#•* 42550.96343
/ , 4255l74^iQ9
Jx/ 16432.62757
d' 42988,17457,86301
j^ j/+ d' 4298M389b,49058
4x/-fD' X J 9785.65466,45604
a' ■ 00443,31579,74695.32791
And b' S,0044S,41365,40161.78395
Case 4. If the number b do not come under one of the preceding cues:
put a for the first five figures of 6 ; n for 101. the least, or some one, of the
(1 n
number?} in tabic 3 ; then — or — = a is lo be had in table 3, with A ita
n m
OF THE TABLES. xxiii
6
lo^richm; let f = — or ba, and a' the first six significant fig^iires of b'
(found in table 3) be an inte^r, and a' its logarithm ; put i for the remain-
ing figures or A*; J the complement of £ to d' ; d\ d", e'", the 1st, 2d, 3d
HifTerences of the logarithms in the same line wiih k' ij*:= J d'" X x -f- I + d".
Then a the logarithm of the number h wilt be
D^ X * + A' ± A = b' ± A to 12^
^ J d" 4- d' X « + a' ± A = b' ± A (o 17 I places of figures nearly.
l^f + d' X « + a' ± A = b' ± A to 20 J
hiample.
Given 6' = 3*141&9|26535,89793,2d846,26434, to find d to twenty places.
Here a = 31413 Lei fl = — = 311.
n
Then V =r — = 001010.15840,95144,02970,57; o' = 101015.
a
S = 84095,14402.97057; j= 0.15904.85597; j + 1 = 1-15905;
©' := 42992.855 74.0633 7 ; d" = 42560,23099 ; d'" = 84263.
Now ^ d'" X jr + I 32555
i/' 42560,23099
/ 42560.5565 4
)fxf 3384,59751
d' 42992,65571.06337
^je/+ d' . . .' 42992.8S95S.66093
ix/H- 1/ X a 36154.93212.03919
a' 0043R.5868I»74054,30961
A 49276.03S 90. 26837 .50555
And B 0-49714,98726^94T33^5435
Or let a = — = 3*216 = 0'536 X 6.
a
Then b' = bn = 10-1033€,19739,44775.0549; a' = 101033.
* = 0'61973.94477,50549 ; x = 38026^055225 ; x + 1 = 1-38026;
o' z= 429S5.1961 S.8076 0; d" = 42545,06747 ; d"' = 84219.
Now 4D^XJr4-l 38748
d" . 42545,06747
/ 42545.45495
J x/ 8089,17910
d' 42 985.19618.60760
ixf+o' 42985.27707.9B670
|x/-fD'x« 26639,67187,88811
a' 00446.32488.03359.618 54
^ |-00-H6.J9127.7I)547,5U665
A 0-5U73l.6O400.764 13,65230
B = d' - A 0-497 14,98726,94133.85435
(II.) To find the Numbert to ^iven Lvgarithnut,
Care 1. When the logarithm n is found in any of ihese three tables ; then
its uumber 6 is in llie line even with it.
DESCRIPTION AND USE
Case 2. Iftlie first five figures (omtUin^ the index) ofa g^iven lo^rithin
b', be between 00432 and 0049*2 : take them as nn iiitef^er, and put a' ard
c' for the logarithms, in table 3, next less and greater iUnn i/, a' and cf their
numbers ; lei d' (= c' — a') and d'' be the Ut and 2d differences in the line
with .'; A = B- - A'; <?= (.Z - 0-=) 1 ; X = ^^ ; « = -;-^-|_,, •
then 6' = a' -f- i, newly true to 17 places of figures.
Example,
Given the !og:orlthra b' =5,00446.59127.70547.507
to find f its number. a'= 5,00445.32488,03339,6 19
tf'= 101033 ^ = 0-26039.67187,888
a 0-61973.944776 D' = 0-42985.19618,808
6' =r 101033-61973.944776 I^ - A = 0- 16345,52430,920
X = 0-38026
d"=: 0-00000,4954 5
ixD" = 000000.08089,1
d' + i X i>" = 0-42»S5,27707.9
But when any other log^arilhm b is given, subduct '004321 from (he first
six figures ofa : mil the remainder r. and let a be the logarithm in table 2,
next less than ii. or next greater than the complement ofn, and aitsnumber:
then d' = B ~ A. ur o' = B + A, will be within the limits of table 3, and 6
will be found as in the preceding example ; and if b' = b — a, then b ^ al/ ;
6'
or if b' = B 4- A, then & := — .
a
Cksr. 3. If a', the first five figures (omitting the index) of a given loga-
rithm h\ be found in table 4 : let a' be its number ; and put a' as an integer,
and £^ the remaining figures of b', and x the complement of d to d'; <f,
d",d"\ the 1st, 2d, 3d ditferences of the numbers in the same line with o' ;
/^d" — ^(T'Xx-J-l: then the number fr', whose logarithm is b', will be
(d^ X A) + «' to 12^
id' - ^x d" X A)+fl' tonj-pli
id' - Jx/ X £i) + a' ... to 20
laces of figures nearly.
Example,
Given the logarithm b' = 000006.933 1 1 ,377 1 1 .69929, to find b* its num-
ber to 20 places. Here a' = 00006.
A = 0-93311,37711,69929; x = 006688.622883; x -|- 1 = 1 066886;
(f = 23029,29742,21293 ; <i"= 53027,52746 ; cf =1 22100.
43422
Now i rf"' X X -f 1
dr
/
And 6
53027. 52746
53027.09324
^i/ 1773.39115
d! 23029,29742, 21293
23029.2 7969,82178
2l4S9,93St>K72060
a* 10001.38164.64943,57474
100015,96535,87452,9474
cf-ix/ ....
(f-Jx/x ^
OK THE TABLES. xxv
Casb 4. If llie lop^aritlim b do not come under one of the precedinsf cases.
Pot A lor the lo'^arithm in table t?, next les.s thun b, or next greater than the
complementer B, and a its number; let 0'= b — a, or b' = u -(- a ; and a',
the first five figures of b'^ may be had in table 4, with a' its number; put a'
as an integer, and lot A be the remaining fif^ures of b' ; x the comptemenl of
A to u'; d\ cf', d'''\ the IsC, 2d, 3d differences of the numbers in the same
line with a' ; f= d'^ — ^ rf"' x Jf -f- 1 : ih'*n the number b\ whose logarithm
is b\ will be
d' x A -^ a' X a = a^ to 1 1 -J
rf* — i X d' X A -j- of X a = oA' to 16 > places of figures nearly.
<f - ix/ X A 4- a' X a — fl6' to 19 3
Erampie.
Given b = 4^46372,61 1 72,07 184, 15204. to find b its number
Let 4 = 1-46239.79978,98956,08733. a = 29.
b'= b - A = 5^00132,81193,08228.06471. a'= 00132
A =0-81193.08228,06471; x = 018806.91772 ; x-|- 1 = 1*18807;
(f = 23096,20835.34 589 ;(f'= 53181.59733; d"' ==^ 1-22457,
Now ^df" XX + i 43496
d" 53161,59733
/ 53161,11237
J x/ 5000,86402
d* 23096,2093 5,34589
d - ^xf 23090,1583474818 7
d'-ix/xA 18752.48284,85771
a* 10030,44036,01963.96855
y 10030.62788.50248.82626
b^abf 000029,08882,08665,72159,6154
Or. given b = T46372,6 1 172.07184,15204. to find 6.
liCt A = 2-53655.84425.71530,1 1205. a = 344.
b' = b -f A = 1*00028.45597,78714.26409. V = 00028.
A = 45597.78714.26409; x = 0-54402.21286; x+T= 154402;
d* = 23040,96629,91521 ; d" = 53054,39634 ; d"' = 1-22163;
Now Id"' X i^fl 62874
d" 53 054.39634
/ 53053.76760
ix/ 14431,21179
d* 2 3040.96629,91521
d^ -|x/ 2304 0.82198.7034 2
(f-Jx/XA I0'b6o.l0496.55627
of 10006,44931.70511.67281
y 10006.5543731008,22908
fc = - 00029,08882,08665.72159.616
SBKTi
DESCRIPTION AND USE
OF THE TABLE OF HYPERBOLIC LOGARITHMS.
This is table 5, in pa^R 219 — 223, which contain the scries of numbers
l-OI. 102, 103, &c., to 1000, with their hyperbolic lognrithtns to seven
places of figures. They are so called becau&c they square the asymptotic
spaces of the right-angleH hypcrlwla ; and ihey are very iweful in tinding^
fluents, and the sums of infinite series. The table, as well as the fuUowing-
rules, were first ^ven at Uic end of Simpson's fluxions, but they were ren-
dered much more correct in the French edition of Gardiner s tables, printed
at Avignon in 1770. beingr very incorrect in the last tif^ure in Simpson's book.
But both those books are very erroneous in the example for finding loga-
rithms by the table
1. fyhen Iht ^ven dumber is between I and 10.
From the given number subtract the next less tabular number, divide the
remainder by the said tabular number, increased by half the remainder ; add
the quotient to the logarithm of the said tabular number, and the sum will be
the logarithm of the number proposed.
Example.
To find the hyperbolic lo^farithm of 3*45678
3 45339) 00678 (0019633
1-23 83742
log. 1-2403375
Here the next less number is 3*45. and its lofcorithm 1*2383742, the re-
mainder or dividend "00679, its half 339, which joined to the tabular number
3*45. gives the divisor; the quotient 0019633 added to the tabular logarithm
1 2383742, gives 1-2403375, the required logarithm of 3 45678.
2. IFTien the gii>en Number exceeds 10.
Find the logarithm of the number as above, supposinir all the figures afler
the finil (o be decimals, then to that logarithm add 2*302.^851, or 4-6051702,
or 6*9077553. &c., according as the given number contains 2, or 3, or4,&c.,
places of integers. That is, add 2 302585092994 multiplied by the index of
the power of 10, by which the given number was divided to bring it to one
integer, or withio the limits of the table.
Example.
To find the hyperMic logarithm of 345-678.
12403375
4-6051702
5-8455077
This number divided by 100 or 10*, to bring it within the limits of the
table, or removing the decimal point two places, gives 3*45678, the loga-
rithm of which as above found is I 2403375. tn which adding 46051702
the hyperbolic logiirithm of 100, the sum is 5'8455077 the hyperbolic loga-
rithm required of 345678.
0¥ THR TABLES.
XXTII
Note The h>'perbolic log^arithm of any number may be also found from
Briggs's lo^rhhmB, viz. multipiyiu^ Brigg^s's logarithm of the same number
bj the hyperbolic logarithm of 10, viz.
Multiplying by 2-30258,50929,94045,68401.79914,
Or dividing by its reciprocal . •43129,44819,03251,82765.11289.
Note 2, There is also now added a supplementary table of Hyperbolic
Logarithms (Tab. 6.) of numbers from I to 1200.
OF THE LOGISTIC LOGARITHMS.
These are in table 7, pages 230 — 233. which contain the logistic logarithm
of every second aa far as the first 88' or 5280".
The logistic logarithm of any number of seconds is the difference between
U»e logarithm of 3600" and llie logarithm of that number of seconds.
The chief use of the table of IngiRtic logarithms Ls for the ready computing
a proportional part in minutes and seconds, when two terms of the proportion
are minutes and seconds, hours and minutes, or other numbers.
When two terms of the proportion are common numbers, their common
logarithms may be used instead of their logistic lognrithms, putting the
logarithm where its complement should be, and the contrary.
1. Tofindtkt Logistic Logarithm of any Number of Minutes and Seconds,
within the Limits of the Table,
At the top of the table Bud the minutes, and in the same column, even
with the seconds on the left-hand side, is the logistic logarithm.
Note^ When hours are made any terms of the proportion, they are lo be
taken as if they were minutes, and the minutes uf an hour as if they were
•ecouds.
2. To find the Logistic Logarithm of any Number not exceeding 5280.
In the 2d row, next the top of the table, find the number next less than
that g^ven ; then in the same column, even witli the difference on the lefl-
hai\d side, is found the logistic logarithm.
When two given terms of the proportion are common numbers, one or both
greater than 5280, take their halves, thirds, &c.. instead of them. But when
only one of the given terms is a common number, and that greater than
5280, take it.^ half, third, &c., and multiply the 4th term by 2, 3, &c.
The logistic lognrithms in this table are all athrniative, as well at>ove as
below 60' ; but the index of those above 60^ is — 1 ; below 60^ down to 6',
the index is 0; and below 6^ the indices (being either 1, 2, or 3) are ex-
pressed ill the table.
XXfUX
DESCRIPTION AND USK
Exampus.
As 60'
To 46' 12"
So 8 7
lo loe.
OOOOO
.. 01135
. . 0-8688
As 60'
To 79' 27"
So 13 53
To IS 9
As 78' 27"
To60
So 18 9
To 13 53
As 24" . .
To 46' 11"
So 8" 7
To 15' 37"
As 46' 11"
To 24"
So 15' 37"
To 6" 7'
CO
cu
• •
CO
lo. log.
OOOOO
18836
06357
As 60'
To 1531
So 40' 12"
To 1179
As 40' 12"
To 1179
So 60' 0"
To 1531
As 24*" , ,
To 76' 34''
So 13" 53'
To 44' 17"
As 76' 34"
To 24"
So 44' 17''
To 13" 55*
lo. lo;.
OOOOO
.. U3713
.. 0*1135
To 6 15
.. 9823
5193
. . 0-4848
As 46' 12"
To 00
So 6 15
CD. 1*8865
. . 0000
. . 0-9S23
1164
OOOOO
0-5193
CO. T-8865
. . 0-4948
. . 000(1
To 8 7
. . 0*8689
0-6357
.. 3713
As 60' .
To 4721
So 37' 28"
CO, 0-0000
.. 1-8823
.. 02045
T-G021
0-US7
0-8688
CO. 1-6021
.. 18941
. . 6357
To 2948
. . 00868
05946
T-8863
0-3979
05846
0-6688
.. 1319
As 4721 . .
To 60' 0"
So 2948
CO. 01177
. . 0000
. . 0-0968
CO. 0- 1059
. . 0-3979
.. 01319
To 37' 26"
. , 0-2045
. . 0-635*7
The lopstic logaritlims may be used in trigonometrical operations, when
two of the terras are small ares, with the lugurithmic sines or tangents of
other arc<); observing-, that in.steuil of the loji^arithmic &ine or tangent, to
take the complement of their lopstic lonrarilhm ; and the contrary.
But this may be as readily and more naturally done hy the logarithmic
sines and tangents themselves ai buch small ares, as taken from the next
fallowing table ofsines and tangents for every second of the first 2° or 120'.
OF THE LOGARITHMIC SINES AND TANGENTS TO EVERY
SECOND.
Table 8, pag^s 238 — 267, contains the log. sines and lan^yents for every
sinfrle second of the first 2 degrees of the quadrant; the sines being' placed
on the lefVhand pa^es, and Uie tangents on the ripfht. The decrees and
minutes are placed at the top of the columns, and the seconds on the left-
hand side of each page, the Ingaritlimic !>ine or tangent being found in the
common angle of meeting. So of I*^ 52' 54" the log. sine is 8*5163420. and
the log. tangent 9*5165762.
The same numbers are also the cosines and cotangents of the last 2 de-
grees of the quadrant, those degrees with their minutes being placed at the
bottom of the columns, and their seconds ascrnding nn the right-hand side
of the pages. So the cosine of 88° 7' 6" is 85163420, and its coUngent
8516576?.
OF THE TABLES
vttx
When It is required to find the sine or tanfi:enf, Ac. to 3ds, &c., or any
other fractional part of n second, subtract the tabular sine or tangent of the
complete secoufls from the next to it in the table, and take the like propor-
tional part of the difference; which part added to, or taken from, the said
tabular sine or tangent, according as it is increasing or decreasing, will give
the sine or tangent required.
EjcampU.
To find the log. sine of 1° 52' 54" 25'" or 1° 52' 54" JJ or -/^.
1° 52' 64" sine 8*5 1 63420
1 52 55 .. 8-5164061
dif. 641
5
12)3205
pro. part. 267
l*" 52' 54" 8 5163420
l°52' 54" 25'" 8-5163687
Here the sine of 1° 52' 54" taken from the next leaves 641. which multi-
plied by 5 and divided by 12. or mnliipHed by 25 and divided by 60, gives
267 the pro. part; this added to the first sine gives that which was required.
On th«* contrary, if a sine or tang;cnl be given, to find the corresponding
arc; take the dilTerence between it and the next less tabular number, and the
didercnce between the next less and greater tubular numbers, so shall the
less difference be the numerator, and the greater the denominator, of the
fractional part to be added to the arc of the less tabular number ; which frac-
tion may also, if lequired, be either turned into a decimal, or into 3ds, &c,,
by multiplying the aumerator by 60, and dividing by Uie denomiuator.
Example.
To find the arc whose sine is 8-5163900.
l^ 52' 55"
1 52 54
I 52 54 45'",
8-5164U61
85163420
6-5163900
diff. .
diff .
480
641
Finding the number is between the sines of I® 52' 55" and 1° 52' 54". take
the differences between the sities as in the margin, and the differences give
If^ lor the fraction of a second, or j J nearly, which abbreviates to |" = 45"';
and then-fore the arc sought is 1° 52' 54" 45"'.
Where the Isl differences of the sines and tangents alter much, as near the
beginninif of the liible, the 2d, 3d, Sec, differences may be taken in, and then
the logarithmic sine or tangent will be expressed by this scries, viz. : —
X—\ Jt—l T — 2
Q =s A +*D'-f- j.-^d''-|-j.-^ . -g-i>"' Ac., or nearly a + (d' — ^ d") *;
where k is the next less tabular logarithm, d', d'\ l/", &c., the 1st. 2d, 3d, &c.,
differences of the tabular logarithms, and x the fractional part of the arc ovef
the complete seconds.
ns DESCRIPTION AND USE
Example.
To find the log. tangent of 5' I" 12" 24"" or 5' 1'' ^ or 5' l"* '206.
Tang. I , I
6*0" .. 71626964,.!! 'iV
5 1 .. 7'164I4l7|}2"J-49
5 2 .. 7l6bbH2V\]Vil.~47
5 3 .. 7-1670178 I
Here a = 71641417 ; x = /j«jj ; d' = 14404 ; and ihc mean 2d diff. i^'
= - 48. Hence a 71641417
J!D' 2977
''-2-'' *
Therefore Ihe tangent of 5' 1" 12'" 24"" 71644398
And on the other hund, when the sine or tangent is given, and fulls near
the beginning of the table, from the same scrips we may find x the fractional
part of a second. For sup|>ose it be required to find the arc whose tangent
is 7 1644398. This falling Uftweea the tangents of 5' 1" and 5' 2", take the
differences, &c., as aljove, and tJ»e series gives 7*1644398 = 71641417
-f. j-D'-f-x."^^^^ d"; or 2981 = 14404j - 24 (i« - j:). or - 24^ +
I4428T ~ 2981 ; which gives r = '2067" nearly = 12'" 24"". Therefore
Ihe arc required is 5' 1" 12^" 24"". Or rather the approximate value a + d'
<* - A 2«8* 2981 ^^^ .
-4" •'= *»' (f"*" ' = n-rrj-^' = T4404T24 = l4428 = '^^^' '^'^
same as before.
OF THE LARGE TABLE OF NATURAL AND LOGARITHMIC
SINES, TANGENTS, SECANTS. AND VERSED SINES.
Table 9. pac^e 268 — 357, contains all the sines, tangents, secants, and
versed sines, both natural and togarithmic, to every minute of the quadrant,
the degrees at top, and minutes descending down the letl-hand side as far us
45°, or the middle of the quadrant, and from thence returning with the de-
grees at tlie bottom, and ihe minutes ascending by the riglit-hnnd KJde to 90°,
or the other half of the quadniut, in such sort, that any arc on the one side
is on the same line with its complement on the other side; the respective
sines, cosines, tangents, cnlangenls, &c., being on the same hoe with the
minutes, and in the columns signed with their res)>ective names, at lop when
the degrees are at top, but at the bottom when the degrees are al the l>ottom.
The natural sines, tangents, &c., are placed all together oo the left-hand
pages, and the logarithmic ones all together, facing ihcm, on the right-hand
pages. Also in the naturals there are two columns of the common differ*
enccs, end in the logarithmic 3 columns of common differences, eacli column
of differences being placed between the two columns of iiitmbers having the
same differences ; s<» that these differences serve for both their right-hand
and left-hand adjacent columns: also each differential number is f^et opposite
the space between the numbers whose difference it is. The numbers on the
same line in those columns having such common differences, are mutually
complements of each other; so thai the sum of the decimal lignres of any
two such numbers i.^ always ] integer, with in each place of decimals
OF THE TABLES.
XTXl
Alt this will bti evident by inspecting' one page of each sort, as well as the
method of taking out the sine, &c., to any de^crees and complete minnte!).
It is, however, lo be observed, that in all the log. sines, ton^nls, Ac, and
in such of (he natural as have any significant tigure for their index or
characteristic, the indices are expressed in the toblc, and the separating point
is placed between the index and the decimal part of the number; but in
several columns of the natural sines. &c.. having fur their integer or index,
both the index and decimal separating point are nuiiltcd ; and wherever this
is the case, it is to he understood that ah thi' figures in <;uch columns are
decimals, wanting before them only the separating point and index 0.
The sine, tangent, or secant of any arc, has Uie same value, or is expressed
by the same number, as the sine, tangent, or secant of the supplement of
that arc; tor which reason the tables arc carried only to a quadrant or 90
degrees. So that when an arc is greater than 90°, subtract it from 180*.
and take the sine. tang, or secant of the remainder, fur that of the arc given.
But this property does not take place between the versed sines of arcs and
their supplements ; and to find tlie versed sine of an arc greater than 90°,
procfcd thus : in the natural versed sines, to radius add the natural cosine,
the sum will be the natural versed sine ; and in tlie log. versetl sines, add
0'3<)L0300 to twice the log. sine of half the arc, the aum, abating radius
10*0000000, will be the log. versed sine required.
I. Given any Arc ; to find \U Sine, Contu, Tangent, ^c.
Seek the degrees at the top or bottom, and the minutes respectively on
the left or right ; then on the same line with these is the sine, Ac. each in its
proper column, the title being nt the top or bottom, according as the degrees
are.
But when the given arc contains any parts of a minute, intermediate to
those found in the table, lake the difference between the tabular sines, Ac
of the given degrees and minutes, and of the minute next greater; then take
the proportional part of that difference for the parts of the minute, and add
to it the sine, tangent, secant, and versed sine, or subtract it from the cosine
cotangent, cosecant, or coversed sine, of the given degrees and rainules j so
shall the sum or remainder be the sine, &c. required.
Note^ The proportional part is found thus, as 1 ' is (o the given interme-
diate part of a minute, so is the whole difference to the proportional part re-
quired; which therefore is found by multiplying the difference by the said
intermediate part Also Umt intermediate part may be expressed either by
a vulgar fraction, or a decimal, or a sexagesimal in seconds, thirds, &c., and
the fraction or sexagesimal may be first reduced to a decimal, if it be thought
t>etter so to do, by dividing the numerator of the fraction by the deouminator,
or by dividing the sexagesimal by 60.
Example 1.
To find the natural sine of 1* 48' 28" }2'".
In the coluum of difference between the natural sines of 1° 48' and I® 49
ia the difference 2907 ; and 28" 12"' being = 28 2" = "47' ; therefore as
1 : 2907 :: "47 : the pro. part -{- 1366
to which add sin. l** 4S' ... 0314106
makes sin. of 1° 48^ 28" 12'" OsIbT?!
ucxu
DESCRIPTION AND USK
Example 2.
To find the natural lan^nt of 8*'9' 10" 24'".
B° 10 tang 1433U94
8 9 1432115
ditf. -2969
2969 :: (10'' 24'^=) n'i : + 515
S°9^ 1432115
gOg/ 10" 24'
1432630
Example 3.
To find the natural coversed sine of 4"^ 6' 5" 40*"
I :2902 (lab.dif.) " i^gV
5" 40" : pro part . . .
4* 6' covers 9285026
}-
274
4" 6' 5" 40"' 9284752
Example 4.
To find the loffarilhmic cnsine of ^ 8' 42".
: 136 Uab. dif.) :: •?'= 42": pr. pt. - 95
6" 8' cosine 9*9975069
6» 8' 42" 9 9974974
Erample 5.
To find the log. sec. of 7° 12' 50".
160 (lab. dif.) : : i' = 50" : pr. pL -f 133
7' 12' secant 100034381
T'^ 12' 50" 100034514
Example 6.
To find tJie lograrithm cotangent of 39^ 4' 12" 20'
I :258l (tab. dif.) ;: 204= 1 -«,
12" 20'": pro. part ... j ^'
39°4'cotaii 10 0905978
39° 4' 12" 20'" 10*0905447
The foregtiing method of finding the proportional part of the tabular dif-
ference. 10 be added or fiubtracted, by one single proportion, is only true
when those differences are nearly equal, and may do for all except for the
tangents and secants nf Itirge arcs near the end of the quadrant in the natural
sines &c., and in the lop *>ine.s, &c., except the sines and versed sines of
small arcs, the langenLs of both hrge und small arcs, and the secants of large
arcs. And when much accuracy is required, these excepted partit may be
* — 1
found by the series used in the last article, viz. q = a + jpd' + x . — - — d"
*- I J- 2
&c. or = A + (d' — Jd") . X nearly ; where k is the
2 3
tftbular number for the degrees and minutes, o', d\ d'", Ac, the Ist, 2d, 3d,
Sec tabular diflTercnccs, and x Uie fractional part over the complete minutes.
OF THE TABLES.
XXXIU
Ac ; at least it may be proper to find the tangents and secants of very large
arcs from this series ; but as to the log. sines, versed sines, and lanj^ents of
small arcs, (hey may also be found, perhaps easier, from their corresponding
natural ones. viz. find the natural sin«| versed sine, or tangent of the (riven
small arc, and then find the log*, of sn<9i natural number by the tst or lar^
table of log^arithms, whidi will be the log;, sine, &c. required. And tike log.
tangent and secant of large arcs will be also found by taking the difference
between 20 and their log. cotangent nnd cosine respectively. And lastly, the
natural tangents and secants of large arcs may also be found by first finding
their log. tangent and secant, and then finding ihe corresponding numbei.
Ejcan\pU 1.
To find llie log. sine of X** 48' 28" 12"'.
The natural sine, found in Ex. 1. above, is *0315474 ; and the log. of this
b 8*4989636. which is the log. sine required.
Erample 2.
To find the log. versin. of 1" 48' 28" 12'",
1* 48' nat. vers 0004934
1 : 92 tab, dif, : ; 47' =r 28" 12'" : -f 43
1° 48' 28" 12"' nat. vers. -0004977
Its log. 1 48 28 12 log. vers. 6 6969676
Example 3.
To find the log. tang, of 2^ 23' 33" 36'".
2^ 23^ its nat tan 04162L0
1 : 2914 lab. dif. ; : 56' = 33" 36"' : + 1632
2'' 23' 33" 36"' nat. tan. . . 0417842
Itslog.2 23 33 36 log. tang. 8-6210121
Example 4.
To find the log. Ung. of 87° 36' 26" 24'".
Its complement is 2" 23' 33" 36"
Whose log. tang, in Ex. 3 is . . 8-6210121
Taken from 200000000
Leaves log. tan. 87** 36' 26" 24'" 11-3789879
Example 5.
To find the log. sec. of 88*' IT 31" 48**.
Its complement is 1** 48' 28" 12'"
Its log. sine in Ex. 1 is 8*4989636
Which taken from 200000000
Leaves log. sec, 88° I T 31" 48"' 11*5010364
c
1
xxxtv
DESCHIPTION AND USE
Examjiie 6.
To find Ihe nal. sec. of 38** 1 1' 31" 4d"'.
89*11'
88 12
88 13
88 14
iiat. s«i'.
31-544246
31-836225
32 133663
32-4367 13
D'
291979
29743&
303050
5459
5612
153
Hence k = 31544246; d' = 291979; »" = 5459; and d"' = 153;
X— I X — Ijt —
J = -53' -31" 48
= -06125.
31 698323
In the 6th exumpli;, the natural secant is found by the ditfer^ntial series (o
he 31-698324. But by taking the number to the loiruriihm of it, as found in
the 5lh example, it is 31 '698329 ; ihc differcnee may be owinp to the logs.
not t)eiM^ fur enuug;h continued. But thin method by the series seems to be,
in many instances, more troublesome than tinding die secant by dividing 1
by the cosine.
2. Gii>en any Sine^ Tangtnt, ^c. iojtnd itt Arc,
Take the dilfcrence between the next le^s and greater tabular number of
the same kind, and the difference between the given number and liaid next
lefts or next greater tabular number, according as the given number is a sine,
tangent. &c., or a cosine, cotangent, Ac, noting its degrees and minutes;
then the two difiVrences will be the terms of a vulgar fraction of a minute* tu
be added to those minutes, tu give the arc required.
And this vulgar fraction may also, if required, be reduced to a decimal by
dividing the less or numerator by the de.iuminalor ; or brought to sexagesi-
mals, by multiplying by 60, &e. Also, where (he tabular dilferences are
printed, the subtraction of the less tabular number from tlie greater is saved.
Example 1.
To find the are to the natural sine *0315474.
Ana l*>48'2fi" 12'" ... 0315474
SuUr. 1 48' next less , .. Q 3UI08
1366
60
Tab. difference 2907 ) 81960 ( 26"
5814
23620
23256
564
60
'2907 ) 33840(12'
OF IIIE TABLES. xxxv
Example 2.
To find the arc to natural tang. * 1432630.
Next greater 1435084
Answer 8° 9* 10" 24'" 1432630
Next less. subt. fr. each 1432115
515
60
Tab. difference 2069 ) 30900 ( 10"
29690
1210
60
72600(24'"
5938
13220
Example 8.
To find the arc lo logarithm cosine 9-9974974,
6** 8' 9-9975069
Answer 6** 3' 42" 9 9974974
95
60
Tab. difference 136 ) 5700
544
260
Example 4.
To find the arc to logarithm cot. 10*0905447.
39«4' 100905973
Answer 39° 4' 12'' 20*" 100905447
531
60
Tab. difference 2581 ) 31860 ( 12"
2581
6050
5162
888
60
2581 ) 53280 (20^"
5162
1660
The above method of proportioning by the first difference alone, can only
be true when the other differences are nothing, or very small ; but other means
must he used when they are large, viz. for the natural tangents and secants
of very large arcs ; and for the logarithmic sines, and versed sines of small
arcs, aiso the log. secants of large arcs, with the log. tangents and cotangents
both of small and large arcs. When the log. sine, versed sine, or tangent of
a small arc is given, by means of the table of logarithms find the corre-
sponding natural number, and then the arc answering to it in the table of na-
tural sines, &c. But when the log. tangent or secant of a large arc is pro-
posed, subtract it from 20, the remainder is the log. cotangent or cosine,
which will be the log. tangent or sine of a small arc which is the complement
c 2
xxxvi DESCRIPTtON AND USB
of that required, which complement will be found as in the last remark, by
taking the corresponding natural number, and finding it in the natural tan-
gents or sines ; then subtracting that complemental arc from 90*^, leaves the
required large arc answering to the proposed log. tangent or aecanL And
when the natural tangent or secant of a large arc is proposed, change it into
the log. tangent or secant of the same, by taking the log. of the pro{>osed
natural number; then proceed with it as above in the last remark. — Or,
what relates to the log. sines and tangents of small arcs, or cosines and co-
tangents of large ones, will be best performed by the foregoing table for
every second of the first 2 degrees.
Example 1.
To find the arc to natural tangent 50*0000000.
20-0000000
Given 50 0000000 its log. It 6989700
•02 S-3010300
"0197830 nat. tan. of 1® R'
2170
60
2910) 130200 (44"
1164
1390
1164
816
go
12960 (44'"
1164
1320
Hencefrom 90« C 0" 0"
Take the comp i 8 44 44
Leaves arc required 88 61 15 16
Example 2.
To Hnd the arc to natural secant 31*6983333.
200000000
Given 3) -6984. its log. 11-50103 6&
•0315474 8*4989635
-0314108 naL sine of I" 48"
IS66
60
8007) 81960 (28"
5814
23820
23256
564
60
33840 (12"'
29U7
4770
Ifencefrom 90* 0' 0^ 0*
Take the comp I 4 8 28 12
LeavcH arc required 88 11 31 48
OF THE TABLKS.
XITVi}
The following rules in reference to the sines and tangents of small arcs,
(riven by Dr. Maskelyne, in hia introduction to Taylor m Logarithms^ will
often be useful : —
1. To find tht sine. To Ihe logurithm of ihe arc reduced into seconds,
w*th the decimal annexed, add the constant quaiilily 46855749, and from the
sum subtract one-third of the arithmetical complement of the log. cosine, the
remainder will l>e the Jog. sine of the given arc.
2. Tojind tht tangent. To the log. arc and the above constant quantity,
add two-thirds of the arithmetical complement of the log. cosine, the sum is
the log. tangent of the given arc.
3. Tojind the arc from the sine. To the given log. sine of a small arc
53144251, add j of arith. cump. of the log. cosine: Rubtract 10 from the
index of the sum, the remainder will be (he log. of the number o( seconds and
decimals in the arc sought.
4. Tojind the arc from the tangent To the log. tangent add 5'314425l,
and from the sum subtract ^ of the arith. cump. of log. cosine: take 10 from
the index, and there will remain the logarithm of the numl>er of seconds and
decimals of a second in the given arc.
*y* See, also. Dr. Maskelyne's remarks, before the directions for the use
of the Traverst Table.
Qn the Construction of these Tahles,
The computation of tables of sines, tangents, secants. &.c. is evidently a
work of i^reat labour; but. considerable as it doubtless is, it has been much
diminished by the employment of various trigonometrical theorenis, discovered
by different mathematicians. A few of these theorems, being of general
utility in the doctrine of Trigonometry, are here presented.
Theorem I. The square f»f the diameter of a circle is equal to the sum of
the squares of the ch^jrd of an arc, and of the chord of its supplement lu a
semicircle.
2. The rectangle under the two diagonals of any quadrilateral inscribed in
a circle, is e<iiial to the sum of the two rectan^^les under the opposite sides.
3. 'l*he sum nf the squares of the sine and co'^inc (often called the sine
of the complement), is equal to the square of the radius.
4. The dilference btftween the sines of two arcs that are equally distant
from 60 degrees, or \ of the whole circumference, the one as much greater
as the other is less, is equal to the sine of half the difference of those arcs,
or of the difference between either arc and the said arc of 60 degrees.
6. The sum of the cosine and versed sine is e([ual to the radius.
6. The sum of the squares of the sine and versed sine is equal to the square
of the chord, or to the square of double the sine of half the arc.
7. The sine is a mean propurtional between half the radius and the versed
sine of double the are.
8. A mean proportional, between the versed sine and half tlie radius, is
equal to Ihe sine of half the arc.
9. As radius is to the sine, so is twice the cosine to the sine of twice the
arc.
10. As the chord of an arc is to the sum of the chords of the single and
double arc, so is the difference of those ch(»rd3 to the chord of thrice the arc,
1 1. As the chord of an arc is to the sum of the chords of twice and thrice
the arc, so is the dilference of those chords to the chord of five times the arc.
12. And in general, as the chord of an arc is to the sum of the chords o;
n times and n -\- \ times the arc, so is the difference of those chords to the
chord of 2 n 4~ 1 times the arc.
XXXVllI
DESCRIPTION AND USE
13. lite sine of (he sum of two ares is equal to Ihe sum of the pmducts
of the sine of each multiplied by the cosine of the other, and Hiiride<) by the
radius. ,
14. The sine of the di(U.'rciice of two arcs is equal to tlie difference of the
said two products divided by rudius.
15. The cosine of the sum of (wo arcs is equal lo the ditfereiice between
the products of their sines and of their cosines, divided by rudius.
16. The cosine of the difference of two arcs is equal to the sum of the said
products diridcd by radius.
17. A smnll arc is equal to its chord or sine, nearly.
19. Ah cosine is to sine, so is radius to tangent.
19. Radius is a mean proportional between the tanj^cnt and cotangent.
20. Half the difference between the tangent and cotangent of an arc is
equal to the tung^ent nf the dilTercnce between the arc and its complement.
Or, the sum arisinp; from Uic addition of double the* tangent of an arc with the
tangent of half its complement, is equal to the tangent of the sum of that arc
and thesaifl half complfment.
21. Tlie square of the secant of an arc is equal to the sum of the squares
of the radius and tangent.
22. Radius is a mean proportional between (he secant and cosine. Or,
as cosine is to radius, so is radius (o secant.
23. Radius is a mean proportional between ihesin^and cosecant.
24. The secant of an arc is equal to the sum of its tangent, and the tan-
gent of half its complement Or. the secant of the ditlerence betv^^en an arc
ond its complement is equal to the tangent of the said difference added to the
tangent of the less arc.
25. Ttie secant of an arc is equal to the difference between the tangent of
that arc and the tangent of the arc added to half its complement. Or the
secant of the difference between an arc and its complement, is equal to the
difference between the tangent of the said dilfereiice aud the tangent of the
greater arc.
26. Sir Isaac Newton also proposed a method of computing a table of
sines by means of multiple angles ; and in which radius, or 1, is the first
term, and double the sine or cosine of the first angle is the 2d term of
all the proportions by which the several successive multiple sines or cosines
are found. The substance of the meihtxl is this : ihe best foundation for the
construction of the tables of sines, is the continual addition of a given angle to
itself or to another given angle. As if the angle a be lo be added ; inscribe
HI, IK, KL, I.M, MN, NO, OP, &c., cach equul to the rudius ab ; and to the
opposite sides draw the perpendiculars bf.. hq. ir, ks. lt. mv, nx. uy, &c. i
so shall the angle a he the common difference of the angles iiiq. IKU, xt.i,
LMKf Ac; their sines bq, ir, ks, &c. ; and their cosines iq, kr, ls, Ac.
Now let any one of them, lmk, be given, then llic rest wdl be thus found: —
Draw Ta and Kb perpendicular to sv and MV ; now because of the equiangular
triangles 4DE, Tta, Kjub, alt, a>iv, &c., it will be ad : ae 1 1 kt : sa
^= J LV + J LS) '.' LT : Ta (= 4 ^^ *** i "^^O ^"*' AB ; BE ', [ LT I 1.8
{= J US - 4 t-v; ;: kt (= J km) : JmI* (= Jmv — Jks.) Hence ure*given
OK THE TABLES.
XXXIX
tlie sines and cosines ks, mt. ln. lv.
pt\)gressions is evident. Namely,
And the method of continuing the
as IB : 2ae
or AB ; 2bb
{i.v : MT -j- MX
mv:nx 4" i-T
{LV : NX — tT
MV: MT — MX
MX
NX
MX
NX
NV + NT, &.C.
OY + MV, &C.
OY — MV, &C
NV — NY, &C.
Ln := LV,
And on the other hand, ab : 2ae : : ls : kt + kr, &c.
Therefore put ab = I, and make he x i.t= La, ak x kt= sa, sa
2aE X LV — TM = MX, &c.
The sense ol Itiese ^eneriil theorems is this, that if P be any one among a
Bencfl oran<^1eH in urithmeticnl progression, the angle d being their common
difference, then as radius or
I -S rn« rf . ■ J^""- P : cos. (P + rf) -H cos. (P - rf)
1 : 2 sin. d
/cos. P : sin. (P + rf) - sin. (P - rf)
(^sin. P : COS. (P ♦- d) - cos (P - rf)
iere the 4th terms of tticse proportions are the sums or tlifTerencch of the
sines or cosini's of the two angles next less ami jrreater than any angle P in
the series ; and therefore siiblractiiig the less extreme from the sum, or adding
it to the difference, the result will be the greater extreme, or the next sine or
cosine beyond that of the term P. And in the snme manner are all the rest
to be fi>nnd. This method, it is evident, is equally applicable whether the
common difference rf, or angle a, h*i equiil to one tenn of ihe series or not :
when it U one of the terms, then Itie whole series of bines and cosiuvs becomes
thus, viz. as 1 : 2 ens. d : :
cot. rf : I + oo». M 1 ; rot. S^ : floi. 4 -f (!Q9. 3,1 ■ or«. U ■ cc«. Si 4. eoa. U
■In id '- km. 3d .f lui. 54, Sea.
rok. M CQI. 3d + iro9. Sd. Ste,
&m.
sin.
ain.
sin.
27. Tlic following values of (be natural sine for every third degree in the
quadrant, have greatly contributed to facilitate the computations :—
0' =
sin. 12° = i [^/3 -f- ^/ (10 + 2 ^5) - ,^15]
sin. 15'=' = I Wl - Ji]
sin. IS^zz^iU^ - 1]
sin. 21'' = J y (15 - 3^3) + ^(5 - ^/5) + ^f + ^i " ^¥ - V4
sin. 24° = 4 [^/15 + ^/3-^^(lO- 2^5)]
sill. 27° = Hy (5 + ^5) + Vi - VII
«n. 30" = I
sin. Sr = J [^/(15 + 3V5) + VV + V|-V(^+ s/^) " -^i " Vil
sin. 36*^
V(10 - 2^5)
sin. 39^ = i[^ (5-^5) -I- ^V + ^4 + ^/| + Vi - V d^ - 3 V^)]
*in. 42=* = HI + V (30 + 6 ^5) - ^5]
sin. 45' = i/J
sin. 48' = i y\S + ^ (10 + 2^.S) - ^3]
Bin. bl'^ = i[V(l.^-3V5)+V(&-N/^) + ^/y +%/^-V4 -VJ]
sin. 54'' = 10^4- I]
DESCRIPTION AND USE
sin.
sin.
sin.
sin.
sin.
sin.
sin.
sin.
sin.
sill,
fiiii.
sin.
60° =r ^ ^
66°= i[] +V(30-6V5)+V5]
69- = i[V(l5-3V5)-^ VSr^+V* + ^4 + VJ-V(*--ys)]
72"=: i ^(10 + 2^5)
78'' = 4 [^5 + V (30 + 6 V5) - I]
8l°=i[V}+s/i +V(^- V5)]
84° = i yib + ^3 -j- V (10 - 2 Jh)]
90° == 1
V 3 = 1-7320508076
^ 5 = 2-2360679775
J15= 3-8729H33462
^1 = 1-5811388301
V V = 2-7386127875
V (5 + ^5) = 2-6899940479
0-7071067812 v' (^ - J'^) = 1-6625077511
1-22474487 U ^/ ( U) -f 2 ^'5) = 3*8042260652
V(IO -2V&) = 2-3511110092
V 05 + 3 ^5) = 4-6.592063629
^ (15 - 3^5) = 2 879547S929
V (30 -f- 6 ^5) = 6-589 n 28284
V (30 -6^b) = 4'072-2956S36
29. The nntnial sines, tanpfents, Recnnts. Ac, beiiifr computed by meana
of those and other convenient theorems, are arranged in order on the left-
hand pag-cs of tabic 9 ; and the logarithtnic sines, tangetitSf sccant% &c,
belonping^ to the same decrees and minutes reRpectively, stand on the oppo-
site ripht-liand paftes. They are, of course, easily ascertained by computing",
one by one. the lot^rithms of the sines, tangents. &c., to wliich they lielong*.
I'hns, 9-3836752. the loir, sine of 14^ is simply the loff. of -2419219, the
natural sine of 14**; 9'3967711, the log-, tangent of 14° is the lo^rithm of
-24932S0. the natural tangent of 14^; and sj on.
29. But, all this may indeed be accomplished with much ^eater facility.
For, since sin. -7- cos. = tan.; tan. : rad. ir'rad. ; cot.; sin. : rad. :: rad. ;
eosec ; cus. ; rad. :: rad. : sec; we may, after havinf^ found the lo^rithmic
sines and cosines ; or, in other words, all the sines, minute by minute, &c, to
flO', proceed thus :—
From 10 -j- sin. take cos. there remains tan.
From 20 take tan., there remains cot
From 20 lake cos., there remains sec.
From 20 take sin.» there remains cosec.
Add -3010300 to twice the log. sin. of half the arc, and take 10 from the
indei of the sum, the remainder is the lo^. versin.
Add '3010300 (o twice the lo^. sin. of half the comp. of the arc, and take
lO from the indei of the sum, the remainder is the log. eoversin.
xa
TRIGONOMETRICAL RULES.
1. In a i%ht-lined triangle, whose sides are a, b, c, and their opposite
angles, a, 6, o ; having given any three of these, of which one is a side ; to
find the rest.
Put s for the sine, s' the cosine, t the tangent, and t' the cotangent, of an
arch or angle, to the radius r; also h for a logarithm, and t' its arithmetical
complement Then
Cask 1. When three sides a, b, c, are given.
Then
And
Put p=i^.A + B-|-cor semiperimeter.
■ V A X B
, 1 /P X (P - C)
s'. * c rr r 1 / .
^ V A X B
L. 8. jl C = J . (L. P — A + L. P — B -|- L' A + I-'b).
l' S. 1^ C := ^ (L. P + L. P — C + L' A + L' B).
c r /a' "* 4- c^
Note, When a :=: b, then s. 1 c = — x -rr. And 8'ic= r \ / ^ — .
* A 2 V A*
Case 2. Uiven two sides a, b, and their included angle c.
A ^ B
Put8s:90°~ic, and t d= — - — X t.s; then a = s + rf; and6 = s - d.
* A + B
And
//4ab X i^ic .
Or in logarithms, putting l. q = 2 l. (a — b), and l. n = l. 2 a -f l. 3 b +
2 L. s. i c - 20,
then L. c = ^ L. (q + k).
A B
If the angle c be right, or = 90** ; then t. a = — r ; t. 6 = — r;
r r I
c =: A, or = — r B, or = va' +
s. a 8. 6
If A = B ; then a = 6 = 90® - J c, and c =
8.^0
X 2 A.
Casb 3. When a side and its opposite angle are among the terms given.
A _ B ^ c
8. a ~" 8. 6 " 8. c
found.
Hien = — r = — - ; from which equations any term wanted may be
xlii TRIGONOMETRICAL RULES.
When on angle, as a, ia 90°, and a and c nrc g^iven,
Tlien B = ^{k* — c*) = ^(a + c) x (a — c/.
And L. B = ^ (l. A -|- c -f- L. A — c).
iVo/<r. When two sides a, b, and an ang'le a opposite lo one of them, are
n;iven ; if a he less than b, then b^ c, c, have each two values ; otherwi«e
only one value.
11. — In a spheric triangle, whose three sides are a, b, c, and llteir opposite
an^es, a, 6, c; any three of these six terms beiu^ f^ivcn, (o lind the rest.
Case 1. Given the three sides a, b, c.
Calling 2 p the perim. or p = J (a + d + c).
p - h)
Then
And
, /s. (p - a) X s. (i
V 8. A X s. D
X «. B
US. ^C=^(l,. S. P— A+L 8. P— B+ l'i. a + t' S. B).
t. s' c =: J (l. 8. p + L. s. p — c + l's. a + l'h. b)
And the same for the other angles.
Cask 2. Given the three angles.
Put 2 ;? = a + 6 + c.
•^ V 8. a X s. 6
V s. a
Then
And
A)
X a. 6
L. s. J c = J (l. «'p + L. %' p — c + L'fl. a + t/s. (f).
L. s' J c = J (l. s'/i - a+ L. s'p — 6 + l's. a + l's. 6).
And tlie same for the other sides.
NoU, The sign > signifies greater than, and < less than ; also -- the
di fie re nee.
Ca«c 3 Given a, b, and iiicluded angle c.
To find an angle a opposite the side a, let r : s' c : : t. a : t. M, like or un-
like A, as c is > or < 90*; also n = b -^ M : then s. n : s. m : : t. c : t. a.
tike or unlike c as m is > or < b. Or let s* J. a + d : s' J. a -^ b : : t' ^ c :
t M. which is > or < 90^ as a + b is > or < 160°, and s. ^. a + a : 8.
A — B::l'^c:tN, > 90°, then a = m + m ; and /» = M — m.
Again, let r ; s'c : ; I. a : t. m, like or unlike a as c in > or < than 90^;
and N =: B >« M. Then s' m : .*i' n : : s' a : s' c, like or unlike n as c is > or
< 90*. Or,
, /s. a X s. a X s* 4 c , , ,
8.ic= y/ ;; i- + s»i.A-B.
TRIGONOMETRICAL RULKS
TtHii
In lognrithms, put l. q = 2 l. 8. ^ ik -^ b ; untl u a = l. s. a + i.. a. u +
a L. •. 4 c - 20 ; then l. s. Jc := J l. (q + n).
Casb 4. Given a, &, ami included side c.
Firel, let r : s'c : : t a : I'fn. like or unlike a as c is > or < 90"; also
fi =r 6 -- fTi. Then a'n : s'm : : t. c ; t. a, like or unlike /t as a is > or <
90°. Or, let s' Jt- a + & = »' J. « -A : : t. J c : t. m, > or < 90'^ as a + A
i» > or < 180*; and s. Ja + A : 8. ^ a-- 6 : : I. J c : t. h, > 90*; then
A = M i n; and b = m :^ n.
A^in, tel r : s' c : : t. f> : (' 7n, like or unlike a as c is > or < 90^; and
n = 6-^ m: then s. m : s. 7i : : s' a : s'c, like or unlike a as m is > or < 6
Case 5. Given a, b» nnd an opposite an^le a.
1st. s. A : a. a : : 8. B t s. A, > or < 90*
2d)y. Let r : s' b : : t. a : t' m, like ur unlike b as a is > or < 90^ ; and
t. A ; I. B : : s'ro : s' n, like or unlike a as a is > or < 90^ ; then c ^ m rt w,
two values ulso.
3d{y. Let r : s'a : : t. b : l. M, tike or unlike b as a is > or < 90*^; and
»'b :y a : r s'm : b'.\, tike or unlike a as a is > or < 90^; then c = M ± N,
two values also.
But if a be equal to b, or to its supplement^ or between b and its supplement ;
then is 6 like to a : also c is = m ± r, and c = m ^ n, as s is like or un-
like a.
Case 6. Given a, 6, and an opposite side a.
Ut. a. a : s. A. ; : ». & : a. b, > or < 90''.
2dly. Let r : s' 6 : : t. a : t. m. like or unlike 6 as a is > or < 90° ; and
t. a : t 6 : : s. u : a. N, > or < 90° ; then c = u + n, as a is like or un-
like b,
3d!y. Let r : s' a : : t. 6 ; t' m. like or unlike fr as a > or < 90° ; and
b' 6 : s' a : : s. r/i : s. ;/, > or <90** ; Ihen c = wj ± 71, as fl is like or imlike b.
But if A be equal 1 1 b, or to its supplement, or between b and its supple-
ment; then B is unlike A, and only the less values of N. n. are possible.
Note^ When two sides a, b, and their opposite angles o, 6» are known ; the
third sidec, and its opposite un^lo c, are readily found thus: —
s. 4 (fl - 6) : s. J. (fl -h A) : : t. J (a - b) : t. i c.
9. J. (a - 0) : s. J. (a -I- ») : : I. J. (a - A) : t. J c
in. In a right-angled spheric triang-le, where n is the hypotenuse, or
aide opposite the rif^hl aufrle* b. p. the other t%vo sides, and 6, p, their oppo-
site angles; any two of these five terms being- given, to find tlie rest; the
cases with their solutions, are as in the fultowing table.
The same table Will aUo ser%'e for the qtindrantnt triangle, or that which
has one side = 90* h being the angle opposite to that side, n, p, the other
two angles, and b, p^ their ojiposilc sides ; observing, instead of u to lake its
x\W
TRIGONOMETRICAL RULES.
supplement ; or else mutually chani^inc^ the terms iike and unlike for each
other where b is concerned, and its real value is taken.
Ca»e
Given
R«,«
1
lot-imoNi. 1
1
H
B
6
P
p
s. H : r : : s.B : 8.6, and is like b
r : t'.H :: t.B : s'.pl • > or < 90** as h is like or un-
s'.B : r ::»'.ii ; s.p J like d
2
a
B
6
B
P
P
r : s.H ; : 8.6 : s.B, like 6
r : s'.6 :: t.H : t.p \ , > or < 90° as h is like or im-
r :s'.H :: t.A : t'.pj like 6
B
6
H
P
P
*'t • LB •• I'l • 8 p1' '"'^'' > or < 90^; both values
4
P
H
6
P
r : I'.B ! : s'.p : t'.H, > or < 90° as a is like or unlike p
r : s'.B :: s.p : s'.ft, like a
r : s.B :; Up : t.p, like/*
d
B
P
b
P
r : s'.B : : b'.p : k'.h, > or < 90° as b is like or unlike p
r : s.p :: t'.B ; t'.6. like a
r : s.B :: I' P ": i'.p. like p
6
I
H
B
P
r : t'.6 : : i'.p : s'.H, > or < 90° as 6 is like or uulikep
s.p : r :: a'.b : s'.B. like 6
8.6 ; r : : a^p : s'.P, like p
The following Propositions and Remarks, concerning: Spherical Triani^les,
(selected and cnmmunicalcd by the Rev. Nevil Maskelvne, D.D.. Astro-
nomer Royal, F R.S.) will also render the calculutioa of ihem perspicuous,
and free from ambi^ity • —
•' 1. A spherical trianjjle is equilateral, isoscelar, or scalene, accordinpr as
il has its three angles all equal, or two of Uiem equal, or all three unequal ;
and vice rrni,
" 2. Tlie greatest side is always opposite the greatest angle» and the
smallest side opposite the smallest angle.
" 3. Any two sides, taken together, are greater than the third.
" 4. If the three angles are all acute, or all right, or all obtuse; the three
sides will be, accordingly, all leas than 90^ or equal to 90^ or greater than
90®; and cicc vend.
- 5. If from the three angles a, b, c, of a triangle
ABC, as pole*, there be described, upon the surface
of the sphere, three arches of a great circle de, of,
FB. forming by their intersections a new spherical
triangle dep ; each side of the new triangle will be
the supplement of the angle at its pole ; and each
angle ot the same triangle, will be the supplement
oTthe side opposite to it in the triangle abc.
TRIGONOMETRICAL RULES.
xlv
*" 6. In any triangle a a c. or a 6 c, rif^ht anzled
in A, 1st, The angles at the hypoteiiti.se are always of
the s&me kind as their opposite sides ; 2dly, The
hypotenuse is less or greater than a quadrant ac-
cording^ as the sides including the right angle ure of
the same or different kinds ; that is to say, according
as these same sides are either both acute or both ob-
tuse, or as one is acute and the other obtuse. And,
vice versdy Ist, The sides includini^ the right angle, are always of the same
kind asiheir opposite angles; 2dly, The sides including the right angle will
be of the same or different kinds, accoiding as the hypotenuse is less or more
than 90°: but one at least of them will be of 90", il'lhe hypotenuse is so "
The values of the sine, cosine. &c. at the extremity of each quadrant, as
well as the changes of signs in passing through the different quadrantb, may
be known from the foUowin'? tables: —
1 ARC =
0'
90"
160"
270"
360°
Sin
R
- R
Tan
cc
— CD
Sec.
R
OD
- R
— CO
R
Cos
H
- R
R
Cot.
09
— OD
ot?
Cosec
CD
R
— CD
- R
OS
The chanct«r od denolai ioAoily.
The chan^^ of signs are these: —
Ist 5lh. 9th 13th.
2d. 6lb. lOlh. 14th.
3d. 7th. 11th. 15th.
4th. Bth. ISth. l«th.
I
tlD.
COf.
g + - - - -
- + -- + '
i
xlvt
THE C:ASES OF PLANE TRIANGLES RESOLVED BY
LOGARITHMS.
In this and the following solulions orsplienoal lriang*1es, it is to be observe*!,
thai when we say the Mue. tangent, &c. we meaD the luf^urithmic sine, tan-
gent, &c. us fbund by the table.
C
A B ©
Prop. I, — Having the an^les^ and one aidt ; to Jind either of the other sides.
Add the logaritbm of the pi'ven side to the sine of the angle opposite to
ihe side required, and from the sum subtract the sine of the angle opposed
to tlie given side ; the remainder will be the logarithm of the side required.
Esamnle. In the triangle d c d, having the angle c d b 90**, c b d 51* 56',
BCD 38^ 4' and the Bide nn 197*3; to find the side c d.
2-2951271 log. of 197-3
9 8961869 sin. o( 51' 56'
12-1912640 sum
9-7999880 sin. of 38'' 4'
2-4012760 log. 251-9278 cd req.
Or you may add the complement of the sine of the angle opposed to the
given side, to the two other logariLlims, the sum (abating radius) is the loga-
rithm of Ihe side required ; as shown in art. 3 of Log, Arilh. And it ia to
l>c observed, that the complements of ihe sines in the table are to be found in
the columns of the cosecants: for (passing over the 6rst unit) the cos cants
of the same arcs are the complements of the same sines, AJso the comple-
ments of the tangents arc the cmangcnts.
BxampU. The sine of 38* 4' being 97899880, the cosecant of 38*4' Is
1 0;2100120, which (omitting the first unit) is the complement of the said
sine.
0-21001-20 CO. of sin 38° 4'
2*295127! log. of 197*3
96961369 sin. of 51*56'
2-401-2760 log. 251 9278, as before.
But if one side and the angles of a right-ant^fled triangle be known, and
you would have the other side, as in the former example, the operation will
be easier thus;
Add the tangent of the angle opposite to the side required, tn the togitrithm
of the given side, the sum (abating radius) is the logarithm of tlie side re-
•quired,
101061489 tan. 51^56'
2-2951-271 log. of 197-3
2-401*2760 log. 251-9278 as before.
OK RIGHT-LINED TRIANGLES.
xlvii
Pnop. II. — Hatting Ittn «dei, and an angle opposite to one of them i to Jind
Uie other two angleSf and the third side.
Add llie Bine of the ang-Ie given to the loparithm of the side ndjohiing thai
ait^rle, and from the sum subtract the lo^rithni of the side opposite to that
ansrle. or add it» aritlinielicul oomp. the remainder or sum will be the sine of
Lhe angle opposite to the adJuiDiiu^ side.
Example. In the triangle abc, having Uie side 4C 800, bc 320^ and the
angle AQC 123^ 4' ; to find the angles bac, acb. and the side A.B.
7 0969 1 00 ar. com. log. 600
2'5051500log. of 320
& S9gl369 sin. 129° 4'
"9-4981969 Bin. 18° 21' bkc.
llavins: bac and abc the angle acb is their supplement to lS0°,
36^ 35'; and yon may find the side ab by the flrst proposition.
VIZ.
Prop. III. — Having two sides and the anffie between therti ; to Jind the other
two angles, and the third side.
If the angle included be a right angle, add the radius to the logarithm of
the less side, and from tlie sum subtract the logarithm of the greater side, or
add its arith. comp. : the remainder or sum will be the tangent of lhe angle
opposed to the less stde.
Example. lu the triangle bcd. having the side be 197*3. and €0 251*9;
to (iod the angles bco, cbd, and the side en.
7-5997728 ar. com. log. 25 1 9
12-2951271 rad. + log. 197 3
969389S9 tun. 3S° 4' bcd.
But if the angle included be oblique, add the logarithm of the difference of
the given sides to the tangent of half the sum of the unknown angles, und
frnm the sum subtract the logarithm of the sum of the given sidts, or add its
complement ; the remainder or sum will be the tangent of half their dif-
ference.
Esample. In the triangle abc, having the side ab 562, bc 320, and the
angle abc 128° 4' ; to 6nd the angles bag. acd, and the side ac.
The sum of the given sides is 882, and the differcuce 242, the half sum of
the unknown angles is 25° 58'.
705453H com. log. 882
2-3S3ftI54 log. uf242
9-68754U2 lang. 25'=' 53'
9 1268870 tang. 7 37
25 59
Angle ACB 33 35 sum.
Angle CAB 18 21 dif.
These 7*^ 37' being added to 25*^ 56' the half-sum of the angles unknown
tliesuni is 33^ 35' fur the greater angle acb; and the same 7" 37' being sub-
tracted from 25" 58', the remainder is 18** 21' for the lesser angle cab. Lastly,
knowin;r the angles, and two sides, the third side may bo found by the first
pro(>osition
xlTlii
OF RIGHT-LINED TRIANGLES.
Prop. IV. — Having the three Mida; to find any angle.
Add the three sides tog^ether, and take half the sum, and the diflVrences
betwixt the half-sum und each side: then add the compiement.*< of the In^-
rithms of the half-sum, and of the difference between the half-sum and the
side opposite to the angle sonj^ht, to the lo^rithms of the dilferences of the
half-sum. and the other side, half their sum will be the tangent of half the
angle required.
Example. In the triangle abc, having the side ad 562. 4c 800, and bo
320 ; to find the angle abc.
H = 941 CO.
H — AC ^ 41 CO.
H — AB = 279..
H — EC = 521. .
AC = 800
411 = &62
Bc = 320
1632
7 0752040
6-3872161
2-4456042
2-7168377
^sum 841 =
sum 20-G248620
Tang, of 61*= 2' = J sum 10-3124310
Wtiose double 128*^ 4' is the aiigle abc.
PLANE TRIANGLES RESOLVED BY THE NATURAL SINES.
&c.
Although it is generally best to solve triangles by the table of log. sines,
tangents, &c. yet. it wilt often happen that the results may be obtained with
more rapidity by means of the natural sines. &c. than even by the aid of the
logarithms.
Thus, with regard to Prop. II., when the sides are given in terms that are
suited for easy multiplication and division, it will be best to work with the
natural sines. As in the example already given. The sine of 128^ 4'. or of
Its supplement 51** 56', is -7872939. Hence
800 : 320 : : 1 : -4 : : •78'r2939 : ?
■4
BID I8*'2r-f = -31491756
Here we have only to consult the table Iwioe; while in the logarithmic
method it must bc donc^biir times.
Again, for Paop. III. Suppose there are given AC = 450, bc = 540. and
angle c = 60°; to find ab. By formula 7, Table 16, we have ab := ^(bc*
-f AC* — 2 BC. AC. cos. c) = ^(540' + 450* — 2 . 540 . 450 . 1736482) = 90
^(6'-f 5"- 60 X '1736482) = 90^(61 - 10-418892) = 90 ^50 581108 =
640*08.
So. again^ examples in Prop- IV. may be worked by a table of squares, and
formula 43 for cos. a, in Table 16.
And the most useful cases in heiglits and distances may be readily aoked
by means of the natural tangents and secants ; the base X tan. an;^U* at base,
giving the vertical altitude, and base X sec. angle at base, giving the slopin^^
or hypotenusal distance.
XllX
THE CASES OF SPHERICAI. TRIANGLES RESOLVED BY
LOGARITHMS.
The resotnlion of spherical tnanj^les is to be performed by the table ni
Rinen, tang-enLs, and secants; which we shall show by the 28 proposition*
following; whereof 16 are of right -angled, and 13 are of oblique triangles;
and first.
Of righi-angied Triangles,
Prop. I . — Having the ltg» ; to find the hypoUmme,
Add the cosine of one leg, to the cosine of the other leg; the sum (abating
radius) is the cosine of the hypotenuse required.
Erfimplr. In the rii^ht-anffled triangle abc, having ac 27** 54', and bc 11^
30'; to find ab the bypoicniise.
9 9911927 cosin. Il^acy
9-9463371 cosin. 27 54
99375298 cosin. 30 ab rcq.
Paor. II. — Having the two legs; to fitul either of the angles.
Add the sine of the leg next the angle sought, to the cotangent of the other
leg: the sum (al)ating radius) is the cotangent of the angle required.
Example. In the right-angled triangle abc, having AC 27° 54', and no 1 1**
30' : to find the angle bac.
9-6701807 sin. next leg 27* 54'
10G915374 cot. opp. leg II 30
10-3617181 cotan. bag 23 30
Prop. III. — Having the. hypotemuet and one of the angles ; to find the other
angle.
Add the coiiine of the hypotenuse to the tangent of the angle given; the
Riim (abating radius) is the cotangent of the nngle required.
Ittample. In the right-angled triangle abo, having the hypotenuse ab 30*,
unil the angle abc 69° 22'; to find the angle dac.
9-9375306 cosin. hyp. ab 30^00'
10-4211896 tang, abc ... 69 22
10 3(jI7202 cotan. bac . . 23 30
Prop. IV. — Having the hypotenuse^ and onf oftheanglet; to find the trgnerl
the given angle.
Add the tangent of the hypotenuse to the cosine of the angle given; the
num (abating radius) is the tangent of the Inig required.
THE RESOLUTION OF
Example. In the ri^ht-an^led triun^lc abc, havinn^ the hypotenuse ah 30^,
and the angle abc 69° 22' ; to 6nd the leg bc.
9 76 14393 tang. hyp. ab 30«00'
9-5noi8S cosin. abc .. 69 22
9 3084581 tang. 8C 11 30
Pnop* V. — Having the hypolenuM, and one of the angle$ ; to Jind the leg
opposed to the given angle.
Add the sine of the hypotenuse to the sine of the angle given ; the stim
(abating radius) is the fiineof the leg required.
Eramplr. In the right-angled triangle adc, having tlie hy|>otenuse AB 30°,
and the angle qac 28*^ 30' ; to find the leg bc.
9-6989700 sin. hyp. ab. . 80" 00'
9 6006997 sin. bac 23 30
9-29U6697 sin. bc 11 30
Prop. VI. — Having one of the legn, and the angle nejct it; to find the
hjfpoteitune.
Add the cotangent of the given leg to the cosine of the given angle; the
sum (abating mUius) is the cotangent of the hypotenuse required.
Uramplc. In the right-angled triangle abc, having the leg AC 27* 54' and
the angle bac 23*^ 30' ; to hnd the hypoleuuse ao.
10-2761563 cot. AC 27*54'
9 9023977 cos. bac ... 23 30
10-2385540 cot hyp. ab. . 30 00
Paop. VIL— Hac/ng one of the leg», and the angle next ii; to find the other
Add the awe of the leg given to the tangent of the angle given; the Mim
t^ahating radius) is the tangent of the teg required.
Example. In the right-angled triangle abc, having the leg ac 27° 54', and
the angle bac 23° 30'; to tinil the leg bc.
9-6701 H07 »in. ac. . 27° 54'
90383019 tan. bac 23 30
9-3084826 tao. bc. . U 30
Prop. VIII. — Having one of the leg*, and the angle next to U: tojSnd the
other angle.
Add the cosine of tlie given leg to the sine of the given angle; the sum
(abating radius) is the cosine of the angle required.
Example. In the right-angled triangle abc, having the leg bo IP 30', and
the angle abc 69° 22'; to Hnd the angle bac.
9-9911927 COS. bc 11° 30
99712084 sin. abc 69 2£
9 9624011 cos. bac 23 SO
SPHERICAL TRIANGLES.
tt
P»op, IX. — Having one of the le^y and theanglt oppotile to it; to Jind the
hypotemixe.
Arid the radius to the sine oi Lhe given leg^, and from the sum subtmct the
sine of the given angle, or add its cosecant; the remainder or sum is the
sine of the hypotenuse required.
EgampU. In the right-ungled triangle abc, having the leg bo 11° SO', and
the angle bac 23° 30' ; to find the hypotenuse ab.
9-2996553 sin. BC ll'^SO'
0-3993003 COS. rac 23 30
9 -6989 5 36 sin. ab 30 required.
Pbop. 'K,^ Having one of the Uga, and ike angle opponle to it; to find the
other leg.
Add the tangent of the given leg to the cotangent of the given angle; the
sum (abating radius) is the sine of the leg lequired.
Ejcample. In the right-angled triangle adc, having the leg bc 1 1" 30', and
the angle dac 23^ 30' ; to find the leg ac.
9'30M626 tang, bc iPSlV
10-3616981 cot. BAC 23 30
9 6701607 sin, ac 27 54
Prop. XI. — Having one of the tegn, and the angle opponte to it ; to find the
other angle.
Add the radius to the cosine of the given angle, and from the sum subtract
the cosine of the given leg. or add the secant; the remainder or sum is the
sine of the angle required.
Example. In the right-angled triangle abc, having the leg BC 11° 30', and
the angle bac 23^ 30'; to find the an;;le abc.
9-9623977 cos. b\c 23^30'
0-00bR073 sec. bc 1 1 30
9 9712050 Bin. abc 69 22
Prop. XII. — Having one of the Itgn, and tfte hypotenuse ; to find the angle
next the given l^g.
Add the tangent of the given leg to the cotangent of the hypotenuse, the
sum (abating radius) is the coi^ine of the angle required.
Example. In the right-angled triangle abc, having the leg AC 27° 54', and
the hypotenuse ab 30°; to find the angle dac.
9 7238436 Ian. ac 27^54'
10-2385606 col. ab 30 00
9 9624042 cnsi. bag 23 30
Paop. XIU. — Having one of the Ifgs, and the hypotmuse ; to find the angle
opposite to the given leg.
Add the rad:us to the sine of the given leg, and from the sum subtract lhe
8in« of the hypotenuse, or add its cosecant; the remainder or sum will be
the sine of the angle required.
■I
III
THE RESOLUTION OF
Example, In the riglil-aii^lcd triaiig^le auc, liavin^ the le^ DC 1 1** 3(K. and
the hypotenuse ab30*; to f\m\ the anjjle bac.
9-299G&53 siu. kfc bc 1 1^30'
0-3010300 cosec. hyp. Ati30 00
9-60II6S53 sine of bag 23 30
Pkop. XIV. — Having one of the legs, and (he hypolenme; to Jitid the other
leg.
Add the rndiua to the cosine of the hypott-niise, and from the sum subtract
the cosine of the given leg^, or add its secunt; the remainder or sum is the
Cf)sine of the lepf required,
Eiample. In the rip^ht-anglod triangle abc« having the leg uc 1 1'^SO', oud
the hypotenuse ad 30" ; to tind the le^ ac.
9-93753U6 cosin. au 30° 00'
00088073 sec. bc 1 1 30
9 9463379 cosin, AC 27 54
Prop. XV. — Having the angles; to find the hypotenuse.
Add the cotuii^enl of one oblique angle to the cnlangent of the other oblique
ani»;le; the sum (abating; radiufi) is the cosine ofthe hypotenuse required.
Esamplf. In the rii»:ht-anf;led triangle abc, having the angle bac 23^ 30'.
and the angle abc 59^ 2i' ; to find the hypotenuse ab.
0-3616981 cot. BAC 23° SC
9- 57 5 S 104 cot. abc 69 22
9 937508^ COS. hyp. ab 30 00
Prop. XVI. — Having the angles ; to find either of the legs.
Add the radius to the cosine of either oblique an^^Ie, and from the sum
subtract the sine of the other oblique angle, or add its cosecant; the re-
mainder or sum will be the cosine ofthe leg opposite to the angle whose co-
sine was taken.
Example. In the right-angled triangle abc, having the angle bag 23^30',
and the angle abc 69° 22' ; to find the leg bc.
9-9623977 cosin. bac 23^30'
002679 16 cosec. abc 09 22
9.991 IS93 cosin. bc U 30
Of Ohlique Triangles.
Prop. XV^II. — Having the three sides ; to find any of the angles.
Add the three sides togetlier, and take half the sum ; also the diOeroncc
h«'iwten the half-sum and the side opposite to the angle bought Then add
SPHERlCAt TRIANGLES.
mi
the cusecantf), or the coinitlemeots of ihe sines, of the other sides, to the sines
of ihe half-sum and of the sniti difference; half the sum of these four loga-
rithms is the cosine of half the ano^le required.
Example, In the triangle szp, having the side zs 4(/^, ps 70^ and pz
3S** 30' ; to find the ans^le zps.
cosec. 00270142
cosec. 0-2058505
tiin ^sxxtn 9-9833805
sin. fiif 9 7503579
2) 1 9-9666031
cos. 1 5° 47' 9 9833015
ZPS 31 34 required.
Prop. XVIII. — Having the (hrec an glen ; (ojind any oftkt sides.
Let the angles be changed into sides, taking Ihe supplement of one of
them ; then the operation will l>c tlic same us in the former proposition.
Prop. \W,^Having two artgl^Jt, and a side opposite to one of tftrm ; to find
the side opposed to the other angle.
Add the sine of the side given lo the sine of the angle opposite to the side
required, and from the sum subtract the sine of the ungle ofipusite to the side
given, or add its cosecant ; llie remainder or sum will be the sine o( ihe side
re<|uired.
Example. In the triangle sip. having the angle bzp 130° 3' 12", spz
31*" 34' 26", and the side zs 40^^; to find the side P9.
PS =
70^ CI
PZ =
33
30
zs =
40
s
urn
148
30
h
sum
74
15
zs =::
40
Diff.
34
15
sin. 18
sm. UP
9-S080675
9 883S294 \
850 j
0-2808858 >
1165 1 ^'^^"^
9'9729ft42 sin. rs
0"
48
40° 0'
J'49 56
fsi 35 .
t -34
rtqd. 70
See page Ixi following.
Prop. XX. — Having two angles, and a aide opposite to one of them ; to Jind
the tide between the anglra given.
Let a perpendicular fnll from ihc angle unknown, on its opposite side ;
then add the cosine of the given angle next the given side, lu llie tangent of
the given side; the sum (abating ratlius) is the tangent of the first arc, com-
prehended between the given angle next the given side^ and the segment of
the side where the perpendicular falN.
And the second arc, comprehended between (he same segment and the
other angle, is to be found thus : add the sine of the arc found to the tangent
of the given angle next the given side, and from the sum subtract the tangent
of the other angle given, or add its cotangent ; the remainder or sum will be
tlie sine of the second arc.
The sum nr difference of these two arcs will be the side required.
Example. In the triangle szp. having the angle zps 31° 34' 26", i.<ip
30* 28' 12", and the side pz 38° 30*; lo find the side ap.
31° 35' ."
-34
38 30
34 7 30
9-9303781 \
440 f
9-9006052
COB. ZPS
{
tan. PZ
9-8310273 tan. PR lat arc
THE RESOLUTION OF
0-74&86981 . „„ J
93-2 J "'""^^ '
r34=
7' .'
. 30
9-7884 529 1 . J
1227/ ^"'"^^ i
rai
34 .
. 26
0*2301404 1
2313 1 ^^^"'^ -
fso
L •
35
29 .
-48
9-7679103 sill, sr 2d arc
52 30
add PR Ist arc
34
7 30
sum ifl sp
70
See p&ge Ui following*.
But when the peqiendicular falls out of the triangle, the diflerence of the
two arcs will be the side required.
Prop. XXI. — Having iwo angloi, and a aidf opptmte to one ofthrm; to find
the third av^le.
Let a perpendicular fall from the anrjlc unknown, on its opposite side:
thon »dd the cosine of Ihe given side to the tangent tsf the adjacent angle;
the sum (abatinj^ radius) is the cutaugcnt of the first angle to be found,
comprehended by the given side and the perpendicular.
And the second anj^le, comprehended by the perpendicular and the side
unknown, is to be found thus ; add the sine of the nnffle found to the cosine
of the ^veu angle opposite to the given side, and frutn (he sum subtract the
oosine of the other angle given, or add its secant ; the remainder or sum will
be (he sine of die second angle.
The sum or diflerence of these two angles will be the angle required.
Example. In (he triangle skp, having the angle zrs 31° 34' 25''. z»p
30° 28' 12", and the side pa 38' SC ; to find (he nngie mp.
9 8935444 cosin. pz 38° 30' 0"
9-78845291 , f 31 34 .
1227 | **^"«?-^^^ 1 . . 26
9-6821200 col. 1st < pzr 64 18 50
9'9547619\
507/
9-93339481
594/
0-06954431
3361
f64 18 .
\ . . 50
J 30 29 .
1 - -48
J 31 34 .
"1. . .26
99598447 sin. 2d < sza 65 44 21
then add 1st < pzr 64 18 50
the sum is azp 130 3 U
Sin. PZR
COS. 3!8P
bee. zps
See page Ixi following.
But when the perpendicular falls out of tl»e triangle, the difference of the
two angles will be the angle required.
Pbop. XXII. — Having ttoo tides, and the ans;U bHvxen them ; to find dthcr
of the other angtes.
Let a perpendicular fall from the unknown angle, which is not required, on
its opposite side : then add the cosine of the given angle to the tangent of the
given side opposite to the an;;lc required ; the sum (abating radius) is the
tangent of the first arc, comprehended between the given angle and the seg-
ment uf the given side where the perpendicular falls.
SPHERICAL TRIANGLES.
W
And the second arc is the diff*erence of that side aiid the Brnt arc, being
comprehended between the same segment and the angle required.
Now add the sine of the first arc to ihe tangent of the given angle, j*nd
from the sum subtract the sine of the second arc, or add its cosecant; the
remainder ur sum will be the tangent of Ihe angle required.
ErampU. In the triangle szp. having the side pz 38^*30', PS 70°, and Uie
angle zps 31^34' 26'^; to And the angle zsp.
9-93037811 f 31^34' ."
440 1 <:<'«'»• "» I . . 26
9-9006052 tang, pz 38 30
9*8310-273 lun. pii, I si arc 34 7 30
taken from ps 7U
leaves SR, 2d arc 35 52 30
sin. PR
ZPS
cosec. AR
{
34 7
9-74S8699\
932/
9-78845291 .
12271 ^ff
0-2320011 1
873 J
tan. XP8 req. 30 29
34
35 53
30
26
30
12
9-769()270
See page Ixi following.
To find both the ttnfmown angles.
Add together the cosecant, or the complement of the sine, of half the sum
of the given sides, the sine of hntf their difference, and the cotangent of half
the angle given ; the sum (abating radius) is the tangent of half the dif-
ference of the angles required.
Add also together the secant, or the complement of the co.sine, of half the
sum of the given sideb, the cosine of half their difference, and the cotangent
of half the angle given : the sum (abating radius) is the tangent of half the
sum of the angles required.
Then add the half-difference of the angles required to their half-sum. and
you will have the greater angle: and subtract the half-difference from the
half-sum, and you will have the lesser angle required, the same as in the
former operation.
Cosec. i sura 009067 19 Sec. J sum
Sin. i diff. 9-4336746 Cosin. J diff.
Cot. izps 10 5486352
PS =
PZ =r
Sum
Diff.
j^ Sum
^Diff.
<ZPS
7(f 0'
39 30
108 30
31 30
54 15
15 45
02334015
9-9833805
10'548635'2
Cot. J ZP3
T. 49°47'30" iO-07298l7'T. 80** 15'42" T0^7654172
Half sum of angles required i.i 80° 15' 42''
Half the difference is 49 47
31 34 26"|'^^* greater angle sap is 130
l<zpfl = 15 47 13 (^^ lesser angle zbp is, as before 30
30
3 12
28 12
Prop. XXIII. — Having two iides, and the angle between them; to find the
third aide.
Let a peqjendicular fall from either of the angles unknown, on its opposite
side: then add the cosine of the given angle to the tangent of the side from
whose end the perpendicular is let full ; the sum (abating rtidius) is the tan-
gent of the 6rst arc, comprehended between the given angle and the segment
of ihe side where the perpendicular falls.
M
THE RESOLUTION OK
And the second arc is the dilfcrence of that side and the first arc, being
comprehended between the same seirmeul and the end ol the side reqaihed.
Now add the cosine of the second arc to the cosine ofihc side from whose
end the perpendicular falls, and from the sum subtract the co<»ine of the first
arc foiiiiii, or add its secunt; the remainder or sum will be the cosine of the
side iequir<?d.
Example. In the triangle szp, having the side PZ 39^ 30', ps 70^ and the
angle zps 31'' 34' 26" ; to find the side'zs.
9-93037811 f3l°35' ."
440 r <^o«'"-=^"'« i . -34
9-9006052 tanff. pz 3S 30
9-6310273 tan. pr, 1st arc 34 7
taken from pb 70
leavert sn, 2d arc 35 52
30
30
9 '908 59981 f 35 53
9-8935444 cosin. pz 38 30
00820236 > ("34 7
429} '^' " 1 - .
30
SO
1-8842553 cosin. za req.
See page Ixi followinp^.
Prop. XXIV. — Haviiui two sides, and the an^k opposite, to <me of them; to
Jind th^ angle opposed to the other side.
Add the sine of the unfile e^iven to the sine of the side opposite to the
angle required, and from the sum subtract the sine of the side opposite to
the angle given, or add its cosecant ; the remaindePor sum will be the sine
of the angle required.
Example. In the triangle szp, having the side PS 70°, zs 40**, and the angle
»zp 130*^3' 12"; to find the angle zps.
1 . r4^66' "
Vain. sup. szp-J ^„
9-8838294
650
9-S080675 Mn. zs
U270142 cosec. Ps
9*7l899fil sin. ZP8 req
40
70
31 34
26
See page Ixi following.
Prop, XXV. — Having iu^ sides, and the angle opposite to one of them; to
find the third side.
Let a perpendicular fall from the angle between the sides given, on its
opposite side ; then add the cosine of the angle given to the tangent of the
given side next thai angle; the sum (abating radius) is the tangent of ttie
first arc, comprehended between the given angle and the segment of the side
where the perpendiculur falls.
Now the 2d arc, comprehended between the same segment, and the end
of the side rcipdred, is 10 be found thus : add the cosine of the first arc to the
cosine of the given side opposite to the angle given, and from the sum sub-
tract the co'iine of the other given side, ur add ils secant; the remainder or
sum wilt be the cosine of the second arc.
The sum or ditfe-cnce of these two arcs wi^l be the bide required.
SPHERICAL TRIANGLES.
Ivu
Example. In the Iriang^le 8ZP, having the side pz 39^ 30', sz 40^, and the
■nglefipz 31'' 34' 26''; to 6nd the Pidc ps.
r3l°35' ."
X . -34
3S 30
9-930378 n
440 1 ''''^^^'^
99006052 tan. pz
9'&3I0273 tang. pr. IhI arc 34 7 30
9 91789081 f 34 8 .
40
9>&842540
0*1064556
cosin. 8Z
nee PZ
3S 30 U
9 9086432 cosin. sk. 2d arc 35 52 30
add PH, 1st arc 34 7 30
gives P8 req. 70
See page \\\ following^.
But when the perpendicular fulls out of llie triangle, the diflereuce of the
two arcs will be the side required.
Prop, XXVI. — Having two tides, and the angle opposite to one of them ; to
find the angle between them.
Let a perpendicular fall from the ann^le between the sides given, on its
opposite side : then add the cosine of the t^iven side next the piven angle, to
the tangent of that angle; the sum (abating radius) is the cotangent of the
hist angle to be found, comprehended by the given side next the angle given,
and by the perpendicular.
Now the second angle> comprehended by the perpendicular and the other
given side, is to be found thus : add the cosine of (he first angle found to tho
tangent of the given side next the angle given, and from the sum subtract the
tangent of the other given side, ur add its cotangent ; the remainder or sum
will be the cosine of the second angle to be fuund.
The £um or the di&erence of the 6rst and second angles will be the angle
required.
Example. In the triangle szp, having the side pz 38° 30\ sz 40^, oud the
angle spz ai^'Sl' 20'^; to find the angle szp.
9 8935444 cosin. pz
9-7884529 > .
1227| ^«"K'
SZP
{
38° 30' 0'
31 34 .
. . 26
9-6821200oolan.pzn, lst<64 18 50
9-63688591 f64 19 .
4^^j-cosm.PZR I ^j-
9-9006052 tang, pz 38 30
0-0761865 cotan. sz 40
9*6137213 cosiu. szr. 2d < 65 44 22
add p^fl, Ifit < 64 16 50
gives SZP, req. 130 3 Id
See page Ixi follnwing.
Iviii
THE RESOLUTION OK
Prop. XXVil, — Having two angUs, and the tide beticetn them ; tojind either
of the other aides.
L«rl B perpendicular fall from the f^ivcn angle^ which is next the side re-
quire<f, upon ils opposite side: then add the cosine of the fpvvn side to the
taD&;ent of Ihe niveii an^lc opposite to the tide required ; the sum (aholing'
radius) is the cotangent of the 5r»t ang!c to be found, comprehended by the
given side nntt the perftcnHicular.
And the second angle is the ditlerence between the first and the given
angle next the required side» lieing <*oiiiprehended by the perpendicular and
thai side.
Now add the cosine of the first angle found to the tangent of the itide
given, and from the sum subtract the cosine of the second angle, or add its
secant; the remainder or sum will be the tangent of the side required.
Example. In the triangle .szp, having the angle spz SP34'26", SZP
180^ Zf 12", and the side pz 38"^ 30' ; to find tlie side sz.
9-893&444 cosin. pz 38° 30' 0"
9-78845291 , I 31 34 .
1227 1 ''*"^- «" i . . 26
9-6821200 cot. pm, 1st < 64 18 50
taken from szp 130 3 12
leaves szr, 2d < 65 44 22
9-636&859\ . ^,„ r64 19 .
9*9006052 tang, pz 38 30
0-8861750X /65 44 .
1028/ '^•'^^'' 1 . .22
9 9238126 tan. h req. 40
See page Ixt following.
Tojind both th^. unknown *irf«.
Add together the cosecant, or the complement of the sine, of half the sum
of the angles given, the sine of half their ditference, and tlie tangent of half
the given side ; the sum (abating radius) is the tangent of half the dif-
ference of the sides required.
Add also together the secant, or the complement of the cosine, of half the
sum of the given onglcb, the cosine of half their difference, and the tangent
of half the given side: the sum (abating radius) is the tangent of half the
Rum of the Hides required.
Then add half the difference of the sides required to their half-sum, und
you will have the greater side: and subtract the half-diiferencc from the
half sum, and you will have the lesser side required, the same as in the
former operation.
RZP
MPZ
Sum
Biff*.
130^ 3' 12" Cosec. isum 00056062
31 ^34 26 Sin. J diff. 9 8793527
"37 — 3Q Tang. Jpz 9 54309.36
28 46 Tang, of 15*="
161
98
\ Sum 80
^ Diff. 49
48
14
49
23
9-4280525
Half sum of the sides rccjuired is
Sec. J sum
Cosin. J diff.
Tang. J PI
Tang, of 55°
0-7968360
9-8148437
9 5430936
10 1547733
55"
PZ
i PZ
3N
19
30
15
Half their difference is , 15
The greater aide sp ib 70
Lesser side sz is, a« before 40
SPHERICAL TIUANGLESL
Ux
Prof. XXVIII. — Hamns:lwo ansles. and the aide bdween than; to find the
third arigU.
Let Q perpendicular fall from either of ihe ang-les given, upon its opposite
aide: then add the cosine of the side a;\ven lo the tan^nt of the ^iven
angle, from which the perpendicular does not fall ; the sum (abating radius)
iff the cotangent of the first nngle, comprehended by the given side and the
perpendicular.
And the second angle is the dlQerence between the first and the given
angle that the perpendicular fell from, being comprehended by the perpen-
dicular and the side opposite to the other angle given.
Now odd the sine of the «-econd angle lo the cosine of that given angle
fi'om which the perpendicular did not fall, and from the sum subtract the sine
of ihc first angle found, or add its cosecant; Uic remain Jcr or sum will be
the coiiine of the angle required.
Example. In the triangle szp. having the angle szp 130° 3' 1:2", spi
31° 34 26", and the side pz 3fi° 30' ; to find the angle psz
pz
38" 30'
34 .
. 26
9-6821200 cot. pzr, 1st < 64 18 50
taken from szp 130 3 12
9-8935444 cosin.
9'7884529\ ,
1227 1 ^"ff »"
{"
0"
leaves szr, 2d < 65 44 22
0045l773'> r64 19 .
101 ] <:o««=»^»-5 , _io
9-9303781 1 ^ .„ „„, fsi 35 .
9'959S246i f 65 44 .
209 1 '^^"'"'^ i . . 22
9-9354550 cosin. Piz req. 30 28
See page \\i fotlowiug.
u
THE RESOLUTION OF
FOR THE USE OF TUE VERSED SINES MAY BE ALSO
ADDED THE FOLLOWING PROPOSITIONS.
pROH. I. — Having two sides of a vphfric triangUt with tht aitgU belweai
than ; to Jitid thr. third si*ie.
Add together the log*, versed nine of the contained angle, and the log*. !«iiies
of the two sides; ihe sum (abotin^ twice the radius) is the lo^iirtthm of a
numt>er to be found, which added to the uaturul versed sine of the ditl'erence
of the two ^iven sides, the sum will be the natural versed sine of the third
side sou^L
Or when the contained anjfle is above 90**, add the log. versed sine of its
supplemenf, and the log. sines of the two sides together; the sum (abating
twice tl»e radius) is the logarithna of a number to be found, and subtracted
from ihc natural versed sine of the sum of the two given sides, the remainder
will be the natural versed sine of tlie third side sought.
Example 1. In the triangle szr, liaving the side pz 3B^ 30', PS 70*^, and the
angle zps SI"* 34' 26"; to find Iht side zs.
91703625 log. vir. sine zsp 31° 34' 26"
9-7941496 log. sine of rz 3S 30
9-9729858 log. sine of ps 70
6'9S7497<) log. of the numb. 865960
Nat. vers. diff. sides SP 30' 1473596
Nat, vers. %8 Of :j339558
Eiamplr. 3. In the triangle szp, having the side pz 3^ 30', zs 40°. and the
angle siP ISO^'S' 12"; to find Ihe side pa
The angle vzp is the supplement of szp.
9-5520590 log. vers. viP 49° 56' 48-
9-7941496 log, sin. pi 39 30
9-8080675 log. sin. zs 40
1426514
&0063-31
91542761 log. of the num.
Nat. vers, sum sides 7 b° 30'
NaL vers. P8 70^
6579S07
This proposition may be very useful in finding the distances of places on
the earth, whose longitudes and latitudes are known ; the distances of stars,
whose declinations and right asceusiuns, or longitudes and latitudes, are
known ; and consequently llie altitudes, or common altitude of two stars, or
two altitudes of the sun, and lime between the ob«er\a(ions, or difference of
azimuth, being taken, the latitude of the place may readily be found.
Prop. 1 1. — Having two an^e$ of a uphrric triangU, and the side bdtwten
them; to ^nd thi: third angle
Let the angles be changed into sides, and the side into an angle; then
proceed as in the former proposition, and the result wilt be the supplement of
Ihc third angle. But if one of the given angles exceed 90", lake its tuppl*-
meut. and ihc result will be the third angle.
SPHERICAL TRIANGLES.
I3U
'Hie followinff remarks ami directions, Ihr rendering the proportional port of
B logarithm always nttditive. and ibr usin^r r -\- t^ c — /, &c., for a or r, &c.
in the foregoiiiif propositions 20, 21, 22, 23. 2b, 26, 27, 28, were cunimu-
iiicate4 by the Rev. Nevit Maskelyne, D.D. aHlrunomer nyul, and F.R.&.,
the fourth case having been invented by him many years Bince, and de-
livere<l to the computers of the Niiutiou] Gphemeris, as precepts necessary
in computing the moon's distance from the stars in some cases; the rest
he has now added on this occasion : —
** The result of trigonometrical calculations will be sometimes inaccurate,
owingr to the logarithms not being carried Ip a greater number of places in
the table, as will suilicienlly appear from the Ingarithmic difTerenees being
small, This will happen where the answer comes out in the cosine of a very
small angle, or the sine of an angle near 90°. The greatness of the difTerences
of the log. sines of small arcs, or cosines of large ones, will sometimes atlect
the accuracy of the result of the second part of the operation, luiless the first
arc be found to a small part of a minute or second : to prevent such error,
and render the computaiiun easier* putting t, I', s, c for the tangent, cotan-
gent, sine, and cosine of the 1st arc or angle, then in the 2d part of the work*
In Prop. 20, if the first arc is very small, for s use c + t
21 angle is very small, for s use c — t'
22 arc is very small, for a use c + t
23 arc is near 9iP, for -c use t — h
25 arc is near 90'^, for c use a — t
26 angle is neur 90^ for c use a -<- t'
27 angle is near 90°, for c use a 4- t'
28 angle is very small, (or— a use l' — c.
Thi» obviates the necessity of finding the first arc to a very minute exactnesfl,
which olherwi<;e would be necessary in taking out the ftine or cosine of the
same arc in the second part of the work.
Where tlic foregoinp* prcccptn direct lu subtract a sine or cosine, it will be
readier in practice lo add a cosecant or secant ; and where Itiey direct to sub-
tract a tangent (which is dune ii> Prop. 26), it vvill be retidicr to add a cotan-
gent. This method lieing used, if it l>c required to find the logarithmic sines,
&c. to the enuciness of a second, and the logarithm is increasing (as in the
sines, (angonts, and secants), write down the logarithm for the degree and
nkinute wiihout the st-conds ; and also writf^ ditwn the proportional part for
the seconds; but if the logarithm is decreasing (as in the cosines, cotungenL*,
and cosecant.«)( write down the logarithm for the next greater minute, and
also writedown the praportiunal part fur the complement of the seconds to
60 ; and proceed in like manner with every logarithmic sine, cosine, &c. used
in the work ; the sura of all the logarithms (ahatiiig one or two radii or tens
in the index, according as 2 or 3 logarithmic sines, t!tc. are u.sed in the part
<if the work in question) will be the logarithmic sine, cosine, tangent, ur cn-
laiigenl required.
Example I . To find the log. sine of 34** 17' 24".
Here log. sine of 34" 1 7' 9 7f>07287
And as CO : 24 or OS 10 : 4 : : 185 3 : .. 741
9 750H02d
Ixii
USE OF THE
Example 2. To find the log. cos. of 55° 42' 36".
Lot,r. COS. of 55° 43' 9-7507287
60 : 24 (60 - 30). or 10 : 4 : : 185 3 : .. 741
9-7508028
Ejample 3. lu the triatit^le pls, given
p r= 20^ 30' 48"
PS = 85 3 40
PL =89 10
lo fin<i LS by Piop. 23
so being perj), pl.
p 20°3r ." COS. . . 9-9715404
. .-12 95
P8 B5 3 . taiu. . W0624350\ COS. found by taking \
. . 40 9814 J iaug. from sine J
8-9349686
PD 84 43 43 Ian.. . U 0349663 110349663
PL 89 10 cosec. pd 84'' 44' ." 100018374
— 17 . . 33
cosin. LO 4 27 ... 9*9986888
— 43 . . 70
LIJ
4 26 17
cOBin. IS 2U 53 24 .. 9 9704714
Here to avoid the trouble of finding the proportional part for the large
logarithm difference of the cosine of ph. thut cosine \h found by subtracting
the tangent of it (already loinid) from the sine, which is easily found, because
the differences are Bmall : and, for (he same reason, the sum of the tangent
and cosecant of pd, are used instead of its secant.
N.B. — The perpendicular should always be let fall from the end of the
side, PS or pl, which didcrs most from 90°, over or under.
OF THE TRAVERSE TABLE.
This traverse table, or table of difTereoce of latitude and departure, inpageb
158, 159, is so contrived, as t<i have the whole in one view, and is so plainly
titled as to want little or no explanation.
The distances I, 2, 3, &c. at the top and bottom, may be accounted 10,
20,30, &c., and the 10 as 100, if the minutes of latitude and departure, an-
swering to the course, be increased in the same proportion ; so that rf the
distance consists of two significant fijrures. ihc difference of latitude, and the
departure, is euch lo l>e taken out «l twice; nnd if of three figures, at thrice.
The chief design of ihi.s table ia for the ready and exact working of tra-
verses ; hut it may ulso he a]iplied lo the soluLion of the several cases of
plain saihng. and tn some other uses
Prof. I. — Having the courte and dUiatiee^ to find the difference of UtlUudc
and departure.
Seek the course on the lef^-hand of both pages downwards, if less than
four points, or 45 degrees; or if greater, on the right hand upwards; and
even with it in the double column, signed at the top and bottom with ik«
distance, is found both the difference of latitude and the departure.
Eiample 1. A ship sails ssw | w 37 miles; the difference of latitude and
the fiepnrture are required.
Find the course 2j points on the left-hand side of each page, and even
with it in the double columns signed 3 and 7. the two figures of the distance
TRAVKKSE TABLE Ixiii
the diflerenee of latitude for 30 is 25* 73i. and for 7 is 6'004. the sum Is
81*736 for the whole diflerence of latitude; and the departure for 30 is
15*4*23» and for 7 is 3' 599, the sum is J9022 for the whole departure. Thus,
Diit. Ditr. Lat. D«p.
30 25*732 .. 15-423
7 6004 . . 3-599
37 miles 31-736 . . 19 022
EiampU 2. A ship sails be 49° 148 miles ; the difference of latitude and
tlie departure are required.
Find the course 49 defrrees on the rig-ht-hand side of each page, and even
with it in the double columns sifrned 10, 4, ond 9» the difference of latitude
at 100 mili's is 65606. at 40 is 26242. and at 9 is 5*248 ; the sum is 97096
for the whole difference of latitude. And the departure at 100 miles is 75*471,
at 40 is 30'18S, and at 8 is 6038; the sum is 111 697 for the whole de-
parture. Thus.
DuL DifF. L^L Ocp.
100 65 606 .. 75*471
40 26*242 .. 30 188
8 5 248 .. 6039
MS miles 97096 111-697
Prop. II. — Hoping $everal courstM and ditlances ; to Jind the difference of
lalilude and the departure.
Malce a table in the following mnnncr, and put therein each course and
distance ; then find the difference of latitude and departure lo each course by
the preceding, and |)tace them in ttie proper column ; Ihe dilference of the
sums of the northings and southing is the whole diflerence of latitude ; and
the difference of the sums of the eastings and westings is the whole departure.
Example. A ship from the latitude of 50° north sails according- to the
courses and distunces set in the traverse table ; the differences of latitude and
the departure arc found at the bottom.
THE TRAVERSE TABLE.
Counev.
OiA
Dim of Ut.
Depa
rture.
Milcf.
North.
SoQtIl.
EuL
We*t
SSE^E
SEi E
S b W } W
S 48*^ W
N SS'^' W
S40°W
79
86
108
112
70
94
6-101
69-671
54 557
101-687
74-942
64*349
37-241
66479
36-384
83 231
69-734
53-994
6*101 365205
6 101
103-7 -20
243-343
103*720
Diir la. 359-104
Depart.
189-623
This proposition may be applied in the surveying of Iarg« tracts of laud,
.IS u cmmiy, Ac. and was made use of by Mr. Norwood in measuring the
*
lUT
USE OF THE TRAVERSE TABLE.
distanue from York to London, as the road led him, observing the several
1)earin^ by Ins circumferentor, and findinijf by snch a table his several differ-
ences of lutitude :ind dt-purture, by which he obtuJned the distance between
the parallels of London and York, pretty near the truth, so longr ago as the
year 1635; as may be seen hi his Seaman's Practice.
Also in plotting the survey of a county thns taken, the circuit station-linea,
though consisting of many hundreds, may be reiluced to a few for the first
doping, and the fike for the iutern:icdiale5 of each line first plotted, by which
every fitation may perhaps be more truly placer! than by any other method:
the distances in the table may 1>e chains of 66, or 100 feet, as well as miles,
or any other measure that the differences of latitude and departure would he
had in.
Pftop, III. — Having the difference of latitude^ and the departure; to find
the course and distance.
Seek the given difference of latitude and departure, taken together, in thei
columnB, or the nearest numbers to them; and the course is even therewith
at the side, and the distance at the top and buttcmi : but if the given difference
of latitude and departure cannot be founrj nearly, take J. J, Ac. part, or any
equal mult'ple of them that can be found ; then the course is even with them
.It the side, and such a part of the distance, as was taken of the difference of
latitude and departure, at the top and bottom.
Example I. Given the difference of latitude 59 miles s, and th^ departure
68 mile* w; the course and distance are required.
In the double column over 9, even with 49° at tlie right-hand side, is found
together the given difference of latitude and departure ; therefore the course
is 49° sw. and the distance 90 miles.
Erample'Z. Given the dilf'^rence of latitude 30 miles y, aud the departure
18 milca e; the course and distance arc required.
Here the given diflerence of latitude and departure, or any numbers near
them, are not to be found together in the table; therefore taking j or the
double nf each, the course is found to be 31° nr, and the distance 35 miles.
Note, A table computed to every miie in the distance up to iOO miles
would more readily solve this eicumple.
Prop. IV. — Having the departure and middle latitude ; to find the diffcrtnce
of hn^itudct according to the method first given by W* Jones, Esq. F.R,S-
Seek the given departure, or the next less nnrnber in the columns signed
lat even with the middle given latitude found aimuig (lie courses, and at the
top and bottom (sigu«'d dist.) is the difference of longitude sought; which,
if not found directly at once, may be taken out at twice or thrice.
Example I. Being yesterday noon in the latitude of 37** 17' n, and this day
noon in 38° 43' x, and by the table the departure is found 70-921 e; the
difference of longitude is required.
In the column signed lat. under 9, even with 38°, the middle latitude is
found 7*0921 ; therefore 90 miles is the difference uf longitude sought.
Example 2. Being yesterday nnon in latitude 46^25' n, and this day at
no*m in 47° 35' n, so that the middle latitude is 47° n, and the departure is
founi 11253 miles w; required the difference oflouiiitudc.
In the column signed lat, over 10 at the l>otlom, even with 47 at the righl-
band ^id»». h 6 B200; therefore subducting 68 200 from 1 1253, the remainder
is 44-33; then over 6 is 4*0920, and 40-92 subducted from 44*33 leaves 3-41,
OF MRRCATOR'S SAILING.
Ixr
which is found over 5 ; therefore the diflTerenve uf lon^tude is 165 tniles
west.
If the middle lutitiide be not on even degree, but have odd minutes ; find
Ihe dilTerence of lon<^Uude, for the even degrees next less and greater, and
add a pruportional part of the diflorence Iwtwecn the two results to the lesser ;
the sum will be iJio difference of longitude sought.
Suppose the middle latitude in the last example had been 47° 20' N ; then,
af\er finding the difference of longitude as before for 47'^, find it also for 48°«
which is 168 miles ; then ^ of the difference being added to the former, gives
the difference of longitude [66 miles west.
Note. Ttiough this method is not in all cases near the truth, yet when the
miles are geographical, it is sufficiently near for daily practice in any voyage,
as well OS easy, and very expeditious.
Pmop. V. — Having the latilvdes and the loti^tudes of ttto placet, tojind the
bearing and distance.
Seek the complement of the middle latitude among the degrees, and the
difference of longitude in minutes among the distances, the departure an-
swering is found in its proper column; then witli the difference t>r latitude
and departure, [in<l their bearing or course and distance by the third.
Ksampie. Let the Lizard be given in the liitllude of 49^ 50' n, and W^ 21'
w longitude, and Cape Ortegul in the latitude of 44*^ lU' N, and 70° 43' w
longitude; to tind the bearing und distance.
The difference of longitude is 142'; and in the columns signed dep. under
10, 4, and 2, even with 43° the co-middle latitude, are found 6-8200, 2*7280,
and 1*3640; then increasing the two former as before shown, their sum ia
96'944 miles w, for the dejiarture; nnd the bearing, or course, answering to
340 miles difference of latitude, witfi 96*844 departure, is found about 16°
8W ; and the distance about 354 miles.
OF MERCATORS SAILING.
Thk uses of the table of meridional parts are fully fiupplfcd by Ihe table of
logarithmic tangents, as is demonstrated in N" 219 of the Phihaophical
Transactions. It is there proved, Ist. That the meridional Hue, or scale of
Mercalor's Chart, is a scale of the log. tangents of the half-complements of
the latitude. 2dly. That such log. tangents of Mr. Driggu's form, are a scute of
the differences of longitude, on the rumb which makes an angle of 51° 38' 9"
with the meridian. And 3dly. That the differences of longitude on different
rumbs, are to one another as the tangents of the angles of those rumbs with
the meridian.
Hence it follows, that ihe difference of the log. tangents of the half comple-
ments of the latitudes, is to the differtuce of longitude a ship makes in Hailing
on any rumb from the one latitude to tlie other, as the tangent of 51° 38' 9"
(whose logarithm is 101015104) to the tangent of the angle of the rumb or
course with the meridian ; so that :
I. If two latitudes, and the difference oflongitude, be given^ the course and
distance are readily deternuned by (hi?* rule.
Take, by help of the tahles, the difference uf the log. tangents of the half-
complements of the latitudes, esteeming the last three figures to be a decimal
fraction ; and add the complement of its logarithm to the logarithm of the
difference of longitude reduced to minutes, and the constant log. 10'1015104*
Ihe sum (uhatijig radius) .shall be the log. tangent of the course. And to
the log. secant of the course, add the logarithm of the difference of latitude
f
Ixvi OF MERCATORS SAILING.
reduced to minutes, Lhe sum (abating; radius) shall be the logurillim of the
distance iu minutes.
Example. Given the Lizard to be in latitude 49" 55' n, Barbadoes tn 13^
lU' N, and their dilference of longitude 53^ 00' or 3180' w ; to find the course
and distance.
IP 1 f -f Barbadoes 38° 25' I. tan. 9-9993082 i. Sisy = 3*5024271
a ^O- '*^ \ Lizard 20 2 J I. tan. 95620477 const, log. 101015104
diir. 3372-605 its co. log. 6 4720346
Log. tang, of the course 49*^ 59' 10" sw 100759721
Loff. sec. of the course 49 59 10 10* 1918067
Log. of 2205' difl; of the latitudes , 3-34340S6
Log. of 3429-378 distance of Barbadues from ibe Lizard 35352153
II. If two latitudes and the course be given, the difference of longitude is
obtained with the same case : for as lhe tangent of 51^ 3S' 9" is to the tangent
of the course, ;>o is the difference of the log. tangents of the half-complements
of the latitudes, to the difference of longitude sought. Therefore, to the
complenieul of the constant log. 101015104, add the log. of the difference of
the log. tangentg of the half complements of the latitudes, and the log. tan-
gent of the course, the sum (abating radius) will be the log. of the difTerence
of longitude in minutes.
Exavipie. Given the latitudes 49° SV and 13° 10', and course 49^ 59' 10";
lu tind the difference of longitude.
Lat. 13^ 10' its i co.lat, 38° 25' I. Un. 9-8993082
Lut. 49 65 20 2J 1. tan. 9 56-20477 co. const log. 9-8934S96
diff. 3372*605 its log. 3*5279654
Log. lang. of (he course 49° 59' 10" 10 07597'21
Log. of 31 80'= 53° for diff. of longitude 3 5024271
By this rule, having two good observations of lhe latitude, and the course
duly steered, the reckoning of a ship's way is best ascertained, especially if
you suil near the meridian.
III. If the latitude departed from, tlie course steered, and distance sailed^
be given; to 6nd the ship's latitude, and difference of longitude.
First, the latitude is obtaineit from the consideration that the distance is to
the difference of latitude, as radius to the cosine of the course, which is com-
mon to plain sailing. Therefore to the log. of the distance add the log.
cosine of the course, the sum (abating radius) is the log. of the difference of
latitudes ; which difference added to the lesser latitude, or subtracted from
the greater, lhe sum or remainder is the present latitude * then having the
two latitudes and the course, the difference of longitude is found by the second.
Eratnj}ir, Having sailed from the Lizard, in lat. 49^ 55' N. on a course
49° 59' 10'' south-westerly 3429*378 miles: required what longitude and
latitude the ship is found in.
Log. of 3429*373 the distance sailed 3*5353153
Log. cosine of 49° 59' 10" the course ^ . .. 98081933
Log. of 2205'. or 36^ 45' diff. of the latitudes 33434086
Now subtracting 36° 45' from 49° 55', the remainder 13° 10* n, is the latitude
the ship is found in.
By which latitude, now known, the difference of log. tangents will be
fuund 3372'6U5, and the further process in nothing differing from itie second
rule, by which the difference of longitude will be found 53° 00'.
CIRCULAR AKCS. Ittit
Thus the dead reckoninnj by the lop;, line, and daily account of a ship's way,
are duly kept* and the trouble very little more than by pluin sailing.
These are ull the cases that occtir in practice ; the rest, which are mostly
fipeculative, are either easily reducible to these, or else nut to be performed
by logtirithms, and therefore come not at present under our cognizance.
But it is to be noted, that both the com]}lements of the latitudes are to be
estimated from the same pole of the world ; which may be from either; aod
therefore if one latitude be N, and the other s, to have their coinptementa,
you must add 90° to one of Ihem, and sublrnct the other from 90®, and then
the o]>eration will be the same as iu the preceding cases.
EzampU, Given St. Jago, one of the Cape-de-Verd Islands, in the lati-
tude of U^ b& N ; and the island St. Helena, in latitude 15° 45' s, and their
difference of longitude 30^ 12' e ; to find the course and distance.
, ,, fSt.Jajro 52^28'. I. tan. 10-114 1965 1.1812' 32591582
^co. ittU -J^sl Helena 37 7i. 1. tan. 9-8790845 con^t. log. 101015104
23i4I20 iu co. log. 6-62SI714
Log. tnng. of the course 44° 1 1' 53" be 99878400
Log. sec. of the course 44 11 53 101445200
Log. oflS41'd.ir. ofthe latitudes 3-2gj0538
Log. of 2567-875 distance of St. Helena from St. Jago . . "3'40957as
Or if it be thought easier, when one latitude is n, and the other s, yva may
add 90° to each nf them, Ihc sum of ihe log. tangents of their halves (abuting
livice the radius) will be the same as the dilTerence of the log. t^mgents of the
fonner. For an example, take the same latitudes as in the preceding.
•PI OAO , /14^56'= 104^56'! ., . ,- J'52°28' I. tan. 101114905
Tlien 90 + 1 ^5 45 ^ ^^^ ^^ ]- its half j ^^ ^^^ , ^^^^ ioM209^l^
The sum (abating twice the radius) e(pml to the former distance. . 2354 1 20
Also, when both latitudes are of the snme nnme, Ihut is both N or both s,
you may add 90° to each of them, the diireience of Ihe log. tangents of half
these sums will be.the same as of the log tangents of half the complenieuts
of those latitudes.
TABLE FOR THE LENGTHS OF CIRCULAR ARCS.
This is Table 11, and constitutes page 350. It contains the lengths of every
single degree up to ISO, and of every minute, second, and thini, each up to
60. The form of it is obvious ; the length of each degree, minute, secoitd,
or third, immediately following it on the same line in the next colunm. And
the two following examples will show the use ofthe trible,
ExampU 1. To find the length of an arc of 57° 17' 44" 4ti"'.
Take out from their respective columps the lengths answering to each of
these numbers singly, and add them all together, thus :
57° 0-994S377
17' 49451
44" 2133
48^',..., 39
the sum or lOOOOOOO is the whole length,
and is equal to the radius ; that is, the length of an art: of 57° 17' 44" 49'" is
ecpial to the radius ofthe circle.
Eramplf 2. To find the degrees, minutes, &c. in the arc I, which is equal
to the radius.
ixviii COMMON AND HYP. LOGS.
Subtract from it the next less tabular arc, and from the remainder the next
less Q^aiu, and so on till nothing remain ; and opposite to the several rum-
bers subtracted* vi\\\ be ihe degree, minutes, &c. ; thus:
Given length 1 0000000
57° 0-9948377
51623
17' 49451
2172
44". 2133
48'" 39
So that tlie arc, whidi is equal to the radius, contains 57*^ 17' 44" 46"'.
TABLE FOR COMPARING HYP. AND COMMON LOGS.
This is Table \'2, and is the upper part of page 361. It contains the
hyperbolic logs, answering to the first 100 common logs, and is very useful
for speedily chongingthe one into ihc other.
ExamjiU 1. To find tlic hyp. log. answering to the common log. 0*9542425.
Beginning at the left-hand, and dividing the given ninnber into periods of
two figures each, including the index, take out the hyp. lug. to each period,
omitting two figures at the 2d periud, four at the 3rd, and six at the 4ih ;
then add thrm all together, thus:
com. log. hyp. log.
09 2 0723266
54 1243396
S4 5526
25 58
9542425 21972246 answer.
Example 2. To find the common log. answering to the hyp. Iog.2'1972246.
Subtract continually each next U'ss tubular hyp. log. from the given num-
ber, and from the remainders ; and the several common logarithms answer-
ing to these tabular hyp. togs, joined together, will be the com. log. required,
thus:
hvp. log.
given 2 1972246
09 20723266
1248980
54 1243396
5584
24 .^526
^~58
25 58
0-9542425 answer.
The remaining tables are often useful in trigonometrical investigations, us
well as in ditfcrent researches in the higher mathematicB ; but they require
00 particular explanation.
TABLE I.
OONTAININO
THE LOGARITHMS OF ALL NUMBERS
From 1 to 108000,
■
B
B^
2 Numbers 1 to tOO, and
IheirLojrs. with Indices.
LOGARITHMS N. 100 L. 00
1
N.
Log.
N.I Log.
150 1760913
N.
200
Log^
301 0300
1
O'OUOOOOO
»1 1-7075702
100 OOOOOOU
^^^^B
2
0-3010300
52 1 716U033
lOI 0043214
151 1789769
201
3031961
^1
^^^^H
3
0-4771213
53 1-7242759
102 0086002
152; 1818436
2U2
3053514
^^
^^^^^1
4
0-6020600
54 1 7323938
103 0128372
153 1846914
203
3074960
^^
^^^H
5
0-C989700
55 1-7403627
I04j 0170333
154 1875-207^
•204
3096302
H
^^^H
6
0-7781513
56 1-7481880
105'o2ll89M
155 I9U33I7
205
3117539
H
^^^^^
7
0-8450980
57 1-7558749
106 0253059
156 1931246
206
3138672
^1
^^^^1
8
0-9030900
58 1-7634280
107 0293838
157 195S997
207
3159703
^1
^^^^H
9
0-9b42425
59 1-7708520
108 0334 23H
158 1986571
20b
3180633
^1
^^^H
10
10000000
60 1-7781513
109 0374265
159 2013971!
209
S-20I463
H
^^^H
U
10413927
61 1-7853-298
110 0413927
160 '2041 -200'
210
3-222193
H
^^^^1
12
10791812
62 1 7923917
111 0453-230
161 2068259
211
3-24-2h25
^1
^^^^1
13
11 139434
63 1-7993405
112 0492180
162 2095150
212
3263359
^^
^^^^H
14
IU0128O
64 1 8061800
113 0530784
163 2121S76
213
3283796
^^^1
^^^H
15
1-1760913
65,18129134
114
0569049
164 2148438
214
3304138
^^H
^^^H
16
1-2041200
66: 1-8195439
115
060697h
165 2174839
215
.S324S8.'i
^^H
^^^^1
17
1-2304489
67 1-8260748
116
0644580
il66 2201081
216
3344538
^^^1
^^^^H
lb
1-2552725
68 1 8325089
117 0681859
167 2227165
2J7
3364597
^^^^1
19
1 2787536
69, 1-8388491
118 0718820
168 2253093
218
3384565
^^^H
20
13010300
70j 1-8450960
119 0755470
169 2278867
219
3404441
H
^^^H
21
1-3222193
71' 1-8512583
1-20 0791612
170 2304489
220
3424227
H
^^^^1
22
1-3424227
72 1-8573325
121,0827854
171 23-29961
221'34439-33| ■
^^^^H
2»
1-3617278
73! 1 ■8633-229
1*22 0803598
172 2355-284
222' 3463530
■
^^^^B
S4
1-3802112
74il 869:3317
l*23'0S99n51
173 2380461
2-23' 3483049
■
^^^H
25
1-3979400
75 1-8750613
124.0934217
174 2405492
1
224 3502480
■
^^^H
2ri
1-4149733
76 1 8808136
125,0969100
175 2430380
225
3521825
■
^^^^1
27
14313638
77| 1-8864907
126 1003705
176 2455127:; 2-26
35410S4
■
^^^^H
28
1-447 15S0
78!l-R920946
127 1038037
177 2479733 i^*??
3560259
_■
^^^^B
29
1-4623980
79 18976271
128 1072100
178 2504200 2*2S
3579348
^M
^^^H
30
1-4771213
80 1 9030900
1-29
1105^97
179 2528530 229
359^355
^M
^^^H
31
1-4913617
81,1 90S4N50
130
1 139434
180 2552725
,230
361727H
^M
^^^^H
32
15051500
8211-9138139
131
1172713
181 2576786 |231
3636120
■
^^^^H
33
1-5185139
83| 1-9190781
139 1205739
1^2 2600714
232
36548^0
■
^^^^1
34
1-5314789
84 1-9242793
133 1238516
183 26*24511
233
3673559
■
^^^H
35
I 5140680
85
1-9291189
134 1-271048
184 2648178
234
3692159
■
^^^H
36
1 -5.^63025
86
1 93449S5
135 1303338
185 2671717
235
3710670
^
^^^^H
37
1 5682017
87
1-9395193
136 1335389
186 26951-29
-236
3729120
^M
^^^^B
38
1-5797836
88
1-1)444827
187 13C7206
187 2718416
:-237
3747483
^H
^^^^^
39
1-5910646
89
1-9493900
138 1398791
188 2741578
]238
3765770
■
^^^H
40
1-6020600
90
1-9542425
139 1430148
189 2764618
I239
37h3979
■
^^^H
41
161-27839
91
1-9590414
140' 1461280
190 27S7536
l240! 38021 12
■
^^^^B
42
1*6232493
92
1-9637878
14ll 1492191
191 2810334 |24l|38-20l7O
■
^^^^H
43
1-6334685
93
1-9684829
142:1522883
192 2^33012
242:3838154
^M
^^^^H
44
1-6434527
91
1'9731279
143 1553360
193 2855573
243 3856UG3
^M
^^^H
4D
16532125
95
1-97^7236
144! 1583625
194 2878017
244
3H73898
^
^^^H
46
1-6627578
96'v98-2-27l2
145*1613680
195 2900346
245
389 1661
■
^^^^1
47
1-6720979
97 1-9H67717
146 1643529
196 2922 61
246;a90935l
■
^^^^H
4S
16812412
9S 1 991-2261
147 1673173
' 197 -2944662
-24'/ 13926970 H
^^^^H
49
16901961
99 1-9956352
148 1702617
1 198 2966652
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41500 L. 618 OF NUMBERS. 69
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4160
6190933
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1246
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1455
1560
1664
1769
1873
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2186
2290
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2603
2708
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3125
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0423
0527
0631
0736
0940
0944
1048
1152
1256
4170
1361
1465
1569
1673
1777
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1985
2090
2194
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1035
1139
1243 1347
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4180
1763
1867
1971
2075
2178
2282
2386
2490
2594
2698
81
2802
2906
3009
3U3
3217
3321
3425' 3529
3633
3736
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4048
4152
4256
4359
4463' 4567
4671
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4879
4982
5086
5190
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5502 5605
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6332
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2140
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3902
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LOGAiuTiiMS N. 42000 L, 023
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7
8
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6232493 2596
2700,2803
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1871
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2909
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■
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IS. 1075 L. 0314 OF NUMBERS. aoT] ^|
N.
1
2
1 3
4
5
6
7
8
y
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Pro.
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1
^■^ 202
1
TABLE IL
■
For finding Logarithms and jWumbers to 20 Flace$ of Figure$,
N.
1
Logarithms
■
N,
Logarithms
•
00000
00000
00000
00000
70757
01760 97936
36584
2
30103
99956
63981
19521
52
71600
33436 34799
15963
3
47712
12547
19662
43730
53
72427
58696 00789
04563
4
60203
99913
27962
39043
54
73239
37598 22968
50710
^
69897
00043
36018
80479
55
74036
26894 94243
84554
6
77S15
12503
83643
63251
56
7491S
80270 06200
41635
7
84509
80400
14256
83071
57
75587
4S556 72491
39S83
8
9030S
99869
91943
58564
58
76342
79935 62937
28255
9
95424
25094
39324
87459
59
77085
20116 42144
19026
10
00000
00000
00000
00000
60
77815
12503 83643
63251
11
04139
26851
58225
04075
61
78332 98350 10767
03389
12
079 IS
12460
47624
82772
62
79239
16894 96233
87488
13
11394
33523
06836
76921
63
79934
05494 53581
70530
14
14612
80356
78238
02593
64
80617
99739 638H7
17128
15
17609
12590
55681
24206
65
81291
33566 42855
57399
16
20411
99826
55924
78085
66
81954
39355 41668
67326
17
23044
89213
78273 92854
67
82607
48027 00826
43415
18
25527
25051
03306
06980
68
83250
89127 06236
31897
19
27875
36009
52828 96154
69
83884
90907 37255
31616
20
30102
99956
63981
19521
70
84509
80400 14256 83071
21
3222!
92947
33919
26801
71
85125
83487 19075 28609
22
34242
2680S
22206
23596
72
85733
24964 31268
46023
23
36172
78360
17592
87887
73
86332
28601 20455 90107 |
24
38021
12417
11606
02294
74
86923
17197 30976
19202
25
39794
00086
72037
60957
75
87506
12633 91700
04687
26
41497
33479
70817
96442
76
86081
35922 80791
35196
27
43136
37641
58987
31169
77
88649
07251 72481
87146
28
44715
80313
42219
22114
78
89209
46026 90480
40172
29
46239
79978
98956
08733
79
89762
70912 9044!
42799
30
47712
12547
19662
43730
80
90309
99809 91943
58564
^^^H
31
49136
16938
34272
67967
81
90848
50188 78649
74918
32
50514
99783
19905
97607
82
91381
3S523 83716
68972
33
51851
39398
77887
47805
83
91907
80923 76073
90363
34
53147
89170
42255
12375
84
92427
92860 61881
65S43
35
54406
80443
50275
63550
85
92941
89257 14292
73333
36
55030
25007
67287
26502
86
93449
84512 43567
72162
37
56S20
17240
66994
99681
87
93951
92526 18618
52463
38
57978
35966
I6B10
15675
88
94448
26721 50168
62639
39
59106
46070 26499
20650
89
94939
00066 44912
78472
40
60205
99913
27962
39043
90
95424
25094 39324
87459
41
61278
38567
19735
49451
91
95904
13923 21093
59992
42
62324
92903 97900
46322
92
9637S
78273 45555
26930
43
63346
64555
79586
52641
93
9684S
29485 53935
11696
44
64345
26764
861 87
43118
94
97312
78535 99698
65963
45
65321
25137
75343
67938
95
97772
36052 88847
76632
46
66275
78316
81574
0740S
96
98227
12330 3956S
41336
47
67209
78579
35717
46441
91
98677
17342 66244
85178
48
68 1 24
12373
75587
21815
98
99122
60756 92494
85664
49
59019
60800
28513 66142
99
99563
51943 97549
91534
50 69ft97
00043 86018
80479
100
00000
00000 00000
OOOOO
.
_J
E
■
■
■
■
^
Tab. 2. LOGARITHMS TO 20 PLACES.
203
N.
Logarithms.
N.
Logai
69472
ithms.
101 00432 13737 82642 57428
151 ' 17897
93169
43<i87
102,00860 01717 61917 56105
152 18184
35879
44772
54719
103
01263 72247 05172 20517
153 18469
14308
17598
80313
104
01703 33392 98780 35485
154 18752
07208
36463
06668
105
02118 92990 69938 07279
155 1903.1
16981
70291
48445
106
025.30 58652 64770 24085
156 19312
45983
54461
59693
107
02938 37776 85209 64083
157 195S9
96524
09233
73676
108
03342 37554 86949 70231'
158 19865
70869
54422
62321
109
03742 64979 40623 63520*
159 20139
71243
20451
48293
110
04139 26851 58225 04075
160 20411
99826
55924
78085
1
111
04532 29787 86657 43410
161 206S2
58760
H1849
70958
'
112
04921 80226 70181 61157 1
162 20951
50145
42630 94439
113
05307 84434 83419 72280
163 21218
76044
03957
80764
114
05690 48513 36472 59405
164 21484
38480
47697
88494
115
06069 7S403 53611 66365
165 21748
39442
13906
28283
116
06445 79892 26918 47776
166 22010 80880
40055
09905
117
06818 58617 46161 64380
167 22271
64711
47583
27998
118 07188 20073 06125 38547
168 22530
92817
25862
85365
119 07554 69613 92530 75925'
1G9 22788
67046
13673
53841
120 07918 12460 47624 62772 ^
170 23044
89213
78273
92854,
121 08278 53703 16450 08150
171 23299
61103 92153 83613
122 08635 98306 74748 22910
172 23552
84469
07548
91683
123 08990 51 114 39397 93180
173 23804
61031
28795
41456
124 09342 16851 62235 07009
174 24054
92482
82599
71984
125 09691 00130 06056 41436
175 24303
80486
86294
44028
<
126 10037 05451 17562 90052
176 24551
26678
14149
82161
127 1 10380 37209 55956 86425
177 24797
32663
61806 62756
128 10720 99696 47868 36650
178 25042
00023
03893 97994
129 1105H 97102 99248 96370
179.25285
30309
79893
16957
130
11394 33523 06836 76921
180 25527
25051
03306
06980
131
11727 12956 55764 26081
181 25767
85748
69184
51029
132
12057 39312 05849 86847
182126007
13879
85074
79513
133
1-23S5 16409 67085 79225
183 26245
10897
30429
47118
134
12710 47983 64807 62936
184
26481
78230
09536
46451
^^L
135
13033 37684 95006 11667
165
26717
17284
03013
80159
V
136
13353 89083 70217 51418
186
26951
29442
17916
31218. !
137
13672 05671 56406 76856
187
27184
16065
36498 06929
138
13987 90864 01236 51138
188
27415
78492
63679
85484
139
14301 4S002 54<»95 08046
189
27616
1HU41
73244
14260
140
14612 803.56 78238 02593
190
27875
36009
52828
96154
141
14921 9U26 55379 90171
191
28103
33672
47727
53764
142
15228 83443 83056 48131
192
28330
12287
03549
60858
143 15533 60374 65061 80996
193
28555
73090
07773
76060
144(15836 24920 95249 65545
194
28780
17299
30226
047 OO
145:16136 80022 34974 89212
195
29003
46 113
62518
01129
146 16435 28557 84437 09629
196
29225 60713
56476
05185
147
16731 73347 48176 09872
197
29446
62261
61592
92737
148
17026 17153 94957 38724
198
29666
51902
61531
11055!
149
17318 02684 12274 03826
199
29885
30764
09706
65010
150
17609 12590 55681 «4208
200
30102
99956
63981
19521
L
_^
^^^H
■
■
^
1
204
LOGARITHMS
Tab. 2.
1
N.
2U1
Logarithms.
N.
25i
Logarithms.
30319 60574
20489 87144
39967 372 U
81039
13934
^^1
202
30535 13694
46623
76949
252
40140 05407
81544
09573
^^H
203
30749 60379
13212
91805
253
40312 05211
75817
91962
^^H
204
30963 01674
25898
75626
254
40483 37166
19938
05946
^^B
205
31175 38610
55754
29930
255
40654 01804
33955
17062
^^M
206
313S6 72203
69153
40038
256
40823 99653
11849
56171
^^M
207
31597 03454
56917
75346
257
40993 31233
31294
53716
^^H
208
31806 33349
62761
55006
258
41161 97059
63230
15991
^^1
•209
32014 62B61
11054
00229
259
41329 97640
81251
82752 1
^H
210
32221 92947
33919
26801
260
41497 33479
70817
96442
^^1
211
32428 24552
97692
66508
261
41664 05073
38280
96199
^^H
212
32633 58609
28751
43606
262
41830 12913
19745 45602
^^B
213
32837 96034
38737
72339
263
41995 57484
89757
86897 1
^^H
214
33041 37733
49190
93605
264
42160 39268
69831
06369
^^1
215
33243 84599
15605
33U9
265
42324 59739
36807
85042
^^1
216
33445 37511
50930
89753
266
42488 16366
31066
99746
^^H
217
33645 97338
48529
51038
267
42651 12613
64575
22202
^^H
21t^
33S45 64936
04604
83041
268
42913 47940
28788
92458
^^H
219
34044 41148
40118
33937
269
42975 22900
02407
98009
^^1
220
34242 26808
22206
23596
270
43136 37641
58997
31189
^^H
221
34439 22730
85110
69775
271
43-296 92908
74405
72952
^^1
922
34635 29744
50638
6293&
272
43456 89040
34198
70940
^
^^P
S23
34830 46630
48160
67346
973
43616 26470
40756
03721
■
^^H
fl24
35024 80183 34162
80678
274
43775 05628
20387
96378
■
^H '
S25
35218 25181
11362
484 16
275
43933 96939 30262
65039
■
^H
S26
35410 84391
47400
91801
276
44090 90820
65217
70659
^^1
227
35602 58571
93122
72010
277
44247 97690
6444H
55378
^^H
228
35793 48470 00453 78926
278
44404 47959
18076
27567
^^^
229
35983 54823
39887
99413
279
44560 42032
73597
55426
^^1
230
36172 78360
17592
87887
280
44715 80313
42219
22114
^^1
231
36361 19799 92144
30876
281
44870 63199
05079
99296
^^H
232
3654s 79849
90899
67297
282
45024 91083
19361
09692
^^H
233
36735 59210
26018
97219
283
45178 64355
24290
23556
^^1
234
36921 56574
10142
83901
284
45331 83400
47037
67652
^^1
235
37106 78622
71736
26920
295
45484 48600
09510
20362
^^1
236
37291 20029
70106
59069
286
45636 60331
29043 00517
^^H
237
37474 83460
10103
86529
297
4 5789 18967
33992
32522
^^H
238
37657 69570
56511
95447
298
45939 24877
59230
95066
^^^H
239
37839 79009
48137
68500
289
46089 78427
56547
85708
^H
240
38021 12417
11606
02294
290
46239 79978
99956
09733
^^1
241
38201 70425 74968 3840S
291
463S9 29889
95907
28908
^^H
242
383S1 53659
80431
27671
292
4653S 28514
4H419
29150
^^1
243
38560 62735 98312
I8G48
293
46686 76203
54109
45624
^^1
244
38738 98263 38729
42431
294
46834 73304
12157
29893
^^1
245
38916 60843
64532
46621
295
46982 20159
78162
99505
^^1
246
390*)3 51071
03379
12702
296
47129 171)0
58939
5824 5
^^^^1
247
39269 69532
59665
73074
297
47275 64493
17212
35264
^^H
248
39445 16808
26216 26531
298
47421 62640
76255
23347
^^B
249
39619 93470
95736 34113
299
47567 11883 24429
6480?; 1
^^^^H
^^^H
i2M)
39794 00086
72037
60G57
300
47712 12547
19662
43730
J
»-
J
1
1
^^^^^^F
m
, Tab. 2. TO 20 places. 205
^1
N
301
Lugacithms.
N,
351
Logarithms.
47856 64955 93S43 3>712
54530 71164 65824 081 OS
30^
48000 69429 57150 63208
35^
54654 26634 78131 01682
^^H
303
48144 26285 02305 01157
353
54777 47053 87822 5655C
^^1
304 48287 35R36 08753 74239
354
54900 32620 25787 82277
^H
305
48429 98393 46785 83867
355
55022 83530 55094 09086
^^^H
306
48572 14264 81579 99S34
356
55144 99979 72875 17515
^H
307
48713 83754 771S6 48475
357
55266 82161 12193 19655
^^1
30«1
48855 07165 00444 26189
358
55388 30266 43874 36478
^H
309
48995 84794 24834 64247
359
555(»9 44485 78319 14782
^^1
310
49136 16933 34272 67967
360
55630 25007 67287 26502
^1
3U
49276 03890 26837 50555
361
55750 72019 05657 92307
^H
312
49415 45940 18442 79214
362
55870 85705 33165 70550
^^1
313
49554 43375 46448 48481
363
55990 66250 36112 51880
^H
314
49692 96480 73214 93198
364
f)6llO 13836 49055 99035
^H
315
49831 05537 89600 51009
365
56229 28644 56474 70596
^^
.
316 '49968 70826 18403 81842
366
56348 10853 94410 66639
^^
■
317150105 92622 17751 49455
367
56466 60642 52089 33799
^H
■
818 50242 71199 84432 67814
368
56584 78186 73517 65972
^^1
■
319
50379 06830 57181 12809
369
56702 63661 59060 36910
^H
p
320
50514 99783 19905 97607
370
56820 17240 66994 9968l| ^B
r
821
50650 50324 04872 07813
371
56937 39096 15045 87635 ^M
^
322
50785 58716 95830 90479
372
57054 29398 81897 50739 ^M
■
323
50920 25223 31102 89008
373
57170 88318 08687 60551 ^1
^ S24
51054 50102 06612 13961
374
57287 16022 00480 16450 ^H
L
325
51188 33609 78874 37878
875
57403 12677 27718 85165 ^H
■
326
51321 76000 67939 00285
376
5751S 78449 27661 05006 ^|
■
327
51454 77526 60286 07250
377
57634 13502 05792 85654
H
328
51587 38437 11679 08015
378
57749 17998 37225 33781
329
51719 58979 49974 29513
379
57863 92099 68072 34193
H
330
51951 39398 77897 47805
380
57978 35966 16910 15675
■
331
51982 79937 75718 73861
391
58092 49756 75619 30154
■
332
52113 80837 04036 29426
382
58206 33629 11708 73285
■
333
52244 42335 06319 87140
383
58319 87739 6S622 74038
■
334
52374 64668 11564 47520
3B4
5S433 12243 67530 80379
335
52504 48070 36845 23894
385
58546 07295 08500 67625
H
336
52633 92773 89844 04886
386
58658 73046 71754 95581
■
■
337
52762 99008 71338 62619
387
58771 09650 18911 40100
■
338
52891 67002 77654 73363
388
58883 17255 94207 24221
B
■
339
53019 96982 03082 16009
3H9
58994 96013 25707 73024
P
340
53147 89170 42255 12375
390
59106 46070 26499 20650
1
[
341
53275 43789 92497 72042
391
59217 67573 95966 S0741
■
^
342
53409 61060 56135 03134
392
59328 60670 20457 24707
■
343
53529 41200 42770 49214
393
59439 25503 75426 69811
^H
■
344
53655.84425 71530 11205
394
59549 62218 25574 12259
p
345
53781 90950 73274 12095
395
59659 70956 26460 23278 ^^^
[
946
53907 60987 92776 60977
396
59769 51859 25512 30577
^H
^
347
54032 94747 90873 71854
397
59879 05067 63115 06589
^H
■
348
54157 92439 46580 91506
398
59988 30720 73697 84531
^^1
■
349
54282 54269 59179 89654
399 60097 2S956 86749 22954
^H
■ I
350
54406 80443 50275 63550
400 60205 99913 27962 39043
^1
k
1.
J
w
■
■
^H
■
i
206
LOGARITHMS
Tab. 2.
g
N.
4i)l
Logaritlims
•
1
N.
451
Logarithms.
60314
43726
20182
30654
65417
65418
77960 53526
402
60422
60530
84470
06666
452
65513
84346
11362 11322
^
403
60530
50461
41109
44887
453
656'J9
82020
12831 87416
■
404
60638
13651
10604
96470
454
65705
59529
57103 91532
■
405
60745
50232
14668
55397
455
65801
13966
57112 40470
■
406
60852
60335
77194
11326
456
65896
49426
64434 99447
■
407
60959
44092
25220
03756
457
65991
62000
69950 22235
■
40S
61066
01630
89879
95148
458
66086
54790
03969 19934
^
4U9
61172
33080
07341
60361
459
66181
26855
37261 24043
1
410
61278
3S567
19735
49451
460
66275
7S316
91574 U7408
411
61384
IR218
76069
20586
461
66370
09253
89648 14507
^
41-2
614S9
72160
33134
59560
1462
66464
19755
56125 50397
■
413
61595
00516
56401
02097
463
66558
09910
17953 13567
■
414
61700
03411
20898 94967
464166651
79805
54880 66919
■
415
61804
80967
12092
70962
465
66745
29528
89953 92175
■
416
61909
33306
26742
74528
466
66838
59166
90000 16740
■
417
62013 60549
73757
51775
467
66931
69905
66 U2 16309
■
418
62117
62817
75085
19750
468
67024
5>)530
74124 034-22
■
419
62221
40229
66295
30985
469
67117
29427
15093 26486
^M
420
62324
92903
97900
46322
470
67209
79579
35717 46441
«K1
62428 20958 35668
30744
471
67302
09071
28896 17406
422
62531
24509
61673
86030
472
67394
19986 34087 77590|
423
62634
03673 75042
33900
473
67486
11407
37811 56716
4^4
62736
5b565 92732
63127
474
67577
83416
74095 OmbO
425
62838 89300
50311
53811
475
67669
36096
24966 57111
426
62940
95991
02718
91960
476
67760
69527
20493 14968
427
63042
78750
25023
86460
477
671:51
93790
40113 92022
■
429
63144
37690
13172
03126
478
67942
78966
12119 6S028
■
429
63245 72921
84724
24725
479
68033
55134
14563 22010
■
430
63346
84555
79586
52641
480
68124
12373
75597 21815:
■
431
63447
72701
60731
60075
481
68214
50763
73931 76601
■
4S-2
63548
37468
14912
09274
482
68304
703S2
38849 57929
■
433
63648
78963
53365
44270
483
68394
71307
51512 14698
■
434
63748
97295
12^10
7i»559
484
68494
53616
44412 47193
■
43d
C3S4S 92569
54637
3294 1
485
68574
17396
02263 65657
■
436
63943
64892
68596
02563
486
6K663
62692
62293 39169
m
437
64048
14369
70421
64040
487
68752
99612
14634 33246
438
64147
41105
04099
53358
488
69841
96220
02710 61953
439
64246
45202
42121
37063
489
68930
99591
23620 244^4
440
64345
26764
86187
43118
490
69019
60S00
28513 66142
J
441
64443
85894
67838
53601
491
69108
14921
22968 47275
■
442
64542
22693
49091
H9296
492
69196
51027
67360 32223
■
443
64640 37262
23069
56023
493
69294
69192
77230 01597
■
444
64738
29701
14619
924 53
494
69372
694S9
23646 92596
■
44f.
64836
00109
80931
58951
495
69460
51989
33568 72013
■
44fi
64933 485S7
12141
86869
496
69548
16764
90197 46052
■
447
65030
75231
31936
47555
437
69636
63887
33332 11691
■
448
65127
80139
98144
00199
498
69722
93427
59717 53634.' ^H
449
65224
63410
03323
17492
199
69810
05456
23399 914171 ^B
^1 1450
65321
25137
75343
67939
500 1 69897
00043 36018 S047»| J
^
J
J
1
I
■
^
■
1
■
■
■
F
V
^^^^H
Tab, 2.
TO 20 PL\CES.
907
1
N.
5ul
Logarithms
•
■
N.
551
Logarithms.
699S3 77258 67245
7172«
74115
15988
51785
04887
^"
50-2
70070
37171
45019
33455
552
74193
90777
29198
90180
^H
1
503
70156
79850
55927
39710
553
74272
51313
04698
25871
^^1
1
504
70243
05364
45525
29094
554
74350
97647
28429
74S99
^^1
1
505
70329
13781
18661
37906
555
74429
29831
22676
23889
^^
^K
506
70415
05168
39799
11483
556
74507
47915
82057
47088
^H
^H
507
70500
79593
33335
97571
557
74585
51951
73728
90044
^H
^^1
508
70586 37122
83919
25467
558
74663
41989
37578
74947
^^1
^^f
509
70671
77823 36758
74657
559
74741
18078
86423
29561
^^1
r
510
70757
ni76*J
97936
36584
560
74818
60270
06200
41635
^^H
^^
511
70842
09001
34712
73179
561
74896
28612
56161
40659
^^H
^H
512
70926 99609
75830
75692
562
74973
63155
69061
08806
^H
^^1
513
71011
73651
11816
27342
563
75050
83948
51346
22909
^^1
^H
5U
71(»96
31189
95275
73238
564
75127
91039
83342
29214
^H
^^
515
71180 72290
4U91
00996
565
75204
64478
19438
52758
^1
^^
516
71264
97016
27211
35413
566 752M1
64311
68271
43077
^1
^^L
517
71349
05430
93942
50516
567 75358
30588
92906
57989
^^1
^^1
518
7U32
97597
45233
02273
568,75434
83357
11018
87173
^^1
^H
519
71516 73578
48457
85186
569, 75511
22663 95071
17229
^H
^»
520
71600 33436 34799
15963
670 '75587
48556
72491
39883
^H
1
521
71683 77232
99524
47424
571 175663
61082
45848
05004
^H
^H
592
71767
05030
02262
15714
M2 '75739
60287
93024
20033
^H
^H
523
71850
16888
67274
23926
573 '7581 5
46219
67389
97493
^H
^^
524
71933
12869
83726
65124
674 7&89I
18923
97973
52044
^^1
fc
525
72015
93034
05956
87758
575 75966
78446
89630
48844
^H
^H
526 72098
57441
53739
06419
576 76042
24834
23212
04587
^H
^^1
527 72181
06152
12546
60821
677:76117
58131
55731
42849
^^1
^H
528 72263 39225
33812
25890
578 76192
78384
205-29
05229
^H
^^H
529
72345
56720
35185
75774
579176267
85637
27436
19789
^^1
r
530
72427
5H696
00789
04563
580 76342
79935
62937
28255
^1
^^
531
72509
45210
61469
06485
581 76417
61323 90330
73454
^H
^f
532 72591
16322
95048
18268
582 76492
29S46
49888
48429
^H
533 72672
72090
20572
26372
563 76566
85547
59014
08638
^^1
534 72754
12570
28556
41723
584
76641
2S471
12399
48672
^^H
535
72835
37820
21228
44562
585
76715
58660
82180
44858
^H
536
72916
47896 92770 01979
586
76789
76160
18090
65146
^H
537
72997
42856
99555
606S7
587
76863
81U12
47614
47606
^^1
^
538
73078
22756
66389
17530
588 ] 76937
7326(»
76138
48915
^^1
■
5^
73159
87651
86738 70217
589
77011
52947
87101
64120
^^1
^
540
73239
37599
22968
50710
590
77085
20U6
42144
19026
^^^M
[
541
73319
72651
06569
43688
591
77158
74803 81255
36467
^^^^
■
542
73399
92S65
38386 92473
592
77232
17067
22919
77766
^^^^H
■
543
73479
98295
88846
94758
593
77305
46933
64262
60640
^H
X
544
73559
88996
9S179 90461
594
77378
64449
81193
54785
^^1
1
515
73639
65022
76642
43999
595
77451
69657
28549
56404
^^
1
546
73719
26427
04737
23243
596
77524
62597
40236
42868
^H
^
547
73798
73263
33430
77881
597
77597
43311
29369
08740
^^1
■
548
73878 05584
64369
15899
598
77670
U839
88410
84329
^H
r
549
73957
23444
50091
90848
599
77742 68223
89311
37983
^^1
1
550
74036
26894
94243
S4554
600
77815
12503
83643
63251
^^^H
k
L
■
■
W
■
^v
■
■
i
^M
'208
LOGARITHMS
Tab. 2.
1
H
N.
Loga
rithms
I.
N.
651
I^ga
rithms.
^H
77867
44720
02739
52089
81358
09885
68191 94767
^H
77959
64912
57824
55233
652
81424 75957
31920 19807
^H
78031
73121
40151
30874
653
81491
3I8I2
75073 92143
^H 1 604
76103
69386
21131
82730
654
81557
77483
24267 26771
^H i^^
78175
53746
52468
88629
655
81624
12999
91783 06560
^H
78247
2624 1
66286
20678
656
81690
38393 75660 27536
^^^1
607
78318
86910
75257
58096
657
81756
53695
59780 77566
^^H
60S
78390
35792
72734
93761
658
81 822
58936
13955 49U34
^^^1
609
78461
72926
32875
35534
659
91888
54145
94009 86128
^^H
610
7S532
9S350
10767
033S9
660
81954
39355 41868 67326
^^H
611
78604
12102
42554
23362
661
82020
14594
85640 23665
^^H
612
78675
14221
45561
19356
662
82085
79894
39699 933S2 1
^^H
613
78746
04745
18415 03774
663
82151
35284
04773 13504 |
^H
78816
83711
41167
67997
664
82216
80793
68017 48947
^H 615
78887
51157
75416
73659
665
82282
16453
03104 59703
^H 616
78958
07121
64425
45710
666
82347
42291
70301 06661
^H
79028
51640
33241
68205
667
82412
58339
16548 96620
^H
79098 84750
88815
83768
668
82477
64624
75545 67041
^H 619
79169
0C49O
20117
97680
669
82542
61177
67823 11077
■i
^H
79239
16894
98253
874S8
670
62607
4S027
00826 43415
■
^H 6*21
79309
16001
76580
19075
671
82672
25201
68992 07464
^H
79379
03846
90818
70077
672
82736 92730
53825 24409
^H 623
79448
80466
59169
61544
673
82801
50642
23976 84648
^H 6-24
79518
45896
82423
98736
674
82865
9B965
35319 82140
^H
79588
00173
44075
21915
675
82930
37728
31024 92146
^H 626
79657
43332
10429
68002
676
82994
66959
41635 92884
^H 627
79726
75108
30716
43958
677
83058
86686
85144 31601
^H 6-28
79795
96437
37196
12719
678
83122
9693S
67063 35530
^H
79805
U6454
45268
92535
679
83186
97742
80501 68250
^^1 630
79934
05494
53581
70530
680
83250
89127
06236 31897
■
^^M 631
80002
93592
44134
31302
681
83314
71119
12785 15740
^H 632
80071
70782
82385
01364
682
83378
43746
56478 91563
^^H
633
80140
37100
17355
10238
683
83442
07036
81532 56340
^^H
634
80208
92579
81732
68977
684
63505
61017
20116 22655
^^1
•635
80277
37252
91975
66903
685
83569
05714
92425 57335
^^1
630
80345
71156
484 13
87336
686
83632
41157
06751 68735
^^H
637
80413
94323
35350
43003
687
83695
67370
59550 43142
^^H
638
80482
06787
21162
32330
688
63758
84382
35511 30726
^^H
639
80550
08581
58400
10068
689
83821
92219
07625 81494
^^P
640
80617
99739
83887
17128
690
83884
90907
37255 31616
^
^^1
641
80685
80295
18617
42225
691
83947
80473
74198 40758
■
^^1
642
80753
50280
68853
27334
692
84010
60944
56757 80499
n
^^H
6«3
80821
09729
21222
07249
693
S4073
32346
11806 74605
1
^^H
644
80888
53673
59812
10001
694
84135
94704
54854 91375
M
^^1
645
80955
97146
35267
76849
695
84198
48045
90113 S8524
m
^^1
646
81023 25179
95084
08529
696
84260 92396
10562 11027
^^^1
647
81090
42806
68700
3844G
697
84323
27780
98009 42305
^^^1
648
81157
50058
70593
33482
698
84385
54326
23161 09175
^^H
649
81224
46968
00369
23101 1
6f»9
H4447
71757
456S1 40948
^
^^^
650
81291
33566
42855
57399 1
700
84509
80400
14256 83071
■
1^
_j
J
^^"
^F
■
Tab, %
TO 20 PLACES.
2oy
^^M
N.
70i
Logarithms.
751
Logarithms.
1
84571 HO 1 79
66658 65706
S7563
99370 04168 38975
702
64633 71121
29h05 27631
752
67621
78405 91642 24527
^^^
703
84693 53250
19823 95834
753
87679
49762 00700 57664
^^1
704
84757 26591
42112 21203
754
87737
1345S 69774 05175
^^^^M
705
84818 91169
91398 70650
755 '87794
69516 29188 24166
^^^H
7oe
84S80 47010
51803 76071
756
87852
17955 01206 53302
^^^H
707
84941 94137
96H99 40499
757
87909
58795 00072 75709
^^^^1
709
85003 32576
69769 01798
758 87966 92056 32053 53715
^^^H
709
85064 62351
83066 54285
759 i 88024
17758 95460 35691
^^1
710
B5125 834S7
19075 28609
760
88081
35922 80791 35196
^^^H
711
85186 96007
29766 30258
761
88138
46567 70572 82637
^^^H
712
85247 99936
36856 37036
762
88195
49713 39600 49676
^^^^H
713
S5308 95298
51865 55853
763,88252
45379 54880 40591
^^^H
714
85369 82117
76174 39176
764 1 88309
3358? 75689 92806
^^^^1
715
85430 60418
01080 61474
765 88366
14351 53617 60792
^^^1
716
85491 30223 07855 56000
766188422
87696 32603 93559
^^^1
717
85551 91556
67S00 12230
767
88479
53639 48980 95947
^^^^^
718
85612 44442
42300 34303
768
88536
12200 31511 999U0
^^^H
719
85672 8H9U3
82882 60777
769
88592
63398 01431 03950; ^^^1
720
85733 24964
31268 46023
770
88649
07251 72481 87146
^^^H
721
85793 52647
19429 03586
771
88705
43780 50956 97446
^^^1
722
85853 71975
69639 11829
772
88761
73003 35736 15102
^^^H
723
85913 82972
94530 82137
773
88817
94939 18324 90897
^^^^^
724
85973 8566 1
97146 90071
774
89974
09606 82892 59621
^^^H
725
86033 80065
70993 69691
77 5
88930
17025 06310 28924
^^^1
726
86093 66207
00093 71401
776
88986
17212 56188 43743
^^H
727
86153 44108
59037 83621
777
89042
10 168 00914 26482
^^^^^
728! 86213 13793
13037 18556
778
89097
95969 89688 93146
^^^H
729 8G272 75283
17974 62377
779
89153
74576 72564 45605
^^^^1
730 86332 28601
20455 90107
780
89209
46026 90480 40172 ^^H
731
86391 73769
57860 45495
781
89265
10338 77300 326841 ^^H
732
86451 10810
5S391 86161
782
89320 67530 59848 00262 1 ^^H
733
86510 39746
41127 94317
783
89376
17620 57943 39922 ^^^1
734 86569 60599
16070 53320
764
69431
60626 34438 4 4228 ^^^1
735^66628 73390
84194 90351
785
89486 96567 45252 54155]
^^^H
736 1 86687 78 U3
37498 85494
786
89542
25460 39407 89332
^^^1
737 86746 74878
59051 47490
787
89597
47323 59064 55847
^^^^^
738:66805 63618
23041 56431
788
89652
62174 69555 31780
^^^H
739 86S64 443S3 94825 73669 |
789
89707
70032 09420 30627
^^^^^
1
740 80923 17197
30976 19202
790
69762
70912 90441 42799
^^^H
741 66981 82079
79328 16804
791
99817
64834 97676 55351
^^^H
742 87040 39052
79027 07156
792
89872
51815 89493 50008
^^^^H
743 87098 88137
60575 29242
793
89927
31673 17603 80309
^^^H
744 87157 29355
45878 70260
794
89982
05024 27096 26109
^^^^1
7i5 872i5 62727
48292 84304
795
90036 712S6 56470 2877 1 1
^^^1
746S7273 8S274
72068 80072
796
90091
30677 37669 040531 ^^^1
747
87332 06018
15398 77842
797
90145
632 13 96112 34727 ^^H
748
87390 15978
64461 35972
798
90200
28913 50729 42476 ^^^1
749
87448 18176 99466 47155
799
90254
67793 13991 39295 ^^H
750
87506 12633 91700 04687
800
90308 99669 91943 58564 |
^^^H
k
1
r
■
■P
1
{210 1JOGAKITU34S
Tab. 2.
-•
1
N.
Mil
Logarithms.
951
Logarubms.
OOWIS ^160 S4297 6V931
99999 9itmf0 &4597 97566
i
802
90417 48082 SI163 50176
852 '93043 95»47 66700 11392* I
90S
90471 554^2 78680 94192
953 93094
90311 67523 03000. |
MM
905-25 04)487 48451 26197
954 93145
78706 89005 05981
flOb
90579 51S80S 67868 51457
955 93196 61147 2S172 64091
606
90033 50418 05090 64409
856 93247
37646 77153 22648
b07
90687 35347 22070 41738
857' 93298 08219 23198 16429
^8
90741 13607 745^6 15992
858 93348 72876 48705 4424?
000
90794 85216 12272 30432
859i 93399 91638 31242 30263
SiO
90648 50189 78649 74918
860 '93449
84512 43567 72162, 1
^H
90902 08542 11156 03069
861 '93500
31514 53654 76252| |
^H
90955 60292 41175 30847
862 93550
72658 24712 79596
^B BIS
91009 05455 91068 16682
863 93601
07957 152»)9 59266
^B eu
91062 44048 89201 23277
664 93651
37424 7h893 28795
^H 015
91115 760^7 39976 61243
665 1 93701
61074 64614 21935
^H i^>^
91169 01587 53861 14669
966
93751
78920 17346 63791
^H
91222 20565 32415 48794
867
93801
90974 762 LO 29438
^H
91275 33036 71322 99S82
868
93851
97251 76491 90081
^H
91328 39017 60418 47451
869
93901
97764 48666 46875
SUV
9I3MI 38523 83716 68972
870
93951
92526 IS618 52463
821
91434 3I57I 19440 77180
871
94001
81550 07663 20336
822
91487 18175 40050 40107
872
94051
64849 32567 22084
HS3
91539 9SS52 12269 83977
873
94101
42437 05569 72637
^H
91592 72116 97115 79081
874
94151
14326 31 403 03562
^^^
91645 39485 49925 0H762
875
94200
80530 223J3 24507
^^^B HUH
91698 00473 20382 21619
876
94250
41061 68080 72880
^^^M HS27
91750 55095 52546 67071
877
94299
95933 66040 51S23
^
91803 03367 84880 14389
878
94349
45159 06102 56585
^H 821>
91855 45305 50273 55312
879
94398
88750 73771 89354
^H
9191)7 80923 76073 903S3
880
94448
26721 50168 62639
^H
911)60 10237 94110 99107
881
94497
59084 12047 91274
^H Ib32
9'^0I2 332li2 90723 94049
882
94546
85851 31819 73123
^H
920f;4 50014 06787 5S996
883
94596
07035 77568 58562
^H 834
92116 60506 37738 71297
884
94645
22650 13073 08817 1
92168 64751 83602 08477
885
94694
32706 97825 43234 |
^H
92220 6277 1 39016 39271
886
94743
37218 87050 75544
^H
92272 54579 93259 99155
■887
94792
36198 31726 39220
^H 83.S
92324 401H6 30276 5U506
[888
94841
29r>57 7864H 01974
^H 83U
92376 19608 28700 27500
889
94890
17609 70213 69496
840
92427 92860 618S1 65S43
890
94939
00066 449)2 78472
841
92479 5!«57 97912 17467
891
94987
77040 36874 7S99S
842
92531 20914 99649 50266
892
95036
48543 76123 06390
^H
92582 75746 24742 33016
893
95085
14588 88546 4>595
H44
92634 24466 25655 05551
894
95133
75187 95917 67077
845
92685 67089 49692 84320
895
95182
30353 15911 97436
H46
92737 03630 39023 53422
896
95230
80096 62125 19721
847
92788 34103 30706 91221
897
95279
24430 44l>92 08537
84}%
92839 5S522 56713 82649
898
95327
63366 67304 37013 1
^^^^ M»l
92890 76902 43952 67285
899
95375
9t»l7 33228 76700) |
H^ 1
tool
92941 89257 14292 73333
900
95424
25094 39324 87459{
^^^^^^^B
^^^^^^^v
Tab. "2. TO 20 places. 211
1
901
Logarithms.
95472 47909 79062 97417
N.
Logarithms.
951
97818 05169 37413 9318!
902
95520 65375 41941 730471
952,97863 694S3 84474 3448&
903
95568 77503 13505 79441 '
953
97909 29006 3H326 40H5a
^^1
9U4 95616 S'130-t 75363 30814
954
97954 83747 04095 11511
^H
905 95664 85792 05203 315081
955
98000 33715 83746 SA2iil
■
906 95712 81976 76813 0693ft!
956198045 7^5922 76100 07543
■
907
95760 72870 60095 255851
957
98091 19377 76843 5653H
908
95808 58485 210S5 11053
958
98136 55090 78544 41531
^^1
909
95856 38832 21967 44887
959
98181 86071 70663 5992h| ^H
910
95904 13923 21093 59992
960
98227 12330 39568 41336
H
yii
95951 S3769 72998 24763
961
98272 33876 68545 35933
912
95999 48383 28416 17969
962
98317 50720 37812 96123
^^1
913
96047 07775 34298 9445S
963 98362 62871 24534 51542
^^^^M
914
96094 61957 33831 41757
964 98407 70339 02830 77450. ^^^M
915 96142 10940 66448 27597
965 98452 73133 43792 5653S
^^^H
916 96189 51786 67b50 38456
966j98497 71264 15493 31209
^^^H
917
96236 93356 70021 09152|
967 98542 61740 83001 67360
^^^^1
918
96284 26812 01242 43564
968 9S5S7 53573 0S393 66714
^^^^1
919
96331 55113 86111 26520
969 98632 37770 50765 32737
^^^^1
920
96378 78273 45555 26930
970 96677 17342 66244 85178
^^^H
921
96425 96301 96848 92205
971 '98721 92299 08004 86280
^^^H
9-22
96473 09210 53629 34029
972 98766 62649 26274 57690
^^^^H
923
96520 17010 25912 05530
973 98811 28402 68351 91117
^^^^^
924
96567 19712 2i)l06 69918
974 98855 S9568 7h6l5 52768
^^^^M
925
96614 17327 39032 60638
975 98900 46156 98536 81607
^^^H
926
96661 09S66 81934 33089
976 98944 98176 66691 81474
^^^H
927
96707 97341 41197 07^76
977 98989 45637 18773 07091
^^^^H
\\
928
96754 79762 18662 06340
978 99033 68517 87601 44015
^^^^H
929
96801 57139 93641 76318
979 99078 26918 03137 32547
^^^^1
930 96848 29485 53935 11696
980 1 99 122 60756 92494 85664
^^^H
931 96894 96809 81312 62296
981 99166 90073 79948 50979
^^^H
932 96941 59123 53981 36262
982 99211 14877 86949 66797
^^^^1
933 96988 16437 46199 94285
983 99255 35178 32135 62275
^^^^H
934 97034 6S762 30093 35830
984 '99299 50984 31341 51745
^^^^1
935 97081 16108 72517 77408
985 1 99343 62304 97611 73216
^^^H
936 97127 58487 38105 22944
9S6'99387 69149 41211 21109
^^^H
937,97173 95908 87778 26303
987 99431 71526 69636 73242
^^^^1
938 97220 28383 79064 46008
988
J9475 69445 87628 12117
^^^^^1
939(97266 55922 66110 92210
989
EJ9519 621*15 97179 40527
^^^^1
940 97312 7S535 99698 65963
990
39563 51945 97549 91531
^^^H
941 97358 96234 27256 90834
991 <
i9607 36544 85275 32S36
^^^H
942 97405 09027 92S77 36927
992 99651 16721 54178 65574
^^^^^1
943 97451 16927 37328 37338
993 99694 92484 95381 17590
^^^^1
944 97497 19912 98068 97 U2
994 199738 63S43 97313 31202
^^^^1
945 1 97543 18085 09262 94739
995 1 99782 30807 45725 45489
^^^H
1
946 97589 11364 01792 76237
996 99825 93384 23698 73156
^^^H
947 97634 99790 03273 41875
997 99869 51583 11655 71988
^^^^1
948 97680 83373 38066 25572
998 99913 05412 87371 1093^
^^^^H
949 97726 62124 27292 67028
999 99956 54H82 25982 30869
^^^^M
950.97772 36052 88347 76632
lOOl 00043 40774 7931A 64067|
^^^M
^^^M
■^^
k
■
^M
^H
P
■
■
2U
UXiAHITHMS
Tab. 2.
I0U3
Logarithms.
1103
Lugurilhms
00130 09330 20418
11880
04257
55124
40 190
59h66
1005
00216 60617 565U7
67623
1105
04336
227^0
21129
50253
1007
00302 94705 53618
00717
1107
04414
76208
78722
80639
1009
U0339 11662 36910
52172
1109
04493
15461
49160
06471
1011
00475 11555 91001
06349
nil
04571
40589
40867
61503
1013
00560 94453 60280
42845
1113
04649
51643 3470S
31364
1015
00646 60422 49231
72283
1115
04727
48673 84179
47k>6
1017
00732 09529 22744
59739
1117
04S05
31731
15609
05702
1019
00817 41840 06426
39490
1119
04S83 00665
28350
042fO
^v
00902 57420 86910
24725
1121
04960
56125
94973
15180
10-33
00Ufi7 56337 12160
15771
1123
05037
97562
61457
78469
10-25
01072 38653 91773
10408
1125
05115
25224
47381
28895
1037
01157 04435 97278
19720
1127
05192
39160
46106
54029
1029
01241 53747 62432
92943
1129
05269
39419
24967
66114
1031
01325 86652 83516
54691
1I3L
05346
26049
25455
29383
1033^01410 03215 19620
57904
1133
05422
99098
63397
24592
1035
01494 03497 92936
55824
1135
05499
5S615
29141
52489
1037
01577 87563 89040
96243
1137
il5576 04640
87734
77923
1039
01661 55475 57177
41240
1139
05652
37240
79100
36269
1041
01745 07295 J0536
15583
iUl
05728
56444
182U
63635
1043
0182S 43084 26530 66897
1143
05804
62303
95281
73884
1045
019U 62904 47072
80707
1145
05880
54866 75906
79891
1047
01994 66816 78842
33384
1147
U5956 34179
01267
67648
1049
02077 54881 93557
859->l ■
1149
06032
00286
88285
17768
1051 02160 27160 28242 2200b;
U51
06107
53236
29791
80185
1053 02242 &3711 854S6 5IS39I
1153
06182
93072
94699
02164
1055
02325 24596 33711
46987:
1155
06258
19842
2j>163
11355,
1057
02407 49873 07426
26758 1
1157
06333
335S9
51749
55393J
1059
02489 59601 07485
00279
1159
06408
34359
63595
99542'
1061
02571 53S39 01340
66612
1161
064 S3
22197
38573
83829*
1063
02653 32645 23296 75697
1163
06557
97147
28448
411391
1065
02734 96077 74756
52817
1165
06632
59253
62037
7769N
1067
02816 44194 24469
89253
1167
067O7
08560
45370
17354
1069
02897 77052 08778
01749
1169
06781
45111
61S40
11070
1071
02978 94708 31855
63385
1171
06855
68950
72363
12990
1073
03059 97219 65951
OS414
1173
06929
80121
15529
24470
1075
03140 84642 51624
13598
1175
07OO3
78666
07755
07399
1077
03221 57032 97981
58511
1177
07077
64628
43434
6S!5vS
1079
03302 14446 82910
67304
1179
07151
38050
95069
13540
1081
03382 56939 58310
34328
1181
07224
98976
13514
79908)
10S3
03462 64566 25320
36037
1183
07298
47446
27930 36918! |
1085
03542 97381 84548
31517
11S5
07371
83503
46122 67008{
1087
03622 95440 862')4
53993
1187
07445
07189
51591
22047
1089
03702 78797 55774
95610
1189
0751S
18546
18691
5M84
1091
03782 47505 88341
8776!
1191
07591
17614
82777 50317
1093
03862 01619 49702
79227
1193
07664
04436
703-41
87278
1095
03941 41191 76137
14316
1195
07736
79052
84156
4*979
1097
04020 66275 74711
13222
1197
07809
41504
00410
66684
1099
04099 76924 23490
56747
1199
07881
91830
98848
67595' '
llOl
0417S 73189 71751
77528
'
^^^H
^^^^H
^^^H
^^^^H
1
■
■
■1
■
■
Tab. 3.
Logarithms
TO '20 PLACES.
213
t
Num.
Differ. 1.
Difi
42572
1%
D.3.
to 1 out)
00432
13737
82G42
57428
42999
24079 66099
67346
84301
lOlOOI
00432
56737
06721
23527
4299S
81505 78753142572
03045
81293
101002
00432 99735
88227
02280 '42998 39933 75709
42571
18747
84295
^^1
\
101003
00433
42734
27160 779S9
42997
96362 56961
42570
34452
84294
^^1
101004
00433 85732
23523 34949
42997
53792 22509
42569
50158
84290
^1
iotO(»r)
00434
28729
77315
57459
42997
11222 72351
42569
65869
84288
^^1
101006
00434
71726
88539
29809
42996
69654 064B3| 42567
81580
84296
^^1
101007
00435
14723
57192
36292
42996
26096 24903
42566
97294
H42S3
^^1
101003
00435
57719
83279
61195
42995
83519 27609
42566
13011 184291
^H
101009
00436
00715
66797
88804
4-2995
40953 14598
42565
28730184277
^H
101010
00436 43711
07751
03402
42994
98397 85868
42564
444 53 1 84277
^H
loion
00436 86706
06139
S9270
42994
55823 41415
42563
60176; 94272
^H
. I010I2
00437
29700
61962
3*1685
42994
13259 81239
42562
75904 94271
^^1
I010I3 00437
72694
75222
11924
42993
70697 05335
42561
91633 94269
^^1
101014 00433
156SS
45919
17259
4*2993
28135 13702] 42561
07365 84266
^H!
101015 00439
59691
74054
3*)961
42992
85574 06337142560
23099 84263
^H
toioie
00439
01674
59628
37299
42992
43013 83238142559
39836 84260
^^1
101017
00439
44667
02642
20536
42992
00454 44402,42558
51576,84258
^^1
1
101018 00439
87659
03O96
64939
42991
57895 89926 [42557
70318
64257
^^1
1
101019,00440 30650
60992
54764
42991
15338 19508
42556
86061
84251
^H
1
10)030 00440 73641
76330
74272
42990
72781 33447
42556
01810
84252
^H
m
101021 00441
16632
49112
07719
42990
30225 31637
42555
17558
84248
^^1
101022 00441
59622
79337
39356 42989
97670 U079
42554
33310
84245
^^^
101023 00442
02612
67007
53435 42999
45115 80769
42553 49065
84244
^^1
101024 00442 45602
12123
34204
42999
02562 31704
42552
64921 [84239
^H
1
l(nu25 00142 H8591
14685
65909
42999
60009 66SS3' 42551
80582,84239
^H
101026 00443 31579
74695
32791 429S8
17457 96301,42550
96343 84236
^^H
[01027 011443
74567
92153
10092
42987
74906 89959 42550
12107 84233 ^M\
101028 0044-4
17555
67060
09050
42987
32356 77951 4254B
27974,84230
^^H
10IU29 00444
60542
99416
S690J
429H6
8990^ 49077 42546 43644
84228
■
101030,00445
03529
99224
3697S
42986
47259 06333^2547
59416
842*25
■
101031 00445
46516 364H3
43211
42986
04711 46917 42546
75191
84225
101032 00445
89502
41194
90128
42985
62164 71726,42545
90966
84219
^^1
101033 00446
32488
03359
61954
42995
19618 90760 42545
06747
84219
^^1
101(134,00446
75473 22979
42614
42994
77073 74013, 42544
22528
84214
■
I0I035 00447
18459
00052
16627
42994
34529 51485 42543
39314
94215
■
101036 00447
61442
34581
69112
4*2983 91996 13171 42542
54099
84209
101037 00449
04426
26567
81283
42983
49443 59072,42541
69990
94209
^^1
10103S 00448
47409
76011
40355
429H3
06901 99182 42540
85681
84205
^^1
101039 00448
90392
92913
29537
42982
64361 03501.42540
01476
84204
■
101040 00449
33375
47274
33038
42982
21821 02025,42539
17272
84199
■
I0V041 00449
76357
69095
35063
42981
79281 84753; 42538
33073
84199
101042 00450
19339
49377
19916
42981
36743 51690 1 42537
48974
94196
^^H
101043 00450
62320
H5120
71496
429SO
94206 02806
42536
64679
94193
^H
IOI044 00451
05301
79326
74302
42980
51669 3S128
42535
80485
84189
■
1
101045 00451
48282
30996
12430
429S0
09133 57643
42534
96296
84189
■
101046 00151
91262
40129
70073
42979
66598 61347
42534
12107
84187
I0I0I7 00452
342 »2
06728
31420
42979
24064 49240
42533
27920
84181
^H
_
I0I04>) 00452
77221
30792
80660
42978
81531 21320
42532
43739
8ilHl
^^1
1
10 1049 00453
20200
12324
019SO
42978
38999 77581
42531
59559
84173
■
■
!
■
i
^
214
LCGARITHMS
Tab. 3.
Num.
Logarithms.
Differ.
1.
Diff. 2,
U.3
IUKKjO
00453
63178
51322 79561
42977
96467
18023
4-2530
7538U
84177
101051
00454
06156
47799 97584
42977
53936
4-2643
42529
91203
84172
IU10S2
00454
49134
01726 40227
42977
11406
51440
42529
07031
84170
iaiU53
00454
92111
13132 91667
42976
6S877
44409
42528
22861
84168
101054
00455
35087
82010 36076
42976
26349
21548
42527
38693
84167
101O.i5
00455
78064
08359 57624
42975
83821
82855
42526
545-?6
84162
101056
00456
21039
92181 40479
42975
41295
283-29
42525
70364
84161
101057
1*0456
64015
3)476 6880S
4-2974
98769
57965
42524
86-203
84158
I0105JS
00457
06990
3-2246 26773
42974
56244
71762
42524
02045
84155
101059
00457
49964
88490 98535
4-2974
13720
69717
42523
17890
84151
101060
00457
92939
02211 68252
42973
71197
51827
42522
33736
84150
101061
004 5H
35912
73409 20079
4-2973 28675
18091
42521
49586
S4I4H
I0106-2
110458
78H86
02084 38170
42972
86153
68505
42520
654.SS
84146
101063
00459
21853
8823S 06675
42972
43633 03067
42519
81292
S4I43
101U64
00459
64831
31871 09742
42972
01113
21775
42518
97149
84140
101065
00460
07803
32984 31517
4297 1
58594
24626
42518
I30<I9
84139
UH066
0046U
50774
9157S 56143
4-2971
16076
11617
42517
28871
84137
101067
00460
93746
07654 67760
42970
73558
82746
42516
44734
84133
10IIJ6S
0046!
36716
81213 50506
4-2970
31042
38012
42515
6(t602
84130
101069
00461
79687
12255 88518
42969
88526 77410
42514
76472
84130
101070
00463
2-2C57
007S2 65928
42969
46012
00938
42513 92342
841S4
101071
0046i
65626
46794 66866
4^69
0349S 08596
42513
08218
84123
101072
00463
08595
50292 75462' 4?9(»8 609s5 00378
4-2512
24095
S4UK
101073
00463
r.l564
11277 75840
4-2968
18472
76283
42511
3!J973
84117
101074
00463 94532
29750 52123
42967
T5961
36310
42510
55856
84116
101075
00464
37500
0571! 88433
42967
33450
80454
42509
71740
84119
UM076
00464
80467
39162 68887
42966 9094!
08714
4250S
876:?7
84111
101077
00465
23434
30103 77601
42966
48432 21087
42509
03516
84107
U)l078
00465 -66400
78533 9868H
4-2966
05924
17571
42507
19409
84107 1
101079
00466
09366
84460 16259
42965
63416 98162
42506
35302
84102
101080
00466
52332
47877 1442!
42965
20910
62860
42505
51200
84h>2
101081
00466 95>97
68787 77281
4-2961
78405
11660
42:>04
67fi98
84097
10i08i
00167
38262
47192 88941
42964
35900
44562
42503
b3lK)!
84095
101083
00467
81226
83093 33503
42963
93396
61561
42502
989i»6
84095
1010S4
00468
24190
76489 95064
42963
50393
62655
42502
I4SU
84090
lOlOfiD
00468
67154
27393 57719
4-2963
08391
47844
4-250 !
30731
84087
101086
00469
10117
35775 05563
42962
65H90
17123
42500
46634
84087
101087
tK»469
53080
01665 22686
4'>962
23389
70!89
42499
62547
H40831 1
10I08H
00(69 9604-2
25054 93175
4-2961
80S90
07942
42498
7846!
K4080I 1
lOIOSS
00470
39004
05945 01117
42961
38391
29478
42497
9 4384
K4078
'
101090
00470
81965
44336 30595
42960
95S93
35094
4-2497
10306
84077
101091
00171
24926
40-229 65689
42960
53396
2478S
42496
262:?9
84073
1 0109-2
00471
67886
93625 90477
42960
10899
9S559
42495
42156
84069
mum
00472
10847
04525 89036
4-2959
6S404
56403
42494
5S087
84O70
101094
0047*2
53806
72930 45439
4-2959
25909
98316
42493
74017
H4065
10109&
0047-2
96765 98840 43755
4-2958
83416
24-299
42492
fi9955
84063
101096
00473
39724
8-3256 68054
42958
40923
.34347
42492
05889
84060
101097
00173
8-2683
231S0 02101
.42i»57
98431
284 5S
42491
21829
84061
10I09S
0047 »
2564 1
21611 30859
42957
55940
06629
42490
3776m
84052
10U)99
U0474
68598 77551 37488
4*2957
I344<>
fi8H6l
42489
53716
84056
^
L
-J
1
1
■
' Tab. 3.
TO 20 ?lJiCBS,
215
I
Num.
loituu
Logaritlims
'
Differ.
L
Diff. 2
D.3.
0O47& 11 baa 91001
06349
42956 70960
15145
42488
69660
84U50
llOllUI
0047;'i 54512 61961
21494
42956 2S471
45485
42487
b56lO
84048
J1U1102
00475 9746S 90432
66979
42955 85983
59875
42487
01562
84046
1 101 103
00476 40424 76416
26S54
42955 43496
5b313
42486
17516
84043
1101104
00476 833S0 19912
85167
42955 01010
40797
42485
33473
84040
|l«ll05
00477 26335 20923
25964
4i954 58525
07324
42484
49433
84040
[loiioe
00477 692S9 79448
33288
42954 16040
57891
42483
653931 84034
IUI107
00478 12243 95488 91179
42953 73556
9249S
42482
81359
84035
^
lOUOb
00476 55197 69*145
63677
42953 31074
11139
42481
97324
84030
■
1U1109
00478 98151 00119
94816
42952 88592
13815
42481
13294
B4028
■
lomo
00479 41103 68712
08631
42952 46111
00521
42480
29266
84025
■
lOUU
00479 84056 34S23
09152
42952 03630
71255
42479
45241
84 026
■
101112
00480 27008 38453
80407
42951 61i:.l
26014
42478
61215
84018
■
101113
00480 69959 99605
06421
42951 18672
64799
42477
77197
S4020
■
101114
00481 12911 18277
71220
42950 76194
87602
42476
93177
84015
■
101115
00481 55861 94472
58822
42950 33717
94425
42476
09162
84013
■
101116
00481 98812 28190
53247
42949 91241
85263
42475
25149 84012
■
101117
00482 41762 19432
38510
42949 48760
60114
42474
41137
8400H
■
lOlllh
004S2 84711 68198
98624
42949 06292
1^977
42473
57129
84006
■
tOlllQ
00483 27660 74491
17601
42948 63bl6
61848
42472
73123
84002
■
101120
00483 70609 38309
79449
42948 21345
88725
42471
89121
84003
■
101121
00484 13557 59655 68174
42947 78873 99604
42471
05118
83996 ^1
101122
00484 56505 38529
67778
42947 36402
94486
42470
21IJ2
83998
■
101123
00484 99452 74932
62264 "42946 93932 73364
42469 37124
83993
■
101124
00485 42399 68865
35628
42946 51463 36240
4246S
53131
83990
■
101125
00485 85346 20328
71868
42946 08994
83109
42467
69141
63988
■
101 12G
00486 28292 29323
54977
42945 66527
13968
42466
85153
ft3989
■
101127
00486 71237 95850
68945
42945 24060
28815
42466 01165
P3982
■
101128
004S7 14183 19910 97760
42944 81594
27650
42465
17183
83981 1 ^M
101129
00487 57128 01505
25410
42944 39129
10467
42464
33202
83978 1 B
101130
00488 00072 40634
35877
42943 96664 77265 |
42463
49224
83978
■
101 I3J
0(l4>i8 43016 37299
13142
42943 54201
28041
42462
65246
83971
■
101132
004HS 85959 91500 41183
42943 11738 62795 |
42461
81275
83972
■
101133
00489 28903 03239
03978
42942 69276
81520
42460
97303
83969
■
101134
00489 71845 72515
85498
42942 26815
84217
42460
13334
83965
■
10113:1
00490 14787 99331
69715
42941 84355
70883
42459
29369
83964
■
101136
00490 57729 83687
4059H
42941 41896
41514
42458
45405
83962
■
101137
00491 00671 25583
82112
42940 99437
96109
42457
61443
S:i9b7
■
10113S
00491 43612 25021
78221
42940 56980
34666
42456
77486
83956
■
101139
00491 8G552 82002
12887
42940 14523
57180
42155
93530
83954
■
101140
00492 29492 96525
70067
42939 72067
63650
42455
09576
83951
■
101141
00492 72432 68593
33717
42939 29012
54074
42454
25625
83949
■
101142
00493 1 5371 98205
87791
4 2938 87158
28449
42453
41676
63946
■
101143
00493 5S3I0 85364
16240
4293H 44704
86773
42452
57730
83944
■
101144
00494 01249 30069
03013
42939 02252
29043
42451
73780
8394 1
■
101145
00494 44187 32321
32056
42937 59800
55257
42450
89845
83938
■
1UIH6
00494 87124 92121
87313
42937 17349
65412
42450
05907
83936
■
101147
((0495 30062 09471
52725
42936 74899
fc9505
42449
21971
h3934
■
10114s
00495 72998 84371
12230
42936 32450
37534
42448
38037
83931
■
luU4^)
00496 15935 16821
49764
42935 90001
99497
42447
54106
83929
1
r
1.
_
^
J
■
^"
■
TABLE
■
IV.
^^
1
216
LOGARITHMS AND Tab. 4.
Log,
Number.
Differ.
1.
Diff. 2.
D. 3.
ouooo
UHHJO 00000
00000
00000
23026
11602
68807
53020 20192
1 22087
ttoooi
10000 230-^6
M6(»2
68607
23026
64622
88999
53021 42279
1 22085
Ot)002
10000 4G052
76225
57806
23027
17644
31278
53022 64364
1 22098
00003
lOnOO f)9079
93869
89084
23027
70666
95642
53023 86457
1 32093
00004
10000 92107
64536
84726
23028
23690
82099
53025 08550
1 22094
000 0!>
IWOOl 15135
88227
60825
23028
76715
90649
53026 30644
1 22102
O0006 loool 3S164
64943
57474
23029
29742
21293
53027 52746
1 22100
O0007 1 000 1 61193
94685
78767
23029
82769
74039
53028 74846
1 22106
0000 s
1000 1 84223
77455
52S06
23030
35798
48885
53029 96952
1 22104
00003
10002 07254
13254
01691
23030
88828
45837
53031 190i>6
I 22114
OOOIO
101102 302S5
020B2
47528
23031
41859
64893
53032 41170
I 221 1«
000 11
10002 53316
43942
12421
23031
94892
06063
53t)33 63282
I 22115
00012
10002 76348
38834
18464
23032
47925
69345
53034 85397
1 32120
00013
10002 99380
86759
87829
23033
00960
54742
53036 07517
1 22120
00014
10003 22413
87720
4257 I
23033
53996
62259
53037 29637
1 22125
00015
10003 45447
41717
04830
23034
07033 91896
53038 51762
1 22128
00016
10003 684 HI
48750
96726
23034
60072
43658
53039 73890
1 22128
1)0017
10003 91516
08823
40384
23035
13112
17548
53040 96018
1 22134
0OO19
10004 14551
21935
57932
23035
66153
13566
53042 18! 52
1 22136
'flOOlD
10004 37596
88088
71498
23036
19195
3I7IB
53043 40288
1 22137
1 00030
100U4 6VI623
07284
03216
23036
72238
72006
53044 624S5
1 22142
00021
10004 83659
79522
75222
23037
25283
34431
53045 84567
1 22141
000^2
10005 0fi697
04S06 09653
23037
78329
18998
53047 06711
1 22140
000-23
10005 29734
83135
2865 1
23038 31376 25709
53048 28857
1 22151
00024
10005 52773
14511
543G0
23038
84124
54566
53049 5 1008
1 22151
00025
10005 75811
98936 08926
23039
37474
05574
53050 73159
I 22156 1
00026
10005 98851
36410
14500
23o:J9
90524
78733
53051 95315
1 22158
000'^ 7
10006 21891
26934
93233
23040 43576
74048
53053 17473
1 22161
00028
10006 44931
70511
67281
23040
96629
91521
53054 39634
1 22163
00029
10006 G7972
67I4I
58802
23041
49684
31155
53055 61797
1 22167
00030
10006 91014
16825
89957
23042
02739
92952
53056 83964
1 22170
00031
10007 14056
19565
82909
23042
55796
76916
53058 06134
1 22170
00032
10007 37098
75362
59825
23043
08854
83050
53059 28304
I 22177
1)0033
10007 60141
84217
42875
23043 61914
11354
53060 50481
1 22177
"00034
I00O7 83185
46131
54229
23044
14974
61835
53061 72658
1 22160
00035
10008 06229
enofi
16064
23044
68036
34493
53062 94838
I 22IB&
00036
10008 29274
29142
50557
23045
21099
29331
53064 17023
I 221&4
00037
10008 52319
50241
79888
23045
74163
46354
53065 39207
I 22190
O0O38
lOOOS 75365
24405
26242
23046
27228
t-5561 53066 61397
1 22192
00030
lOOOH 98411
51634
11803
23046
80295
46958 53067 835^9
1 22195
00040
10009 21458
31929
58761
23047
33363
30547 53069 05784
1 22196
00041
10009 44505
65292
893nK
23047
86432
86331 53070 27980
1 22209
01)042 lOOOy fi7553
51725
25639
23048
39502
64311 53071 50182
1 222021
00043 IOO09 90601
91227
89950
23048
92574
14493 53072 72364
1 22206.
00044
10010 13650
83802
04443
23049
45646
86b77
53073 94590
1 22209
00045
10010 36700
29448
91320
23049
98720
81467
53075 16798
1 22213
00046
I 00 10 59750
28169
72787
■>3050
51795
98265
53076 39011
1 22213
00047
10010 82800
79965
71052
23051
04 87 2
37276
53077 61224
1 2221-i
00048
lOOll 05851
84S38
08328
23051
57949
98500
53078 WM42
1 22219
00049
lOOll 289113
42788
06828
23052
11028
81942
53080 05661
1 22224
1
L
L
_ J
i
^^^^^^^H
^^H
^^^^H
^^^^^^1
1
^
^"
m
1
Tub. 4.
NUMBERS TO 20 PLACES.
217
001)50 1001 1
Number
Differ. 1.
Diff. 2.
D. 3.
1 22225
51955 53816
88770
23052
641 OS 87603
53081
27885
00051 lOOll
75008 17925
76373
23053
17190 15488
53082
50U0
1 22228
00052 100 11
9S06I 35115
91861
23053
70272 65598
53083
72338
1 22232
)
00053 10012
21115 05388
57459
23054
23356 37936
53084
94570
1 22233
00054' 10012
1
44169 28744
95395
23054
76441 32506
53086
16803
1 22238
00055 10012
67224 051 86
27901
23055
29527 49309
53087
39041
1 2223S
00056 I 00 12
90279 34713
77210
23055
82614 88350
53088
61279
1 22244
00057; 10013
13335 1732S
65560
23056
35703 49629
53089
83523
I 22245
00058 10013
36391 53032
15189
23056
88793 33152
53091
05768
1 22247
00059 1 10013
59448 41825
48341
23057
41884 38920
53092 28015
I 22252
00060. 10013
82505 83709
87261
23057
94976 66935
53093
50267
1 22254
00061 10014
05563 78686
54196
23058
48070 17202
53094
72521
I 22255
00062 10014
28622 26756
71398
23059
01164 89723
53095
94776
1 22261
00063 10014
51681 27921
61121
23059
54260 84499
53097
17037
1 22262
00064 10014
74740 82182
45620
23060
07358 01536
53099
39299
1 22263
00065 lOOM
97800 89540
47156
23060
60456 40835
53099
61562
I 22270
»
00066 1 10015
20S61 49996
87991
23061
13556 02397
53100 83832
1 22270
00067 I00I5
43922 63552
90388
23061
66656 86229
53102
06102
1 22273
0006ft 10015
66984 30209
76617
23062
19758 92331
53103 28375
I 22276
00069
10015 90046 49968
68948
23062
72862 20706
53104
50651
I 22280
00070
10016
13109 22830
89654
23063
25966 71357
53105 72931
1 2225:2
00071 10015
36172 48797
61011
23063
79072 44288
f'3106 95213
I 22284
00072 100I(J
59236 27870
05299
23064
32179 39501
53108
17497
I 22287
00073
10016
82300 60049
44800
23061
85287 56998
53109
39784
1 22290
00074
10017
05365 45337
01798
23065
38396 96782
53110 62074
1 22295
00075" 10017
2S430 83733
98580
23065
91507 58856
53111
84369
1 22295
00076 U00I7
51496 75241
57436
2.3066
44619 43225
53113 06664
1 22299
00077 10017
74563 I9SGI
00661
23066
97732 49SS9
53114
28963
1 22301
1
0007B 10017
97630 17593
50550
23067
50846 78852
53115
51264
1 22305
00079 100 18
20697 68440
29402
23068
03962 30116
53116
73569
1 22306
00080,10018
43765 72402
59518
2?06ft
57079 03685
53117
95875
I 22312
00081 llOOfH
66H34 294SI
03203
23069
10196 99560
53119
18187
1 22312
1
00082 10018
89903 39678
62763
23069
63310 17747
53120
40499
I 22315
t>0083
10019
12973 02994
80510
23070
16436 58246
53121
62814
I 22318
00084
10Ut9
36043 19431
38756
23070
69558 21060
53122
85132
1 22324
1
00035
10019
59113 88989
59816
23071
22681 06192
53124
07456
1 22321
000861 100)9
82185 11670
66008
2307 1
75805 13648
53125
29777
I 22329
00087
I0t>20
05256 S7475
79656
23072
28930 43425
53126
52106
1 22329
00088
10020
2S329 16406
23081
23072
82056 95531
53127
74135
I 22332
1
OOObD
10030
51401 9S463
18612
23073
35184 69966
53128
96767
1 22336
1
00090
10020
74475 33647
88578
23073
883 13 66733
53130
19103
I 22339
1
OOOOl 10020
97519 21961
55311
23074
41443 85836
53131
41442
I 22339
1
00092; IU02 I
20623 63405
41147
23074
94575 27278
53132
63781
I 22346
1
00093; 10021
43698 579NO
68425
23075
47707 91059
53133
86127
1 22345
w
00094! U»02l
66774 056S8
59184
23076
00841 77186
53135
08472
1 22351
00095 'l0O2l
89850 06530
36670
23i»76
53976 65658
53136
30823
I 22350
1
00096 1 10022
12926 60507
22328
23077
07113 16481
53137
53173
1 22358
1
00097:10022
36003 67020
38H09
23077
60250 69654
53138
75531
I 22355
1
uooys 10022
59081 27871
08463
23i»78
I33S9 45185
53439
978.^6
1 2:^363
1
00099 1|0;;22
82159 41260
5364s
2j07h
66529 43071
b314l
20249
1 22:i«2
L
L
*
^"
■
^
^B
^V
218 LOGARITHMS AND NUMBERS TO 20 PLACED
Tab. 4. 1 1
Log.
00100
Number.
96719
Differ. 1.
Diff. 2.
D.3.
10023 05238
07789
23079
19670 63320
53142
42611
1 2236H
OOIUI
10023 2b317
27460
60039
23079 72813 05931
53143
64979
1 22367
00 102
10023 51397
00273
65970
230S0
25956 70910
53144
87346
I 22374
00103
10023 74477
26230
36S&0
23090
79101 59256
53146
09720
1 22374
00101
10023 97b58 0533 L
95136
23091
32247 67976
53147
32094
I 22374
00105
10024 20639
37579
63112
23091
85395 00070
53148
54472
I 22S&oj
UOI06
10024 43721
22974
63182
y30s2
38543 54542
53149
76852
1 22333
00107
10024 66803
61519
17724
23082
91693 31394
53150
99235
1 22396!
00108
10024 S9986
53211
49118
230H3
44H44 30629
53152
21621
1 22390
0U109
10025 12969 99055
79747
23093
97996 52250
53153
44011
I 22392
001 10
10025 36053 96052
31997
23084
51149 96261
53154
66403
1 22393
0011 1
10026 59I3S
47202
2S258
23085
04304 62664 '53155
SH796
1 22396
I»0112
10025 62223
51506 90922
23085
57460 51460 53157
11194
1 22400
00113
10026 05309
08967
42392
23086
10617 62654 53158
33594
1 22403
00114
10026 28395
19585
05t)36
23096
63775 9624S| 53159
55997
1 224U7
00115
10026 51491
83361
012S4
23087
10935 52245
53160
78404
1 224<n
00116
10026 74569 00296
53529
23067
70096 30649
53162
00811
1 22412
00117
10026 97656 70392
H4178
23088
23258 31460
53163
23223
I 22IU
001 IS
10027 20744
93651
15639
230H9
7G421 54693
53164
45638
1 22416
0OL19
lOO.n 43833 70072
70321
23l»99
29586 00321
53165
6S054
1 22421;
noiao
10027 66922 99658 70642 | 23089
82751 68375
53166 90475
1 2243i;
«J012l
10027 90012
82410
39017 123090
35919 59850
53168
12H97
1 22425*
O0122
1002H 13103
19329 97867
i:3'>90
99086 71747
53169
35322
1 22430^
00123
10029 36194
07415
69611
23091
42256 07069
53170
57752
I 224*»
00124
10028 592S5
49671
76683
23091
95426 64821
53171
80192
1 22434
00125
10029 82377
45099
41504
23092
48598 45003
53173
02616
1 22438
O0126
10029 05469
93696 86507
23(»93
01771 47619
53174
25054
1 22438
00127
10029 28562
9546H
34126
23093
54945 72673
53175
47492
1 22443
00123
10029 51656
50414
06799
23094
09121 20165 53176
69935
1 22446
00129
10029 74750
59535
26964
23094
61297 90100
53177 92391
1 22448
00130
10029 97 84 5
19833
17064
23095
14475 82491
53179
14829
I 2245i>
00131
10030 20940
34308
99545
■23095
67654 97310
53180
37279
I 224M
00132
10030 44036
01963
96955
23096
20835 34599
53181
59733
1 22457
00133
10030 67132
22799
31444
23096
74016 94322
531 82
92190
I 22459
00134
10030 90229
96S16
25766
23097
27199 76512
53184
04649
1 22463
00135
10031 13326
24016
02278
23097
80393 81161
53195
27112
1 22464
^^1
00l3fi
10031 36424
04399
S3439
23099 33569 09273 53 186
49576
I 22469
00137
10031 59522
37969
91712
23098 86755 57849 53187
72045
I 22409
00I3S
10031 92621
24724
49561
23099
39943 29894
53188 94514 1
1 22475
00139
10032 05720
64667
79455
23099
93132 24409
53190
16989
1 22476
00140
10032 28990
57900
03863
23100
46322 41397
^3191
39465
1 22478
00141
10032 51921
04122
45260
23100
99513 80862
53192
61943
I 224SS
00142
10032 75022
03636
26122
23101
52706 42805
53193
94426
1 22iSS
00143
10032 9SI23
56342
69927
23102
05900 27231
53195
06909
1 224<M
00144
10033 21225
62242
96158
23102
59095 34140
53196
29393
1 22490
00145
10033 44329
i>133S
30298
23103
12291 63533
53197
51883
1 22495
00146
10033 67431
33629
93S3I
23103
654S9 15416
53I9S 74375? i
I 22499
00147
10033 90534
99119
09247
23104
18697 fr9794
53199
96S77
t 22501 1
00 US
10034 13639
17^06
99041
23104
71897 86671
53301
19378
I 22510
00149
10031 36743
99694
H57I2
23105
250^J 06049
53202
11881
1 225»Kl!
J
1
V
^M
Tab. 5.
HYPERBOLIC LOGARITHMS. 219
^
101
Logar.
N.
1-51
Logar.
N.
2 01
Logar.
Logar.
0'00995U3
4121097
U-69S1347
0*9-20->828
I 02
O019HO26
1-52
0-4187103
2-02
0-7030975
2-52
0-924-2589
103
O02935!^H
1 53
0-425-2677
203
0-7080358
253
0-9-282193
104
00392207
1-54
4317824
2-04
0*7129498
2*54 '0*9321641
105
0-0497902
1'55
0*4382549
205
0-7178398
255
0*9360934
106
0-05S2689
1*56
0*4446858
2 06
0'7->27060
2-56
9400073
107
00676586
1-57
04510756
2 07
07-275486
2-57
0-9439059
108
0769610
1-58
0*4574248
2*08
0-7323679
2-58
0-9477h94
109
OOS51777
1-59
0*4637340
2*09
0*7371641
259
0-9516579
rio
0-0953102
1-60
04700036
2*10
0*7419373
2-60
0-9555114
1 111
n- 1043600
1-61
0-4762342
211
0-7466879
2-61
0-9593502
1 12
113;}2s7
1-62
0-4824261
2*12
0-7511161
2-62
09631743
113
01222176
1-63
48S5SOO
2-13
0-7561220
2-63
09669S38
I !4
0I3102S3
1-64
0-4946962
2-14
0-7608058
2-64
0-9707789
115
01397619
165
5007753
2-15
0*7654678
2 65
0-9745596
1 16
OM84200
1 66
0-5068176
2-16
0-7701082
260
0-9783261
117
0-1570037
1-67
0-512S236
217
0-7747-272
2-67
0-9820785
I 18
01655144
I6S
0-5187938
218
0-7793249
2*68
0-985MI68
M9
1739533
1-69
0-5247-285
2 19
0*7839015
2-69
0-9 S9 54 12
1-20
0-1823216
1-70
0-5306283
2-20
0-7884574
2-70
0-9932518
1-21
0-1906204
171
05364934
2-91
0-7929925
2*71
09969486
1-22
0-19.SH509
1-72
05423243
222
07975072
272
1 0006319
123
0-2070142
1-73
05481214
223
0-8020016
2-73
t-0043016
1-24
0-2151114
1 74
0-5538851
2-24
0-6064759
2 74
I 0079579
1-25
0-2231436
1-75
5596158
2*25
0*SL09302
2-75
I 01 16009
1-26
0-231U17
1-76
5653138
2*26
0-8153648
276
1-0152307
1-27
0-2390169
1-77
n-5709795
2 27
08197798
2-77
1-0188473
1-28
0'246SfiOl
1-78
05766134
2-28
8241754
278
1-0224509
1 29
0-254 64-22
1-79
5H22156
2-29
0-8285518
2 79
1 •0-2604 16
1-30
0-2623643
IbO
0-5877867
2 30
083-29091
2*80
1 0-296194
1-31
0-27 00-27 1
1 81
0-5933268
231
08372475
2-81
1-0331 84 5
1-32
0-2776317
1-82
0-5988365
232
0-8415672
2-82
1-0367369
1-33
0-2851789
1B3
6043160
2 33
8458683
2-83
1*0402767
134
2926696
1-84
06097656
23-1
0-8501509
284
1-043H041
1-35
0-3001046
1-85
06151856
2*35
0-8544153
2-85
1-0473190
1-36
0-3074847
I 86
6-205765
2 36
8586616
286
1 -0508217
1-37
0-3I48I07
1-87
0*6259384
2*37
0S628899
2-87
10543121
1-3H
If3-220S35
1-88
06312718
238
0-8671005
2-8y
1-0577903
1-39
0-3293037
I -89
06365768
239
0-8712933
2-89
10012565
1-40
0-3364722
1-90
1)6418539
2 40
0-8754687
2-90
1-0647107
1-41
0-3435S97
191
0-6471032
2*41
0*8796267
2*91
1-06«1531
1-42
0-3506569
1*92
06523252
2*42
0-8S37675
2*92
1*0715836
1-43
03576745
1-93
6573-2(>0 2 43
08878913
2-93
1-0750024
1-44
0-3646431
1-91
6626880 2-44
0-8919980
294
1 0784096
1-45
37 15636
1-95
6678-294 2*45
0*8960880
295
1-0818052
h46
0-3784364
1-96
6729445
246
0-9001613
2-96
1-0851893
1-47
0-3H5-2624
t 97
n 67S0335
2-47
9042182
2-97
108856 19
I-4H
0-3920421
1-9S
6830968 2 48
9082586
2-98
1 0919233
1-49
39S7761
1-99
688(346 '2-49
0-912-2827
2 99
1 0952734
L
l-5«'
If4051651
2-00
6931472,2 50
0-9162907
300
1-0966123
k
■
Ir
-
_
-
■v
-
^ ^
^p
1
IHI
1
1
ff
1
H^
221
► HYPERBOLIC
LOGARirnMs. Tub. 5.
N
3*U1
Logar.
N.
3 51
Logar,
N.
401
Logar.
N.
4-5 1
I^igar.
1-1019401
1-2556160
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311
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3-12
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317
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329
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^^^^^^^^^1
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333
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334
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^^^^^^^H
330
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336
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^^^^^^^^^B
337
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338
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339
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340
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Tab. 5, HYPERBOLIC LCG\R1THMS. 221
N.
rrOI
Log'ar.
N.
5^
Logar.
N.
6-01
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6 51
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1-7065646
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1-6733393
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1 6131299
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602
1-7950873
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^^^^1
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1-7I01S78
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1-7967470
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^^^^H
504
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554
1-7119945
6-04
1-7984040
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1-8779372
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1 61933^3
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17137979
605
1-8000583
655
1-9794650
^^^H
5-06
1 6213665
556
1-7155981
606
1-8017098
6 56
1-8809906
^^^H
5-07
1*6233408
5-57
1-7173951
6-07
1 8033586
657
1-882513S
^^^^H
5-08
1-6253113
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1-7191888
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1 8050017
6-58
1-8810347
^^^H
5-09
1 C272778 5 59
1 •7*209793
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1-8006481
659
1-8955533
^^^^^^^^^^^^^^^^1
510
I -6292405
5 60
1-7-227666
6 10
1 8082888
6-60
1-8870696
^^^^^^^^^^H
511
16311994
561
1 7245507
611
1*8099268
6-61
1-8885836
^^^^^H
5M2
1-633 1544
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17-263317
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662
1 '8900954
^^^^^^^1
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1 6351057
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1-8131947
663
1*8916048
^^^^^^1
514
1-637053.
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1 ■7-298841
6- 14
I-S148247
6 64
1 8931120
^^^^^^^1
6-15
1-63S9967
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1-7316555 6*15
1-8164521
6-65
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^^^^^^^H
516
1 6409366
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5-17
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^^^^^^^^1
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1-8309802
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5-75
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1-6601310
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1-9110229
^^^H
5-27
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6-27
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6-77
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6-28
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6-78 1-9139771
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5-31
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536
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1-9500284
6-86
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5-37
1 -6808279
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1-7693546 6 37
1-8515995
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5-38
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6-91
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1*8656293
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^^1
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1-7011051
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1 8718022
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1
222 HYPERBOLIC LOGAHITHMS. Tab. 5.
N.
701
Logar.
N.
Logar.
N.
L gar.
N.
8-51
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1-9473377
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1-9558C05 7-57
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7-08
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1 9586653
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1-9615022
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1-9629077
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1
■
Tab. 5. HYPBHBOLIC LOGArtiTHMS.
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^H
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N.
901
L -ar.
N.
936
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N
9-71
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2 1983351
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9-10
2-2082744
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9-11
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2-29I524I
^^^ll
9 20
2-2192035
955
2 2565411
990
2 2925348
^^^^^1
9-21
2-2202893
9-56
2-2575877
991
2 2935444
^^^H
9-22
2'22I3750
957
2-258633:
9-92
2 2945529
^^^^M
9-23
22^24590
9-58
22596775
9-93
22955605
^^^^^^^^^^^^^^t
^B
9*24
2-2235419
959
2 2607209
9-94
2-2965670
^^^^^^H
^B
2-2246236
9-60
2-2617631
9-95
22975726
^^^1
^B 9-26
2-2257040
9-61
2-2628042
9-96
2-29S5771
^^^M
9-27
2-2'^67s34
9-62
2-2638443
9-97
2-2995806
^^^^M
9 28
2-2278615
9-63
2-2648832
9 98
2-3005831
^^^H
9-29
2-2289385
9-64
2-2659211
9-99
2-3015846
^^^H
9-30
2-2300144
9 65
2-2669579
10-00
•2-3025851
^^^M
9 31
2-2310891
9 66
2-2679936
100-0
4-6051702
^^^M
9 32
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9 67
22690283
1000
69077553
^^^^^
933
2-2332350
9-68
2-2700619
10000
9-2103404
^^^H
9 34
2-2343062
969
2-2710944
100000
11-51292546
^^^H
^M ,9-3&|
2-2353763
9-70
2-2721259
^^^1
^^^^^^^^— __W^ H
J
^^^^^^
■
22A HYPERBOLIC LOGARITHMS. Tab. G.
1
N.
Lo^ar.
N.
Lo^r,
N.
iOi
Logar.
4^6151205
N.
151
Logar.
1
DOOOOOOO
3 9318256
5017279fi
■
2
6931472
52
39512437
102
4-6249728
152
5 0238805! ^M
3
109H6123
53
3-970-29 19
103
4 6347290
153
5 0301379, ^1
4
1-3862944
54
39889840
104
4-6443909
154
503695-26
■
5
1-6094379
55
4 0073332
105
4 6539604
155
50434251
■
ei
1-7917595
56
4 02535 17
106
4 663439]
156
5 0498564*
^
7
1-9459101
57
4(1430513
107
4 672b-iss
157
5 0562458
J
8
2-0794415
58
4 0604430
108
4'6>521312
158
5-062:i950 ^^
9
2- 1972246
59
4-0775374
109
4-6913479
159
5 0689042
■
lu
2 -302385 1
60
40943446
no
4 7001804
160
5 075I73S
■
11
2-397S953
61
4-1108739
111
4-709530-2
161
50814044 ^1
12
24849066
62
41271344
112
4 -7184989
162
5 0875963
^^1
13
25649494
63
4 1431347
113
47273878
163
5-0937502
^H
14
2-6390573
64
41588831 :II4
4-3'5l984
164
5-0998664
^^1
la
2-70S0502
65
41743873 115
4-7449321
165
5M059455
^1
16
27725897
66
41896547 116
4-7535902
166
51119676
^1
17
2-8332133
67
4 2046926,117
4-7621739
167
51 179938
^H
1ft
2-8903718
6S
4-2195077 1 118
4 7706846
168
5 1239640
^H
19
2-9444390
69
4-2341065 1 119
4-7791235
109
5-1298987
^H
20
29957323
70
4-24849521 120
47874917
170
5 1357984
^^
21
3 0445-224
71
4-2626799 121
4-7957905
171
5 1416636
^^
22
3 0910425
72
4-2766661
122
4-8010210
172
5-1474915
^H
23
3- 1354942
73
42904594
123
4-8121844
173
5- 15329 16
^^1
24
3-1780538
74
4-3U40651
124
4 820-2816
174
5-1590553
^H
25
3-2188758
75
43174881
125
4 -8283 137
175
5 1647860
^1
26
3-2580965
76
4-3307333 126
4 836-2819
176
5 1704840
^1
27
3*2958369
77
4-343*^054
127
4-8441871
177
5-1761497
^H
28
3 332-2045
78
4-3567088
128
4-8520303
178
5 1817836
^^1
29
3367-2»58
79
43694479
129
4-8598124
179
5187SH5'*
^^^
30
3 4011974
80
4 38-20266 130
48675345
180
5-1929569
^H
^^^^M
31
3-4339872
81
4-3944492
131
4-8751973
181
5 1984970
^1
32
3-4657359
82
4 4067192
132
4 88-28019
182
5-2040! )67
^^1
33
34965076
83
4-41K8406 133
4 8903491
183
5-209 4 S62
^H
34
35263605
84
4 4308168:134
4 897K398
184
5-2149358
^H
35
35553481
85
4 44-265131 135
4 9052748
185
5-220355H
^H
36
3 5935199
86
4-4543473 136
4 9126549
186
5-2257467
^^
37
36109179
87
4 4659081 Il37
4 9199809
187
5-23 U0S6
^H
39
3 6375862
88
4-4773368 133
4 9-272537
188
5 2364420
^^M
39
3 6635616
89
4-4886364 139
4-9344739
189
5-2417470
^H
4(J
3 6888795
90
4 4998097 140
4 9416424
190
5 2470241
^1
41
3 7135721
91
45108595 141
4*9487599
191
5 2522734
^1
42
37376696
92
4-5217886 ,142
4-9558271
192
52574954
^^1
43
37612001
93
4-53-25995' 143
4-962S446
193
52626902
^H
44
3 7841896
94
4-543294S 144
4-9698133
194
5-26785S2
^^
45
a 8066625
95
4 5538769
145
4-9767337
195
5 2729996
J
46
3 8'386414
96
4-5643482
146
4-9836066
196
5-278M47
^H
47
38501476
97
45747110
147
4 9904326
197
5 2832037
^H
48
3 8712010
98
4 5849675
148
4-9972123
198
5-2882670
J
49
3 8918203
99
4-5951199
149
5-0039463
199
5-2933048
^J
50
3-9120230
100
4-6051702
L50
5 0106353
200
5-2983174
^1
^
J
1
^^^^^^
^H
11
Tab. 6. HYPERBOLIC LOGARITHMS. 225
V
N.
201
Logur.
N.
LfOgar.
N.
301
Logar.
N.
351
Logar.
5-3033049
251
&■ 32 5 1529
5-7071103
5-860786:>
1
202 5-30H2fi77
252
5 5294-291
302
5-7104270 352
5-86363 !-<?
^^^^^1
203 5*3132060
253
5 5333S95
303
5-71373-28 353
5'86646W|
^^^^^1
204 5 3181200
254
5-5373343
304
5-7 170277 '354
5-669296!J
^^^^1
205 53230100
255
5 541-2635
305
5 7-^03118 355
58721178
^^^H
20t5 5 3278702
256
5 5451774
goG
5 7235851 356
5-8749307
^^^H
20T 5-3327186
257
5'54!}0761
307
5-7268477 357
5-8777358
^^^^^1
208 5-3375381
258
5-5529596
308
5-7300998 358
5-8805330
^^^^1
2l>9 5 3423313 259 1
5*5568281
309
5-7333413 359
5-8833-224
^^^^^1
i
210 5-3471075
260
5-5606316
310
5 7363723 360
58861040
^^^H
\
2ll'5 35l«581
261
5-5645204
311
5 73979-29 361
5 8888780
^^^H
\
212 5356-1863
262
5-5683445
312
5-7430032 362
58916442
^^^^^^^^
!
213 5'361>922 263
5572 1 340
313
5 746-2032 363
5-8944028
P^^^^^l
2U 5 3659760 264
5-5759491
314
5-7493930 '364
5-897 1 5:J9
^^^^^H
215. 5 3706380 '265
5-5797298
315
5-7525726 365
5-8998974
^^^^H
1
216 5-375-2764 266
55834963
316
575574*22 366
5-90-26333
^^^^^H
217 5-3798974; 267
5-5872487
817
5-7589018 '367
5 9053618
^^^^^^^1
218
5-3S44951 1268
5-5909870
318
5-7620514 368
5-9060829
^^^^^1
219
5 3890717 '269
5-5947114
319
5 7651911 369
5 9107966
^^^^^^M
220
5 3936275 j 270
5-5984220
320
5 7683210 1370
5 9135030
^^^^^H
1)
221
53981627
271
5 602 i 188
321
5-7714411 371
5-916*2021
^^^^^1
222
54026774
272
5 60&902I
322
5-7745515 372
5 9188939
^^^^^1
223 5 4071718
273
&-609471H
323
5-7776523 '873
5-9215784
^^^^^1
224 15-4116461
274
5-6131281
324
5-7807435 '374
59242558
^^^^1
225 [5 4161004
275
5*6167711
325
5-7838252' 375
5*9269260
^^^H
226i 5 4205350
276
5-6204009
326 5-78689741376
5 9295891
^^^H
22715 4249500
277
5-6240:75
327
5-7899602 377
5 9322452
^^^^^t
22S
54293456
278
5 6276211
328
5-7930136 378
59348942
^^^^^
229
54337220
279
5-6312118
H'£9
5-7960578 379
5 9375362
^^^^^M
230
5-4380793
280
5-6347896
380
5 7J>909*27 380
5-9401713
^^^H
231
6 4424177
281
56383547
331
5-80211841 381
59427994
^^^H
232
5-4467374 282
5 6419071
332
5-8051350
3S2
59454206
^^^^^1
233
5-4510385 283
5-6454469
333
5b081425
383
59480350
^^^^1
234
5-4653211
284
5-6489742
334
5-8111410
384
5-9506420
^^^^H
|233
5-4595855
285
5 63-24892
335
5-8141305
385
5-9532433
^^^H
i236
5-4638319
286
5-6559918
336
58171112|386
5-9556374
^^^H
1237
5-4680601 -287
5 6594822
a37
5-8200829 387
59584247
^^^^^1
;238
5-472-2707 268
5-66296(>5
338
58230459 38S
5 9610053
^^^^1
239
5-4764636 289
5-6664267
339
58260001 389
5 9635793
^^^^^1
240 ' 5-48063S9
290
56696809
340
58289456 390
5 9661467
^^^H
24li5 4H47y69
291
56733233
341
5-8318825
391
5-9687076
^^^H
242
5-4889377
292
56767538
342
5-8348107
392
5-971*2618
^^^^H
243
5-4930614
•293
5-6801726
343
5-8377304
393
5-9738096
^^^^M
244
5-4971682
294
5-683579S
344
5-840G417
394
5 9763509
^^^^^1
945
55012582
-295
5-6869754
345
58435444
395
5-9788858
^^^H
246
5 5053315
296
56903595
346
5ft1643H8
396
59814142
^^^^1
247
55093883
297
5-6937321
347
5-8493248
397
59839363
^^^^^1
248|5-5I342H7
29H
5-697(>935
348
5 8522025
398
59864520
^^^^1
24915 5174529
299
5-7004436
349
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399
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^^^^^1
250!5 5'n4«l)i*
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5-7037825 1 350
58579332
400
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^^^H
1
^^^H
^B
1
H^
226 HYPEHBOUC LOGARITHMS. Tab 6.
1
N.
40T
Logar.
451
Lo^df.
N.
501
Logar.
Lo^rar.
5-9939614
6*1114673
6-2166061
6aU734«
^^^^^^^H
402
59964521
452
6 1136S-22
502
6 21S.60UI 1552 ^SlSStiMJ
^^^^^^^^V
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5^89366
453
6-1 158921
503
6-2205902
553 6 3153561)
^^^^^^^K
404
6-0014149
454
6 11S0972
504
6-2-225763
554 6^17 I6M
^^^^^^ft
405J6'003SS71
455
6 120-2974
505
6-2245584
555 e^L^MSI
^^^^^^H
406 ; 60063332
456
61-22492^
506
6-2-26534.7
556 6-3297«a
^^^^^^^H
407 6-O0S8I33 457
61246834
507
6-2285110 5->7 6-a-22565«
^^^^^^^^H
408 6011*2672 45ft
6 1-268692
508
6^304^14 1555 6*3243500
^^^^^^^H
409 60 137 15-2 459
61290502
509
6-2324480 559 6 3261495
^^^^^^H
410 60161572 460
1 1
6-1312265
510
6-2344107
|560 6 3279366
^^^^^^^r
411 601 8593-2
461
6-1333980
511
6-2363696
561 > 6-32»7i09
^^^^^^^B
412 6-0210233
462
6- 1355649
519
6-23S3-246 ' 562 6-331 50lR
^^^^^^^^H
413 60234476
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513
6-2402758 1 563 6-333-27f5
^^^^^^^H
4l4|6 025ft660
464
61398846 514
6-2422233 564 6'3350548
^^^^^^H
415
6-0282785
465
61420374 515
6-2441669 565 6 3366257
^^^^^^H
416
6*0306853
466
6-144l856|5l6
6-2461068,566 6-3S6594I
^^^^^^^^H
417
6-0330862
467
6-14632931 517
C ■2480429 1 567 6-S4l>3599
^^^^^^^^H
418 e0354fil4
468
61 484683 1 518
6 2499752,568 6 31-21214
^^^^^^^H
419 6 0378709
469
6-15060-281519
6-2519039 1569 6 3ISS904
^^^^^^H
420 60402547
470
6-1527327 j 520
6 2538296 1 570 63456864
^^^^^^H
421
6-0426328
471
6154858! '521
6 -2557500 671' 63473892
^^^^^^^H
422
6-0450053
472
61569790 522
6-2576676 572 6 3491390
^^^^^^^^^
423160473722
473
6 1590954 523
6 2595815 573 6-35088»7
^^^^^1
424
6-0497335
474 61 61-2073 524
6 2614917 574 6-3526294
^^^^B
425
60520S92
475 616331481 525
6-2633983 j 575 63543700
^^^^H
426
6-0544393
476 6 1651179 5-26
6 2653012 576 63561077
^^^^^H
427
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6'2G72005 ; 577 , 63578423 J
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428
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6-0614569
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^^^^^
430
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530
6-2728770
580 6 3630281' ^M
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431
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^^^^^H
432
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6- 177944 1
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533
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58316 3681875?
■
^^^^^^
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6 0730445
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6 18-20849,534
6-2803958 584
6 3699010
■
^^^^^
435
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6 1841489 |535
6-2822667 585
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■
^^^^1
436
60776422
486
6' 186-2086 {536
6-2S41342 5S6
6-373319S
■
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437
60799332
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61H8-2641|537
6-2S59981
587
6-3750248
^^^^^H
439
G0S22I89
488
6 1903154 538
6-287 S5S6
5S8
6 3767269
^^^^^1
439
60S44994
489
61923625 539
6-2897156
5H9
6-37S4202
^^^^M
440
60B67747
490
6-1944054
540
6-2915691
590
6-3S01225
^^^^M
441
60=190449
491
6-1964441
541
6-2934193
591
6 3818160
^^^^H
442
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492
6-1984787
542
6-295-2660
592
63835066
^^^^^^
443
6093569S
493
6-2005092
543
6-2971093
593
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^^^^^V
444
6095H246
494
62025355
544
6-2989492
594
63&6rt7»3 1
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60980743
495
6-2045578
545
6-3007858
595
6'3"-856l4 1
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6- 1003 190
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6-2065759
546
630-26190
596
6-3902407
^^^^^H
447
6-10255S6
497
62085900
547
63.144488
597
63919171
^^^^^H
448
6 1047932
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6-2100001
548
6 306-27 53
598
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^^^^^^
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6- 10702-29
499
6-2 126061
519
630S0984
599
6 395-?616
^^^^m
450
6-1092476
500
6-2146031
550
6-S099183
600
6-3969297
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4
Tab. 0. iiyim:rbouc uigahithms. 227
N.
Logar.
N.
651
Logar.
N.
7"oi
Logar.
N.
7T1
Logar.
63985949
6-47S5mi6
6-5525079
6 6214057
60?
6-4002574
652
64800446
702
6-5539334
752
6 6227363
^^^^H
603
6-4019172
653
64S1577I
703
6-5553569
753
66240652
^^^^1
604
6-4035742
65t
6 4R31074
704
6-5567784
754
6-6253924
^^^^H
605
6-4052285
655
6-4846352
705
6-5581978
755
6 6.>67177
^^^H'
606
6-4068800
656
64861608
706
6-5596152
7S6
6 0-280414
^^^H.
607
6-40ft52Kh
657
6-4876840
707
6-5610307
757
6-6293633
^^^^H
608
6-4101749
658
6-4392049
70S
6 5624441
758
66306834
^^^^^^M
609
64118183
659
6 4907235
709
6-5638555
759
6 632^)018
^^^^^^^M\
6tU
64134590
660
6492239H
710
6 5652650
760
6-6333184
^^^^^H
611
6-4150970
661
6-4937538
711
65666724
761
66346334
^^^^^H
Gt?
6-4lfi73'?3
662
6-4952656
712
65680779
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6 6359466
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613
6-4 183649
663
6-4967750
713 6 5694814
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6-637-i580
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614
6'4 199949
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6-49H2S21
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615
6-4216223
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6 4997870
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1
765
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^^^H
616
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6-5012897
710
6 5736602
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6 641182-2
^^^1
617
6-424869(t
667
6-5O27900
717
65750758
767
66424868
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6IH
6-4264885
6GH
6-5042882
718
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768
6-6137897
^^^^1
619
6 428 1053
669
6-505784 1
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6-5778614
769
66450910
^^^^H
620
6-4*297195
670
65072777
720 6-5792512
770
0-6463905
^^^Hi
621
6-43I33II
67l'6 50H7691
721 6-5S06391
771 6 6476884
^^^H
622
6 4329 JO 1
672 6-5102583
7-22 6-58-20251
772
6 6489846
^^M
623
6-4345465
673 6-5117453
723i6 5n34092
773
60502790
^1
624
6-436 1 504
674 6 51323U1
724 6-5M47914
774
6 6515719
'
625
6-4377316
675 6 5147127
725
05861717
775
6-652K630
626
6-4393504
676 6 516I93I
726
6-5875500
776
6-6541525
627
6-4409465
677
65176713
727
6-5889265
777
66554404
628
64425402
678
6-5191473
728 65903010
778
6*6567-265
629
6-4441313
679
6 5206211
729
6 5916737
779
6 6580110
6S0
64457198
680
65220928
730
65930445
780
6659-2939
631
6-4473059
681
6-5-235623
731
6 5944135
781
6 6605751
632
6-4488H94
682
6-5250-2y7
732'6 5957^'i)j
782
6 661h547
633
64504704
6S3
6-5264949
7331 6 5971457
783
6-66313-27
634
6 4520490
684
6-5279579
734 6-59850911
7H4
66644090
635
6 4536250
685
6-5294188
735
6-599h7U5
785
6-6656S37
6S>i
64551986
686
6 5308776
736
6 6012301
786
6-6669568
637
6 4 567697
687
6 5323343
737 6-6025S79I
7S7
6 6682282
63B
6-4583383
689
6 53378H8
738
66039438
7K8
6 6694981
639
6-4599045
689
6-5352413
739
6 6052979
7S9
66707663
640
6-4614682
690
6-5366916
740
66066502
790
6 6720329
641
6 4^30295
691
6-5381398
741
66080006
791
66732980
642
6-4645883
692
6-5395860
742
6609:U9-i
792
6 6745614
643
6 4661447
693
6-5410300
743
6 6106960
793
6 6758232
644
6 1676987
094
6-5424720
744
66120-110
794
66770835
645
6-4692503
695
6 5439118
745
6 613SS42
795
6 6783421
^\6
6 4707995
696
6 5453497
746
66147256
796
66795992
647
6-47-23463
697
6-5467854
747
6 6160652
797
6 6808547
64S
6-473S907
698
654H2I9I
748
6 6I7403<I
798
6-6821086
649
6 47543-27
699
6-5496507
749
6 6187390
79<»
6833609
650 6-4769724 1
700
6-5510803
750
66200732
800
6 6846117
i
1
■
^^^^^^^
1
228 HVPBRBOUC LOGAJllTHMS. Tab, 6.
T
N.
801
Logar.
N.
Logar.
N.
901
I»gar.
N.
LogBT.
6-6858609
851
67464121
6 8035053
951
6 •^5T5UI
BOd
fl-687l05s6 852
67475665
902
68046145
H
803
6-6883547 853
67487595
903
6-S057226
9hJ. . — ^^-4,^M
804
6 6895993 854 6-7499312
904
6-S06B994
954 16-MO^^^H
805
6^08423 655 6^511015
905
6-8079349
955
6d6t7fMH
80«
6-6920837 856 6^522704
906
69090393
956
6-8627579 ^H
807
6-6933237 1857 675S4379
907
6S101425
957
6^638084 ^1
808
6-6945621 85816^546041
908
6 8112444
958
6-SM8476|^|
809J6 69579S6 859 !6"7b376S9|909
6-S12345I
959
6-M&S911^H
810 [6 6970342 S60 6-75693241910
6^134446
960
6-fi6693S3
H
811
6 0982691 861 6 7580945 91!
6 8145429
961
6 8679744
■
812
66995003 862 6 7592553 '9 12 ' 681 56400
962
68690145
■
813
6-7007311 863,6^6041471913
6-6 167359
963 [6 6700534
■
814
6-7019604 864 676157281 914
68178306
964
6S7109I3
■
815
6 7031881 865 67627-295
915
68189241
965
6S72I281
■
816 '6-7044 144 866 67638S49
916
6-S200164
966
6-8731638
817 6-7056391 667 6 7650390
917
6-S211U75
967
6^741985
SIS 6-706S623 S6S 67661917
918
68221971
963
6-9752321
619i670S0S4l S69 6 7673431 ! 919
6 8232661
969
6-8762646
820 6-7093043 670 6^684932 920
6 8243737
970
6-8772961
821 6 7105231 871 | 6 7^96420 921
6S254600
971
6-S7S3265
822 6-7117404 fi72 67707894 922
6-6265452
972
6-8793556
823 6-7129662 873 6-7719356 923
6 6276292
973
6*8803841
^_
824 6-7141705 874 6-7730804 924
6 8287121
974
6'8614I13
■
82567153334 875 ; 6-7742239; 925
6-8297937 1 975
68824375
m
626 j 6-7165948 ' 876 1 6 775366!
926
6-S306742
976
6-8834C26
1
827 6-717S047 877
6 7765070
927
6 6319536
977
6-8844667
828 1 6-7 190 132 87S
677764661928
6 6330317
978
6-8855097
829 ! 6 7202202 ; 879
67767649 i 9-29
6-6341067
979
6-8865316
830
6 7214257,860
67799219
930
66351S46
980
68S75526
831
6-7226299 ' 881
6 7810576
931
6-8362593
981
6S8S5725
832
67238324 8S2 6-7821921
932
68373328
982
6-8695913
833 6-7250336 853 6 7S33252
933
6-6364052
983
6-8906091
834 ; 6 7262334 SS4 ' 6-7^4457 1
934
68394764
984
68916259
835 6 7274317 885 6 7855S76
935
6-8405465
985
689-26416
836 6 72862S6 8S6
67S67170
936
6-8416155
986
68936564
837
6*7298241
8S7
67878450
937
68426833
987
6-6946700
■
838
6-7310161
SS6
676S9717
938
6-8437499
988
66956827
839
6 73-22107
889
6-7900972
939
6-8448155
989
6-8966943
840
^6-7 334019
890
6 7912215
940
6-8458799
990
6-8977049
841
67345917
891
67923444
941
6-8469431
991
68987145
842
6-7 3 57 SOU
892
6-7934661
942
6-8480053
992
68997231
843 6 7369670
893
67945866
943
6-8490663
993
6-9007307
844
6 73^*1525
894
67957058
944
6-8501262
994
6-91M7372
845
67993366
895
67968237
945
6-8511849
995
69027427
846
67405194
896
6-7979404
946
6-8522426
996
6-9037473
^
847
6-7417007
697
6 7990559
947
6-6532991
997
6 9047509
■
S4ft
67428S06
89S
6 6001701
94S
6-8543545
998
69057533
^
849
6-7440592
S99
6 601-2830
949
6-6554066
999
6-9(»b7548
1
850 67452363
900
6 8023946
950
6-8561620 1000|
6 9077553
J
i
1
^M
Tab. 6.
HYPERBOLIC LOGARITHMS. 229
^
N.
1001
Lograr.
N.
1051
Logar.
N.
1101
Logar.
1151
Log.ir.
6-9087548
69574974
7 0039741
7046aS64
1002
69097533
1052
6-9584484
1102
70048820
1152
70192548
1003
6-9107508
1053
69593985
1103
70057890
1153
70501225
1004
6-9 U7473
1054
69603477
1104
7 0066952
1154
70509694
1005
6-9127428
1055
6'9612960
1105
7 0076006
1155
7-0518556
1006
6-9137374
1056
69622435
1106
7-0085052
1156
70527210
1007
6 9147309
1057
6-9631900
1107
70094069
1157
7-0535657
1008
6 9157234
1058
69641356
1108
70103119
1158
7-0544497
1009
6-9167150
1059
6-9650803
1109
7-0112140
1159
7-0553128
luio
69177056
1060
G9660242
1110
7-0121153
1160
7 0561753
1011
69186952
1061
6 9669671
nil
70130158
1161
7-0570370
101-2
6-9196838
1062
69679092
1112
70139155
1162
7-0578979
1013
6 9206715
1063
69688504
1U3
70148144
1163
7-0587582
1014
6 9216582
1064
6-9697907
1114
70157124
1164
70596176
1015
69226439
1065
6-9707301
1115
70166097
1165
70604764
1016
6-9236286
1066
6 9716686
1116
70175061
1166
7-0613344
1017
6-9-246124
1067
697-26063
1117
70184019
1167
7-0621916
1018
69255952
1068
6-9735430
UlS
70192967
1168
706304B2
1019
69265770
1069
69744789
1119
70201907
1169
7-0639040
1020
6*9275579
1070
6-9754139
1120
7-0210840
1170
7-0647590
1021
6-9285378
1071
6 9763481
1121
7-0219764
1171
7 0656134
1022
6 9295168
1072
6-9772813
1122
7-0228681
1178
7 0664670
1023
69304948
1073
6-9782137
1123
7-0237590
1173
7-0673198
1024
6 9314718
1074
69791453
1124
70246490
1174
7 0681720
1U25
6-9324479
1075
6-9800759
1125
7-0255383
1175
70690234
1026
6 9334230
1076
69810057
1126
70264268
1176
7 0698741
1027
69343972
1077
6-9819347
1127
7-0273145
1177
7-0707211
1028
69353704
1078
6-9828628
U28
7028-2014
1178
7-0715734
1029
6-9363427
1079
09837900
1129
7-0290876
1179
7-0724219
1030
6-9373141
lOSO
6-9847163
1130
7-0299729
1180
70732697
1031
6-9382845
1081
6-985641S
1131
7-0308575
1181
7 0741168
1032
69392539
1082
6-9865665
1132
70317413
1182
7-0749632
1033
6-940-2225
1033
6-9874902
1133
70326243
1183
7-0758089
1034
69411901
1084
6^884132
1134
7-0335065
1184
7 0766538
1035
6-9421567
lUbo
6-9893353
1135
7 0343879
1165
70774931
1036
69431224
1086
6-9902565
1136
7-0352686
1186
70783416
1037
6-9440872
10S7
6 9911769
U37
7-036 I4S5
1187
7 '0^91844
1038
6-94 505 U
1088
6-9920964
1138
7 0370276
ns8
7•080(^265
1039
6 9460140
1089
6-9930151
1139
7-0379060
1189
7-0808679
1040
6-9469760
1090
6-9939330
1140
70367835
1190
70817086
1041
6 9479371
1091
6-9946500
1141
70396603
1191
7 0825486
1042
6-9488972
1092
6-9957662
1142
70405364
1192
7-0833878
1043
69498565
1093
6 9966815
1143
704U117
1193
70842264
1044
6 9508148
1094
69975960
1144
70422862
1194
70850643
1045
6-9517722
1095
69985096
1145
7 0431599
1195
7-0859015
1046
69527286
1096
6-9994-225
1146
704403-29
1196
7 0867379
1047
6-9536842
1097
7-0003345
1147 7-0449051
1197
7-0875737
1048
69546389
I09b>
7-0012456
1148
70457766
1198
7-0884088
1049
6-9555026
1099
7-0021 160
1149
7-0466473
1199
7 0892432
1050
6-9565454
1100
7-0U30655
1150
7*0475172
1200
7 0900708
1
1
1
fiao
LOGISTIC U>OABITHMS,
Tab. 7.
<io
3'55G3I-77I0
3'07I« l-7'>70
2-!>.'i42 l-7'V'l
2*8d73|l'7-i»4
2-7782 I
3-7ll2|i
2C-»32!l
9J2 'tOJj 1
l0 2-.~jfir*3 I
11
12
1ft
14
15
)6
17
le
1»
3U
21
122
[23
'24
I 25
26
27
802
SB 2
90 3
73cn
73()2
72:«
717.''
71 II'
70jO
tlUflO
(ID 30
»W7l
6ai2
2-5U» I
2*4771 '1
2-4424 1
2-4]U2|]
2-3802 1
2-3622 t -6755
2-3253 I'WiDir
2-3010' lfW;42
2-2776 l-f'AUJ
3-2553 1-6632
120
I-477I
I '47:15
I ■ 4fi2fl
1-4594
lito
240
1-3010,
1 • 20W)
31 Ml
1 ' 4550 I
1-4525 I
J-4157'l
'>Wi2
2d3!>
2f»I5
2JICfl
2tM5 1
31
32
133
34
135
I3G
37
■ 3H
|3U
U\
43
44
45
40
47
48
4!»
5(»
ftl
63
A3
64
55
56
67
•66
1 69
L
00 1
2341 I
2n» I
liMt; 1
1761 1
1584:1
uis'i
124»1
lo.'il I
0»3M 1
0792.1-
647n
6425
C37S
632<i
K2*W
G216
6tUH
UWti
6021
3-0C49 l'6ft73
2 05 12 l-5f»-25
2'037J l'6fl7a
2*0248 l'6S:i2
2-0122 1-6736
2 uoon 1
i-Dm(i!i
1-H765 1
J-!J652|l
I-H542 ■
I 11435
riJ33i
r»22tt
1-Ul2f{ 1
l-tH)3t 1
1-8035 I
I '1842 I
5740
5695
5651
5607
5663
652l>
5*77
5435
53!»:t
5351
6310
52U0
i-43;jo
1-4:07
1-432.'
1-4202
1-4260
1-4228
J-411'6
1'4I(>5
1-4133
1-4102
1-4071
1--10-10
1-4010
I ■ 3071'
\-3iUU
1-3010
1 - :ufMt
I • :w6o
r:ui3)
I • 3;i«a
2H21
2; OH
2775
377^*
3745
3716
|-36H8|i
1 3660 1
i-:w;3*j
1 ■;i576
t - 354tf
*52J
1 -3495 1
34(»K 1
3441 1
1 34lfV 1
I-33881
I -ai62 I
I • 3:t36 I
I 8751 1-5-22!)
i-B66lil-dl80
1-8673 1 5140
l|.
1-8487
1-8403
I 'B:i2o
82:w
81.i9
5110
607 1
5032
4901
4050
3310
1-3284
1-3259
I 2753
I •2730
1-2707
1 - 2005
1-2663
1-2640
I -afiJH
1 -2506
2574
2553
2531
2510
2I8B
2467
2424
•24o;i
■2382
■2302
-2341
■2:«fl
•2300
2270
2250
2230
2218
2108
2178
2150
2130
-2110
2'«I0
3<»80
2061
2041
20-22
■2003
i084
l!H»i
1761 I
1743 1
1 7251 1
1707:1
•070-.*
•0777
6
420
360
00(»0 0331
4H0
tOMK OSSO'KT-IS
8751
9
510
81"
10 1 ill 12
ton}efn]Ti»
)CH9 I-Oi
1671 1-07J0
1654 1
1636 1
I6l!t|l
1601 I
1584 1
I5Cg| 1
15401 1
1532 1
15 1 51
UOH I
0040 !«70
iwss.oaifo
0093 »0I«'mS0
0706
1481
1464
1447
143<1
Ui3
1397
13^)0 1
1
I
13^:3
1347
13;^!
0678
0663
0G4y
063.*i
06-.' I
0001 1
0504
0500
•0566
055-.*
• 0530
-0525
•0612
■0408
■0484
■0471
9906 9S49
0893 '9236
O/mi 9228
0060 9218
0ti58 0208
00469108
OB34;01I{8
0H-23 017fl
i
-, I.. n_.
8706 l8lr
H6!l7'8l!
6668 81.
6670 hi;
6670101 07 177 17 7JW«.
a6r.i|Hi5o'77ioJ7sw3J
8652
8643
8635
8020
8617
■0
-tnei
2|aM6
5»tt
aftuam
8608
0811 Mir.8
IMOOUf..
i*78H Jil
0777 »i;mi (...n
8152 770317296 «m
8i4r:';'i';7:mrmn6
Bi:. :\W\S
8n2'7W7 Tent
:446R77
0765 9128 (;573 8081 ;7G39 7238 6871
0754 91
t74i !.'!■
)731 00:
:ie»S
0458 !>720 OWiy 8530 0050 7ff 1 1 7213
1-1946 1
1314 1
12m 1
1282fl
I2IJ6 1
1240 )
1233 1
I2]7il
6824
681S
18081 1
1-8004 1
1 702911
I- 76.^1 1
77821 1
49I8!1
4681
4844
4808
4771
3233 I
33081 1
3183il
3158' I
3i33Il-
3108 I
3083 I ■
3050 i ■
3034 I-
3010 1
1027.1
1008,1
1880 1
1871 1
1H52 1
1834 1
UU6 1
17l'7ll
177IH1
1761 11
'1201
1186
•1170
Il5'i
1138
1123
1107
1001
1076
lorn
1045
1030
1015
OJ»f»0
0084
0060
<»1»54
0030
Of»24
OIKIO
mtin
OHHO
0865
005'»
0821
0806
0702
0444 0708 0070 fCi30 8043 ;7«»04 /'OC
043119607 0070 (1522 8035:7597 7200
0686 9060 8513 802;;;5!M 7196
0875 oo.'.o 8ai»4 0020 758;i 7187
0664 0041 U4!lf! 801:2 7.j77 7IBI
9*'»52 9031 8187 IK*04 7570 7176
9C41 902r84;'' 7^1- 7.''637ie«
iwcto ;ki 1 2 8J : *;7
W>10 OtM>2 m'._ . f 7IA(U«gi6
0608 8002 845.} r'i* ;.>4J 7I4:»
0507 8983 8445 ' 7066 !7r«35 7143
05)10 8073 84:17 lUC'i " 7
»57.T 8064 84:.»8 70."> f isyjl
:»5tj4 8054 84-iO ^7044 , , . .4^«7«(
!f5.-i3 8045 84 1 1 |7f>:{6 7508 7 I MSM$i
•1542 iW35 8103 7020 7501 'JUalaJM
-0418
0404
■o:m)1
•0370
0365
(»35
o;»;to
0.3 J6
0313
0300
0287
0274
020 1
024II
■0235
' o-_*-j:;
-»2lM
■0107
0185
•0172
OKjfl
0147
0135
0:22
1 oiin
I 0008
1-008.-.
I -0073
l-IKtOI
I 0040
I 0038
I ■ (K)'24
L0<tl2
1 0000
6647
CB4I
«7«*
6764
«77»
0532 8026 830^17021 74M|;i06!c746
0.121 8017 8386 7014 74887100 8741
t5io 8007 8:^78 7!'06 7481 !7ofW 673fl
1490 8808 83711 'Jii'M 7474|7«87 6732
;>48a 8888 8:i61 '7001 |7l67|7081 (J726
0478 8879 83537884 74*11 '707'. P7.'l
»4«7 6070 834ri7H77 74j I
I45<;8861 8:137 78*JO 741,
0446 8851 8:t28J862'744l
0435 8842 83J0 7855 7431
0425 8833 8312 7847
04)4 8824 Item 7B4<
0404 8814 (L'O'i ~" '
)303 "805 82i
KI83 87^8 8^*>7'.
J372
0362
!f:i51
O.'U 1 1
o:i3il
6787
0778
8700
87ik>
8751
827 1
8263
8255
8247
8239
7811'7.'K"
7803l73.'i:
77:"
77(i:',-,
7782 7:wo (^ou"6w;
Tab, 7.
LOGISTIC LOGARITHMS.
231
13 14 15 16 17 18 \9\2u 21 22 23 24 125 126 27
7H0 j n40 I 900 ; 9C0
6643,
16637
9 6631
36036
4 6630|
6 6614
66660
7
a
f»!6598
1016687
na-iu (toil 6740
caL-v W'i»;:,;3(;
6310 <Uil! ,'»73l
6305 «J0« 6727
0300,6001 '6722
62M 6097 5710
6SltO 6003 5713
6S84 6087 6700
erjObUf^ 5704
6S74|6i»77 5700
6-200 61*73 5«>6
II 6681 C.>r;4 6008 6691
I a 6676 ''"^-''O siMJ^i fl««o
6670.6254 5i)r>ii &6V)'2
6666 «24« 5I»ii4. ',077
6650 G243'501tl 6(i73
fl554 0-230
6543 fi*22B
6638,6:223
6632 6318
I
0527 6213
6521 6208
0616 0203
6510 61 im
6606 6103
6500
6404
6180
20 1 6401
30G478
31 6473
33 6467
618B
01 83
017B
6 1 73
6160
filM t 5fifi0
5:i3!» r.(i»i4
bu:M> 5'j(jtt
51130^6655
6926 6051
5320 6046
5016 6642
5911 6637
5006 6633
5903' 5620
6007 5624
.'i«!»2 5*J20
imio
5220
5236
5231
6217
5213
62(«
5JtK](
5878
6402
Oi67
6451
6446
6141
G435
6430
64-25
B103
6t5A
6153
6148
6143 6866 &68&
6874
5860
5804
6880
41 0420
43,6414
4a'640f>
44 6404
46 6308
46|g303
47 c:uui
46|G:i83
49 [6377
M G372
0I36;6860
6)33.6816
6 1 2H 6841
6)23 6836
6118 6832
6)13 6827
(EI 00! 5833
(1103 6818
(>090;5813
6094 15800
608!t 5804
mUU 15800
6079; 5705
6O74 6700
6009 6786
61 03f!7 (;on4
53 636*2 0059
A3 0357 0055
64 tiCiol 6054»
60 0340 0045
60 6341 now
57 0:00 #;035
60 6331 t}*t:i{i
_ 69 6325 6025
1020
6I77
5473
5469
5464
6460
6456
6453
6447
5443
54 3»
6435
5430
5426
5422
5418
5414
.''►409
5405
5401
531*7
)3y3
5ria9'
6364
5:t6n
6370
6372
6368 6126
53*14 6122
5359 51lfl
5355 61)4
5351 6110
6347 AlOO
6:il3 5l02
6339 509B
6336 6094
6:»1 609U
6326 60^U!
6323 6002
63 lU 5079
6314 54)76
6310 6071
6559 '5300 5007
666416303 6063
5660 6396 6050
6646 6304 6056
5641 5290 M)51
1 140 1 2U0
4994 '4771
49«M» 47<f8
49H'; I'itU
4UH:\ i'VM
4979 4757
4976 4763
5015
5011
5607
6603
6608
6604
6580
6680
6676
6673
6667
6663
6306 4071 4760
6201 UfHti 4746
15197 4964 •17-i2
5193 4!»fi») 4739
'6IW)!4956'4735
6185'4952'4732
51 HI 494!M72fl
5177 4945 4724
5173 4941 4721
516g4»37!4717
51C5 4933 -1714
5)(JI 4'J'Mt 47II'
5157'49J6 4707
5163 49-22 4703
6149 49in'40in«
6145 4915|469G
6141 4911 4692
5137 ^'MfJ 4685*
513:14903 46^(5
6129 4900 4082
1260 13-2it
4559 4357
4r,50|43,'>4
4r.52l4:i.M
4549 4347
4344
4341
4338
43:u
4331
4546
4542
4530
4636
4532
452HI432H
4525:1325
4522 4yt2)
451k'|3)8
4515:43 16
45n;43ll
4508 4306
4505M:{05
4501 4302
440
4164 'to79
4161 3976
41 58 3973
4155 3970
4152 3967
5537
6633
6638
6534
&d30
57HI 5510
5777 6511
5772;.v.o7
57fWJ' 5-103
57«3
57.^
5754
5749
54!)»
5494
4498
4494
4491
4408
4484
4481
4477
4474
t8D6'4676'4471
4892 4«75 4167
48K9!l671 4464
4mi6 4668 44';^)
4881 '4664 445?
I I
4«77 4ftff0 4454
4«74 4057 4450
4«7« 4fi53 4447
4IU;0 4(mV> 4444
4m:i 4646 4440
1
4059 4043 4437
4855 '4G:m u:u
4ft.'i2 46:i0 4t3(»
4048 46:12 4427
1844 4629 4421
4841 14635 4430
48:t7 4022 4417
4833 4618 44 1 4
48:iU 4616 44IU
4826 4611 4407
4298
4295
4293
4289
4285
4282
4279
4276
4273
42«;9
42(;0
420:1
4200
4256
:4253
:4250
4247
'4244
1380
3803
371m
379<:
3793
, . 379)
4149 3.'>(;4 13788
1500
1660
3632
3629
3«jr;
:h023
3621
3018
4l45'3m:i'3785!30l:i
4I42:«I58'37B2|3612
4139|3955'3779 3C10
4i:Mi 395213776 3007
4l33'3949 3773 3004
4l30 3(MO;377o{3001
4127 3943 376n'3598
4124 3!t4o 37(;5 ;»5:h;
4120.3937 3702'3593
4117 3934 :i759|3Al>0
41)413931 3756I3507
411l|3928:$753
4108'31W5 3750
4lOo!3023 3747
4)(>2|39)»3715
35 (Ci
35B2
3579
3.^70
4099'39)7 3742 3574
4096^3914 37:*9;357l
4092'39ll 3736'35(;«
40Jt9J3'K)8 37;*3;:<5f)Vi
4086 31K>6 37 :»0 3503
52115 5048
5281 5044
6277 '**»I0
5273 5030
6269 5032
I
5266 5028
6361 6025
6257 51)21
53.')3 50I7
5240 6013
;.245'6009
4:»0 52JI 5lt0'i
54afi|.V.'37 5002
5746:5481 5J:*3 49'JH
6740)647716229.4994
Ht-22 4608
4819 Mil)i
4Ftl5 4001
4811 4597
4806 4594
4804 459'»
481 HI 4587
4797 4584
47! »3 45Jt0
4789 4577 1
47804373
4712 4570
4778 45«>0
4776 45(i3
4771 465y
4210
im
4234
4231
4228
4224
4221
4218
4216
4312
4404 4-20!)
4100 420:1
4;ii»7l4202
4:t94 4199
4390 4196
4:Vt7'4l93
43Jii'4l89
4:U»» 4186
4:t77 4183
4374 4180
4:1704177
4307 4174
4:«;4!4i7i
4:if;i 4167
4357 4IG4
408313092
40;)0|3099
4077'38!*6
4074
4071
3727 3560
37253557
3722!:*555
:(7 1 913652
3893
3890 3716|3649
4008 3887
4006 [3804
406213881
4060 3878
4066 3876
ta53'3872
404013860
4046'3ftC6
4043' 3863
4O40i:(800
37133546
:<7103544
:*708j354l
3705 3538
3702 ;*5;t5
3609 353:1
3606 1 3530
309? '3527
36if 113525
3688 3522
35)9
:(5)f;
3514
4037,3857 3WW
40:i4 38.'.5 3fyi2
4031 3852 3*;79
4038;:UI49 3077 351)
4036 3846 3674 3508
4022l38M3n7l 3506
iOI9 3n40:i608|3503
4010 38:0 soGsia-soo
38:14 3003 3497
383) 366013195
40)3
40)0
4007
4004
4001
3998
:il*95
39i>l
3888
3086
3983
3979
3828
3825
3JI22
38-20
:i8l7
3814
3811
3808
3805
3B0S
:«i')4'3J«9
3651 34H7
3619 34114
:UM6 348I
3643 3479
:i640 3476
3(i;i7 347:1
3035 3471
3632l340Hl3310
1630
3408
3465
Mm
3460
3457
3454
3453
3449
:i44«
3444
3441
3438
:i436
3433
:i43i
3428
3425
3423
3420
3417
3416
3413
34 03
3407
3404
34i>l
3:i90
3:i96
3303
3391
3388
3386
3383
3380
337s
3376
3372
3370
3367
3365
3302
3350
:i:i57
3:154
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3349
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:i34 1
:i338
;i336
3333
3331
3328
:i:i25
3323
:i320
:ni8
.1315
3313
232 LOGISTIC U»0\R[THMS. Tab. 7.
/
•^s
•29 1 3l>
31
32 33
34
3d
36
37 1 3BI 39 1 40 ! 41 42
an 10
1740 18' >0
3i:»»30lO
umo
28li8
1920 iimo
2730 Lwx;
'2040
2467
2100
2160
2220r22(tt»|2:W0 2400 2400 2520
2341
2218
20!Kn904|lK7l I7OI 10.64 1649
1
-SM):
3166 31H>K
2800
2728 2694
2406
2339
2216
20flH'lJMJ2 1H09 1769 1652 164?
i!
XHih
3i.vi:ii>i»6
2803
272."^ 26I*J
2402
2337
2214
2090 iiuiotoo? 17.'J7 ir;.-io 1646
d
3302
3160 3<Hi3;21J0l 2723|2.M»<i
24(;(
2:1:1;.
22 ll
2094 1978:1 8(^ 1766 1&18 1644
4
3300
3 1 48 30 1 1 2809 272 1 , 26»«
2460
2;J33
22 K
2(J92!l»70 IW;3 1764'l(;47 1642
A
3297
3146 2998 286C 2719|2685
2460
2331
2208
2090 1974' 1802 1762 1046 164U
6
3294
3143 2990 2864
2710,2683
2464
2328
2200
2<»08 l972'lK(;o 1760 1643 1639
7
32!« 3140 2!»Ii3'2Bri2
27I4I26KI
2462
2:120
2204
2000 l970ilH.''f8 1748 lft41 163?
8
32H!t:*i:w*>:»iH
21)49
2712 267:'
246(1 2324 122(12
20H4 1900 Ui:>ii 1740 1040 1636
:i>ii: •m:\5 2im
2B47
27 1 M 2677
244H|2:(22 •J2(HI
2002 11(07, ia:.4 1746 1038 1634
10
32H4 3133 2iHHi
2KVi
2797 2^»74
244.)
23202198
2030 1906
1862 1743 l«Ui 1M2
]|
3U«2Hi:i0 29U4
2fl42
27O6 2672
2443
23 lu' 2 190
2078' 1963
I860 1741 IKM 1.630
13
a27i»|:tl28 2y8i
2840
2:031 2.-P70
2441
2310 2194
2070,1901
Ui49 17:19 Hi33 1628
i:\
3^7t;,ai-.»ri ^nvX'-^u'w
2701 2.if;)i
2439!2;U4 2l!(2
2074 1969
IHI7 1737 1031 1527
u
3274 3123 2977
2ii;tr»
2b-98
26f;o
2437,2312 2190
2«l72 1957
UU6 17.36* 10-2!i 1626
lb
3271 3I2(» 21*74
283:1
2090'
26fi4
243.'!
2310,2188
2070! 1966
1843 1734! 1027 1623
If.
32(W 3118 21173
2H3I
2094
260 1
2433
230b'21«K
2(H;o'l963!Hi4l'l732'»'">"*''-"'|
17
32*16 3116 ^'Miii 2li2a
2(;92-r»o9
2431
2;*O0 2184
2(k;o 1961
Ui'AU I73u
in
32fW3M3-.>l«;7
■2H2ii
20H9 2667
2429
23*»4 2182
2004,I9*.0
lo:*8 172.'; '
19
32(;i 3ll0 2!tG.'>
•2H-24
2087
2666
3426
3302 2 IIH)
20ri2 1948
I0;i0 1727, 1(j24J 1610
20
3260 3108 21)02
2H2\
2086
26&3
3434
3300 2178
2001 1940
1(134 1726 1619 I6U
isi
32.VJ 3106 2!>(»0
2UI9
2083
2551
3433
3398 2170
2069 1 944
1JU32 1723 1017 1613
33
3263 3103 2y.>K':;HI7
208 1
2!fi»
3430
2290 2174
2067,1942
I0:tO 1721 1016 15IJ
2.^
3261 3lHl i'ur>5 2U16
J078
2640
24I8I2294 2172
2066 1940
1028 1719 1013 161(1
U
3248 3IKH1 2\t:t:i\Ml\2
2070;2644'24l«
2291 2170
2(153 1930
1827 I7I8 I0r2|l5rt«
25
324C:^>(>2964J|2UIU
2074
2642j2414
2289 2109
1
2061 luao
1826 1716 1010 1606
1 ] 1
20
;«43 3003 21I4B 2808
^2til2
2640; 24 12
2287 2107
2049 l!f34
1823 1714 llinR!lA04
V
3241 :«>91 2y4C 2806
2603
2638 2410
228,^2106
20i7 I'JXi
1821 1712 16<»0 |:h»3
2Jl
323lt 30»a 21U3|2803
2*^7
263^1 2J(UI
2283 210:1
2045 l'j:il
1KI9 1711 I0<».-,;i6(H
•iii
323(1 3<»8« 2941121101
2066
2533 2406
22H1 2101
2043 1929
1817 I7fm 1003 1499
^]
3233 3<»83 2931*
2798
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2631 2403
22792169
2041 1927
1816 1707 161 1| \ii99
1 1
[31
3231 mm 2!)36
2796
206<»]2529
24i»l
2277 2167
2039 1925
1814 1706'l6l»y 1496
32
322il 3078 2U:W 2794
2(;6« 2627
2399
22/6 2166
2037 i!ni3
1012 1703 1698 I4IM
33
3226 *>7'J 2;»31
2792
2G.Vt2J26
2:t97
2273 2153
2036 1921
1810 I7(»2 16:^6 1493
34
3223 3073 '2!»-_»;)
2709
2064
2622
23;*6
2271 2161
203:* 1919
1008 I7(H( I&94IU9I
36
32S0|3071 292/
2787
2062
2620
2393
2201»2149
2032 191 U
1806 1098 1692
1
I40
3«1
3218 *>00' 2924
278i'
2019 2618
2391
2267 2147
203(» 1910
1806 1090 1691
1487
37 3215 »►«« '»r*-2
2782
2047 2610 2389
'2266|2U6
2(»20 1914
1803 IGJ14 l.'-f!*j'll«n|
3ti :iji.'* ;f"»i 2!>iMt .i7'«'
V04,V.».-,U|2;187
2203 2143
2020' 191 2
loiu i09:t 1
3!l).'lJlO ."iiHM 2!H;:-*77H
204;i 2612 2304
22«l;2Ul
2024 1910
1799 1091
4n 3ihwi :jom 2JII.. -'775
■.'0111,2610 2382
2269'2139
2022 1908 I797jlli«9 l..a-. nai |
41 32«W> »>.-«!iiM2 '.»77:i
•2ii:W 2607 2300
2257 2137
202(» 1900
1796 1087 1682 1179
42f3i.M»:*j:«r»4'-' ' ■""■ :';:{(;':'.-.o:.':j:i7K
2266 21 :i6 201811904
1794 1080 1600 U77
43 -TJiki ;i(»r»i' >::u j.'.u;[ lM7«;
2263 21 332010 1903
1792 1081 1570 1170
44,:naji :i»i;* . . ,, .'.sj j.yil j:i74
2261 2131 20UI901 l71M'il082,16;7: U** |
46
3196 .-(I'l; -'.ii , -7(i4 lm;». 2499'2372
2249 21 21»-2»»l2l 1899
1788! 1080 1676
U7i
46
3193 304-4, Jimi 27*:-' ■:t;2-4 24;>7'j:^7o
224721272010 1097
1786 1078 1573
1470
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3190
304:2
2Jt;m,J7(;"'20Ji» 2494 -SMm
224;i 2126 2009 Ui:»6
l7ai!lC77
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1469
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3188
3039
28:J(i 27n7'2(i2:t,-J4;t2.LMW
2243 2I23'20()7|I893
I7«3
1075
1570
1467
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3186
3037
28;i4 2766 2021 24:MI 2304
2241 2121 '2IMJ6! 1891
1781
1073
1608
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60
3183
3f)54
2«i*l.27r'3
1
2018 248B 2:102
22:i;»
2119,2003
1889
1779
1671
1560
1404
61
3180
3032
2889,2760
20102480 2:»69
2-237
21173001
18B8
1777
1070
1666
1402
62
3I7K
3030
2887 27 4H
20N;2484|2;i57
22:16
2116 1999
1886
1775
1068
I?l03 I4f»l
63 3l7i>
3027
2HH4 2740
20l2,24«2!236:i
2233 21 1311997
1884
1774
i(;o(.
64I3I73
3025
21IM22744
20IU 248(1;
2:i63
2231 I2IU 11996
1882
1772
100 1
66
3170 3022
2UH0 8741
2U<»7
2477
23.-1I
2229
2109
1993
iBfK)
1770
166^ii.j.in i^jj
M
31G8 3020
2877 37311
3606
2476
2349
2227
2107
1991
1878
1768
1661 I5S6 14M
'•7
3106 3(118
2876 2^(7
2(MKl 2473I
2;M7
2226 21(16! 1989
IH70 I7«<;
I06n'"-* ■;'■
:*»
31<;3 3(il&
21173 27;t'">
2(^01
2471
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2223 2HKt 191(7
1876 l7f->
1057
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3100 3013
2*170:2732
26*fy
2409
2:J43
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18/3 I7'i3
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tat
316U|3010
2«Wl!2730
-2690
2407 234 1
2218 309tf| 11)84
1871 1761
lti54[l649U447 1
Tab. 7.
LOGISTIC LOGARITHMS,
233
43 I 44 i 4!S
■i50O''J(>4O 27(KJ
1447 1
i44:t
144->I
L44o!
i4»ai
6 U37
7 UAh
14:1*1
\41M
11 1420
12 Ui7
1»,I426
U|U2:t
16,14-^2
le'uLNi
17 1418
IH 1417
1» UlA
20,U1»
3l!l4l2
321410
23ii4n»
3411407
261 UUA
an'uoii
27 I40L»
38 Uthi
30 1 3117,
I I
31 I »',«.'>
3-j'i:»y:{,
33,i:««
:i4;i3iM>|
36 I'Mm
3c'l3JJ7
37 1385
38|l3{Kt
4<j;i3Jio
4)|]a7»
4a 1377
43 1375
44^1373
4611372
46 1370;
47 i;w«l
48 13(i7!
49'l3<;6|
60 1363
6l'l3t?2|
1360
1367
1366
1364
1362
i:i60
6» 1341) i-i61
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347
313
3-14
342
.^0
33y
337
335
:w2
:i3i
329
327
32«
324
■S22
321
3ia
317
3IC
314
313
311
30!)
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0422 0342 0265
0420 034110364
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0148
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234
LOGISTIC tXKSARlTHMS.
'I'Ab.
77
58 59 GO I 61 62 I 63 64 65 66 67 Gb 69 70 71 I 7t)
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0147
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28 0112
29 0111
30 0110
31 Olllli
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34 OlOA
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37 0101
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30 0098
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67 »»77
68 0075
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9310 9249 9180
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9283
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9280
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9240 9185
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94888183
8181
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Tab. 7.
LOGISTIC LOGAnirilMS.
233
' 73 74 I 75 76 77 7B 79 80
43»U
9U0
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0089 0031
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8534 IMKi
I
8534 1 84 82
8533 8481
((532 8481
(t.'^ll n4Wf
8530,8470
8687 8G34
mv* 8703 *(730|00«5 803i
8114^ 8702 87:01 8084 80:(1
8847 8702 8737W»;SO:)0
8581 8520
8580 8528
8570, a52»
8570 i'527
yU07 1HI00;H!(.'i2'K0!I5
0O0«0lHm8l*5l|8((0i
IK& 9l24!00(>o 0007 8050 8803
20 OI23{0'>(;4 9006 8040 8092
27 0122 !IUt»3 0IMI6 8040 S^lOl
28 01JI ;K)O2 0l>O4l«047
20
Ot20,!>00l OO03 8040
9119 9000 9002 8945
9n8';W59 90«l «0(1
0117 !iii5Ji oiKm;ftii4:t
ti'.njt
00 11
8040
33[y|i0 0057 woo
34 0115 OOuOHOilB
36loil4 0055 8097
36'01l:i'00<>t
37 0)I2,!K)&3S9£I6
38 0111 0052 8<>04
3!ll>||u0()5l 8003
40,Uli»ulm}5O80U2
8030
8938
8037
8036
8036
4l|01flniK)40 8992 8936
420107 !t048 8091.8034
4:f !)ion!Kt47 H:nm ii'js.i
8C40n79rfl73G!
mi45 87!io h7:ij|
8014 nimt 8734!
8843 878H8733
8842 8787, tf73;i
8&11 8780 8732
8«J0 8783H73l|
«8;to«7H4'87:.'j
88;ia 8783 87:iO
8837 8782^8728
8837 878 llll7?7
WirOi 8781 «72ft
««00!«i:i5 «7J« 8725
8H80 88:t4 8;70 8724
8808 a«3J 8778 0724
ilMHS ;88:i2'8777'*7-*3
Ii087i88:t| 8770 872J
mtOO 8830 8775 8721
miU 8774 8720
8828 8773 8710
8682 8029
mitll 8028
m»8l 8027
iWiU 8027
8079 8020
8078 8626
84*77 tB024
8076:6023
0876 8022
807 4 8821
8O73 8020
B<i72 8(;ht|
8071,8618
80*70 6d 17
8678
8677
6576
8676
8574
8673
8638
8625
8924
8623
8522
8522
B478
8477
(t470
U47n
8476
8474
B437
84 :o;
84:*.')
1(431
84 lU
K432
8431
8431
M4:«)
8420
8428
8427
8420
M420
8425
6'I34
8423
047:1 ;I14-2J
047218421
0471 8421
8470.8420
8672 6621 8409 8410
6572 6520 8400 8418
8671
6070
6500
8AI0 8408|04I7
8518 8407 8410
8517 84U0|8410
H!>Gti 0516 040618415
85n7'85ln 840418114
8500 85 15 8404 6413
8J(85
8884
888a
8881
8860
I
6627 8772 8718
6830 8771 8717
8*C25 877l "710
W(25 6770 071'
8«7P|«824 8700 871a
6078'R't23 H70;i 8714
8077 002i 0707 0713
8a70iw:2i H7(:o H71J
44.!n05
46
9104
0(U0 HMUmSJ 0875 0820 8705 O7IO
9045 8!m8 8031
46 9103 9044 0087 8o:io B874 8818 n7o:t H7<>0
47 0102 9043 nviitiiiHnu 8H73 8Jtl7 87(i2 8708
48 9101 9042 89t(.'> 8020 HH72 8010 8701 87(»7
40 0100 9042 8804 8j;27l»871 18815 8701 870f:
6O00gv0O41 8983 n020 8870|08U 8700 87(»5
61 0008 9040 «9(w'»1t-J5'8«(i0;8813 6759 «7'M
62 0007 iHKVJ m»!ll |w^24'8.'{f!8'8813 87fi8 87U:(
63 IMJOO 0(138 8:«UJ H02;i «JI07|8012 8757 8703
54 0005 00;{7 8!i7!l'80-22 OJIM; 801 1 Oj.'iO H702
65|;»oo4 itu'Mi 0^78 m»j 1, 8805 8Jtto 8755 0701
6010003 9035 8077:8:>l.M) ||8(J4
0002 'Mi'M 8070 8<)l0 8mi3
OdOl 90,W0'J75 8018 8862
Ov>0«) 0032 8'J7t OOlollttKIl
9009 !KI31 lt:i73 U0L7't0t01
BtSOV 6610
0(;iill 8016
0007 6014
800061! 19
6(M;5'6013
8005 6612
8W4 8011
8(W3 8010
0t:f;2 iim*
8001 60O8
d(HM}8607
0(U9 8(;0fi
8(k)0 8(;<h;
«Ik)7 0(;o.j
80.i7 0004
mv>o iHitKi
0055 8002
805 4 80l»l
aiihli HOOO
8052 &599
I
8(i5l 8599
8f;50 Oo'Mt
HtibV 8j»97
OIUO K.'iiH;
&i-itl B596
IUI4)0 8754 8700 0047 8504
tUiOfi 8753 8000 0040 8503
8HO7 «752 HOOO 8i;V) B:i92
8806 87>2 8<tl»7 0044 0502
mfcl5'875l 8607 00-Kl 8501
Bft75 ttttlO U704 8710
U565
8606
8564
8663
8663
8661
8600
8660
8669
((558
8557
8550
8666
8554
lt.'.5:t
0553
0552
6514 BlCht
8613 8462
B612B461 R4in
8412
6411
8611 0401»
8610 645<»
8510 64641
8600 6466
8608 8467
8607 6456
R50<i 8455
8505 04:14
R604 B463
8410
8409
6400
8407
8406
R406
8405
8404
H40:i
8402
8401
8504 11463
8503 6452
)(:.02 0451,8400
r(.701 0150 84<m
8500 U440iH:UIO
a%51 8409 8448'8308
865lt 84i;8 8447 8:('l7
6540
6648
8547
K498 8447
8497 6446
6496 8446
83:hj
8396
8396
B547 0495 64 14 6394
8540 0404 8^4;( 830:t
H54A 8403 8442 8:t02
8544 8*02 84 4-2 H'.VM
8543 84!t2 8441 83!>0
B541
840 18 140
8541
85411
841)0 6439
Kiai».84:)8
0540 0406 6437
K5:io 8407 8>:j;
8300
8:I80
6:m8
8;ut7
«:u»7
87
■.220
It3*(5
8385
8.(1U
mm
838)
H3m
JU70
«;i7H
0377
n:47«
n;i70
0:175
8374
0373
372
o;i7l
8:171
M370
ft3<J0
mi08
a:HS7
8306
6:iGS
8366
8304
Kui:t
8302
8361
0301
8300
8360
H»6«
6367
8366
6366
0:t56
0354
h;W)3
8352
6:15 1
8351
ri:i50
6:149 I
63^48!
0347 I
o:u7 '
8346'
8346
8344
H:I4.1 •
8342 I
H:t42
8341
8310
633:1
S:(38
8336
8337
TABLE VIII.
LOGARITHMIC
SINES AND TANGENTS
TO
EVERY SECOND
IK THE FIRST TWO DEGREES.
240
ODeg.
LOG. SINES.
Tab. 8.
7'36UH1&7
1 33077106
S7'368r»lft
3 7 3695310
4 7 3704 1 OB
6 7 37l3l(t-i
673722107
7 7^7:^ I "'w
tl 7 ^T'^'J'M'A
y 7 :i7488:i2
10 7 W7706
11 737R0&A9
12 7 :t7;d;i:(«;
9' I W \ IV \ V2f I ly
7-ll7!*OHI 7 4S37:Ki6
7 4I»77I<>7'*«U487
7 4i;),'.7:i7 74WI707
7-4203742 7 465«!» 10
7 42n7:*:i 7 46661 12
7 42l!»7t'0 7 4673800
7 4227070 7-4690408
7423;»fiI7 7-40f»7B20
7-424:i.'.4;t 74'irw778
7-42Ai4/;7 7 47011II&
7-4369:170
)
7*42072
7427&IH4
13 737H42I4 7-42««ff)A
ir
7 6U6lltil 7 6421MMW 7 Ji770ti«4 7 <i*M»HA3(t
7&0677.'i0 7 /»4a.MKI2 7 A7K224!* 7 0|(»:«W7
7-5004321 7'544MI2 7A7"7BO« 7fll080Afl
7 6(>7<m7fi 7 544712:1 7 A7»:i:c.(i; 6i 14012
7 fio77422 7 54:»:U2ol7i7f)Jiiii»!» 7 01 lOUil
7-60aaOA8 7 M6OI2O 7 6U044:i.'>j7 0I24:UI4
7-60110483 7-A40&lO(; 7 &00'j9U4 7 0l2»44U
7ft09flniW7:»47itHij 7" *'; :6i;i4;i7l
7-ftlo3&4>G 7 w"?*'.'.; ; Ri;«m*».i
7'.'ino()«r2 7''i""'' ■ '■' '•"'■'
7-47otw(4i 7'''nf;4mi7''i
7-47232&7 7SI20434 T^i}i)tiipOi:*M2ififi) 7<;iwi;ij
7-4730347 7-S133a02 7 WOC77oi7 6ft4«470 7 0105227
14 7 3703O14'7.i2:>ofl4l 7'473742C 7AU234n 7 A6l27(K)'76«r.3;»4:i 7617U3IA
U 7:i80l7!»J 7 JLH»K«73 7 47*4403 7 5UH770 7 WIrt«lM 7 A«fl!»40i* 70l7a:i»7
7-47fti'i4;»'7ftl'>v.Nm7f'''^ '.4Wffl 701«O474
7 475Koj)4 7-''>ltil';2B 7'' :"32l 70IWM4
7 47(L'>627 7 AIOJKKUI 7 £»^..'. . '•■.;67C7 7'C1000(KI
no
A7
&5
16 7 3Klt).V>l,7 t:MW4;ii
17 7-3in;»»i8 74:5i42iw
le 7 :f028038i 7-4322005
10 7 3H367;ioi7 4329061
7 4:137024
7 4772049
7477afi.'it>
7 4:t4.'>;i72i7-i7w(;Mi
30 7 3n4fi444
21 7:t«.'»4122
2S 7-3«<»27a2 7 4.V».'110« TlTJ'Mi-m
23 7 3^t71424'7-43flOa27 7 4000023
24 7-:*HJW()5*lj7 43fIBS34 7-48076IW
25 7 3nB«O.S«|7 437(^22H 7-4814542
20 7 3«0724U17-4.l«:i!H»H 7482 U85
27 73l»058«4(7 4:if>l574 74«2«4I7
58 7-aOI43ai r-43!'!i227 748:{:.:i30
59 7 3!«2922i7 440080*J 7 4H42248
30 7 3031440 7-44U4M2
31 7 3!(3!)!»M 7 44-22104
32 7 3!Mfl4li 7 4421*703
s.H7:i!».'>*;i*iM]7-44y72ft9
34 7 3IK!5375
3A T^ll-fWHi
36 7 3l>a224
37 7-3D0«)«60
3*J 7 3IirK»4-J
:ty 7-4007418
40 7 4«i.'i77«
41 7 40241
42 7 40:12449
43 7-4040701
44!? 4049067
46,74057337
40 7-4006001
4774073850
487-4082083
49,74090301
7 40<ja50J
7 4ioooaj>
7 4114800
74123016
7 4131150
74139-282
7 4l473i'2
7 4 I .V»4U7
7 41»kV>67
741710:11
7 4I70W'1
51'
7 44448R2
7 44.'i242l
7 44.'>yi»(«
7-4849147
7-4S680S5
74862913
7 48B!>77!»
7-4M7(;t;:i4
74jim:u7:»
74y!Mi:*l3
76174431> 7 AS 42 KM 7 6801206 70195060
75IitU8;H) 7 ft54«ii:.7'7 5a8W;3« 7 f "» - *■
7.'. 1/172 1 2 7.''''.:i:i!>ji 7 .'iii!*2ofi:t :
7 61y3ili5 7 5061^770 7 '>*tl»7l«l 7 '
7 5199»48 7 6d65627 Ta0O2liU:i 7<i2I.V
7-6206302 7-6671469 76«»82!m 7 »'--'2o:
7521S64G 76577302 7-69I:
7*6218982 78685I27 7 691:.
7'5335308] 7-6688946 7^f244;:i ,
7'523ie8i|76694765 7 5J*2i(«.'>l 7
7-6237933|7-6e0O657|7-6u:io223 7 r>::i;.:(;u
76^4423. 7 fOOC352i7 6940588 76250920
7t3lJ61tfU
7040SM3
76407S0O
7 0« 1261 2
70417419
70423221
7'M27UI7|&4
7fI43iriQ0|A3
7 04366d3|&e
7tU(lAl;itt4«i
t If ■!>« I til ■.
7048aaaBl4i
7 626062 I
76266801
76303073
7^2755f»
7 6281833
7-4407501 7 4897130 7 5288068
74475021 7 4l#o:t;i4» 7 5294296
7-4482.','>t> 7 n!f'7.''0 7 5300612
7 44'>iH II 7 53(Mj721
7 44!I7 J 7 6312920
745*MUi.i / .;r..Mi.*2 753t:illl
7-4513420
7 451987!
74527302
74^4719
7 4.%42I24
7 4649516
7'4666890
74664263
74.'»71C1»
7 49:1786
74944(iOO
7 4»5133»
7 49584K(7
74904784
74971492
7 49701 88
74984876
7 4ini5AI
7 457HOOOl7'4IW«2l7
7 ; ■ '' '.iM)487:i
7 .i<ll.-»l9
7 <'i'»":M.'
7 40oo2o:r
7 46U48(t
74638704
7*463001 1
7 4037255
7.'iitl8l54
7 5024700
7-.Mi( I •(■.-.
7-.'>
17 -V'
760^11
7 5:t2.'.21M
763:ii4«7
7-53:170:11
7-5:u:i7K7
7 534i);»:u
7r>35(i073
7-6963902
7*6366334
7 5S7443fl
75380540
7 63/Mfrh'lA
753U3723
763U68rM)
7 6404870
7-661 21 :tJI 7 5!)4.'i!)4G 7 025^19 1 7
7-6617;H7 75I»&12WJ 70->ttM*ol
7-662:1680 76966043 7 0*265878
7-6629458 7-6861901 7 6370650
7-6636308 7-6967313,76275016
7-M40967 7*597363017-0380777
7-5646698 7-60779S8'7 6386732
7-6062431 75.'>8:t270 7 62;NklH|
7-666816717 '•>0K(l.'\7(; 7 62066W
76663875 7 ; '.3(m502
7*5669685 7 ';3(».'J495
76676289 7 w,^.*^..., 7 6310421
76080984
7 Of;<»2363
7 5fil»8036
7^^703603
7&70D361
76716003
75730046
135
134
7 6A406«3ia<k
7-064583 IIV
7 6649803 S8
7 6664650' 'J7
7 6659303 -iff
7flw;34i.-.(i ■-*'.
7<i577702-'J
7 06frj3i>u'^f
7 6607O13|M
76ft&1639{l9
7 6600343 18
7GOO9735 7'h>I6342 7 0000850
7-60l;WH»!l 7 «.1.'02.*.H 7 «i«5453
76020277 7 6:i-».-.l(it{|7 0610053
7 60355^8 7 6:t:ioo7:ij7 0(;i4645
7608O7U2 7 0:1:14971 7 '»;ii»2:i3
76036040 7-6:n!mf;^|7 ';62:i8i7jl*<£
7*6941282 7
7-6946518 7
';2B3»A, II
'.32969,10
7-57WJH2 7 0<»fll747 7 6:V*4dI2
7 573 1912
75737633
7 5743148
75748755
75764356
•.7.'.<>«lJ'i
7 0050970 7-6350384
7 0963187 7-6304S6O
7O067397 763691I9
7 607S693'7 6373965 79655797
7-6977900 7-6878015 7*8690019
7-fif»ftooftf {7-6383659 7-6994889
177 7-0388408
.:t.VJ 7 (►303332
4^
I 7 .'>42:hk;u;7 u7;t;4.JU;; f;inm6ao 70398loo
18' I 47' I 4G' I 45'
7 6637&B8
7 0049103
70646693
76651317
70*173919
7 0678445
44'
LOG. COSINKS,
89 Def;.
i
ODeg.
LOG. TANOKNTS.
241
«
\y
'i^tmiiiu i4[TJ*i\*o
3 7 w;:».»j^« 7 ^i2^f^^'o^
4 7:i7<>4JHi!7'<-'ll74«
fl 7 37i:ii7J 7J'J1:*724
«.7r.7i2Hy
7 7 3731040
d7a739s»5
f^ 7 374BB45
10 7 37 'J? I fl
11 737(MW72
13 7377A40B
13 7'*7«*22«
1 4 7 3;:ao2«
lA 7:1m
Itf 7.'<«ii
17 7 3*11'
7 4i27t»«6
7>42aft83a
7-4243MU
7 4351482
742&u;iR<;
7 42C7275
7 4276 1 Ml
7-42«»0lU
7 42yt>JV>7
- i"-");k:i
"'7
l(y 11' I 12' 13' I 14'
f« 7 3«2tw;»l|7 43-"JlO| 7-47tt:Kt4(l
Il)73fi367rt3 7 432»877 7 4;72*iC8
'2» 7 3H454v'i7 7 4:137040 7 ■*77t*tl7l'
21 7:w.*'I1:{j7 4.iia:i.'i« 7 i7«fJ''7»
7 4*a7i.-:
74*^4..
7 4'jJ!ii;-'(;
T-iik'itiVM
7 4fififil30
74fi7.'»3l5
74fl«>4tt7
74187048
74«n47I*7
7 47«»U*W
7 47rK>0Wt
7471017:1
7472:*27';
7473<>3*;«
747:(7445
7 4741013
1 7 A77t>7 1 fi 7 'iO(»8Jti([
» 7ri7822mi 70103733
ly
7.'i(Mi4:t»:i
7 507attUO
75077444
7^508soao
75000&06
7.'>097022
7;iioa62ir
75110025
7dn(;Ai:
75122i»a<;
76129457
7*AI35tfl«
7-6l4£l63
7514U802
7 47.'il.M.';i 7.''i5ft-.>:ti
747.'i(WJl3 751(ilWI
7 .'i4 4i i;i«
7 A447 Ulf
754A3152
764MU7
7&4G5t33
7w7nn
7o477oao
75483042
7&4HH095
7 549494 1
7650087^
TMtfemn
7-5512728
7 67U7a37 7 GIOHHIM
7-67y3:w7 7«n4«4;i
7'67i'tiu30 7f'nu]f)7
7«a0446«
7*Aa09906
766I&61
7-6821032
7-^820640
7-6832041
75&17ft36
7'&B43022
75848503
7a8A3&7a
7-55 1 «e40 1 7 5859441
7.V>2454Si7 6IWJ4(rtH
7-6124340
7*;I21>4 77
70134W7
7«I3I»732
70144850
7014I>0(.'3
70155000
7C1601C'»
7 0UW2'H
70170352
7017543s
7 5100001 7 5530331
75l7ii'i-*'T''»122I2
rr-'. 18084
7.''1 -3049
70431850
7fi43(;n:t:>
7 044 1 4 10 51
7044011M :>u
7 04.v>jw;i:4u
7 04:u'>725 4fl
704004K:) 47
7«^'w2;i!» 46
(:4t;0!>KU:+5
7 0471732,44
7.'»A3O442J7 5if;o;V»3i7 01K.'»5KL> 7 0479471 43
703002OI
7-0403024
76407ft42
7 C4 1 740 1 50
7 0422202165
7 'i42705y 54
7A«7571»t',7 0l3O647
7 588IS38 7 0105705
22 7:i8(,j' . .';(il7 5i;i;»iu;i
23 7 3Jj;i ij
24 I CUtblHiif/ii / i.Hto-).!! 4 -Iftii^riOH
25 73nHflii7ll7 437«244 7 48U5C2
20 7 ■; '- ; .ri4 7 4«2150>'i
27 : ':»»j7 4«2tU37|7
211 , i:i 7 iJic.L.'i :
2;)
3u ,-
7668O070
7589209(1
oaoc! 7 6807514
76902920
70200758
70205805
7|t2I0847
7 0216882
7 5lmMJ72 7 5505066
7 520*1320 7 5571497 7590«33l'7 022091 1
7 62I-JG70 7 55773:w) 7 5tfl373<l 7 0'2259:fci
752l!M)U0 7-55U3IfiO 7-5019121 1702300 "
:/j32 7 5:.08974 75{>24.%00 7023.*';"
ti;i!> 7 5.'.ii47M4 7 .'.!i>!».'!Ki 7 024o:i;_
: 7 50fioAt«; 7 " '.'245J#7a
' 7 5000380 : , 0250907
!'.O545{76til2107i7'5!f4.yj80 7 0266050
. -.f;7i20|7 .-.'MT'i »':': .Vi.-.l33l i7-C200939
■ ';77 7 0205917
.|||5,7C270rt«l
■' / .'-'/.-M.. .(I7J7O2758.V1
l|75JH185; :';73i7 0280810
31 7 39:w;>07i7 442-.
32 7 :v\tni:'iu i'-"
33 -
34 :
3.-, 7 '.r
ao 7-1!.. .■
37'7:»-- ;'.... :
38,; ■,.■...-,, ;
3y 7 j(»fi^ ■
40 7401 .
■*» 7 lO-M . ! _ .
42'7 40324t):i|7 *MHJIM\] 4u:H I 13 7 <*31til37|; ^i7.V318^ 7 0«>044:ft»7 t>;ilo40l
43 7'404/t7T '■''' i''i'Ji"i T i'i:t7;i7 '!T ;.:i_>.'.:il'i T ;.<;,: in 1 1 7 (imi'i"*! 7 C-U.'.iii -
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(/
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V
LOG. SINES.
Tab. 8.
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5 4r;a72i;i
5.VM)fi7'-»9
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57^r^
LOG. COSINES.
89 Deg,
Deg.
(y
V
LOG.
TANGENTS.
239^
o'
I 4 0S5A74
S 4!KMiU<M!t
10
I II
12
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6dS44340
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17 A-0I602.18.6-A730fUWt
15 &-&40B474 15776095
19 6 f^3.}8A
90 6-0866040
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• 6473027
6^0667861
Sfi 6-0836140
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66886849
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6-6993887
7 1(I'J6904
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7I«70J7»
i; -j-jrumw G iuno'jfii 7071 1»13
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fl 71124849 ClKJ27<(i7 7 <'747ll2 ^ICUHJ.MI
C7(«>0455 6f>a50tt79 7-07''<>ll»-i 7'1713f»66
0769378G 6lW7nGfi'70782:-'" 7 1 7271 ^^I
0"7»S7H49 6-D.V»7:iJH 70H(H»J(iH 7 I74l25f»
6790ie4G6962ii3';8 70Jtl77U 7 H.Vi.W;
0-7996183 ft06432ll0 71)H:t.^l.>l 7 I7(>!t:^i!i
<r80284G2 60666084 7 <>a:)24ltlj ; l78a:K»(J
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0-8IA04>87 6»750<f;NJ 7<':'21 U3 7 l8:iUH5V
68191138 B!»7783l I 70*»:tK15| 7 |K.*.2(JJ3
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6 843U374 U 9952052 7' 10? 1790 7 1901202; 7
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7 2572842 7 322 Mi34 4?
7 2584409 7 3230052 46
7 2598068 7 3240048 46
7 2f»(7032 73250020 44
7 2011)167 73260570 43
7 2fia(Hi72 7-3270490 42
72042146 7 3300400 41
7 2053590 7 3290282 40
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7 207*i3Jt7 7 33(M«i7B ^'
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6-8409278 69994422 7 1104567 7 19H792U 72721627{73349UM 34
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7 3088348 60
7 3008676 69
7 3IOB879 68
7 3119158 67
7:ii2;wi3 5«j
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7 :{l04Ht:U 53
7 3i70i;a52
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7:iUM»440 50
7 3Joa;.j« 49 '
7 32iO;>92 48
085870)2 7*»<»572!M 7 1 153274 720277M
6-8610002 7 0077943 7 1109389 7^040(102
6-8646619 7 0098575 7 1 1't5444 7-2*t540:*2
686741B5 70M9I09 7 12iH44il 72i>*t7133
&I62696U66398I74
6 1 769:i6C 0440163
6*1007248 Oli4<»:*(i27
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6'34I8774 6 007840110 8700995 70200-288 7 1204842 7 2119145
(^S637766 672:i400 088147^0 7 (>22<l34rt 7 I2«0549 7-2l3-iOo2
6'S66»6«5|667080IO 6 8842:120 7('24<»:il'> llHtGWfJ 721419-20
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6-S07634O'6685574<.l 6 8890!M9 7037W(77 7 1327332 7 2170342
0-3983687 ;6 6K98!N;:I 0-893400H 7 (^*mM;7:i 7 i:i4-Jlliri 7 2IJI321i6
6-8060900 7 0319280 7 1358242 7 2h>OOI4
7 2755250|7-:t:»782iM31
7 270«;4oo.7 3:tJi708i Jf^
7 27775-21 17 3:i!*7.V2l 29
7 27HWil5 73407140 2H
6'306tt342 6 6(f4i73|
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7 2H21 72:1 7 34;(,ȣi70 25
7 28:*27'Ki 7 :i4454'>4 24
7 284:Mi.'.;( 7-3454018 23
7 2854505 7:1404411 22
7 2fWtt4ra 7 ;i473^JH3 21
7 2870354'7*M83334 20
7-2887108 7 :i49-27«5 19
7.2tt960l6
08977620 7 o:«:mi799 7 1373010 7 2'208fi:M
0!KHHlfl8 7-0:iA8231|7 I38a;*:t5 7 2'22KW7
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0-73O8979 0018571 1 7114911170
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6-7380634 6-9234121 1 7 1V>2<»3lO
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7 1419412 7 2240.-. 1 4
7 I i;U570 7-225IHU8
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7 2370253
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72418778
54'
53'
73502170 10
7aOO««06 7 35IKVl*i 17
7 2oi!t508 7;vv2Mo;«i i«
7 2930:1414 7:i5:iu-j8o 15
7 204 101517 35:i!Milo N
7 2!J5|(i08;7 3,J41l02o 13
7 2;>02;t50 7 3554>-2l5 12
7 3972*187 7 3507485 11
7 29a:i503 7 357'i735 10
7-2l)IH173 7 3.V»5905 9
7:HMW727 73.»95176
7 3016-255 7 3O<l4308
7»025758 7 30134140^
7 ;4O30235 7-30226931
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7:iori7!i5 7 3040940'
7:i(t075i7 73(i5oo:i5
7»U778')5 7 3<;591I2
7 3(»n«24« 7:M*081(f9
52^
LOG. COTANGENTS.
89 Deg.
240 Deg.
LOG. SINES,
Tab. a
8'
07:Mj«ai57
i:7 3fi77iy6
2 7^WMU)2I6
3 7 3«95*216
4 TAHunm
9'
i<y
ir I 1/ I 13' 14'
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LOG, COSINRS
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LOG. COSINES.
89 Deg.
1
1
^^^^^^^
^
Deg. hOG, TANGENTS. 243
I
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16'
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1 lb'
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LOG. COTANGENTS. 89 Deg,
k2
J
244 ODeff.
LOG. SINES.
Tab, a
2V
u 7-K4:i;*:t;w)
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7-99l9i»2!tj«(KM87:io8 0li;'»I>l3
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7 9795934 7 9928358
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81)4152979 017tXH3
8 0055059 18 01 78034
8 )HI57 137 80180055
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8 0402607
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7-9811:^63 7 fK>4 1322
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8 0001 29 180 1 84003
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8 0OG&44I 80188127
8(1087514 »0 1901 42
8(HMJ!)587|8 0l:hi157
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24'
23'
22'
21' asy
LOG. COSINBS.
89Deg.
ODeg.
LOG. TANGENTS.
24
32'
3S'
TwuuimG
7IMJ1UU8
7I)W»792.'i
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8 0585058 40
8 05«(W;»8 39
8^47«982 8U5WI737 36
7-975C224,7-9887847
70756461 7 9891 1007
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7-97K0670 7 9692180
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35 797fj7:M6 7Wt9Wa7|8»W2K076!«0U98«3 8 027025818 0;i8738
8 01 3561 9
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8 0376615
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37 7!»77I787j7096a946
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7 9798338 7 9928709 600552H2 KOI 78270
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80408522
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60412354
60414269
8 04if;in3
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8 03018(1:; 80418098
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8 0309851 804257:19
8 0311613 8 0427648
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8 03174'19;8 04:i:t309
8 0319448 8 04:^5274
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6 0493930 60605255 29
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8 0497687 606069 1 6| 27
8 0499564 60610748|26
8 0501441 60612577|2d
8 050:^317 60614406 24
8 0505 1 92 606 1 8'2.33 23
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8 Oo:i6!*43
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8()625359
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8 Wi29005
8 0(;3O82(;
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8-063628C
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8 0546094 60650057
21'
20'
19
18
17
16
15
14
13
12
11
10
9
8
7
5
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LOG. COTANGSNT3.
89 De
rj
248 Deg,
LOG. SINES.
Tab. 8. i
4(y
8U6A7763
8^59672
8-066I3S1
8-0(;r»I88
806(M90A
B-OtHiQSOl
aOOGSGOG
1
2
3
4
6
6
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I0,8)>«75H20
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8^88832
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8-0991984
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14 HimH,'^rj2 H07m>4i4l Bort!):i7iM> Bf>!(»5;i54
15 BmifMrtyl «07!U.1J(« 8fi«!l.'»4ll( Btt!)!»700«
17 ««t;mt4IC S^07it4i»n4;«(tHi>«Ji44 « iiH>«:i:i;i
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8(1782814 8 0886845
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8 07881 29,8 0890277
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8 1001528 8 li78W'2 8l2741 1
19 8WI02'K)n
20 mm'xmm
21 8 0«!I.V.!>7:
22 8of;:»7:nn»
23 8 08*WI83
24 8-07mW7/i|
2.1 8 070276fll
26 807(W.'>37|
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8-I0930O1 8II90I21 81285117
8-|094fi:i8 8 II91722 8 I28(W;82
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8 l(>99o44 8 1190019 812:il.i70
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8 0f^2II23 80J»24445
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8 144U470
8 1441987
M 1 143497
8 1445006
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61448024
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LOG. COSINES.
89 De^.
ODeg.
LOO, TANGENTS*
249
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4(y I 41
42^ I 4;y I 44' I 46'
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8-0861344 008374/
8 0863070 «0*)fi54 33
8 08647116 8 0*107 Mu
8 0806522 8 (KM»8804
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8 ioi73f«i 8 1110221 a i-,»i28.j:t a i;i(i7:iH3
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8 1086807 a 1184080
8 1068446 6- 1 J 85001
8 I OOOOB.-. 8-11 87204 » 1 2H2375
8-10017236 llaSHOOJU 1283042
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8 lOiMOOJi a 1102008 a 1207075
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8 1125981 !ai222300 8 1316723 8 U00O43'27
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8-U43919
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12'
LOO. COTANGENTS.
89 Deg.
250 Deg.
LOG. SINES.
Tab, S.
48'
49'
8 I -I -195 33
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ft 14.'>-J0.>4
8 U5M570
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LOG. COSINES.
89 Deg.
b
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LtiG. TANGENTS.
•2^1
I
48'
49^
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252 Deg.
56'
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88 Deg.
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1 8'2120U1«
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89 Deg. I LOG. COTAN,
88 Deg.
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8:15I08I7
8 3.717754
8 3518600
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Tab. 8.
83567835 B3i;l3ia0»
B 35607 t."J 1 8 30 1 40M 09
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88 Deg,
I2f
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LOG. COTANGENTS,
88 Deg'.
258
2(y
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LOG. 61N&S.
23' 24'
Tab. b.
25'
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8 382d4tf£fr 3880483
8-3829364 8-3881348
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1 Deg.
LOG. TANGENTS,
261 I
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8 4643302 84587402
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8 474(U94
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8 4710776
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8 47656h8 8 47^7763 |6
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8 4763416
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84801253 U
848U1950 10
8 48U:*648 u
8 48033451 C
8 48O4042 7
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268 I)eg.
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9803287 7^ 145827 Oi:Mi728'73 138991
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39 8 483.>995 8 4877324 8 49 18263|8 4958821 8
40 8 4.'t;i6687 8 4878009 8 491«!M2 a 4;i5;i494 8
4l,tf4837:s;u8 4878695 8 4919621 8 4960167 8 5(KW«8 8
42,1)4838071 84870380 R492(K{(K) 8 1960839 8 500 1004 8
498565218
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.OG. COTANGENTS.
88Deg.
26G
1 Deg.
LOG. SINES.
Tab. 8.
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86I31!>(>2
8-&I32548
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31 8-5148054
32 8 5U!»207
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r.OG. COSINES.
88Deg.
1 De?.
LOG, TWGEVTS.
267
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LOG. COTANGENTS.
88 Deg.
272 2 Deg.
NATURAL SINES, &C.
Tab. 9.
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NATURAL SINES, &C.
Tab. 9.
' I Sine.
I «:r.ioo2
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30:0430194 ■y„j!iy5*i3808:22 925580
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32!0442O(MJ'.';;„.j95.S7994 '2+824120
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LOG. SINES,
&C.
277
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1 1 2240048|oi»733l4l 10-0007726
11 22I886J '9 07:11800 IOO(K>7803
II 2197782 0M7;<045h'|O(HHI7878
D. Conine.
19487
I040l»
10314
io2:t4)
10140
I9U*:2
18980
18808
1 881 7
18737
1865*
18578
II 2176801
Il21.'>5i*2l
It2i:{5130
11211445/)
II 2(KJ3870
11 2073380
11 2052986
i I -2032687
II 2012481
11 H<92:i68
ill 072347
11 1'J524I7
11-1932578
II 1012828
II 1893166
09720117
9727774
972*U31
9 07-25088
10(HHl7y54
IO(HH»i031
IOOOOKIO8
100008185
9 0723745; 10 0W*8283
9 9722401 10-(KM»8341
11 1873503
II Ui541O0
II 183471k;
II 1815302
II 1796102
11 1777010
11 1757954
U 173K974
111 1720076
111 17012^9
'.lU i««2fl22
11 I6(.:mh;8
18400
18422
18344
1 8208
18192
11-1645288 9002735
9 9721057
99719712
9-07l83(J7
0971702
lO(Hf08420
104(01 »d499
100«>OH578
10 0008*158
;^07i5*;75jliMM>087.'i8
<Mt7t4329/lOIMM)88l8
0712082
9 971I0:iA
09710288
9 0708JU0
9 0707 ■•'92
07***;243
O07"4894
oo7o;to4:.
9 070211*5
(* 9700845
9609494
99698143
9-9C96702
9 9605440
9*194008
It 16267/(9
II I6(*8367
1 1 l.'i9O023
II 1571755
II 155.V.63
10 0008891J
1 0008980
10^0009062
IOOirf>OI44
IOOlH«l22f?
10000030^)
10 0(NI03tf
IOlHH>017.i
10 0009559
1U0009<;43
100009727
IO(K>Ot>812
(0lN»OO807
lO0<Ht0083
la00lOO*J9
10 0010155
10 or* 10242
10 0010320
100010410
9»«0i;*fl2
:i 960*K)-29
068732lll0 00l05(*4
9 0685087 10-001051*2
no*
67
07
OH
68
08
69
70
09
71
70
71
71
72
71
73
72
73
74
74
74
74
7.1
76
76
76
76
77
77
77
78
78
79
79
79
BO
80
i»
81
81
82
82
82
83
83
83
84
tu
B4
85
85
88
86
84i
«7
87
87
6H
8.1
Cosintf. I Diir. Secniit. Covers. | Cntanp-, Ditl". Tana;, Verseds. Cosec. D
t2
9 909404-1
|9f>99.'i97fl
9 91W30I1
0!»I»03844
00903770
Jfr 91*93708
9 9]*;*:iri4o
99!K*3572
99f»;i6(t3
9 00034:1:1
9993:tOJ
9-9i*9329;i
9f»931G2
9 999308 I
99993009
0-9992038
99992865
999'2703
90092720
9^990204*
99092572
99992408
9^9992424
9-9992349
9^9992274
9 00.'2l08
l*0!*02t-22
9 9992040
9090t!100
JHJ99ltf02
9-9991815
90991737
*9t*0l650
M*!t015JtO
991)91501
9!K*9U22
99091342
* 9**01262
99I*;iinfj
9 9001101
9 9901020
9^9990f»:ta
999(m56
!^90tM>774
,0 999*1001
00!«Pfi(i8
9 000(152:^
9 991*044 I
9^9990357
9^9J*J*0273
9!*:*9<»]8U
9 91*94*103
991*9<K)I7
9 9989931
9 9980845
99989758
9 9d6)x;71
99089584
9 0980496
9 0989408
Sii
86 De^,
276 4 Deg.
NATURAL SINES^ &G.
Tab. 9.
Sine. |Dif. Covers
3 07)i(i'J7(».„ft, y-iKiy^o
4 07oi>i7r-;'"Vy«»o«.>j)
Cosec. Tanp. Cotuug.
ft7(>-iJ!Jl
07(t6ll5'
(t7rt«03«
C07U^7i5|S2
512B502«
7 07I787rtL,uft, 9282121
B 0720777 :.;m;i!»*-27!)'J23
W1072367M :;r"t927«:t
to
I
07!(
I
le
13
H|07:miH4
■|2!M)I
SZ:!i;:!!^?'29«i
21MH
32i;j7I7
».'i<t7'iio«:>
itJ074:*»m; ;;" y2&«ou
10<l7r;28!tfl|.,_,, 'l»2473l2
2o|o7r:A5mv',5^>^44iu
21 O?^^^^! -;';"'l!l24l5ll
22o:<ji3!t<A*;;"jUj:ia(ii*i
■900,. j:
i»!*(K*
2.1,e(7<!-i2w
24 07«7li>u
25'077«IMH
2«07729!>l
27 077^»«:n
2«,07;h7!iI
S807r}lf»ia
S0 0784S<>I
Slif>7ft7Jf>»
:i2 ii7!)o:t!n
:<4 07im;i;>()i.;;J]^
35,07ll!H»iH}-;f~
30 0801989 jj[;j2
!:i67io
<>2:i2tiUi
2U01
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9224 HHi
9221 2iyj
921031)9
9216409
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JUIMJ
21)1X1
2900
21199
3Bnft(^77mt
I9:tiui ™:'9iao(iir.
39'(l(UtM>Ji7
40|f»KI
41 OK
42,.,Ki:.:«uv^^^
4:iO0-322«4l
4^»B2&iti:ij^;^
45,mi2mKt-:'^^
920y*iiH(
92mi7U»
9203610
92(»09lU
919U0U
919,'VIII
!Hi»22l2
l!Jl«;)3l3
49
ftO
61
62
63
64
66
M
67
68
60
Oft39fi77
0);42u7(i
OB4M74
OB48373
OftAl>7l
OB&70fi7
06611008
0809664
0066702
OH7i.'>r.7
Cnsine
2rat9
2ft!ttt
2aMfi
S8!)fl
2Rnti
2n9H
■imn
2897
11177710
9174817
:H7191K
9l(i9Ul9
<J\fSV20
91(13222
9160323
9157424
9l&4.^2fi
9161 G27
9140729
9116^131
:Jl42tl33
9U04)3l
:M37i:Mi
:M:«i3a
9131340
912044
I4 3.'»JJ87
l4 27(i2<M>
U-217304
l4l:i»094
U HK»Wi3'07lOf)(i|
l4(l43J04|07l3Uti;>
I3 9»0ol4 0710009
I3 92imHV07l9733
13H739I3 U722(i.'i7
13(110291
13 70311a
13 7W0379
I3OWO77
O725.-JKI
«7i?ao«)5
0731430
0734364
14 3<K>li0fi
1 4 2411:^4
14 IH2ntiJ
14 Ij3ri:i6
U(Mm4.*i9j
U'Ni;85U
13950719
138J» 104ft
13K37)t2i
13 7RJ0(K>
13-72073aj
13 071056
13 0I74U9;
Secant. Vers. I D. <
1 3 000J05 0737279
13,V|i;7o8'0740203
13 493731 0743128
l3 44lll0,O74tJ0.->3
13 5G:{3!II
13 509799
I345«i25
13 40;UM>7
I3;««9l4|0748y79 13301518
13-:t3711(>;O7ol904 13 299574
13 2411031
13 1 90083
13 140 1 27
13095757
13 04&709
12990100
I3 2H57I9 0754829
132:117170757735
13 lH41OO|O7UUiH0
13 l33Wf2O30;M>lM;
l30O4(M0 070<>53-2
13 03^1570 0709458
12 9854Ro'o7723a4
I2 9307*»|0775»U
I2-8H04UHi;7«237
I2 84iul0ll78t UJ4
12792779 OJHJOIM)
12 745496 070701 7
I2C9 8500 0709044'
lJ05l:*7l|o79J«7r
120(10724 0795798
12 559ai.j,079O726|
12 514240 WIOIO53;
12 40U995 0004581
I
12-424070 08075()9
I2 3794K4
12 335210
12 291252
12-247M»6
12 2<I4274
12-101240
12IIH522 W!2BiW>7
l2 07<i)»9K (tH:nrj:t(J
I2n33!t79 UHXMitWt
11 992137i<^J307l*4
11-950595 08:19723
1 1 909340 Ikt) I2r.:i3
1 1 800.3700.^4550:1
II 827'i03 0848512
01^'il4'l2
«H54:t72
OR57JW2
(H;00233
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0024359 I .
(H)246<i I
(H)247f.7
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,0025178.; '
002530i ^ L
^",2*19
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0086260 ^ V
0020431 r '
i002G643 .,.*
0020066,;!;
'0027000.,,,
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0029705,0029006 .,.,,':
1-0024419
1 (Hh!4G23
1 (M>24829
I 01t2.iO35
I 0(h.»524 1
1 0025449
1 04)25058
10025867,
IOOS6O76I
I002<»B»
1 002(kV)I
101I-J0714
10020920
HKW7142
I 0<I27358
i (M127574
1 0027791
1 ()(i2.SIM)9
1002022a
l-002fM4a
10020009
1-0028090
104J29112
n»02y3:«;
1 0029500
;*97a02a.J7
l^73oO:> ai
in»73557 4l»
in)731 .151451
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»07loa3 41
12 940024 I
12 898056 UK»300lO'4)029920
12849557 I
UlUlUI? 1
127530:W I
12 700206 1
0810437
0013306
00IG2B3
0819321
0022160
0825078
II 7H7274
11747141
11 707282
II (;07r;!)3
1 1 02)!372
II 5893 Hi
I I 550523
II 511!1!H)
11473713
12 059125 I
12 rj 12390 1
12 505997 1
12 519942 1
12474221 1
12 420J31 I
12 303708 I
12 339028 I
12 294609 I
12 2505(15 I
12-200710 1
12 10:12:10 1
I
12 12(K»02 I
12^077192 I
I2 0:U022 1
1 1 ^9234*1 1
1 1 950:t70 I
II 908r»02|l
1 1 RG7262 I
lUt2«107 I
n 7tt533:i 1
II 744779 1
n 7045(m 1
U(;«U40& 1
00:UI237 (M):Utl4l.
(N):«u(i4 oo:w37j
0030093 0030591)
0o:U>u22|003O82;
003n52'003lft5.-,
01131303 «m;u2e5
003li;l5 0031515
00:11847 0«t3l74(i
0O32li(Jl lK»3l97li
0032315 00:t±21 1
003355 1 1 0032445
00327H7 0O;V207!i
00:i3024 iHl329i:.
00332K1 t«i:Ulol
(.Ki;i35(Kt «t33:t«i,
0<.)3374O0U3302<.
0<i3398o'*Mi3:Mt6.-.
(H);i4-22i o»):*4io:
0O344(i:i*H)3i:i4:i
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0035195 0035071
■.►■.»! :
2M\
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oo:t5oa7
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0034;(i81|UOJO54:
O03.Vil5'„,,l
00:1
"I I
1 1 824701 I niO(*!l32in03079(i
1 1 585294 I tH)37103JtH):»7tM(;
OJinO()94l 1 1 54(>4I93| I <M>:i7430'0()37-2tH,
0809025 1 1 507154' I 0037«i«9lO03754J:
0871950,11 400-174 I 00:t7»43 00378iM»
4Deg.
LOG. SINES» &C.
277
6K
o
1
o
a
7
«
to
II
13
i:(
14
I&
16
17
18
19
70
21
33
34
25
3tf
«7
38
29
30
31
3:i
34
3.-,
3G
37
3K
3!»
40
41
42
4.'l
44
4A
4(i
47
4H
4M
All
SI
52
A3
&4
AA
&6
57
A8
line.
f|-8435H4.5
HH471H'J7
DifT.
IBr>2!»
17!*.»3
ft«4jm707i;i!!!!?
RW2:.245*"*
a-HM04U3
a-8578010
88695457
8 Ml -2833
I75I7
I7«7
! 1 7376
;i730G
Conec.
VVrscHs.
7 :i:*(i->7»:,
7.i!i:iM7;t'>
88647376 ly^-^J
8 ft(K;4ri45'
8-808 Mi4A
8'86:iSC60
8 87l5fI4fi!
8 8732A4*;|
U B74:i38 1 1
8875Cl."iO
3 87«2«o4l
d883'^81
8-8849031
88805418
8-8881743
88808007
8-89U3(KI
8^89:)035l
8-8940433
17101
17034
I nwu
IfiTMHI
H>(t35
lHM(y2'Xi 7 3!*74:»3:i
II [4747-^5
11-14671)95
II l43U.'>n7
II U'iimm
llll0454;i
II 1387167
II I3f :■)«(; I
11 I:i5-i634
1M33A456
II I3l«354
Ul.1lfl:(2<l
IM-21M5:)4
II 12«74.'>4
7'4i»i()i5ff;
7-40457<»'J
7'40fll»7l
7 4ll(K!t3
7-4151372
74i;t6:ui
7 422HO;#
742.>:.7'i7
742»(>2a«
7 4324^73
7-4:i:in!»2i
7 4J!i:i03.j
7442701.-.
7 44ti<)H62
Tanj
II ]2.'iO(ilU 7 44U4o7H
n 1333850 7 4S2WI63
11 I2l7l4f: 74.Miniin
18704
1<;U39
l*»76
IIJ0I2
16450
18387
18325
jSlii 11 110I9!'3 7 471(2264
Si.«|lMW«-''7IH 7 41?247l!l
n«4»2j!*7
«HftlK4*
HtlYMiJillH
{I8.3o40a4
88,17171:1
3«nHit:t2l
88(;24327
«K(:4172.'i
8B85<f065
88676317
8R6!I35M
Dilf. Cotana:.
II 1200:107,7 4ft!>4^»4«
11 nH:i;i3i 7 4iWHi4(;
n Ilri74l»'7 466l210
llll50!m9i7 4<IU4l6(;
1 1 1 134582 7 472698!)
11 11IK257 7'475!)688
tf-H744«!»4
««7«1023
88778487
8«7;»ri-iHf;
K HH'JRtiOi
H «H<,'j:ioa
8«W>I850
8 887fi:i:i4
888947.17
8891111!!
8-«;»2742n
iMnnvi i i loO'.mu 7-4*»57<V»2!il flfM.'i/WO
18022 • **<*^^**''7i7 4881)265 880i0842
8-8962455 ,„_-ll 1 lOS?^^'? 492135y 8-8n7.'ifl6:i
88;»7H4 Ifil *^J!J;^; 1 1- l»21aH2l7 4n5;i;»3r»l8 8!»(>202li
i^«:t!>i.'^22 ;;,,', 1 1 lOlkltj^S 7-49«''ii:»3|81)(H(Hi»:Ul
'■^""' n-*>l»fll»833 7-50!*;jKt4 8902:^77
J iW7ioi,v7 '■vo4U.j6o;Hw.'i»Hfi(;
1 1 U95U31&I7 AO8OO7I |8*9()od(i07
8f((»lO|liJf
8-iM>25r);i.i
800411146
89057358
J^ 9072976'
8 !»08853A
89l040:t9
8!I11»4S7
8!M:M88I
U7«7
Ia730
150731
1WJI7
15560
15a04
1 '1448
I o:i!)4
1,5338
M;nowo4| ,'-11;;
8 9(00734 ' ""
H»l95!lll
8 9211034
8;r>2tJloft
81*24 112s
8 !»J.VJ08tl
HJ»27i(H):i
H-!l?8.'t84;f;
8-y:i(Hiii7K
8-U3 1.14311
I-M77
Inl23
15071
loOlB
14966
I49I4|
I48n:{|
14812
14701
14711
1 1 0942642 7 51 1 UG8;8907I472
1 1 092702517 5142751 !» Wt87l!»0
II i)!HI4(;5;7Al73!»2:i 8 9in2«r.:i
II (>Brf5!)6r7'&2il49n2 'I91l8t(;0
II 08110513 752159:11 a9l340l'J
1 1 08«5H!t;7 52667f;!> 8-9149509
II 0B4!l78l i7-52974!)8,8-9l64fl.'i2
1 1 083449<! 7 A328I 198 0180340
II 08l»26(; 7ft:i5Br;.T2'H!ll95C75
1 1 «804lt8:> 7 5.1H9H3J( 8!t'_M0!»,-,7
11 0788966 754l93,t8;8922(;i86
1I077*I895!7 54495:12 8 9241363
1 10758877 17 547r*'.'21 !« 92.'Vfi487
1 1 074;t!i| I 7 5oil!»(;n7 8 "ti*;! ,VJO
1 1 072a!>!»7 7-553'MMO 8 ;*-2m;5)n
li((7l4lH4 7.'V.=)fi92';8 8 0301. '>.i2
11 0fJ9!l3j2 75.Vifl.'M« 89:il647l
II (mH45«l 7 562i«»22
K93:ini50
89344811
8 9;i5!U22
U 0669850 7 56J7*)98
II 0(M>5189 7 5687*173
II Wi40,%78 7-57l66.i0
JM»:*7;<!»H:»i"'*?' 1 1 062*iitl7 7 574-'i828
8 !*:i«M41lf;| j^*[U0*;i 1504:7 5771908
tf04»296»||1105970W|7 5803801
14661
14611
4.->6l
Co«nr, Dirt*. Secant. Cover*.
89331:^40
8934GniO
B9360929
H93750.'.O
89390321
8 04O4ri44
8 0419518
C'ol&iig.
IRII7
nioiH
I706.'J
I 78!*.-
1 7822
I77^'>l
17679
1 760B
I7.'"i:*8
I 74rj8
1 73!I8
17330
17262
17194
17127
1 7O6I
1 6995
l6!iJ!*
16H64
16700
i(fi;7_'
lOtilfO
16547
l(;484
HH2A
lii'Mii
Ui'MH
102411
UilK2
16121
l60R:t
UiOJt4
15947
I5U8D
I58:ti
I. ''775
157 18
^5m^
15552
15497
15443
in.'iNB
I.V>82
I6l»2!I
15177
15124
15073
I5(r-'i
14971
14!»I9
liHti'.t
1 4H2tl
14769
14721
14(i71
1 1623
I 4574
11 15535fi3
II 1535446
11 1517103
li 149f)4:t4
M 1481530
H I4i;:^7i7
U I445:y06
I
Covcr'4.
Secant.
DiflT.
1420287
1410679
Il-I30:il4l
II I37.v,7:i
II i:i,^i{-„'75
11 134(^5
11 13236B:i
Ill30648(t
lll28y:t«2
H 1272301
II 1255306
II 12;i8377
II 1-221513
II 1204714
II 1187!*78
III 17130*;
I11I546H7
11-11:18150
11 1121066
II 1105243
I L 1088881
II ]072.*»80
II 1056340
II 1040158
II 1024037
9-im4tA007 10 0010,592
9-96K4r;i-j|inimlor>8i
9 96«32.'if;| I 0*14(17-7(1
9968iaol I0001085:»
996805141 10 lN>lim4fl
967!M88J0O0IIO38
99677831 10 00II12J
99670*74 10(K1II220
99675II0 10 001 131 1
9f>67:i758 190^111402
9;)f!72:iM;i; 100011494
007 1 04 1, 10 00 1 1 58<!
9 9660681 lOOOl 1679
99668322 lOOul 1772
99f>G6961 lorMJll'^jA
9966d6lU I0-U0lirf5!l
99664240 UI00I2053
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99661517
9 9660155
9-96587o:»
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10 0012242
10 0012337
10 0IM2433
9!K?57430 10 0(11252!)
9*>5*HH;7!lOOOIJfi*J.i
996a470:f 10 00)2722
996633:^ 100012811)
9965ir)74|l000l2ni6
9966O6lOil0')O].?0l4
9-9649244! 16 00)31 12
09647879100013210
9-9648513' I OOOniiOO
99645146!l90OI3409
89
89
89
89
00
91
.91
91
91
92
92
93
93
03
94
94
94
95
05
96
!Nl
!>0
07
97
97
98
08
98
99
100
99
Cosi
ne.
100
9 9*J43779 lf>*>OI3fi<»8l
II 1007974 996424 12! 10 00i:M;08i,
0641044 10001:1708 ™
9 0C39676 I0 00i:^80'» '"'
It o<mi97n
I 1 0076023
U 0H6OI34
I I 0944303
II 0928528
II 0912810
It O8O7147
II (1881540
tl (OIC:.»RU
II 0850491
11 0835048
H 08198190
no804:V»o'9 9'!24*«t
11 (i7(mo43 jKi2;i22;)
II 0773814
1 1 0758637
n 0743513 f>9*:ioin8
!10728440i9!l«l77:*:t
11071:1410 9 96163.^0
llmi!m448 9614983
II tM;8:i520 9!Kil3608
liiHiUMUm 99612232
9 9638;W8 UHmri'MlJ
9 96360;i9 lOtHJUOli
9-9635570'! 0-0014) 14
9!)6'342Oo'l0tK»U2l6
!)0fNl283O lUOt)t43l8
9 9631460 10 00 1 4 421
O'KrtOOBO 10 00145^5
99^:20718 1OO0U62H
9•96a73^6 190014732
9-9625974 10(MM4K:I7
IO(K)I4042
10 0015047
100015152
I9IN)I5258
9 !)62 1 858
9 9620482
II iKi5:Hl40 996I085O
110639071 0y609478
Il<»624:t50 996O8IOI
II wiy»9673;9-eoo<n23
110505056 9-9695345
110580482 99603967
Tangf. Ver«eds.
100015:164
100*115171
IOO*Jl5;i78
I900I5G85
190015793
10 0015901
lOOOlGOlO
10 00l(;ll9
lO(M>lG2t28
10 001ti337
l(MMi|*i447
10 0016658
Cosec,
101
102
103
102
102
l(U
104
103
104
105
105
105
105
106
106
107
107
107
l(k8
I08
109
109
|0*i
I ("J
110
111
9 9981>408
99089319
99089230
99989141
!)90890&2
99088062
99988871
9988780
90988689
90088896
9 UUHHbim
99!m84l4
99088321
99988228
99988135
9 998804 1
9 9987947
09087853
99087758
9 09876*13
9 !l**87,Vi7
9 0987471
9go8737&
90087278
9 9987 1 81
9 09/17084
901I*;!I86
9 9986888
0-9986700
9086691
09986591
90966492
00086302
9 9986202
9 9986191
tt if.mw.ti
9-9;Uld986 24
9 9085886
99085784
U 00856H2
09085579
9 9085475
99985372
99085268
09!t8&IU3
99985058
99984053
9 9084848
9984742
09984636
99084529
90984422
9 9984315
91*984207
999840<i0
a 9983*190
99983681
9 !»983772
9 99834>63
9»98355;i
9 91)83442
o.
Sine.
60
59
58
•w
60
56
54
A3
62
61
50
49
48
47
46
45
44
43
43
41
4t)
30
38
37
36
36
34
33
32
31
39
29
38
27
26 i
25 I
85 r^.
278
5 Deg.
NATURAL SINES^ &C.
Tab. 9.
Di(
Sine.
ttHlUUHti
!BI»fi
ift'tH
2K!»7
0801840
OB947:iO
oiMi:*42y
uyi79ia ;
2ft?)H
28I»7
2HI)7
Ci)vcrs
UT28U3
;»l2->«47
:it i»74!t
Otlt>Jto2
<iii:{:iA4
»U10a7
9l08ltiO II 312770
yio:>-2C2|ii 17W«:.'
yio2:w.j iino;tH!*
iHH»it4l«i II l(JI54i>
OH7-iKJ(7
0«77»1»
Otl8U741l
Colan^J Secant.
431KI52
355(>7<l
3l#;U(t4
278885
241712
2047KO
Vera. I T>. Cosine
OKKUm 11 IBSOttU
0898:t4i 11 I3w:;*5
ON(M27:f Il(l!>fi41(j
0!m4joi;!ii uoy4:u
28r*7
2«!Mf
tHj2;i7o«r4;2
0!>2*>(Mt:
9tm6.'»7I;ll ot]8:Mt) Wi07i;i8ill«2a(i7»J
lH)l>3(i74 1 1 0335Gl> U9 1 IK17 1 1 1 U 98U 1 5<>
iMXKt777 10 ff984(Hi(Hll:i»0 I 11^952850
!MW7aHlIlOmi347(i!tWlf.y3B '
ix>a4i>tt4 io»2(i7««lyyH*87i
mmi'Ji uituami
!M)7«2y4 ia«25957
im'j
»!)2;*4!m,
oii:J2.t:j:i ,. !
OM8I87i-;^
oa4in8:.,-;;^«
25 0fl4:if>7!*l.»,,.H.
2«oiM«8;o,-^^;
2701MJ17711- ;,3
28|oiJ.i2*i(>«
29!ou.'i.-i;,(;2
30 ooa84.ia
»i odtiiSAS
33 0064248
33:f>087l44
34 007(»039
35 097W34
3c!a97r'«*io
37!(>fl78724
38 ooaioio
39 0»H4aU
40 01187408
41 0dtM)303
42 00031U7
43 0006003
44 0008986
45 I 001 88 I
40*1004776
47,lf>07(f4)0
48 lOlO:i(K)
49 10134.17
60 IOlK:i.-jl
1019245
1032138
I0SA032
1027^25
1030010
1033713
I036G06
1030400
A't! 1042303
GO 104A365
28fl0
2«1«'
28951
2895
3890
2895
2805
2895
2895
2805
2895
2894
2B95
2004
2896
2094
3805
2094
2804
2894
2U:i4
2894
28;U
2893
2894
2803
2894
2803
3893
3804
90733981
1N>7U50| I
OlMi/OO:*;
90f;iHi:J
0003017)
00541021
Wt53l25.
90502291
9047334
904443U
00415421
10792117
lU7oH4U8
10725070
10 891059
1 (;.}8U54
1U8200&4
10 593455
105(j|057
10528857
1 0490864
10 40504 1;
1^433431
(^21804
0924738
0927872
093il(»(i
0»;i354«»
09:m;474'
093! 1409
0942344
0945278 1
0948213
09511 48
0954084
0957019
l»95<*U65
09628001
0917775
10 882921
10 848288
10 813872
10-779073
10745087
10711913
I0«7K:?48
ioe44!n»2
10611841
10-678805
1 0038108 003JX)53|
I <MI38154
1-)MI387I1
I ik.)38;m:9!>>
1{)<)39227|I'>
1 003:>J8tJ t>
1 0039747, 0u3:(im:(
|fKI4mHl8 003!)tt48
r<HI4027() 0040108
I tH>4(l,i33 00403(19
1 0«407!M; OiM'w ■'"
1 (H)4UKit U< .
10041328 01. 1
I 0041592 001142"
1 004I859'(MU18I! .
10042127 0041 9.-'i
I0l>4239t; 0042217
I0042«MieOOI24ii..
I00429:<7 00427.'./
'r.*4
|25tf
1 2*; I
'2<;i
!»SMik>024*d«
99604trM
0«MH>I53&3
HHM320H 004:i022
10043480 (K>43292
rO(>437''3'iH)4.t.'.i:3
1 IMM4028 )Ht43H35
l(>0443*t2 0041107
0044380
10044678
10044855
10045133
10546151
10513607
10481261
10449112
10417158
10365307 10046251
270
271
272
27j
27:t
275
0O4465r.
004493^1
1004541 1 1004620:> -_
l<Kt4561K> 0045482 iJi
1 4H>4.''>97(M)045760 Z^^
625I,004»K»38Sf:
90364i47ll0 402lN)7 09658-26 l0 3&aI^27
90:i5752 1(^370772 09«iH76.'t 10322447
9032856 ll^33:l7J^; 00;i*«09 10291255
94»29IHil \o:MUUUHi 0;»740a."i 10 260249
I#027066| 10 :i7lfl90 n;i77572 10229428
W»V*417l l0 247'i''7!098O500 l(H9ti789
279
■JMI)
I0046533;004mi7
I 1)046815 tMti
HMi47lH(9 *>.'
1 oo47:mj3 "fii,
1 (K>47Ci;9 I»0i741.'
10047955 m>477-''' ,
10048242 0048010
I 0048;)30 WM829J
9021276 1021738(, 0983446 10 168;i32
90l838li|0 IJI7254 098fNl8:{ 10 138054
04)15488, 10 |5734)1»'0989320 10 107954 14H)488I9 004(1581
1M>12592' 10^ 127522 '•9!»2257 10-078031 I 0049108 tH»4m{6H
90006971 10097920 41995194 I004H283 I 04)49399 0049151.
0006803, 1004*8491 ;09U8l33 10O1874>8 1 (H)49<;90, 004944 1
286
0053663 29
•1/53123 37
9001000 33
0*>6l7a5 3S
!»95UItl 21
9803
9003908
0001014
8998119
8905225
it992:Kn
8989437
6066643
8083849
8O8O755
8!»77862
6974968
8973075
8960181
8988288
8983395
som)5oi
8957608
8954716
Cosine Dif.l Vers.
10039234
iaoiou7
9 98 12291
99524787
9 9236943
98954744
9 8672176
08391327
O8111R80
9 7834124 1
97557944
9-7283327
070 1 0260
9 67;M(730
6488724
9 (.21*0229
;'5933233,
9 5'i67722l
UK) 1(»71 9 9893050
IOIM009 fJ9»;4M»724
14MHK»47 9 931(H>«8
1INI9886 9!Hr2U25
1012824 9 8733«2:i
1015763'98448I66
•-".1 1
294
I0l»74t2
KrjKMl
1U245(H»
I0275a(t
1030480
1033:i90i9 6766000:
9 8I(;4I40
9 7*W1732
9 7»;4H>;t27,
97321713!
9 7044075.
io:w;;i4o
I03<>.>80
1042220
1045101
1048101
1 05 14142
|9(;493475 l<H»5;i657
9(J220J84i
9 5949022
|i»-0879088
|9-54lOf;l3
lf5l(3645
10049082 00 i97:Wo(j^
1 (m6O275!0050024 rJV
1 mir>fl569'04»503I5
1 o4>r.o84:j!oo54H*rf>:
1 tHlnH60 0054t8N:i
I()05l4n6 0051193
I 4Kh'il754'M>''UiiT
1 (11152052 '»•
1 0052.V.I "•
1 4KK.J'
1 005 J
I 00532.14 niM^;».
005327 i
vjiouwj
J
. 1
'3
13
"'" i'»l3 III
17
tu
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«
Secsiit. |CfiUn.| Tan^.
1 005:i860
I 4t054l64
1 0054470
I (io^'.477(i
1 005.'»083
?*J
00;
(Ml.;
Cosec.
(M)5447:
IH>5470i
Covprs|D.| Sine. I
84 Deg.
6Deg.
LOG. SINES. &C.
4
279
Sine. Oiff. Cosec.
8 !»4!737« ;. '-1 1 1 O.-iJri'C-.M
n;»4:il743 ]:J;''|llo.7*;«2-,7
« !*nfi(H;3 ^:,:. . 1 1 no;».i;»:i7
j::„;no52A4:«i
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flIM74.'»0l
Ha4«»7'W
8 9flOe87l
8-f»544N!ll
H »o&W>40
a-l»&7*<£»43
B>fi68n7o»
B!>f»4l(i97
ftQ668n34
»9IW24a7
,j„oJM04(i7l'il»
;![«n«4H:i.M:.
Vptsetls
7 5Ho:**H»l
7r>H:i-J77»
7 :.mii.'i(i«
7.iy|iij(tii
7.'i!M7a7M
7 51*75 7IW
76004103
7f(U3:e33l
Trtfifr-
imu4m:.2;»
H !U77a:«i
ltU4]>lU7(i
HU:>Ud!XI7'
8 9.^>34410
Diff.
7(>1l'Mf)t(
7 61 443;):!
l.lUli
13771
i:s72«
i:i(i40
i:i.vi7
!i!ili!;M-<)44io«o
IM60| ""*-"•''
110413207 7fil7'-l'W'
II oaJi.-.7ij 7 ';i*^7:i'*''
n(>;i7i!*i[(i,7t>Jj4LKJU
1 1 OS-IHCioa 7 «-'i«a30
IIU.144f;(;Si7 63iKl688
7'6000468|tff>.548564
H;i6(ijfi7j
8 ii:i7«7:i.-,
8»&!N>7*34
13&53
i:i5ii»
M 0331006 7 fisctcoao
n 0317313 7 C3<W0««
11 o.'KMoni 7B3!in(i7
II 02r»(t:»327(J4lfil«4
8D722AUd |!h!^J 11 0277I0.WBJ4O078
B- 3736280
D-9741)e?4
8-9762»2»;
R-978940n
HfW 14729,
H 3S M64lnH9
8^854010
ftMaOA34
••98037A7
•9010420
ff003-i-Jl7
a9044!)'i8
a-99A7't)l(
IHW703.i«
8 !):i»'_>!l!J4
8i*m»,'j5!i.->,
i^ootmuii)
9 0O3iHI«7
!HM»33I7:»
1^0045634
nii»7Mi:*fi
H><»/«704
HM07374
!Hlll9lilft
133^)5
13344
13:102
1 32fiJ
13*i20
131/11
13140
13100
I30<>0
i:t02l
12'»/Il
1 2;U3
12D03
j 12865
!l2fl?7'
12788
i?751
12713
1 2(;7A
Ufi:t8.
12fi01
1 2.Mih
12527
1 24!)2
124.S5
12419
1 »m3
r.':ii8
lJ3t2
1J278
\2ir2
Ii-O2o:<72o!7e47i908
11 02.W37«i7'>4J»866:»
1 1 02371174 7 «i25:iiO:H 9782483
fl-W;04728
/^!M;I8f;5J)
JI !H;32.'i4.'.
8 UUiGUmi
ft- 9060188
»9673944
8 IM»87r>a8
8 970i:i:*O
H Ul I i'J.V.t
H ^728.^47
8 !*742092
8 07.>5597
«^;»7«f>o6o
11 o>i:ifli2 7'Jj''>u*03
l!021(>,-,;>3 7'i'i7WO4
II 010741 117 (>«0482a
110184271 7 6*aU««
8-97UoJi<>6
8980920f;
8 9822607
1 1 OI7ll7li76'w7427 89848991
I l-OCiKI 1 1 7-M»:J«i08 8 08(i2173
uoii:i09o,7C7'>y7ii
II 013210017073^735
II 0U!M6f>|7 0781682
II 0100263 7fi787660
8 9875317
89888421
8 9901487
89914614
1 1 0(»9339B|3 0813342 69927503
1 1 (H)8057l|7 t>83:>«>W 8 91*40464
11 fHM[7783i7 68«46!l7l8 09533II7
1 1 0055032 7 689O2)i0'8-yiWl»«43
II 004231!* 7«rtI*'»74U|H9'J7jmni
II002:m;44 7C94llR2iH9»!U8B3
'M-(K)l70(W;i7f;!M[(M02 !*(K}04647
I10<H>4405,7 0;t;»l7«7 9<M>I7375
lO!)!i:ilN40 7 701695!* !*00:t4H)(;0
1^9079313 7'7'>'*-"7'*i'* (M)4272l
l0 99fMia2i TV>*il\'i^\OOi)itb'Mn
I0-9954308 7-7«i*200a!9 (H)07(>24
ii09:»4i!>477-7n:" ' »7i
io!»if.>;i5(;i 7 714 114
io!hti72i(; 771*;'"'- •-■. ■■■i'ii
i09rK)4:»oi 771U'-"' :nMi7;»'»3
lO!lJ{;j202li 7 72l5!HMt|!>OI.t(l3|«
0131823
014391*8
1.,^-, 10 9^08177 7 7264;»30 90I6M>21
-J';; Ift;ina6(»ft4 tth^U'W
!)oi.vii35; J ;;;; io-08438«5 7 7'^i:i''«»
f*0l6fi23!( -'"j IO»«3170li7;;i37058O0I!*IH31
*OI8(i:»00 !*"/_ 10 !)ttl9(J!*l|7-7:i<i*'l04 19 020 1(133
f*0192;i4fi| ' 10 0807054 7 7^'^^ l'02l(;202
00 107325
0179501
I 452ft
N47!'
J 4431
I43*(4
l43,nH
I42<K
14244
1 1 1 99
14154
I4I0K
I 40*i3
14019
13074
13931
iriBHti
13N43
l:i/UK>
I37A6
I37I4
13072
1 302;*
135HM
13545
13506
13403
13123
I33H2
13:141
i3:u*i
13202
13322
131B2
13144
13104
1 301)0
i:jo27
I2!*U9
12961
12913
1 2870
12838
12002
12764
f'ntanp;.
Cover*. [ Secant
1 1 0590482 9 9003907 1 00 1 6558
) J -0506950 ]M*002dR<) IO-Ol*Ui(i68
1 1-0561477 9 9'JOI209IO<Nt 10780
n0537<M'j|0 9599R29ilO(MllO/!Wl
1 1 Ou22iioji:f uriiim ir*' 10 imh 7003
J I 0508324 !»-9597lMl9 I IHU 7 II 5
9-1*595088 ,10 0017228
It U4940.33
1 1 0470789
n04C65!*0
II 045l4:ii;
II 0437328
9959430*Ha0(*17340
90592925 I000iy454
9f*>9l543 IO<M)|7507
9 0590HW, I0imi7«»2
1 I 04232tM !*!»5J(8777 IOOIH77IWJ
U 040924 lj
1 1 0395272
U 0:{8i:t41
1 1 0307455
Il035;«;i2
II03;*90I2
II O320050
II 0312342
1 1 0298670
11 0205041
M O27I4&3
11-0257908
110244403
1 1 O2:ki040
110217617
11 0204(36
II oi:mi7;i4
II 0177493
11 CP 104231
110161009
II 01:17827
II 0I24G83
II 01 11579
II 0008513
9 9587394 10-901791
9^96fu;oio iof>oino20
9 95H4620 10 00 181 4 1
995U:i242 100010257
9-95BI8."i7 I0001JI374
9958IM7I 100018400
9'*57m*8(;'ioooiH007
99577699 10 0018726
9- 957'f3I3 100018842
99574920 IO-0OI0!*6(»
99573539,100019079
9'!»d72l5l IOmil9198
9 9670763' IOOOI93I7
9-9609374 1 0(H) 1 9437
9-9A67ii*i:iliowi9557
99flfi65y6'l000|iw;7;
* 9605206 100019798
»956:un6!lO00l99l9
!^9502426 1 0020049
99*'itil034il0flO20102
9-»669643|l00O2O284
9-966826 1 [ 1 90020407
!* •J5508.Y9 tO-lNI205:t<l
9 95554<;*i IOlH»-.MWfc'i3
ll-(M>85480l9 9554073! 10 O(>20777
12728
1 269 1
1-2055
12019
12684
12647
12513
12477
1-2442
1 2407
1 1 0072497
11 0051*646
110046633
110033767
II 0020919
1 1 00081 17
99652<UJ0
99561206
99MD89S
90646497
la003U»25
100021 150
10^0021275
99547102 IO-002U01
99645700 109021627
10-9996363 99644311 100021663
19^9983626 9^9642014 10-0021780
UYUim'XKU 99541518 I0002l!*07
10 9957279 99340120 100022034
U>^9944<i60 9-9638723 1O0O221O2
I9 9932076p9637326 1^0022290
10^9919629 9 9535927| 10 00224 IK
IO9im70l6 9534528 I (MMt22r>47
10 989453910 95331 29| 10 0<(22(;77
10 !*8B21*97 9 .'*53l 729 1 r«»22«00
o^7» lOOBOtMilM) •* 9530320! l(VOO-229:i6
1 -i'ttO * '^^^'^^ 1 8 9 9528**291 1 a 992:1067
10-9844970 9 9627528 10-0023197
10 98:121.75 '9932(1 1 27 I00023:*2e
1O982O4O0 99524725 la(M»234l»
1 23<t4
12209
12237
12202
12169
Co^iintf. I Ditr. Secant. Covers. J Cotaiifr. Diff. Tung. |Verseils. Concc. D. Sloe.
10 9808109 9 0523323
10 97959fI7 995211*21
10-9783798,9 1*320610
la<M»2:*592
iooo-i:t724
10 00-23867
D.
Ci
>Kine.
110
112
HI
112i
112
113
112
114
113
It5-
114
116
115
116
no
117
110
117
118
117
118
il9
119
119
120
120
I 20
12 1
121
121
122
i22
123
123
123
124
124
90
59
58
57
50
56
54
53
5S
51
50
49
48
47
4n
45
44
43
9 998131*3: 42
9!*981275 41
9-99H1158 40
9 91*81040 39
9-9980921 38
9 gtMO0O2 37
99960083 :iO
9 9983442
9 !*9833:t2
9 99«;i220
9 9903I99
9 9982097
91*982085
9 9982772
96982660
9 9!*82540
9^9982433
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99983204
99!483089
9 9981974
99981859
9!»981743
9^ '^8 1 0-26
9 9981510
L
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9!*9It0 4l3 34
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9 91*79i.'<Wj30
9-i*97!»an' 29
9 91*7;*7IO 28
9*»979593 27
]:>9:»7047o 26
|!>.'t979:*47'25
124
125
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12*
126
126
99979223
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131
130
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9 9970072
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Tab. 9.
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l>|l04.ViB5
1 10-18178
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64 J30130H!:Jj^', 8708032
50 1207144, ,:!!; 8/02 150
67 »-i*»<>^i .>unN h7'ft'o«;o
Wi;12l2;Hir.^|^"^ 8787(Un
so 12l5H(K;:g^';H784l04
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4:mJ2()33
4 i05 1 84
3840738
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8 83:iC7l5
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" 8785880
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8 415O8L'0 IIU2428 83862510 1 O*»70843 0070;i45 ^^: ImiilWJM 111
8 085O04:r 1 fNM;i73l 'lHMii:t52
8 0822800 1 <KM;2057 OOOIO74
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8 80I85(»5 I fl4H;;i04O 0002045
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8 8455103 I (Hiii;v7»i O(>»;:i207
8 0225IWi I n(Mii((.TJ 0(MKl/i25
324
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1151144
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1 182:KiO 8 5!Mt02!M) Il>087:i04 IHM^043 «_
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1 I88832|8 55A.5408 1 CNlCMO?; iHMi;0]i; *, '
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1 177070184012772' I OmJOlOO IXI88«33'.^. .
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1 1805-Jii 8427!*5;il I «H)70l40 .00<(58 ;ti'.lyi»:
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8 1837041 I iH)74380 Oi»7383l
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Tang. I Cosec. [Covers
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LOG. SINES, &C.
281
Sin<».
!> 0204 348
D-022B254
9^02401.^7
9-0252027
1> 0*^63865
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12002
li;*70
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11870
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11804
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904ft27Rfi
9 05njl!l4
9-0.MG354
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9-05(>t»7'>'l
90371723
9 05827 1 1
9-0004804
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9^062(;38f;|
9^>fl:^723.»
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9 0850832
9-08ti96I9
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10701761
f> 0712421
lt-0723055
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9 0788310
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9 0827088 1
) 08:^8317'
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773
11740
11708
1 1677
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11G13
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10 9807854
lO07t»5652
1 9783882
1 977 1 748
I0y7-''f>813
109747973
10973tiI35
109724331
Vorseds. Tanp
7 7:wif;:«>:i 902ifi20.i
7 7410375 9 0228338
7 7434380 90240441
7 74nR3I0'9O2r.25l0
7 74R:I9J f*02845^fr
7-750,'i999|9 0278552
7 75297-*2 9 0288524
7 75534lo'9 03i>0484
03l237;i
9 0324249
90347908
9^0359888
I097!25:.87 7'''7703i
109700818 7 78iKK'>80
109889110 7 7824084
10987743317 7W7485
l»9885788l7 7'»7*WU3
IO9654l757-709*'l38 9^0371439
1098425937 7717371 90383159
,,., 109831042 7'77-*OflJl 9tt39484«
I tinii »W 0ii\Ur,'2:i 7 776.'M>49 90406508
11582
Lt55l
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11458
11428
11397
ll3*]fl
11337
11307
11277
11248
II2I9
1 1 189
1 1180
1I13I
Mt03
11073
1 1045
IIOI7
10088
10981
10932
109O5
; 10877
10849
1 0822
1(1795
10787
1U74I
10714
I08B7
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10634
1060R
10681
10 9';<»8034 7 778«698;9 f)4 18134
10 9598576 7 7WW682 90439731
109585148 7-7'*''*2G^7 90441299
1095737.^1 7 7855472 90452a'tt;
109562303 7 7878276 90464343
109551046 7 79(U02I» 90475821
10-9539739 7 79237(»5 9 048727"
90498880
9 05 I 0078
9 052 1 439
9 0532771
9o:jJ4o74
9 (»555:U9
9 0566595
9 0:.77ni3
:) o.'.Hwoo:;
9 080<ll(;4
90611297
90622403
9 0633482
9 0844533
90606558
9 0680553
9 Of.77522
9 0f;88485
90710270
9 0721133
9 0731989
10555
10530
10503
10478
10452
10427
10401
10378
10351
10328
10302
I Difi:
Ifr9528462 7 7948331
10 9517214 7 7968897
10 950;J995 7 791' 1 405
10 9494806 7(J0J3855
109483648 7a03*J248
109472515 7 8058580
109461412 7 S080850
109450339 7 H 103075
1 943929 1 7'n2.'j-J37
io;i41!8277 7H1-17343
I0 9417.'«9 7UI69392
10-9408328 7 8191388
10 9395390 7 8213324
1O938440I 78235205
1093736U 78257032
10^*362705 7 8278804
109351943 7 83(M»522
10-9.3-11148 7 8322185
10 93:103817 8:143794
10-9319640 78365349
10-9308928 78386851
10 9-2!I8239 7-840B2W
10 9287570
109278945
109268337
IO92.V1756
10 9245201
109_'34R71
109224188
7 84 2]h;95 90742779
78-151037190753583
7H472:t27 9 0764321
78493585
7-8514751
78536A86
7 8556968
1092138907 8577999
109203238 7 8598980
l09192Bll|7 8''I'' *''
10:H82410 7 8^il'
|O9l72034
109161883
109151357
I09U1055
Secant
7 8(j82397
78703128
7 (i72;uio(;
Covers.
9-077^053
90785760
»079S44l
»^00070iK>
9-081 7728
9 0828331
■r-^-;:::ill
'188
. ■:,<:j98
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9 0880981
9 0mH438
CotDIi^.
12138
12103
I206'f
12038
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1197
11940
1(909
1 1 878
IJ844
1181:
1173
1 1 320
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1 1 858
11628
11597
11568
11537
11507
11478
11449
IU19
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11361
11332
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11246
11218
11189
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1 1 1 0tJ
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10943
10916
10869
10883
10836
108 10
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lt)978;*798
10 977 1 *W-'
109759559
199747490
1097:15452
I09723448
109711476
109699536
Covers.
99520518
9-9619115
9 96177M
9 9516307
99514902
99511497
9- 05 12092
Secniii.
I0 0023<{57
100023989
I00fr24123
10^0024257
10{«)24391
10 0024525
100024660
9^9510686 100024796
O9rt87»;27j99509280 1000249:11
109075751199507874 100025063
1 09663!H)7' 9 9506487 1 0025203
IO9852094[995O5059| I0OO2534O
10 9640312 99503652.100026477^
l0!Mi2a'>6l!9M5(t2243 lOWISSfiU
10JM;i6fl41 9 9500a35 10 W>2.5752
10 r»605152|9 949942ri 10 0025R90
109593494 9 9198018 10 0<h>8029
10 9581888 9 9196807 I0(l02f;i87
109570»8U 99495190 10 (MI-2t;:W7
1 955870 1 9 9493786 1 0026446
10 9547IB4 9 9492:t75 IO0O26.^86
lO-9.Vi5857 9 949IKH:3 10(H>-J8727
10 95241 79!9-948y.*»5l 1O0«»_'8868
18 95l27:{0'9948»i:t9 lO01»270lt9
10950131 1 ;9 94U6726' 100027l5t>
10 9489922
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109455928
109444651
1094:13405
1 0-9422 1 87
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109399836
t0 9:{88703
109377597
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t09:i55467
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10 9333447
10-9322478
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10 93IN)619
to 9289730
10 9-278867
10 928nii:t|
10 9257221
10 924f;437
I0 92;j/i679
109224947
10707
1 088 1
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l0 9l50.Vt4
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10 9ll!N)l9
10 9100562
9-9486313 IO0027292
9 9483899 100027434
9 94824K6| 10 0027577
9 94810/1 100027720
9 9479(w8
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& 9476826
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9 9468323
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9046.5486 10 (H)293I8
9 9464066 lMlH»'i94G5
9 9462846 lU002mM3
994612261 10 IN)29761
9 9459806!l0(>029910
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:»94589*;3;10(to:t(»208
9 94555-1 MO 00:tO:i58
10 0027863
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10002 fll51
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100028441
10002B68f
100028732
10 0028878
10 0029024
10-(M>'J9I71
9 9454119
99452696
99451273
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109214240 9 9449850
il0!»2<»3.'>5f|l9944»4'J8
10;M!i2!K»» 9'M17(K)|
(»9|Hl'274 99445577
99444151
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9 94:iir87;i
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Dirt'. Tanff.
Verficds.
l0 00:tO50H
100030fia»
loon:«»809
10 003(1960
iorKi:iiii2
IoOi'3l364
lOIHi3l4lti
100031569
10(M)31722
lotHi:(iH75
1000:12020
10 1)03.; 183
10 00123:18
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Co sec.
D.
132
i:u
134
134
134
136
135
Cciflin*.
9:)978l43
9 99760 1 1
9 9975877
99975743
9JW75809
99975475
9-9976310
,^99975205
:„^y9!i7.io69
'■"'999749:13
138
137
137
137
1381
1 381
i:i9
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140
139
140
141
141
141
141
142
'99974797
.> 9974660
99974523
99974386
9 9974248
9J»974llO
99973971 1
9;m7:t833j 43
9 9il7:i893 42
60
59
58
57
56
65
54
63
?I
60
49
48
47
46
45
41
142
143
143
143
144
144
145
145
145
99fl7:i564
9-9973414
9 9973273
999731:12
!»9f»72!Wl
9 9972850
999727O8
9997-2566' 34
I>9!»72423 33
9!»972280 32
9 9972137
9!»y719;»3
36
148
146
147
147
147
148
148
149
149
149
150
150
150
ISI
'9 997I84Q
'9 99717(U
9 9971569
9 997 1414
99971268
99971122
'99970978
9 9970829
9 9970*182
9 9!* 705 35
9 9970:i87
,99970239
09970090
9 996!m4 1
9990979;
99089642
9 996*1492
99969342
,- I9 91HJ9I91
i«9'9IW»!HM0
j^., 9 9!MHWI88
;.; 9 9!M;»(738
'^"9 91Mi8584
j^ 9 9968431
,...9 9968278
-J 9 9**68 1 25
^>9!H;7971
;,:^:99967ai7
*■ 99967862
D.
83Deff
98-3
Deg.
NATURAL SINESj &C.
Tab. 9.
Sine.
1234 lti»
I227.H5A
12»»24I
l'2.1R!>rM
I2417)(K
lJ44t;74
I 2504 46
I2A3332
125!) 1 04
12GI!)!>0
!2tJ4«7.'»
I2«77«l
127064«
1273A31
12764 1 U
i27»303
12R2l8fi
1285071
12879&6
1390841
1293735
\20Gmt
I2m)4,14
1303378
1305362
31
32
33
34!
35 :,
3«ii;t.!25W
Dif.
2U8U
2Ba7
2»n7
2H8(;
2Kd7
21t«7
2K<I(»
21107
28841
2^(80
zmiti
2080
2liHG
2B85
2R8(i
281*:.
2885
2885
2884!
28A4
2885
2886
3885,
2884
2884
2885
2884
2884
S684.
Covers
«7«T307
U77841&
8775A32
87 7264 s
87f;n7:,!j
87f;<iK72
87t;3!*85
Co!;ec. Tans.
8 20:»M>lfO
818(>ll&7
8 1(>(>ftl45
I 227 H 40
r2307!m
12337^12
8 l47W)4H'123f;70S
l2:t'J«.»H
1242(il2
1245560
Cotatif?
B\-2HiHtXi
8lo;»4n7:i
8 0905103
a I44:i4fj-i
8- 1 2-1 81)7 1
8-lO*i3,"»l»!t
8 081^104:;
8 iHHil'Mti
80475G47
802847iW»
8 00!>4S35
7W05750
7tf7l7555
7 9530224
7IKI43758
7015U151
8743782 7 Dfi04003 1206249 7'8073390:
8740«'J« 7y-l2l5nrt l2W»2rt5'7 878!»48;)
87:j«(Hol7 uHiO'j.-jt} i27_Mfil 7 8(Mw;423
a;:*.'. 1 l»:> 7 doaii i 7i» 1 2751 1 7 17 8424 1 u 1
87:*-'2:W 7 R87f»-'38 I27HO73 7 82427fW,
87'29:iJ4i7 0700120 1281030 7-8Wi22rj
87filOI)9 8 0710681 '1248520
U7<'>II2I2 8firi2<KHi2'I25U74
8755320 8 0:t42321 12641439
8752440
8749554
8746668
8 0150450 1257384
7-997 M45 1200339
7 9787238 12C3294
Secant. Vera.
I 00750MH 0074538
1 (M»7 - '<;*
nw; i't
l(H>7fC>4'i 0078903
I -00701^8 flojaaii
I 0077273 0076681
I 00776:W 0077041
I tM)71«Ht.'i 0077401
10078:172 00777«3
I 0070741 iKi7)ti2t;
1 0t»79llOlHt7H489
i 007^80 0078853
100798510070218
I O080222 0071>584
I (Kt}1059o0o7996l
1 0080908 ofiftoain
I 0081343 0080686
1 0081718 00B1(»56
K7264fl9 7 8521821 I2839B6
«72;t584 7 8344335 12^(6943
H72(m;i« 7 nifi70.'V« 1289900
87I78U 77rwil778 1292858
6714929 7 7«i 0*2*7 ! 121*5815
8713044 7 7642406 1298773
1308146
1311o:mi!
i:*i39i:v
i:ii(i797'
13I!n;»i
2884
2883
28ft4
28(14
37
38
39
40
41
42
43
44
45
46
47
48
40
1 50
51
53
53
54
55
56
57
58
59
60
1325447!
132^030
13,Tt2i:i
l3:uofi«;
133097'*
1339802
,2883
)20«3
2883
2883
2883
2««3
2««3
2Ji82
1342744
1345627
13485 Wl
13.'.4274,2gjj;
2883
2882
2883
13571501
2082
2881
2882
38B2
2881
2881
1360038
1361»10
1305801
1368883
1371564
1374445ji3g,j
1377327 Oftfll'
13ai089,^*J
iruma-.o-""'
I39173l| **
B70JH59 7 746H90I
8700275 7 72y<>i7«
870;(.i;M 7 7124227
U70<i:,oo 7 0953047
WR»7022j7 0782631
6a»4738 7 6612976
I I
8891 854 7 6444075
H0S8il70 7 0275923
R(»(;ofl7 7 6iOt;;.i«
8083203 7 594 iy49'
8(>803I9 7 5775916
8077436 7 5010713^
8674553 7-<'i446236
JW7 1070 7-6282478
8668787 7-51 19437
8«6fi{K>4 7 4 957 1 06
fl«6;«)21 7 4795482
8f»ini38 7 I0345(io'
8657256 7 4474335
8054373 7-431 4fl03|
81W1491 74155959
8(;4Rfi*Mt 7 3'W779B
8045726 7 3H403I8
8042844 7 3683512
B«:«»9C2'7:*.'»27377
8637081 7 33711*09
8/;:WI9f» 7 32t7h»2
I10;(l."il7 73(M;2954
U02«4:i0 7 2i«»9400^
8625556 7 27A66 10
8022073 7 2H044 17 1390580
8019792,7 2452059 1393546
OfilOOl 1 7 2:tf>l9lO 1396510
H014030 7 2151G53 139947c
m;i 1 150 7 ^ooiatje 1402442
80082*19,7 1852905 1405408
1301731
1304690
1307648
131»m;07
I3i:vi00
131G525
1319484
1322444
1325404
13iH;t04
1331324
1334265
1337246
13411207
1343108
1346129
i:W909l
1:J52053
135r7015
1357978
1300940
1363903
1360806
1369IU0
1372793
1 375757
1:170721
13JJlf:85
1384050
1387615
7 7802453
7 7703500,
7 7-^25:WJ0
7-734 0028
77171486
7-6005735
7-6820709
7^646584
7 64/3174
7030053:1
7«l280.-,7
75957541
7-87a7l7»
7 5017567
7 54480!»9
7 6280571
7 5113170
7 4946514
7 4780570
740l53.'i7
74450855
7 42870<I4
7-4123978
7 3961595
7-3799909
7 3638916
7 3478010
7 33189891
7 3160047,
7 30<'1780
3Co'
302!
3fK*
363
3C4
365
366
3(57
367
3^m
370
370
04182094 OOH1426 .,^„
35fi
3ft7
Cosine
»92M83;eO
9925107 M
9934751 M
P9229M>ft3
9922237 51
it*.ri 1 874 50
91/21511 43
992U47a
9930783 47
9930040 4S
9»IW3U«3
1»!»18»44 43
irjlB574 41
9918304 41
1917893 S
1 (K>82471 mtni7)M;::i;;
l-(HMr2849 0C)HJl(.« .*'
1 0083228 00(1254 1 :'',
1 008300? 0082914 ill*
I 0083988 008:1288 ?.ti
.1|5
1 0(»843(» 008:«t(rj ^-.,'0916337 3»
1 0084752 008403,9 'tiJi 99l59til 34
I OOILM:^"* Oft " •>•''' ■'■' '.".fLl 32
1 0005i;i5(»f
I 0085519
1W85904 (M
10080290 0085651
3IIO
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J J-28 31
^,(14449 30
1 0086076 008593 1L|, I SgUufiS 39
I 008704;4 00(}63l2i^ 9013688 Sfl
10087452 OOm;«9l'^''9Tll330e 39
100878420' "»23aB
1 01I8U-233 01 .40 38
1 0088G23 0lMi«r, .t,,. ;r.iii'|55 24
1-0089015 O00823oi..nf-'j*«»n77O »
1 0089408 01»a«H.' .-J
1 0089803 0080011;^
l00tW196 0(>»^*^''- I
1 0090592 0' '
100900B8 0^
7 2844184
72087255
72o3t«H(7
72:*75;i78
7 2220422
7 2066116
71912456
71759437
7-16U7056
7 1455308
7 i:i04i90
7 1153697!
10091386 009065.. ij \:
1 (>09 1784 009094 ' > .t W'
1 0092183 01 f^^ lA
10092583 01 jrmM
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I 0093788 00921^ i ; i.U U
1 00ii4l92 009331 ; ';fl7 l"
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1 00«J54(»8 OCKI454I'. J
1 00M815 0004905 '^^jilrtHliOMd «
1 0096233 0095306 .^, l'i'»'iM:<i« A
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10007041 ODlXilOl) :":. :• A
I (My<i7452 wvM'Ai 1 1 : * '.*m»;t4<iy 2
KM >97 803 00!)6y 1 5 * ' * 9' H t.1IMio I
I 0< ►98276 OtH»73i9 tflK^SObl
C(»ine!Dir.l Vers. | Secant. ICotan. Tan^. i Cosec ICoversI D.
82 Deg.
^
7 Deg.
LOG. SINE^, &C.
283
n
4
ft
fi
1
n
9
lo
II
la
13
14
I&
le
17
18
19
90
SI
2-:
25
24
25
26
27
28
29
30
31
33
33
34
n.'»
3f;
37
38
3!»
40
41
42
43
44
4:i
4t;
47
4U
<0
50
b\
5-2
A.'t
54
S5
57
5fl
iVU
GO
Sine. I DiH*. CoReo.
»0H*>Hil4n
90mi:ii'21
!i(m7:(47:i
D-O88U701)
9-0899003
» 09 10082
in>y4i>474
w ouAoriMj
y<m7of:/.i
ni27«
HI2d7
10203
109UI055
lo-ui:io77!»
I0»I20527
lOf)MtM(K)
" ;. IO!>fl8tWl«
loi:w »*>y«7i>763
,,,,«- io9i)o;«i:i:i
Ver?icds. Tan^.
7K723lWHJj9«miU3H
7«j4-i43«ii)-(>yoi(((J!*
787W»')17!>*«'l'-'i;7
7«78.v>:.ol9oy2j'i(rt)
7 Maiiiio:i:i|!> o:i:t:t4)'jo
7«fritf4<iy|yoy4a:tv.
7 Kti4ti»6C .■>tj»6:t(i(;7
7fl8G71Pfi(H)Hf;:*IWi.'»
7H8«7I«7:!>0074-21»
7 8IM»77;i'i:!)0!>H44«()
Diir.
100 341
■ iiHdi
fHHK»08AI
IMOOOtfltt
» 1O1O&60
0-1030177
r>- 1 0.10372
» 1040240
9-1050006
0-1050934
!> lOflU739
L» 1070512
O I0fl»372
9-1009010
9I10872«
9-lllB420|
9 \\2miV2\
11377421
9-1147370
&1I5G077
0^11RG562
0-117'il2J
ona&w;7i
oil www
0-12l4l(!7
.')'l223(i24
01>33(»(tl
0-1242477
91251072
U12(il246
9-127<»«H)
279(»34
9 12»<J247
9I208.)31>
i»'i:t07Hl2
9 l317tKl4
9•132C2*^7
9l335:iO:)
9 134J70-J
5*- 1 3531175
!H3<^t02a
9 1372101
M 38 1375
91390370
91309115
•M 40850 1
M417S37
!J U'ifiri'iri
9- 1435553
I0 903!»3K5 7H927y21J 901»9|*.7H
I0 9(t-2!»34JI 7^M»41i07« i* 1 004872
j^3^p|l090l93:WU8960l«ljH 1016044
„fj-r ! 1 9fM»fl34;i 7 «9BH23«t ft- 1 025 1 »2
m^ 10 mWl'3il4 |7 JK>0H24« 9 1035317
;,;',r IOB;*Ha4J2!7 W2a2l2 :MIM542»»
J;:!' .1 I0fi;»7!*a23 7 904al3o!9 In5.i500
jj^^.j IO";»(;w;27 7 9n«mK)2!91i>r*5657
9950
0805
10 8^59754 7 9087«29
10-8940904, 7 0107610
l&894007(; 70127.'i4fi
q^:^i 108930271 79147038
flii^l 10-8920488 70I«6C84
"'IJ^j 100910728 7-9186386
971ti lt>^'J»(>0990l7 0305844
^jn.'loai9l274'7fi325358
'WT' ''*''i"8i-''^o 7n244H27
iw-rn 108n7l:M»B 7!^2fl4253 9 I
la(Wti2Jn« 7 0283636 01174724
10W(52(;30 7f>302975 9IIH4518
1088430-23 7 U322271 1 194201
910755UI
9 loa5(J04
910955^4
9 1 1055(13
9 1 1 155 OH
9 1 125431
9-11353:<3
91145213
9 1155072
9628
0607
9M5
«»63
9542
9521
9500
9479
9457
9437
9416
9395
I1374
93.-»4
9334
9313
9292
9273
9252
92.1:1
9212
9103
9173
9153
9133
9114
0095
9075
9II5(J
fM}36
m)i«
K998
IOmta3438 7'9<')415-23|1»-1204043
108823875 7 9360734 91213773
I0H«I43:J3 7937I«JOl 91223482
10 8804812 7y:jJ»9027 9 12:i3l7l
108795312 79418110 91242K39
10 87858:13 7 9437151 91252436
I08776:i7« 7 9456160
10876*1939 79475107
IO8757.V23 7:14940-23
10 87481-28 7 9512898
10 8738754 7 9531732
10 8729400
I0-872006fi
11)^8710753
7 9550525
7 9569276
7 9587988
10-8701461 7 !*6iW;.'i!»
10-8692188 7 9(;-J52!M)
h>86839:i6 7 96i:J8tt<>
10-8673703
7 9662431
10-86644!)! 7 9680942
I0865529J! 7 989941*
I0864612.'. 797178^6
I0 8«:i(."!»72l7 97;if^2;vy
10 86278:t!t 179754593
IO86I8725I797739O8
10 80^9630 7 97911 84
1 08600555 7 !m0'l422
108591499
10 8582463
IOJI573445
)0 85rj4447
91262112
9 1 27171 8
9 l2Hi:t03
9 1290868
9 I3lK)413
9 1309937
91319442,
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9 i:i:i83!)i
9i:u78:i5'
9i:i57260
9 i:i/iGRB5
IM 37005 1
9 1385417
9-1394784
9 1404092
9 14134 'K)
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9 1431059
91441310
7 98:^762119 1450442
798*5782'il U59655
1 043 J
10 108
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10286
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10034
10013
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99
9902
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Colatig. Covers.
Secant.
1 tJ 9 1 085821 9-943559T 10 0032493
[ 9098 131 l> 94:i4 1 63 1 0032648
IO'*08;7J3 9 94;i27.'i5llO(Mi:i2804
io*Hi77:uo
109086i>80
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10 9046:t33
9 943l3(Ki|lO-yo;(2960
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9it4 28447 100033273
9-9427010 100033430
10 90:t6045 9 9425586, 10-0033588
IO9025781 94-34165 I O003:»74G
IOfKlI5540 99422723 10 0033'H>4
to j».M)5322 9421-291 j lO 00;U083
1 1» M!t95 1 28 9 94 1 9859 1 0034222
10 8964956J9 9418426 IOIKI34:i8l
10 8!(74808!994 1 6993 1000:14541
l(»fl9fl4fl83j9-94I55G0;li>'iM»H47U|
10 )i9545H(l 9-94 1 4 ! 28, 1» (Hi;*48fi2
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108934 143 9-9411256
10-U924409|99409821
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IO00:i5l84
lO0035;t45
7 9863905
7 988l99t»
9 1488849
9 1 478025
9859
98:i7
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970!*
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10 88;>44:i»|994055l3< 100035833
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10 8815482
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10 8795957
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10 0738-282
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10 8540345
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9 9403638
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10 0041589
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9 9I»67;*52
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;j 99!»62lfl5
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lJ^'9 9!W1174
i"i9996l004
''"99960834
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9 99G0663
99960493
99960.121
0-9900149
99950977
9 09508(»4
99959631
,-.99959450
i.. 99959284
i^|99959Ill
Ji^9 9!»589:Mi
i^ 9 9958761
^^|99!>58586
1^5
,.,.'99958411
1^90958335
[!!: 9 9958059
" 9! 957882
177
177
9 9957705
9 9957528
69
56
57
66
55
54
53
52
51
50
4Q
4S
47
46
15
44
43
43
41
40
38
37
36
36
34
33
32
31
39
29
38
27
26
25
34
33
33
SI
90
19
18
17
16
15
14
13
12
II
10
9
8
7
8
5
4
3
2
S2 Deff.
I
284
8Deg.
NATURAL SINES, &C.
Tab. 9.
Sine,
i:i974!»2
1400372
MO:J.'.'rJ
UOGKi'i
U0!^0I2
Dif.
2ani
•J8H0
2ttao
Covers
86063fl«
Cl»S(
Tanp.
7 lt{:*L'!(tio 14(U'i4(JU
7 170455(1 1408370
!tiC<i2dou|7 i&5t;7r>4 I4ii:u':
8d9i}<>-2f) 7 l4(>!fS87 l4U30n
8&!)09mi
7 lUTO-M) l4)Hf2A;i
7 0'i7l7«l> 1 4232 1
'» ;^»;
7411
iJtiir:
UUn92S5B8\0H Timuui] I l*2«I7;>
(414772 ;„,,, «ftB.V22H 7 »';»2777 U2;iU7
l-n7'I.'>l ^"'*;iH.'S»234f> 7 0.J3!I206 U32II5
1420531 "'j!JJj«57!»4(m!7n3IM;220 14:i.'iOfl4
1423410 o«7« fi57«50o|7 02&3ir20 U38053
I42(;28'» ;(*i I "^7371 1 7 01 12001 U4I022
,JH70 [
_ lB57O832'6!»9707fi0 I4439IJI
^J:^;[ B,5f;7953;«98;MK)!l2 l44rt'JOl,
J i; H565074 It tMMIIiyJM 1449931 (iK9««7!'9
-"^ 'HiV;2l96 f;;(5504W l4a2!M)| «;«827H07
U29irt8
1432047
1 43492^1
U3780.'i
17'14406VM
i6i 1443662
Colaiiff,
7 li.'>;«J97
7 lfM>382«
7(HI.'i4n73
7 07n.'.;i:t4
7 (l.io7!Ht:.
7 04l')482
7 02ti3G«2
701
Secjint Vers,
1 (NKIflJ7fiOO07MI9|
lO<HIM/iK!» <Mt97725;
I 0(»9!»I03 (WJKiai
i (M»!»:jriiH (h»yB538
I 0()!);i!l34 iHK* 945
1 oiuo:ii>i (>0!>9:id4
1 01 O07OU 00911763
lOI0nn7 0I«»174'
1 oi()if;i»7 0I0058&I
9820781 [IO|02«27 0I001>97
69f:ir233.') I 0102449 OIOUIA
G9538473 10102871 0101833
l)9:iUal92 I 0103294 0l(»22a8
C9252489 I0I03718 0102053
9110359
Cosine! '
287!'
287"
J(55!)31(> 09411490 145.'i872'0 8f;87370
o«-To O^'iOlSfl 9273089 146UU42 C WJI/iOU
ig!U4G440 ^^^lOAflSAfiOilMUriiSa l4filHI3'en408l9«
449319
1 4 .-,2197
1455075
1457953
2879
2878
2878
2«7«
2877
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8547U03 OWKU 195 I4(.77.*.« 0813122
8644925,0 »72499f> 1470727 « 7U93o05
8542047:0 8;.«9338 1473«1»9!« 7866440
8539170 U454222 1470072 6 79) 9U4i7
853*i*292;«-8319rt42 1479'J44 7583820
nirsfi «'''''*-'*^'5 08185597 1482017 «744H3I8
-"*" aA3(KV*7|0K(».'i2OM2 NHfWJKMJ 731331 1
., ''*(527<J00 7919095 I48lt5«a 07I7H89I
"^"'''^1024783 77U*«':»3 1491530 7044900
^V*""^*^2«78
26Uffll708* _
2fi;146«aa5*"''
2711409403
28 1 472:^40 .;";;il*'527<Joo (
3911475217 ,
3o!u7*tOy4Sfl?L«52I9Uti0-7('54e9l 141*4510 0«91l5e
All 1480971
32
3:t 1 41107.
.ULilWiy 7523208 149/484 fi77R'"77
tJ 73923(W I6l>i>4.>H 01(40307
48:0148 -"'/.OOlOl:
4 "J!;, 8;.i327(; 720i;»o.-. i^WMXi 00614149
34 1 489001 ',''.«.') 1031190 7 1:{2079 i5or;4o8 oc:iK;tioi)
35 1492477 „1,\ 0507523 70<»2fi99 I5()9;t03 0252258
36 1495353 „j' ' 8504647l« 0873822 1512358 G'til219l9
37 14982301
38 1501106
^2877
2870
39 1503981. ^"^5
4011606867 ooi!:
B50177o;« 6745446 16153X3 C 5992000
849ttHai;6«017't6«il5l8»t9'0 5»J2739
41 I&OD733
2876
42| 1512608 ^2
43 I5154A4I
44 1A1B359
2875
849001U 04 90184
8493U3'o030":i293
8400207 frSMiiVMl
8487392 6110973
S4845l6'ff5g86A40
8481041 'G5800r>87
45 Ifl2l234i.'^^j,* 84787(;0 .'>73*J1 12
46 I624l09.:;"''*]847589l|0.'i0l21l3
47 I62*tt*84i' (, 847:«010,6.'>4885m>
48 I529ti58|';i;: 8470142 65363528
28 /A
1532733
1535607
1538482
1541350
1544239
1547104
1649978
1562061
1556725
1558598
1561472
1664345
2874
8467207 16 52429:18
I52l28A6 573;iffi»2
1524202 50055:i0
l3272:to (i 5477072
15302)5 G53,j0293
1533102 6 522331>6
1530170'fi5O96981
15:*HI47 64971043
I:i42l2r» 04845581
1.''j45103 472059 1
]548082^G 4596070
isoimii 64472017
8464393,6 5120812, 1554040 6 4:*48428
""ij 0401518,6 4;«*!I148! 1557019 6 422534)1
;;"'■: 8458044 e 4077944' I .^.^(ua! 4 1020:1:1
r_Z"VB455770i647d7l96J60-2i»78 03980422
2874
2874
2873
2874
287:1
2874
2873
Cosine Dif. V«is
8462890 6 463690 1 1 506958 6 3B58«i<;5
8450022*6 4517059' 15089:19 3737:Vi9
B447I49
8444275
0441402
0438528
0435655
6 4397006 1571919 03016502
6 42787l9,l574!MiO fi :u;i6092
6 4i6(»2i0|l577mu i; 3376 1 20
6 4042 154 1 5H0863 325rrfi0 1
3924632 1583844 63137515
Secant. { Cot&n.| Tang.
40G
I 4117
407
4IMH
400
41!
I
411
4IS
413
413
415
415
4lCi
I 0104143 oim;hk;9 ::"
41
419
I 0104568 0lo:t480
I (» 1 04995 Ol03!M»4
t 0105422 0104323
1 OIO686I 0104742
I'O|O028r)OlO5IO2
I 0)06710 O10,'»504
10)07141 oi(m;uoo
1 0107573 0)00120
lOlOOOW; 0106852
1 0108440 0107277
1 0108875 OI07702I
10)09310 D10MI28
1 0109747 OlO?t.^>55
1 0110184 0)08903
1 01UH;22 0)(K)412
10)1106) 0100811
1011)501 0110272'...,
101 11942 0110703 T'/,
I 0112384 0111133
1 0112827 0111568
ioii;*27o 0112002
) 011:1715 01)2436
10114)00 0112872
10114«Hjl0ll3:in
0)I5(WJ4 011371
01155020114!.
0116951 0114'.
91M>2?7&!&tl
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9e:K;6)4 45
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;»«9567i43
98;:fo-2.ifl 4i
'9tin71Q8
10116400
I 0116851
10117303
10117765
10118209
10118003
10II9I18
) 01 1 9575
012(8132
1 01204B9
1 OPJWMH
1-0121408
10)21809
1 0122330
1012279:1
1 (1123250
1 012:1721'
0124185
10124651
OM5U4»l
01 155021
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0110:1
OIIOJI.-,
0117272
0117718.
0118162
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01 20862!
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'.-.'il; :.-■
u
10
Oft70«»
.1
7
•
4
t
9H;t»tftt4
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SlDsg.
8 Deg.
LOG. SINES, &.C.
285
n
o
to
II
1-2
la
14
la
Hi
17
18
IS^
90
SI
92
S3
24
2ft
26
27
38
29
3U
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32
S3
34
35
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37
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41
4.1
41
45
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55
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67
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J#-N;ia5M
9 UJ4532
J) 1 i.i.'Mff.t
U U7UJ8
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897!>
8116
81»0I
8867
9-1-I080I,'.
g-isisK-ji JJJIf"
l>-|52».'V"7in- '^
.J lM2(.7«|«j;^
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fl704
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1 9 1637434
|9-1C45!»'JH
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&l(;8Bd69
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86 j I
0634
861 A
8699
8581
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9I70S4B5
9^17138'M
9-l7*)*»»9
9-l73tfi>77
9-1747431*
9 1 7A.'V7'J4
9 1784112
9-1 772425
9 178*>721
9 17890IJI
9-1797285
91805613
9l«i:t744 ;-*;.-
9 itiiunm
> 1838344
9l848'i)'.>
10 8584447
ll)8:».V>4«8 7 9900(138
10 8.'i465r>7 7 9:M8U4
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!oBji!)73a 7;>;'7i«''3
10 8510862 7 9989713
io«6oi!m.-. «ooo7:.37
10 8493138 JMK>J532.i
I0 84H4308 8 1)043078
lOflJ7ft4;)3 8 00C07W»
101)488899 8007U4C8
10 8457024 8 0098110
10844:1168 8 0U3716 9 I595G46
10 8440426 8 0131287 9 180JA60
19 8431704 80148822 91813473
10-842:MOO 8 0UMI321'9I82238I
10 8414314 8 018378,^,0 1831231
14780251
U 1487 1 82'
I4!M>32I
9 l.)0544l
9 1514543
9I52:MJ27
9 1632802
91541739
9 1550780
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91588773
9 1577748
9'l6m;708
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10 8:198996 8-0218807
10 0:(8lt38l 8 0235965
10-«:i70746 8 0253280
10 8371147 8f»27057H
I0 8:i82.'i68 8028783:4
l0 8:V>40ffJ 8 0300063
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1875322
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|si67
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9120
9102
9084
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80 y 3
8075
8058
8040
8428
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8378
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9 1701572
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1 744988
9 1753822
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10 83:t6!t2H 8 033:81.01
10 83284 U 8 035fi50i
108319019 S()373.'.:*2
10 631 U4 1 8 0300843
10B302!f79 8 040786:'
I08>0i:)35 fl-0424812
108288107 8O4tl.'i02
10 8277805 8 0458:.rltlj9 1770840
1O828O30I 8 0476303,9 1770425
HHI2O4)023 80492243io 1787303
10 82J2J61 8 0509081
10 8244216 805258O:
I0 82:C.8H8 8 0542500
IOB227575 8 055031;i
loB2l;»279 80578U07
lO82100i»;» 8 0502883
I0 82027:i6 8 080{)288
892:*
8904
8888
8870
8852
8838
8818
8801
8784
8787
8750
8733
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9 1854805
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10 8104488 8 0626878
10 8188256 8-0842438
108178040 8 0658986
10 8160840 8(W75463
108181858 8 0691928
10 8153I88|8 0708362
10 6145.335 8 0724764
108137108 80741138
10-81 JOO77 8 0757478
10812o;i7l 80773788
10 8112880 8O70t)O85
ll)8104806'8 0S0ti:il3 :i l!M7S02
l(ViW08748 8 0822531 IH,»8060
lit 8088701 8 0838718 J 0843(12
10 8080872 8 0851875 (072530
10 8072658 8O87H'02 I9.J07J3
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9 1706546
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10-8521976
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10 8503'J70
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9 0347705
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10 0061623
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10(8)52212
10 0052409,
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178
178
170
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170
180
181!
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182
182*
182
183
183
183
184
184
184
185
186
999676-28 l»0
99957:150 69
09957172 68
9 9956903' 67
9058815 66
9905e(>36
9 9066456
1 9 9966276
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1 9 9956916
19 9966734
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9 9965370
9 9966188
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9996408?' 41
99953902
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9 9061854 28
190
190
191
191
l!>2
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192
193
193
194
194
194
194
196
196
196
9 096I4(U 27
9!i96l274 26
9 9961084 26
9 99.*>0B93 24
'99950702 23
9 00505 1 0| 22
9 0950318,21
it 'MftJili^ 20
;^:»04o:^:w 19
09940740^ 18
9949546, 17
9 9949362 j 16
9 9949166 15
9 9948964
9 91M8760
9 994t(673
,_„0 9(»48377
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iJS 9 9947986
o- :'9947788
^J' 9 9047501
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,„ 09947195
;^"9 9946»:i7
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.'•^ 9946690
*" 0994(C190
^ 9iM6l90
Cosec. D
Sine.
81 Ih'o;.
I
286 9 Ueg.
NATUUAL SINBSj &C.
Tab, 9,
19
2U
21
22
124
Sine.
1364345
1567218
I570091
I5725W3
157'»»:m>
l57H7flB
15816fil
lA8-44.'i3
\mnin
lA96a40
1606813
1001683
1004555
1007436
Dif.
2n73
2K7:i
2U72
2&73
2072
2873
2872
2«72
2«72
Co sec.
Cov<
8433655 6-3il24ft:« 1583844
84y2782!fi 3«<l73-t7 1586826
Tanjj. Colanpf.
B42iHM>9 «3/J!J05(|5
84 27037 |<i 3574*76
8424164 'f! 3458386
8421292 8 3342923
84I84IV63227BH4
«U,V'i47l<13II32R;t
*; K4lJi;7;. (;2Mfw»7M
1589806
1592791
1&9G774
1696757
1601740
in04721
16('77(>(|
63137615
6 301 8866
62900651
63782868
62665515
63646666
63432086
Secant,
l<M24(t5l
1U1201IK
1 «12.'i:>«*l
lOI-J'.
1 fll2<.:;
IOI27406
Vers.
0123117
0l2.V»72
<>l24(>*fl
4A5
4r.K
Cosint
tf6;C6&l
m7e4tmm
-^^7|840*a>31 ie 277l!'33i 16I3«77
rn;l8404'J(;f)'0 2658!»«4!t«ia(W2
'*"^"-' 8401188 6254644«I«I!M^(7
2871
2U73
3671
28711
2ff70
623!fiO(t7'l*Oi279:i9
(i221Mi;U7 I ()IL»«4I2
<i20K.'il(Hi lOliiWiU
oiy7'>27y ioi2i»:wil
G lK558i;7 1 Ml2t»«:i7
6I74I860 l-ui:u>3i4
0398317 62434310 1622632 61028272 I OlSO?!*!
8395445 63333594
8392574 6321 127s
8389703 62100359
1636616
1B315W)
61515085 1 0131270
6U03303 I013I7->0
G 1289933 1 (»132UM"
lCl(K>38!ii!!Z!|8383i»(;
«:iH(iK:(3 6i;m;iH43 iC3457(i « 1177^43 i 013271 1
0i258«2iiJijii#fl7ll3AM
'460
1618909
1 02 1 779
I*W4ImO
I62752(»
1630390
16S3260
i636l2!l
1638999
1&I186K
1644738
29! 1647607
30 1650476
an 053345
32 1 f;5i;2 1 4
33J«3i»082
:i4'l661951
35 i(;ti48iy
1607687
28711 ,'»"^''-'
.^„_j83HHmi 61770003
-"47 8378221 6I(I«I>«74
-"4„ 8375350 «15A17:t6
'„'" 837248(1 6 1443189
*Ji"H;WJ;KiIO 61335028
jJ/iQ 8:166740 61227253
012632?'
OI267Hi
012724'
012770:*
0I28I7:
Ol28(i:[7
oi2yio:j
oi-jy:.(;:f
oi;Mt;.Mi
01:10:17
ji..;
)(>375G3 61004i3(iU, 1 0l33194!0l3U4;v ,. .
Itt4055o'fr0fl55l74l 0133677 0131913! . .4 1
1643537i6084438l!l 0134101 01M.'i--<-. -"^-i
1«4«.VJ5 «073a'»7M 1 0134«46.01
104M5K16 0G23967 1 0135132 (M.v
16A2A0ll605I4:*43 1 0135618 0l33;,U4
Iti5548l4'60405ia3 1 0136106|0134278
1670556
1673423
1676291
1079159
1682026
1684894
1667761
1600636
1003405
I6B6362
1609338
1701005
1704961
17078-26
1710694
1713500
1716436
I71929I
1732156
1725022
1727887
1730752
l7:i:^Ji7
r73fi4«2
Co'-inc
8363871 6 1119801,1658478 6029*ri47 10136595 0134754
4741
476}
476
; .' U
UK(MI087 4I
»f»67«U 40
1'86714»3»
:*806670 30
9866196 37
!MI6A7^36
H« fi:W1001 61«1286i»'IWIl467 601877/2 1 0I37OB4 0135230 *i^
™!* fi;i,^j!|,i^. (;)i:«»,il!(l(;*;44o6 6 0079676 10137574 013A7(t7 *!',
2870
266JJ
■'x<:y2i'.-2 t:.
n:\ iii07446'5 997i9.'>7 I oi3H<Hir:oi:oiiii.
2609
28611
2869
2868
2668
38691
2867
2868
2868
2867
2808
2867
3867
3867
3667
2866
2867
2866
2867
2866
li;.152393 U(;L'40H^'>
8340524 6 0568580
I
8346655 6 0483445
ti34:i786 (i ()37JI<;80
8340tJlB f;027^-'82
8338049 6 1 702:>0
8335181 hU066581
8332313 5 0003374
8329444 5 9860336
1670436'5{)8646I4; 1 Ol38558,013i;60j
1073426|5 9767644 I 0139051|0137144
16764 17,5 1)651045' I 0139545 OIT' "
in79407|5 9544815 1 OIKHUOiOi
I(;e.>3!l6 5 9438!l52 1 0NU536 0):.:
-»;.'
J., i
■1:, 1..
16S53!H» 5 0:1:1.-1455 I 01 4 1032
1688381 5 9228322 10l4l530
1691373!5 912355U l0U2029
()i:i:iti7i
013955:.
ouo(un
ouo;i2:>
''V
1694366 5 9019138 10142528
8326577 5-9757737 l«9735«|5 tt9l54»84 1 0U:«>2J( OUlOl::
8:1237119 5 9655504 1 I70l»351 58811:18^: 1 nl4:i:>:t4j'ul4l 49:'
«:t2084l 5'9553«2o 170:1344 5 870:fO42 I Ol44l>:t2 014198;
8:117974 5 94520981 1 7<MKi:(8 ^ttUUKiiKtl I Ol445:i;) Ol4J47(
2866
2866
2865
2866
2865
2865
2865
2«6;»
Dif.
8312239 5 9250(t!f5
8300373 60140614
8306605 '6-0049479
8303038 6-8940688
fl31Mn72 58850238
8297905 5875 11 20
8295039 '6*8662356
8292172 6-8553921
8289300 6 8455820
628fU40 5 8:i58053
8283575 6 82606 17
8280709 6 8163510
8277844 5-8f>6673«
B374978 6 797028O
827211316 7874153
B269-248
57778:150
5 7f>82867
5 758770ft
Secant.
i4 IJ
.4 13
^3 II
■7 |«
1712325 5-8400117 10145544 Ol43t5(;
1715320 5 8298172 10146050 014.194; ,
1718314 5-8196572 I 0146556 0144439 ." «
17213(M> 5 8095315 1 0147064 01 449:t-J ,;. ,
172I3U4 5 7!m440u'l Ol47572{Ol4.>l2r
1727300 5 7893825|l 01 48062 0145921
1 730296 5-779:i.'>88 101 48592 01 404 1 7
17:1:1292 5709:1688 nH49l03|ol409i:i
17:16288 5 7:)94I22 1 Ol49<J16;01474 I"
173928.'! 5 74!»48rt9 r0l5(ll29jOl479O.'l
174-2282 5 73959K8 l*0|5IHi43,Ol48407 :.„.,-, .... ,
1 745-279 5 72974I6 1*0151156 01460071^ 066|OUa 6
1748277 57199173 1 015I673IOI l'»'"^
17512755-7101250 I (U52l9UjOU
1754273 5 7003»W3| I 0I527O8 01..'
17.'7272 5-6906394 1 015:1226 iU5o9U
17'H)271 5 68<HM46 1'0153746|OI5141^|
1763270 5 6712818 101542661015193
Colon.
Tang. I CosecJCoverii
D
19
16
i-i
!fMi}i(i78
13 5j
■M 4|
3>
1
78 6
Sine. I '
8U Deg,
Deg.
LOG. SINES. &C*
287
o
I
2
3
4
6
6
7
a
lo
II
12
13
14
Id
16
17
18
Sine.
ft 194^324
9 l!)Jl2U:i
0-l!JJ*»2l7
»-l»(i7imi
Dif.l Coaec.
7!*54
7u:w
7'J'-M
7»oj*
7B80
0-2030 1 «7
30a7!)74
tlOa«.'MMt7(i
^''"*'au 8018707
i|0Ut(4t»753
il0flO2-*n;m
ilOUUlli<t&l
1 1 SlKKJOa?
Vcrseds.
Ro:tr»iifm
Tang.
!»l!ii»7l26
!l-2Ui:t44!)
Dir.
firt;»(>7l.'W i»-'<i2!'7U;
7«3«
1782-2
l7Wt7
77^2
a204:.7);«
{)-2nj:i54.'i
loiitKiian?
IO-7!*77W5
ll>7i>«it)Jti
I0 7il&4'234
n/tll0 7U4«45.-i
0-207tf793lli:!v I0 7!«:i:^0j
20a45lfil'i.'f,VlO7yiS184
i7/'*Oi
0-301)3224
7693
I7B80
20 9'20!JI*«J!7
31 »2l073U7|i^^!^ 10 78»2403
^ In ill i«L.«i*.!760O in^iiufi,.^^
24
Il2ll5-2'rj;
7fiai
: 71*24
lo7SH)7776
10 71)00083
10 7884737
10 7877086
l0 7B(it>446
9^2I3«l76i-,j,
10-78*11824
92183e:i5-, , I0 78I«:W5
»2Ull I fij' '*/:;. l07«0H83ri
i> -2 1 !»«()itii' ^;J ' ^ 1 fr 780 1 320
22O(;iH2!^^'!r io77y3aiR
n2ai:w7i|ij?^ 107786329
9 222n47'jjj? 10 7778853
9222nfl(«»L, I10777
9 22m):>ii'. *]?!;. !077«394l
!»224:i4;W ij^! I0 77a6«)5
92250iil8!i,7;; 1(^7743082
9 22ft032Kli''" I0 774lfi7'2
fr82R5725 ij^Jl IO773427A
8 01>«30:i j
K 0U!Ht»44
Ui037825;
9-204oU22i
!l'2»)fi4lM>4|
I*20<i-2<I72!
;»-jo7i)i2«!
0^-2O7KI*Wi
!f'2oatiiai'
9 2094203 ?!j,' i?
» 1014801
HI03O<i;t.7
H I04f)4:i7
H I0<>22)1
K 1077:)5?»
« I093ti7l
6 11V0358
8 112.5017
81I4(M>47
8 II. 18249
81171023
«I1873«9
8 1202887
8- 1218377
8I233840 9 216.V6B3
H I249274!;i2l7:v».'»(i
8 1284881,9 21814)7
8 128008119 21892841
ti\tVj
815
8139
8l2fi
8111
8097
8Uli2
81)88
80.) I
803!)
H0'2ti
9 2102200
{12110184
yaiiui.wj
9 2128109
9 2134061
9 2141980
7984
7H8'!I
79i«
7942
7929
7914
9 2140894, ,,jn,
7873
78iil
7847
7833
Coianp,
Covers,
108(M>2876 9- 9261188
lO79947(Miy!«59709
I0 798«a6r9jr268229
l07y7*W12:992,Vf749
I0 7970288'91»2ao28tf
107982175
1^7954078
l0 7!»-i'*'998
l(t 7937928
10 7929874
10 7921835
10 7913809
IU71W57M7
U 9253787
IM»25230U
9!W50824
9 9249341
9 924785H
9 9248375
9 9244891
9 9243407
SecnnL
I07897800i3924l922
8 1-29.VII3 92197007
&13l0738l9"22049l7
8 i:tt0O38 9 2212724 i",,
8 1341307 9-2*2-20,il8|ii;*
8 I3.M;6rjli9 222829alii
7820
7«07
8-1371788 223GO(Mi
1113889*8 9 2243819!
77f»7
77M
H U02r2r9 22A158l
81417258 9 22^,9209
7742
7728
8 U323G8 9-22«7l»04Ujli';
8 U474:.2;9 2-274708 ^^'-
8 1482610 92282305 '
1 788:131 'J
10 7881847
10 7873891
107865949
10 7808020
10-7850106
10-7842205
10 7834317
10 7826444
10 7818583
IO7HI073*;
10 7802903
10 7795083
10 7787278
10 7779482
107771702
10 77(Ki93d
10 77581 81
10774ai3!»
107740711
10 7732998
:3!ll
9-2273110
9 2280481
9 2287839
9 22!>5I0.-.
9 2302518
9 23098:18
9^317145
92:124440
9-2331722
9-2338992
9-2340249
9^2353494
>238fV728
*-2;Mi7948
7371
7;u8
7348
7333
7320
7307
7295'
728:2
7
10-7728890
I0 77IJW19
107712101
I0770I8I:.
107897482
10 7890182
10 78U2855
10 7f;755(>o
10 7808278
''J 10 7«81l>OH
7257
7245
7232
7220!
I10 7';j3751
10 7840500
-Hi- 10 7832054
9 2:i75153::,/.|l0 7*J24847
92382349 '„!;|107CI7651
9L'n8:i532,' "■ lO70H>488
9 2398702 * ' I0 700:tt9«
L'oftinp.
Dif. Secant,
a 1477M1 9^2290071
8l49254fl,9229773«
8 1507525 ir230a3HCI
8 1522478 92313024
8 1537406 92320650
8 1553307 92388263
8la67182'9-23;j5803
8 1582032|923434ril
H ld!>68d7 923&1036
8 1811656 92358509
8IU26430 9 238Ci;W
8 1841 178 92:17:^:78
8|fi55!H>J 9 23K1203
8 I87O8O0I9 2388717
8 I88.'.273
« 1899921
8 1714545
729144
8 1 7437 1 8
8 1758287
8 1772792
8 1 78721*2
8 1801788
8 1 SI 8220
7670
7604
7651
7638
7626
7C12
7601
7588
7576
7563
7550
7539
7525
9 9240437
992aaMr):j
9 92374t;8
992;i591iU
9 9234493
90233lX)6
99231518
99230030
99228541
99227062
9 9225583
9-9224073
99222 >"i 83
99221092
9 92l9<iO)
9 9218109
9 921&il7
9!)215125
91(213832
9 92I2i:i8
9 9210844
!(► 772529419 9209150
107717605 9 9207658
10 7709929
10 7702265
197694614
10 7flflffl»7«
I0 7679:i50
10707 1 73it
10 7664137
10 7668.VI9
197648974
I0764U11
10 7633861
10 7626322
10 761B797
10 005:1801
100054001
10 0054202
100054403
IOOOn4i;<»4
1U00J180(J
10-0055008
10-0055211
1 000554 13
109055617
10 00558-20
I00056(»26
10-0056229
10 0056434
10 0056839
101)056844
I0<K>57050
10 0057257
100<157463
IO0067870
10 0057878
10805 8088
108058294
109058502
18 00587 II
100058921
1(MH)59130
U>0059:MI
10 0059651
10 0059762
10 0059973
iono(y)iB5
10 0060397
100080609
IO<M)60823
100061035
1O006I248
100081482
100061670
1000618!)!
10 00821 06
10 0(>82:t-21,
9 9206100
99204665
99303169
99201672
99200175
90198678! 100082537 1
99197180 100082703 '
99195082| IOOOG21»70'
99194183 190f>83187l
99192884
99191185
9 9160685
Covers. Cotan^. Dif
99168184
1076112«3>91U66B3
I076037B2'99185IB2
107598292,99183680
107588815 99182178
107681360>9180675
I0757:i897 90179172
10 7588457 9 0177889
10 7559028 9 9178185
IO755I6II 99l746fiO
10 7544208 99173155
t0 7536812|99l71850
Tunjr. Versedh.
10 0063404
I0')083C22
100083840
10 0064058
10 0064 277
IOD(M;449fi
lOtK«;4715
10 0084935
100065166
100065370
10 0066697
I0IN)65819
10 00<iflil4l
IO(MW82(Ki
10(>0(M485
Co sec.
D. Cosine.
200
201
201
201
202
202
303
202
201
203
205
304
206
205
2^»5
206
207
206
207
208
208
208
208
209
210
9046199 60
9 9945099 1 69
99045798 56
9945597167
999453981 56
9 9945194 66
9 9944002 1 64
99944780' 63
909445871 63
9 9944:183 61
9 0944180 60
9^9943976 49
99943771 48
9 0943566 47
9 9043361 1 46
90943156 46
99942050 44
9 0042743 43
9 9942537 42
9994'233o'41
9 9042132' 40
99941911 :iO
9 9941708 38
9941498 37
99941289 36
99941079 35
9 9040870 34
J99940650, 3:t
<99940449 33
99940238! 31
209
211
210
21 li
^{2,9 9940027 119
!9 9930813 29
^{.,! 9-9930803 28
f;:,0993039ll27
99930178 26
9 9938965
9938732
2t3l
213
313
214
rt, .I9003*i5.'tft
,^9 9038324
1^ 9 9938U»!)
^^9 0937B:»4
;^9 9!i:i7879
<^jjj 99037483
217
217
217
218
218
218
219
219
219
220
221
220
321
22s
222
222
00 ■»
25
34
S3
22
r>|
20
19
18
17
16
00368131 15
9 9937247
99937030
i9 90:«;506
9O034n178
9936160
190936942
99035723
;9 0935504
9i/93.)-285
09935066
00034814
99934634
9 9934403
99904181
9933!)5y
9 9933737
0033515
D.
Sine.
SODeg
NATURAL SINES, &C.
Tab, 9.
' Sine. l>it
1736482 2«64
1 I75!»a*6
1742211
2»(n'
l/-Jao7.'i
4 17471K1H ^^^.J
7 I75IW3I .,y^.
lOjIitiAl-JI jy.
I li''/!»H4 .,^.
12|i;70847jS;i
14 Ii/(K^i.l ..,
Ifi I77«4:ia -"!:.
I6| 17822^8-2^,:;
i7|i7»5t'Jo-^*;i
18!7tf8022-^:^
1911790884 oon.2
2O|!70374C-^J
24 laosiDi^lU;!
26 1 808052 ,»,.,..
26 iflio'.ii:*.': !
27!lHi:*:74.^ :
2Bjl81«6;i.|- :*
30| 1822335-1;;;^
3l'l8252l5' .,„,.,,
32:iW807n2^
33 lH3<»yna **^;5
:i7 Ifl42373.,n5n
2HoM
2KriU
2tf.-.H
:iy|]H4«o'ji ;
4fltlHj(H.U'.|
III.VttlOM
2tt.'>U
1B5»524'.,„.H
_'2o.jn
2K:>8
2808
2 HAH
iK(;2:t82
l(lf;624U|
L ntUHmi
I ft7«i:" .,or,„
l87»''28^-J-«
lUK2:t8j'-"^^
I Ka^ri 41
2KJ(i
!Bamii;8:
28.'i'
1 t{JUt).J4
2ft5ti
2867
iiifl:wjii:
iKi>G);(i7 " .,.
l!»02:<7!*
2ao:i
286«
Cosine Dif.
L*f)\ers
K24.14«J»
U240»ia'>
H2:i7742
H234H7f»
a2:t2(»io
8229153
822fI290
«223427
8217702
92] 4840
iJ2liy7B
C{»sec. Taiitr-
.')7^tt7705|I
a74»2tMJri
o7:*)wi2i 1
5 7210223 1
bJMGti'Mi 1
d 70233*^0 1
7(J:i27i'
7f;(;2fi!t
7(;y2*ii»
77.i2(it»
775271)
t'olimj^. Secant
.IU7I2F1B
jtid-2aAi6
.i 64248:t8
5 6329474
778270 n«2:W42 1
781271 3 6139680
Ol542l»J
ers.
D.
0U1922
6 693n3*»3 1 784273 5 G045247
5 6837734 1787274 5r.95112l
.'ifi7453tW I7l(027'j 5 5857303
56653331 I79:*279 5 5763780
5 656I6K4 179(J28) !& 5670574
5 647014U 1799284,5 5577t>t>3
56378995
5 6288148
5Gl;»75:*9
5 61(17345
5r>Ol7:t86
6 5927719
8209116 ^583(i343
82116254 5-5749258
H203;«I3 5 56W460
^r2lHl531
819767U
JID948U9
8l9l;>4B
8l(t:i087
ai«'i226
8i833(K^i
8)80505
8177845
817478.^
8171925
0169065
8166205
8)63316
81 61)486
5 5571951
5-5483726
5 5395786
1802287 '5
1805291 15
1808295 '3
18112990
18l4:i4i3 5
lUI7:i(»8 5
1820313 5
1823319 5
1820324 ft-
1829:i:UI 5
183233716
1835343!5
5485052
53y2740
530U724.
5209005
5)I7.'>79
5026446
1
I OI547H7 015242B
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10 74tllfi8 8 2197531
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107213555 H 2802307
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10-7194'»I2 8 2841757
Secant.
Covers.
9 2587099,
92594285 4 "
717(1
9-200 t4(>l
9 2mMl(i25
9^2815779
9 2822;) J 1
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9 2844283
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7132
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7110
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107441700;99I62040
107434^.28 9915052S
10 712731)8 9 9149016
10 742:iO:)9|9 9147504
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10 7:191375,99141450
10 7384221|99139935
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107:189947 9 9U)890i
107:1828-27 9 9I3538Jr
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",\[, 9 1*9:12171
'■^-19 99:11946
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231
231
231
232
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9 9028753'39
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239
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NATUKAL SINES,
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Tab. 9.
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VJHidbG
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U»2««74
I
1
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Tan». Colanp.
t<l43Uli:t 5 1445540
5 I3&'»7'!3
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Secunt. Vers
I OIH7I67 018372H
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I 0I88K99OI
I Oia947«l'l: - ^
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506,
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5 0158517 2034523 4 9l6157(i; 10.»048(fe 0200753 -
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in 2022176 ouI;,'7977624 4 !I4..|6M7 '.'0648:U 4 8J30045 I 0210952 02ntia;(j
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LOG. SINES, &C'.
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240
240
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9!>!fl9220;59
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8 3249532
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250
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9-901B645
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2'J:> \2 Deg
NATUUAL SINES, &C.
Tab. 9.
Nine,
aoTMUT
;i.M»»l>4!f7
i20!i:t:ui
3IO)H7-l
2tn47ift
21i>75fll
2110400
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2121777
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217'W»3
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2 1 84 271 1
2187110
2I9WI24
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>,... 7!'20KH.^ 4KtM*7:n:<
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2102077
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2180353
2183400
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2180400
21U2.'>44
2105603
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2201602
2204742
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L' J 10844
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2210047
2210000
2223051
2226104
2229167
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2235265
22:10:110
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4-7040301 102234IHJ
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4 6*t452iB 10225:W.7
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4 0712124 10226678
4004A832 I02272I6
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4 on 13708 1 0228403
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4-6107086 1 ■0242795 0-237040
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4 47:17428: l(124O77«!02 40032
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4 4016489' I 024RI 10,0242103
4 4564750 1 (1J4077'' "'*■'" '"
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4 4373500 10260700,024;
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22i»KOI3
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2275012
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100131/092
100137014
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100137000
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H700001o'ool7:i3o3
i{7mi7nfMi'y.'>i77rjo«
iI70l.»7.V»|»nlJIU{,'K'i
»7023(;i7 youwiioi
8 7<>3]47lj'J.''l!»0344
8 7*>3y3l8jy^51»45a3
«7047138'9.'}ia88l9
y7(>:>4yyo!y.v203o:j2
l{70(;281.^|y .5207282
«7070«33yr>2 11508
8 7078444|yi>2Iii73O
«70KG247|yr>2luy50
»70»4044!>5224inn
8 7l0l833;y.'>22837y
Dif.
421*7
4294
I2W)
428(1
4280
427<'
4273
4270
42«*i!
42(;3|
42:iy;
420(j
42o3
42 ly
12 JC
4243
423y
4230
4233
42:io
422li
4222
4220
42ld
Cotan^.
Covers.
10 4882240 •»«3»4(j74
10-4877943 jrjttirjyii.'y
10'487304y'yH39lly.'i
i\)Aitn'Xi.vj yiKiiiyi.V)
10 4/100073 9 831(7714
l0 4Kt>0790 9 838:>973
I0 41C005IU ya3U4231
10 46622:(4'9 8382489
10 4847IMM|y 8380740
10 4843(191 yB379003
l0 48:«M2.»;9H377i?iy
H^4Jt:»:»I(i2i9H37.'>.')lS
J-^
10 4830903
H^4tt2R(hl7
10 4822394
10 4818145
l(»4tll3M'J9
lO-48(»y<J5(J
87'-*JlJ7 y52i(i:):»9
8 7132918(95240199
8 7U(M7I 19 5249394
8 7148418, 952.'>;i;.80
8 71 J(iI57, 9^5257779
8 7l(nJ8a9,9 52(»l9(J«
fl7UI'jl4|9.'i2«CI50
8 7l7^3:^Jl9 J27o:«i
8 7187044'y 5274508
8 7194748 9 5278082
4213
4210
V 42il(i
42114
4200
4198
9 8373770
9^8372024
rt37027«
9 h;m;8532
9 8;m;o7u5
y n'Mib^>:il
10 4805417'9 8303289
ia-480118r9 83615 10
I0 479(;;M8 9!135:)7:M
I047927l8 9fl35}!04l
l0^478IN92 9J{:ir.«29l
10-478(270 !»«3545IO
I&4780050'9 8:t52789
10-4775834198351037
10-477i(!21 198349285
1047"i4!lln8347532
I0 47(;3205'9 8:t4."778
8 7202445
8 72lOi:i5
8 7217818
8 7225494
8 7233Ifi3
8 7240825
" -■' "'I!IO
,770
H727i4(»4
8 727JWI32
it 728/WVi3
ii72942*.*7
Jl 7301874
JE 7:109474
8 731 7t«7
«7»24fl54
8 73322.; .
8 733';,:
j;73J7:^;-
il 7;t-»493j
8 7382485
Covers.
9 5282853
9 5287021
9 5291180
9529:1347
4194
4 1 90
4187
4184
,4181
4177
4174
4171
|41(i8
14185
4181
41MI
95299505
9-5303(U;|l
4l.-|(i
■'•••*"'"''*in4n
!'531I;h:i!J -^^
;»>:»l'-i»7i; {S
9-5320250'
9 5324389
9532Ii52(;
it 533 Jfi59
9533/J78!!
9 5:i4<)91(!
9 534 jf>4t»
fi 53491 B|
■ r.i
:. <i5
f»5o;'.i;i3
9 .'>3<»'i7 1 11
14139
:4I37
i4l33
(4127
4124
14121
^117
4115
4112
4 ion
4108
Cotung.iDif,
141 I7.V.MMH
10 4754801
I047508(»5
Ut 4748411
104742221
I0473HO34
10 4733850
10 472:»(J<i'y
9 8311024
9 ll'M-i-JV'J
!V 8340.^ 14
9 8338759
U 8337002
;i 8;U.f24(I
9 833:i48H
94t:i3l731
9 8329972
9 8328213
9l^12(i454
U 8324«^94
9 8:*22933
94(;i2ll72
9 8.3194)1
9 8317049
:»831.VHU;
98314123
98312359
rt- 8:110595
1 04725492
10 47213111
104717147
104712979
10 4708814
ia4704*M'>3
10 47<Ht495
I0 4fi[i(;;i:i'j
10 4092187
lo-40f:8o:i!i
1040M3893
10- 4879750
l(V4fr7501 1 9-8308830
104071474 08307004
IO400734r'^83(t.V.*'l!^
10-40(1321 I
10 40590; .
10 4054901' I nz-.r.r.r.i i
|0-4«5O«39'iMt998229
10 i-: , '. : J Mljor
10 1 14092]
10 i' '■'■'
I0-;
10-1'. :,...,
Secant. D. | Cosine.
|(Kt2l7y37
I0(>2IJ»47|
IO(t218759|
10 02I9170(
100219582'
IOO2I9994I
10 0220407
410
4l'J
411
412
412
!9 9782003 (jO
9 97f(H;53|59
9 9781241 58
9 978(H*30'57
9 9780418150
9 9780000 .Vi
10 0220820
10 0321234
I0(»221047
10 0222002
10 0222477
I0(»222m»2
10 0223:U»7
10 0223723
1 0224 1 40'
In ((224550
10 0224974
10 02253911
10 02258091
10 02282281
l(H»22700(;
Km»2274/W
|{H»227905
10 0228320
10 0228747
10 02291(^8
HM)229.V.I0
10 02300 1 2
1 0234)434
10 0230857
10 0231280
l0 02317fH
10-(»232128
l(t0232553
10^0232970
10 0233403
Ia02;i3829
100234255
10 0231082
10 0235109
IO()23.Vi3(i
I0 02359C4
10 0230392
I0fr>3O82l
100237250
100237079
10 02381 0!t
Ifl023a539
10 0238970
lo(C23;it(il
IO0241I30
10 0241503
lOU24l!f90
(11 (I > t ')■<"
M3ii'!>77y5a3
417
418
419
418
4*20
419
420
421
9977502014
9 0774009142
90774I91I4I
99773772,40
9y7733;"i4 39
99772934 38
9 9772515 37
99772095
..„i9»77»«74
]* 9 9771253
].■;' 9 9770B32
:^il 9 9770410...
^*" 9 97(J9988 31
422;
423
9 97095(;(;
,.,« 9 97^*143
J-** 9 97OK72O
;^-;^9 97'i82;,(i
^-;9 97'i7872
;;.T' 9 9707447
]|-^ 9 9707(^22
,' J997(i0597
j^^;997«OI7l
J*, 9970.5745
'::ii997053l8
■t37i;
* 9704891
'*i;?, 1 9 9704404
428
428]
9 97G4o:W
429p;
9 9;(j'3008
9703)79
*;; 9 970275.1
|-^ 9 9702321
;J:||j!>97oi39i
" 9970U01
*: 9 9701030
,;^.' 1 9 9700599
;^;;r997ooi(J7
J. ' 9 975:»7;Ht
,;::i9y759:«)3
.9 9768870
j;:;|9 9758i37
,: , 9 97.V{004
'^* '. .7.7570
, 135
■ . uTol
Tung:. IVers«ls,l Cohcc. I D. ( Sine.
1
sm
19 Defr.
NATUKAL SINES, &C.
Tab. 9.
Sine.
Dif. Covers
.■;';'\»;73'E«ii{
:«7.ii7i'r,i;;;;i;7-'7y-'i
3274!>-ifi" j|f;726072
:<277ti7'i.;ijolf;7i;a;(j4
Cosec, Tail jr.
loyii
j:i:.i;u4.Mi7''
:tmu;:t7:(i':u4!i7«5
Coian^.
■2 liiKAr.m
3 i»«;t7mHt;:n:t;uuu
:t o(;i2i 1 1 aidO*2:»';|'2 «;)y27fM
:i ujiM;:i7o S451KI33 2 «i>uoir;7
;vo5Wi(i7.-i
3«,'iXi02«
.t o:i4H)42:f
:i2f !(i424 1 .:' :, ' i;7 1 ^7*^1 3 04ii:iii(;4
't2nr,iHit :*']* t;7U"HI]30432flJM
•ViUHwii ;
2747
(i711334 3U4U7402
:UU21U(i 2-««7tf277
:u(i;):»L'7
:U72'»»';
317u/U(i
r.. .,_,« ..,oit.'iji7|3(i:iJE2'i({4;:t4«.'>f;:tii
»2iJl4Kl
32!)4i(io "i;;. (;7«:.;uo::t(i:i.v;7,vj,:ujiijji:i:i
32siiyo(i *i"J''|/;7«:(ii!M 3o3;ii4i;4 ;i4;/2i:)(;
'M'JWi.y.\ f/*i (;7(M)J*7|3():j(k;22I :i4;jri420
:no2:«Mi :;^::! r>(;;>7(i(>2;3 02Ki02:* :j4!m(;i[.''»
asoiuoo
332430U
3327U0n
132!I)I4 1
j:w2.*.a4
:u:i;i:i2i;
'sxmxju
.-.^WI7i'04" 3 0081024 352482«
."74'J M»72!(ii2|;i iM»:>(;22i :*ri2Hiu»ij
^1:^ (;<:7oi.>u 3(H»3i4o'2 ;i-i:u:u;)(
-•712
2743
■i741;
(;«m74Wi
«(Wi4fl74
l(;fMiUt3l
3343.*tj2|:;i"i G«ri(;44«
334(;2i/3,.';^][ (;«5:i707
334!»o:ui.';^^ •■"•
33ol77i'''
2741
2740
3:Wi4jjl(ii
3:i;.72r>*;|
33««2i4,"i;;
r.. -i.r.i
(;f;454U4
2710
:KJ70!»o3
t:^73r.yi
3:i7«i2:»
:t;i7i'i(;7
3;»hi;hk".
331*73 7»
I31HII Ui
t.'.y2nr.2
3:(!;:».'.Mtj
13:»I32it
t4))HHt(i
34037y«i
34IH;53I
I40!»2f;o
:t4l20(M)
WW 2744
U4;41H)|)4
(;/;:i72(jj
)iti3jri2.'.
-^Ijjj (HJ21W47
«fi2/i30U
273M
27:i«
27 3H
);(i23r»7 1
;iirt20ii:f3
3 0(HM;74f; ;3.'):uti4(i
2 Hi>Ji2<»7:i :u37i>12
2»'f.'>7443 3.'i4ll;((J
2-J)!f32.'t.if;,3a444(;0
2!»'Mm3I2,:i547734
2umii\Qi\ :to.'iii)i(i
2!Mfoli:i.j2<U:*42»(i
2 »«34i>3(i :ioo7rp(i2
2 9tilU5(;3':i-jUUU40
2 9780231 '3.JC4U8
2U7fily42 35(i73!»7
:/ l)737tii>j 3j7o(;7(J
297134:10 3."i73l»5(i
2WWi)327;t''77237
2JWKK".2«j3;)ltl>5IH
i*t;ui2A s.-iasr.oi 271*03339
2 9«i7on7 ;tdn7(»K:i 2 7«77B02j
2 9.V!»30l>(> 3.'i!Hi307 2 7S.V2307
MMui'Xi '£UMi:)iii:i'^o'j:Mi:u 2 7)i2(;»o3
>54o22l 3:i!»6U'iU 2 7>10I440
r,*:i'(Wl53:>H2!
Secant.
2HH24033
2^(f7l*«y79
2 H7oyy7o
2 8743007
2U7ttn>jm
|2)Ui;t!»2i:»
'2mj(J23i;(;
2i(';:!o(!a2
2 ii*;u»uf;3
2H:.Ii2lOH
21lu 55517
2nA28911
2-i;0023«fl
21(475831
2 It44936U
2«J2292«
2 8396530
2^8:*70I»C
2 8343R!>ti
2-a3i7(:;i9
2»29li2(;
2f;2(M2.'.(:
2«239129
2 8213045
28U17003
2«IGI0(U1
2ai3504;j'
28109134!
2 80832(>3
2 8057433
2IU>31fU0
2t{00.M»0l
2-7uaOl98,
2 7951537
2 7928917
Wil202l 2 952134H 3(i0O222
2737
2737j
.,-^^1 0«09«84 : 2 94975 1« 3(J0a508
.';i:, ' WM»714H' 2 9473725 3Wie;795
:,!,?.;. mi>4i\\ |2 0449U7A 3(!I(>0«2
"' .-...w.-T- I., .»4.j,;.j(;;, ^(113371
(iOOWi?:.
'i: ;. «.'i9H9iO,2 !l402:ili7 :Ui\*HitUy'2 7041)02
2 777«o«i>
2 77.''073H|
27725448
2 77*M)I99!
2 7(i74IHH)
173:.
(w9(;2fMl2 937OUCB 3/;iU949,2 70J4IW5
„-.jj 0593409 2 9:i553PO 3023240 2 7jl>y«<»«
.,^:J: 05907361 2 fiX'i 1 8:« 302r»53 1 12 7ft745f; I
r':!^ 05«HOOo'2t»30tKi20 302'.(«23 2 7.'4*>.V»4
34I47:m;.;:::' 05Ho2t>« 2;*2H4»5« 3033115 2 7^24500
34174'W|.,':!^ 0582532 2 9201431 30:W.>408 2-7499G0I
342U20ir^*",05797fly 29230044 3i;3y702 2 7474771
Cosine
Dif. I Vers.
Secant. iCulnn.l Tauix.
0570207
Ver-
0544AI4
0577207 0545702
,„.........,,.-,,-...
057:1
05; ;i'.
0501.- 1 ; '
05«_'.. .:: >
0583049|(ir>5I4(i
05«4717'i>.*.r.„Ml'
050' '.
0587:»-''i"-'r'.t"_*.'ii>
05i(«999 055K2:tfi
05iH>a72!(t;. I .
0591 I40|<>
0592221 V
05932;Mt " '
0594:^70 •'■
0596454 050I;HM>
05%*534 O50-2l»52
0597(;i5{05(;39J5
0598097;o.v:iR7R
0590701 Ml
00001(05 II
0001951 U;it.iji.i
00«»3037 0508740
00O4l25y50!}7O7
(►0O52l4'|n.'.7iiiT(;
0000.304 *t57l«l'
^.|Co*inel '
\\*>7
•.'tu;:»' 49
;94437ti4 48
l.J«J43«iOB6[4n
im;7
mu
0007395
0098487
0«09ft»«)
0010075
0*; 11 770
0CI28(i7
0429934'
057201 1
a'»7;t5^i..
0574AM;
057.W20
05705^1.
05774 7
OCI3!'05 0570450
0015004 0579425
0010104 li5aU02
00 172(:5 05H 137(1
00I83U7|" ■
tK;i947lV
o(;20575]o.:. 1,
0021 f;8 1 0505205
oo'2--':'-" "'"^■■'"■"
00-.':;
OO-.V'M
00201 1611'
0027227
(HJ2«3:t9|o5Jll9J
Dfi2!M53 0592170
0030508)05931*;'
0031084 05941. V
0032801 05951 I'
00:^3919 05901'.'
051*711:^
973I
97.''
y77
977
081
042M44; 3d
.'U2Ui7frl M
[9414706 IR
■•"•^724 17
;43 10
,„,.h^n7.iC2 II
O0:i6038
0030158
0A98l01f
0037200 0599101
0(;3n403Joi;iHHi:i3
oo:ti»527|00nlnuo
0040052 t)0(rjo79
0011778 ooo:v»74
992
9!>2
993
993
U05
71
|9401K9l
i4(H)399
93'.»4e>14,
1397921
y3y*iS20.
Cuscc, [Covers ! U. Sine. 1 '
70 Deg.
19 Dog.
LOG. SI.NES, &C.
307
' I Sin.
1 ii-5i;ti»n)ii;
-I&-:.U10G7
5 95144721
6 9^514»371
7051521)17
no JI55G<J0
!i o5i6n:toi>
10!>5IG2!»:RI
11 a5i&;s<>!)
12 9-5170198
K3 fro 173824
14 lJ.il77J^7
15 U51«10(;6
Iiifl-5l84fi8-i
17 ;>dl8tt2D5
]U051ftl004
19 05105510
20 I>-5l!)Dn2
21 Ui»2rt27n
22 9 520n:K)7
2:),9520!»8!t!J
24 9-52134afl
239^5217074
2<i'!»522(Ki.*»f
27|9r>2212M5
28 !»-ri227Bn
Dif.
:iGrt7
:«;(;<»
3i;.j7
3054
9650
3046
3«4:»
3010
:Mi3;H
3029
3G2C
3023
3f:i!t
•Mil'A
3r»09
3(U>(i
:vin2
:*5<i»»
3.'v:j(j
:<A'j2
3,')«9
:i5HK
Cosec.
M>41{7:i5ltl
MMi{(i!l!ll4
|fMJl«2o!*0
erseiis.
Tauff.
JJ 7:10:2485
;' 7;i7iii».'Ki
H 7377''7»
H73Ji.M02|9'i3«20l7
9 538til 10
95390200
953«97i!>
9 537382)
953771>20
95304287
29,95231383
\
»Tj234953
. 35 R2
3:
3:)7«
3o72
3570
3oy>5
9-0X18518
95242081
1) 5245(;4ii
_.9o24!}lJ»C
35 95252749
95266298
9-5260844
»-6a633«7
!» /i'2«6*!)27
9 :i-'704(:3
95273*J!*;
9527752(!
:i5fi3
3559
3.V.fi
.3oo3
3549
354f;
3543
3j |(»
:*.'.;*«
3.'i:*4
;i52!»
:i527
281053
jt-52HM)>;*; :J;-!,
f»52!»l(il4 '
1(5205 1 2H
a o20(J(;3H
9 5:102 1 40
0-5:fO5ti5()
!^.i3l2*;4D
:i5i4
3.ilil
:)5()8
:4o04
:i5oi
34mt
:i4»4
0.'.3I«143„ ..
953IJG35^{;^
95:123123
0-533rMiOU
95330090
95333569
953:»704l .^-.,
95:140517 '
3485
34H2
3471/
3475
Conine.
Dii:
»63!>8371
95402453
9540653!
9.'*4l0606|j,,-.,
a»^u«7H:'/*
9-5418747
10 48.'*«!^•U H73y20iU
I (►■Itt56'270 87400147
lO- 486 H;29 8 7407^(50
104H47983 8 7415165
10-4844340 8 7422064
l(»4H407(to'87430l5«
1 4837004 8 74:^7642
ll»483:i43l ^7445121
10-4029802 a-7JS2593
IO'4B2rtl70'8 7-t(;00.M» 95422813
l(» 48225ri3 8 74f;7.'i 10 954'2*>n77
10 4HI8:jm4|8 74741171 9 5*:iO;)37
10 48I531H 8 7*82117 :i543i!l04
lO 481 1/05 8 7i8:;857 954311048
IO4(tO809(;^8 7497290 95443100
I9464M490 8 7504710 95447148
1 4800M88 H 75 1 2 1 'Mi !t 545 1 1 j»3
lo 47372IW » 70I!»n4!» 9.'.4552:W
I047!):UJ;»3 8 752Ci)5« ;» 5459270
10 47yOlOl 87534:157 54*Kt3l2
10 4780512 8 7MI 7^1 95487340
104782f)2« 87549l.'»8 95471377
10 477I»:i44 K755fWI0 •t547.i405
I0 477.'»705 H7&038JU f»517l)(:il»
10477.MH9 87571202 !I51(|;U52
I4U708017 8757H(;23 !> 5487471
10 J705O47 »7''>»'':»7y U 541(1487
Oil.
4102
4o:(o
4(K*7
40!i3
40<>0
400/
40JM
Coianp.
4083
4078
4075
10-4701482,8 7503327 95405500
I94757!)in 8 70m>fi70 U 54!r!)5l I
10 475i:W0 8 7WM(O(»0 9 5.W):t5ia
I047501t04 8 70 153:W 95507523
i947472."'I 8 7022*W!»i0 55ll525
104743702 8 7ti2i»97r>|955!5524
104740160 8-7637280
I947:«:«13 8 7044591
10 47:1:1^*73 8 7«,M8«;>
I0 472!J537 8 70"'illB()
10 4720003 8 7(k;04 00
10-4722474 1 8 7073745
9 5519521
95523514
5.V27504
;155314!»2
95535477
9553945U
Ift-47I8947187G8I018 95J434:i0
I947154J3 f{7ti^l«284 ;J5oJ74lii
10471 ii#o:i 8 7f;y55 44 |ei 5.0:1 i38)j
10 47(MKmo' 7702708 55.'i53.'i:(
lO47O4872J8 77»0O4fi 95o5y:i27
I0'47013<i2 8 7717288 96503292
104(;!)7854 87721523
10 4004350
l04'nM)849
10 408735 1
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I0 40m>305
I04G70877
10 4073:102
UfAiUilfiiU)
10 4f;4i0431
19404{2050
10 405r»4l{3
Secant.
D-773I7V2
877:18975
8 77401
8 77r.:i .
3 7700'..'. ,
9551)7255
95:171214
95575171
4000
4O04
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105
4054
4052
4048
4045
4043
4010
4o;w;
4034
4o:ji
4028
402
4022
4019
4010
4013
4011
4008
4004
4002
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3997
MUKS
3!n8>
3080
3985
39K2
3:»70
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10-4*i302ai 98281*381 I002i;»2!)l*
10402017!) 982a7f;0!l 10024:1735
10 4023080 98286837 10 0214170
10 4017083 98384065 I0O244f;O0
1(» 461.1890 9B2B2292 10(1215043
10 4009000 98280518 100245470
10-4005713 082787H 1O024.W17
10-460I639 98270970 10 0246:154
I0 45«I7547 8275104 10^0240792
I»45mi46!i 9»27:t4lU KV0247231
10 4589304 98271042 100247070
194585:122 9 8269866 10024'IIOO
10-45^(1253 9-R2G8088 100218540
I94577l87l9'82663l0 I0024n!m9
1 4573 1 23) 98264632 1 024 !t4:iO
10-45600';"'-' '•"■■-■.:( ioo24;/H7i
194665011 ;| 19025031
10-466005-: J /.:.';i|IO02507ii4
I0-46»6000i962674l2 10-0261190
194662862 9B25563I 1 10 025 IWiiO
10 4548807 9 02.^:(84!» 10 0252082
Secant
D. Cosine. I '
10^4544764 9ir25'JO«7
194540724
I0 45:i(iOJtn
IO-4532IW4
10 4528623
10452451)5
10452O57tt
10 4516648
194612630
1 0-460861 S
10-4504500
I9450948f(
1 944^648 1
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10-4488475
19 4484470
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194476180
10 4472400
194468508
1944645-23
l944tM>54l
10-4456502
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10-4444041
194440073
194436708
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98240717
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190253525
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10 0254748
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U 8239570
98237789
98236002
982342 1 4
9112:12425
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98-2281147
911-227057
9 822.VJW;
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98214511
98212717
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lo^02:»(;i)87
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190256982
1002574:WI
I0 0257M78
19 0258327
1011-258776
10 0-250220
100259070
100201)127
■'.'1029
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10 0202385
10 02028:18
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43^1
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4:17
438
4:19
439
4.1.9
440
440
441
441
441
442
442
443
443
443
444
414
445
445
445
446
447
440
447
448
D975r;70l m
9»75«2fi5 69
!)9755«:tO 58
9 ;i755:f.>4 67
9!I75I!)57 56
9 9754:j2I 66
9 9764083.54
99753646 63
99753208 52
y9752769j5l
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19751891(40
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Covers. Cotaiig.
Dir.
982073;«Hl0 9263745
9 8->05.'i3.1 10 0204199
9 8203736J 1 09204664
104432745 9B20l9:Ht 100266109
10 1428781; 982lM(l 40 10 0205565
1 4424H2J) 9 8 1 9834 l' 1 (»-J0t;02O
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. : . ;..J9«I02941 109207390
19440!)(>2!I 98191 140;I00267B48
1 i U\M)m 9 81 89:i:«l l O 02*iiUUMi
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10 4:i!»7208 !» 8IM57:0 lO 0209*223
1 4:t!)3273| U 8 1 83!)3f ) 1 (r2(ft>6'.{2
10 4:189341 19 81 82 1 -2(; 10 0270142
448
418
419
419
450
450
451
451
451
452
452
452
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45:1
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454
455
455
456
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467
48
9 9751011
9 975057(»
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9 974908JIJ44
99749240 43
43
9 9748804
99748361
9 974791 8
99747475
99747031
9 0746587
9 9746142
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9;»744806
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0:174:19 1 3 j3l
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9 9743018
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70 De^^
I
308
20 Deg,
NATURAL SINES, &C.
Tab. y.
' I Sine.
\\'U22'j:i6
« :t4:Mi5!»7
»;3i4471M
I0|;ii.i7vjl
ir34.5(l2o2
lSj34o2'JH2
I3 34;»57I2
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15 31f;il71
1 7 :> M:fiii2H
18 :tiG!):^7
l!>;i472085
2rt :»474«12
21,3477540
22':UHni'ii7
2J :Wi2'J'M
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25134 HU417
2ti! 341)1 17:*
27|34;»:ii!;»H -'i;'*
2U3i;H;ii24r,i;V
ao 3502074 jgj^,;;
3604798
Dir
27:ii
273a
27:1
27a;i
27:1-:
27:t
2732
2731
2731
2730
273
27.'i<>
2730
27
2730
272!l
272i!
272a
272H
2727
272H
2727
2727
272(i
2727
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31
32 H&07523
2726
33 3:iI024K^7|^
34:«l2!i7oL;4:7.
3(i35184iu'''„
J/ 23
49
3521130
3523062 -i-,-J
3526*564 :':^%
2721
2721
352! 130(1
3532027
H53J74U
35374«W
;i:i4(ii;»o
3.>421*1()
3i>^'t*j30
2721
2721
2720
2720
•'720
:t-.4fi:t.2o-Co
»56lo7o.j^-!;
35.'i378f)
50 3.Vi(I.Vm
51 3:».'ifl22f;
52l:i5fit!t44
3 3r»(:i*i(J2
30tJ73HO
3670097
3672A14
357^^1
3678240
3&60tf(f4
3583670
Cosine
27 1 1*
2718
27 1 M
27I'
271;
2717
2717
2717
2717
271(»
a'i7;i7!«»
O«77o(;5
^574332
(m7i(;oo
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Ko 1 1 553
C.'K>fl(J27
(;5(m;io2
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(;50(KJ.'i I
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Cosec. Tanir.
2 U23H044 3«3I#70.'
2'!»214»W7l3ti421»y7
2I»ija3«|» 3(;4(>2!J2
2-!*H;HI21 'MA'.lhm
2":*l448y2|3<i52mi5
2!»12I703
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20075443
2'9»52372
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27474774
2 744;m27
27425120
27400352,
2 7375(i23
2 73J0!(34
3651*41*0 2 732(;i«4
3662771»l2 73t)1674
36CG«7!t!2 7277 103
!Hli9339 3W>rt37It 1 2 7252561*
1'-J*(hj(i34fi
2 8*f83;tOI
2 8*J(i0475
2'8f»3750»
3672(i«0
36751181
:«7«284
2722BO78
2 72U:«20
2 71 79204
2 7l54K2'f
36R25«
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2 HH(."?M:(8|3*;!(250O ■j-7r»iii;>23|
2 Hf) I6474 36I»5«(k; 2 7<'57«!)y
2^8«237«l*l36i)!* 112: 2 70:W513
2^8«on42i3702420 27(W)!*3(!4
2 8778532 37O572H 2 6:*«525l
2-875ft»(;i ;370!H)3(i 2';;*til 181
i 8733428 37l2:t4tt 2*;iK(7l47
2()710!*32 37I.'.*tj« 2«yl3l4U
2'8(J88474 37IUmi7 2 688UI!fir
2 8fifi«053'372227H 2 r»Hi52(i7|
2-8fil3*;70 372551*0 2f;H4l383i
8*121 324 37281(03 2 «M 1 75;i.vl
851*9015 3732217 2 »I7lt3725
2-857(;744 37:i5.vi2 ^*;7tii*t>5l
2 8554510l3736847 2U746215
Vers.
Oif.iCoMnt-l
64*15202 2 8532312 3742163 267225ir,
6492477 2 85101d2|3745479 26r;i>8853
6489764 3-84SB028 374879? '2 6675227
6487030 2-8466941 3752) 15 2-6f)51ti38
(U84307 28443891 3755433 !2^(i628(l85
0481534 28421877 37o«753;2 60045(i9
Ii478mil 2-839i(899 37fi2<t73 2 6581089
tf4 76 1 38 2 8377958 : 37C5394 ' 2 f,557(U5
<J473JIH 2 835i;u54 37W17W; 2ri5:i4238
i;470^il)4 28334185 3772038 2 6» 1 0807
64«7"73 2 8312353,3775361 2 8487531
6465252 2 8290556:377a685i2 6464232
6462531 28268796 37820lo'2 6440969
64o9JllO 2 8247071 37853.15 2 fJ4l7l4 I
045701m 2-8225382 378H<ifi| 2 631*4549
6454370|2 82o;*729,379lya)J 2 6371302
(ilol65U;2 81821 11 37953l5!2t;34827l
64489;i0|2 8 160521* 3798644 12 63251 B6
84462H '2 8138982 380197312 C30213(i
0443492 20117471 38«.'.3iri 20279121
04407742 801*5995 3808033 2 Oi.VOUl
.; '-vr' ,■■ ' .'1074554 381 11104 2 (lilUlltO
.i»5:il48 38l52II0;2 0210286
;io:ii777 38Uw:29|2ui874ii
8429903 2-801044 1,3821 962 2 8164571
842718<; 2 7981*140 :»t2521M;<2 0141 7'i6
0424489 2 7967H73 3828631 ^2 01 18995
0421752 279i(iK41 38319(i7'2 (;oy6j.>9
0419036 2 7925444 38353032 (;07355n
2 7904281 38:J864U'2 (;050l{Dl
^^'"1 0416321
Dif. Vers.
Secant. I ColHii. Taii'T.
10641778
I 0642905
I 064403:t
I 0645103
I 0«4«2!M
1 0847425
I 0(hl8558
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03:i&iim
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69 Deir.
20 Deg.
LOG, SINES, &C.
309
9-54 127-2
ai
!>-64l;*.V27
0-&42ti'J2ri
I
U 6a47462
» 535001.-,
9^5364:H7a
9^&357633
9-fi»6 12041
D-53fi4:.H7
9^637 Itiit'
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'l Sine. Dif. Cosec
H4(:u
34 bt;
34(i;u
;j4f,7
:i4r>4
:t447
:i445
3411
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9 54024H!I
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9 5543292;
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3293
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l0-4'wl»4a3
[(^4iiiilU\\4
I0 4(J52:)41I
l94G4IMI}i5
l*>-4(>i:.fl2.'i
1U4U3U714
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10 450751!
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104580473
10 4677074
1 45731579
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I0 45<;(;fi!f7
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1045(:m27
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10-4653370
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10 453061 1
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10 4523107
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1 4.-, 13073
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I0 4f^03O»J5'
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l<U49:tOft4
l044H97fi3
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IO-4470flWi
104470500
10 4473199
10 4409K95
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104403290
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Covers,
TmyfT. Dif. Colany.
9 5010059
9 5014566
9 5018515
9 5022439
9 5«i2<i:WJ0
9 50:t0270 ^
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3929
3927
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9-6638107L,.,,
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10-4090131 8-8972:$OI 90200932
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Cnsine.
Dif.
IO-4tHI3l44 8 8978532 902(;-l454,... ,
lO-40tM»t51l «8y847.''7 902«7973i'*;,:,
10 40871 77|H8y:»o;»7« 0271401;::;,;
1 94084 1 ui ntiUW; 1 04 »;275(HHi j ) '* *'
10-41181 220|/f90o3400 9 0278519 **'"
Secant. | Covers. | Cdtanf]^.
Dif.
I03739008
10373.5540
103732l>27
103720509
10 3724904
1 0372 1 48 1
Tanp.
9791fl3<Ht
970 104 13
97014525
970 1 2037
9-7010749
9 790085')
970o(;y7o
9 7!Ki507y
9 7903188
97901207
97Hyil405
!^7H975l2
9 7095(;l«
97893725
9 78!»1B;MI
7Wt9{J35
9'7'«tH039
9 7080 1 43
9 7884240
7082348
7H8045<t
97070551
07870052
9 7874752
07872Jt52
97870950
97801H>49
9-7m;7i40
9-78fM243
97O»;3340
9 700U:MJ
9-7a5'*53l
97057020
97055720
7053813
9705190*;
;»7849998
97040090
Verseds.
I0 032tt:t4
10 0328852
I0 0320:{03
100320075
1 0330381;
IOO:W009!*
10 0331412
10 0331925
100332438
10 0332952
100333407
|O03:i:i902
10 0334497
10^0335013
10(1335629
10^0330040
1903;«w03
I90a370}10
100337590
10 0338HO
IO(l3300:Vi
10 0339154
10-0339074
10-0340194
10 034071
10^0341230
100^1757
100342279
10 0342801
I0 034:i323
10 0343847
100344370
1(M1344894
10 0345410
10 0345943
190.340408
100340991
10 0317520
IOO:i4JtOJ7
10 0348571
100349101
10 0.'M9029
ini»:t50I57
100350000
I0 03.'il2l5
100351744
IOlt:t52274
10 0352805
100:153:1:15
1003538<J7
|0 03.)4:HO!
1 00:15 493 1
!0o:i55403
tOO:t55990
1003505:^)
100357003
HV03:.7598
Ioo3;>8i:i2
H^035((008|
190359203
100359739
O.
511
51i
512
511
513
513
513
Costne.
1T907T059
9907 II 18
90700*3
99070125
90(;0014
90009101
9 9008508
99000975
9IM;07502
99WJ7<t40
'.t 900G53:i
9 900f;o|8
99005503
613
514
515
515
515
510
.,^190004987
"^9!M;C447I
517
517
518
518
519
5 19;
620 1
520 i
521
521
M;C447
9000:i954
90oi;:m:*7
9000'2920
9 9002402
<9 900 1 884
'9 900i:$4*5
;90000840
\*j *>of;o:i2U
9 9059806
99659285
521
tf966«7A4
9 .0058243
9 90157721
i99ri57l;»»|32
i9y<»(;077^l
[99050153 30
522
524
523
-„j 9905503o|2fl
?r»jl9!H;55100 2fl
J',';;l9!*f;545.'{2 27
."? 9 9054057 2(i
","9lH»5;i632'25
■;"'99(is:ioool24
520 1
!9 9(»24B0 23
99051953 22
527
??2 '99051420! 21
" ,'. 9 9050809
„" 99050371
,:-,f, 9 9049843
529
5-29
>30
09049314
0904078.-1
99040250
'"V 09047720 14
.';" 9047195 13
(904W05
5:111
532
531
53:(
532
5:1:1
5;t4
yxi
5:15
5:u
530
h'Xi
530
;99fM0133
91»0450<t2
9 904.'>009
99*;44537
9 9044004
9-9t;43470
9 9042937
9 90424(»2
9041808
9 90413:12
9 9f^l0797
19 9040201
Coscc. I D. I Sine.
67 Deg!
i
d
314 23 De^,
NATURAL SINKS^ &C.
Tab. 9.
Sine.
:i!M.V14;(
:):tl(toi;i
Oil.
2678
2«77
•2tJ7c;
Covers
Cnseo
R093titt9 i 5ri!i:t047
aMWOUi2 5.*i755il
Tnnjr.
4*J4474«
42JBIH2
Cotanff.
*2;tri.'i».v-M
i* :t.'.:i'.i4H:i
42alfil6 2Xt20itiU
42a/il».'il
,., .^ finHl»HI ■Ju.'i-JSKU 4'jr)m)J7
i:»-j(M;fij,;; /' v«;i»7ii:ntj :^.'^-.|^.^»;?|(» 4-J'il!i2i
-*''-**'*'' h;07(i
:W2G047L„^
3a2tt722i:; :r^
:mi:i:»7':':'j
Jt>74
-Ni74
3!)34071
(i(»7(j«;:;fi 2 rj4iijfL'j;4 42(;j:i(ii
rti)7:«»:>n 2 :.47m) I s 4J«fi(iO(i
co7i27^rj54o:v.7i,427J2:$ft
<i(yi(j«o:i 2 04:m2>'ia 427*i*(8(t
limif>;»2M 251IIW«I 427!H*JI
5I01«!U 42«2:.(j:i
mi4:i:^ 42n(k)u,^
au3*»4liii.t !'':tJu(io.jHi 2;i:
,20741
3!1421W:J|. i«W.'"i71»07 2S3y72:i8 42mU4!>
:*!)447f!« r/^:: m:*o-i^t 2Vp35IMMH 42;»2iJ94
;i!»474:i:» ;':':; i;ii:.2;.(n 2:>:i:*2Kn:i 42y«i:«!>
i!»J01 1 1 : !lr. *»"4!Wi!l 2 5:iKi744 42:jy7B5|2 .T-V.fiy?-''- 10(!(1.V.>2<: 0(U:*2:i7
23jVU4KI
2:i4U2.'>I)*
■J :t4u;t5»2
2-3444{J72
2 :W2ii787
2 34afiif2H
2 :i:t(utoii6
2 :«oo6o«
2:t:uu748
2a:U3oi7
2 :f20431 1
2 :*27.'j<i:«t
Secant.
Vers.
07D41).'il
07:'7
iiT:'
1 oji(>j(;<)4
1 ntl041»4fi
I-ow;m:i7"
I (11170:1::
I ■OH7:i024 0803*127
1 OK74:}75 ()MU<Nm
Dif.
IOB75727
10H770»0
1087tM35
l(Nf7U7&l
I0KK114H
1 mi\:\iU'tii
0805212
(1807501
0aU8G47
()m>!)7!i:t
(lj{|ih)4ii
<lHl2(lIUt
'Mi!i'27illi\i*'l'i *il)472 1 7 2 :i2;m«:*ll 4303232 \ 2 323H345
3a5a455|.„4- W)44d4o, 2 62ai64l|430Wi80 2 3211*740
3f)-"iKl27!., .- '6041K73
:i:*(;<j7.''»c;:^' <;"3!'20J
:i!M:34(;)[ :.:'', WMi^ysi
3;»7i47y
3074148
307'iHI8
307041U;
3982155
3964823
3987491
39901 58
*y92H2i'i
'.rr,\
-.'■.2f;447H|43lnl2It
62*7^^0 43I3A71'
n2:«M2(i,4:n7o:{(t
.- «i»;i:*8(;i,2 52i:i4;m432u48i
:J1" «03I \Ul 2 5IlM;47ii 43J3;a3 2 31
iliiy *'"-"^-* 2-5179037 4327380
•2r7ft ''1>'2A852 2 fi I (^2fi24 1 43:i084rt
•In-H ''*'*'^'*' "^ - ^ * ■*^' '*^ 4334295
o*! 'ft *>l»205l4 2ol28H7l 43377nl
2f;«8
2Wi8
2(;«7j
26C7
0017845
OOIAIJ?
00l2otia
6009812
0007 1 75
399&J92|.7' I/. 6004508
3998158-'!^:* 6001842
400lOi25;^ 6099170
4003490^6996510
40061 56., --,16903844
4nOHK2|l-'7^!ft99n79
40ll4)t6l';"™591HC.14
2W/4 -
2-5112032
250:t.VJIfl
2 5078428
2A0<n663
2 M)4 1023
434 1208
4344665
4346124
4:*5 15B3
4355043
4UI4I50
4016814
4I>1947»
4l>22l4l
i 024604
40274U7
46|4u:ti>l2:)
47 40327!*1
46 4036453
49 4036114
504040775
51 4043436
52 40460*16
53 4048750
51 4U5141U
56 4064076
56 4066734
57 4069993
58 4002061
60 4067:m;6
2664 V
985650
2664
26r.3
i9U3l6(i
5UU0522
,,-03'5977a-,.M
2663
»;(75i;i(;
■>:t.3
2ey|5!KI454;
j^: 15959225
Hum ■^!>-'t.^64
2 5026207 4:t5 8504
2-51)11515 43619611
2 4994641(14365429
2-49782U4 14366893
24901586 4372357
24944901 4375623
2492tM2l 4379269
2 4911674 4362756
2 4695;t.j2 4366224
2 4676654 14361*693
24662:M10 4393163
24H4592!I 4396631
2 4629503 4400105
24813100 44035/8
2 4796721 ;44O705l
2 4760:U»j 441 0526
2 4764034 4414001
ir 4747726 4417477
2 4731442 44-20954
2 32011601
2 3162606
2 3164076
23145571
7092
2 3106637
2 30902061
2:*07l60li
2;«»53420
2 ;*0350*i4
2-3016732
2 2999425
2 2980143
2 2961685
2 2943651
2 2925442
2 2907257
2 2869*396,
22870959
22652846
2 2634756
2 281(;693
2 2796653
2276U6:«J
2 2762643
2 2744»;7l
2 2726729
2^2706807
22690:h«»
2 2(i730:i5
2 2655184
2^2637;i57
2-2619554
I 081UI56ir
1-0867952
10889317
10«!K)662
1 08;»2050
1 06934 IB
r08;i476H
1 0896159
I0mi753l
I (»6!0i904
I 09(»0279
1 0:M)1055
1 09O;iO32
10904411
10tm579l
10:>07172
1-090M5.'>4'()}1321Ut2
1 09<Kl!l36 OJCttOC.
I(K»11323|o6;i
109127090a;''
08l438tl
(I8l55:i6
Ofllf:'"'":
08 1 :
061!
062l»l45>
06212;KI|
082245-1
06234>O!»|
0624 76f>
OK259l'3
I0t27011|l
<t82a24o!
0tf293;n»
08305(iO
0631721'
10914097
1<»9154«:.
HK»I6876
I 09lfi'j67
I09l06.'»9
0H375H8:
06:01703
0839670
OJMI037
0)t42205l
Cosine
',' 5953904 2 4715I6r4424132j2-260lV73,
.'^,!jr 5951244 2^4698943 4427;no ■Ji»564(H0
.'i/lRft!5946584,2-4682729,443i39Ul2 2566263,
iG&9\ I
5-4«l5945925 2 4666538 443467112 25485721
^^|6U4326f] 2 465037 1 14436352 2 2.^30865
Srf 6940607
.>«&-? 5!»3529l
'**^^!6932e34
Dif. Vers,
2-4634227 4411634 2-2513221
2-4618106 4415316 2 24 9556
2^4(W2006 4448602 2 2477i>62
2^4586933 4452287 3 2460366
im»210A3mi43374
1-0922446 0844544
1 09231145 01145714
I 0925-243 '0846665
1-0926642 084mi57
I 0928U42 Il8492:i0
1 0929444 0850493
1 0930646 0851576'
H«)3225i;065-J753
1 0933656 0653928
I09;t.i063OK55]O.V
1 o:i:Mi47l 06:.(i2»2
1 0937660 06.*746u
1093I»29l]o856639|
|-f»940702 06:);i8l9
I t»;»42116 06(;09!t9
1-O94:i530 06(;2l8l'
1 11944946 <1863n63
r0946:i«r3 <»864545,
1137
1 i:i:;
1142
1143
1144
1 1 45
1146
1146
1147
1146
1149
1119
1150
I 154
1155
1155
t 1,.9
I I -.9
Ittil
ll'll
1165
1167
1167
llt;6
1109
1170
1170
1171
1172
<'n«:in#.l '
:554i
9I9J499 4V
'.1191353 411
9I6IIG4 42
"' " ' *1
91 773 16 36
9169440 29
9t02
9lfM
'.1 '■ ■
462 aa
--•7 22
UlM'A
.■26 lU
9 1 55
9154
9153
156
^66
115
17
Hi
1 p.j^9l5lll43 14
jji;,|9l.Ml770l3
1175
1175
1175
1177
1 ,
ii7:t
1160
1160
1162
1162
1182
9149597 12
9146432 II
91 47247 10
•.tHiU»'J2 9
'»5 B
3 7
>iiJ G
91413111;
'.* 140181
9l3iKl01
9137619
9i3tn;37
91:15465
SeciiiiL |C()tan.| Tonir. | Cosec. lCuvcrs|Dif. Sine, j* 1
60 Uejr.
23 Deg.
LOG. SINES, &C.
6 I :j
Sine.
» 59 18700
9 5921765
9-69247S8
»fi037a9B
9-5030666
9-A833(;3l
6t9-A(}5G51M
Dif.
2975
2973
2970
211 C^t
20«6
VJiiX
7,0-503a665
8yft!»425IHLf;'?"
n 9 6l>46-i(i:.. ■;;[';;
Mi9f.y5i:»7;ii;;^,„
12 9 0954322 .";;,:
2940
Co sec.
&5.')57268
9-5!)C()'212
9-5063154
&59G9003
9-5909030
9 5971065
0-5974807
(►6977827
96980754
959B3<;7^»
9-69066(f2 ;
2944
2942
2030
2037
3035
3932
2930
2927
292^1
9608U523
2923
2921
'2918
fr599244II^,.
^ftoosso;!.;; I;
i^«w827oi.h;J';
S8»0OO1I8L!
fr6D04U!M^
9*600<t9!>7
9-6O09901
OGO 12803
06015703
9 0018000
9^602 1 495
9^24388
9^6027270
1^6030 100
0-60a*i052
9 C035930
9G<»3eHI7
OG041G90
0-6044573
9^6047448
!M;ii;>;ti:iit
«8|9-605892»
'2Mm
iWl
2904
2902
2rMM»
2m»7
2895
'289.1
28iK)
2808
tifUUl
28fi4
28^11
2«79
2«77
287:*
2(t;2
•jtr,o
2H63
10 4081220
10-4078245
10 4075272
lO-407i'302
104O09:i34
I0-4O06369
10-4003400
10 4000445
10 4057487
10 4064531
104051578
10 4048827
Versed s.
8 9003400
aoofKmis
8 90 I 5H 10
81MJ22IH3
8 9*12(1207
H9y:t439f.
8 9040579
8-904 G759
89052934
8-9059104
89005270
fl-9<)7U3l
ia404507« 89077588
10^4042732 8 9083740
10 403.')788'8 0089887
l0 4irMii\iG^HU0Ur,(}'M)
1114033907
10 4030970
10 4028035
10 4025103
8 91 02 1 fill
8 910B303
8 9114432
8 91205.17
ht-4i>22I7.t 8;iI2WJ7«
Ilt40l!i24(; 8 9i:i27!l4
l»4nl(;321 H9l3B90:i
104O|;i3'.l8 89145012
10 40l0477]89l5in5
Tang-.
9(;27«ol9
9(J2H2(»31
9 (;2H.Vi40
9 fi2K!»048
9ti2J«.*>53
9t;-29f;i)57
9 0299558
9 0303058
0630055'!
9-631006
0631354
9 6317037
9 032O527
9f;3240l5
9 03*27501
9 »j:«i»9Jtri
;MJ:134408
9t>a37it48
9 0:i4U-26
aC344903
9(j:i4H;j78
Hi:t5t850
!ifi:i55321
9 0368790
9 6362257
Dif.
:i.M2
:t5uy
3506
3505
3504
;15U1
3500
3498
3490
3493
3492
3490
34tf«
34Krr
3i84
.'WB3
3480
Cotan^.
10 372I48I
103717909
103714400
103710952
10.1707447
I0 3703:i4;i
IO37U0442
10.3090942
lo:w:9:«44
10 3(i89948
I030or;4ri5
I0 3CH29C3
103079473
103(J75985
1O307249J
Covers.
9 78.'W715
9 7832801
9 78.'MMH(8
9 7828973
9 7827058
9 7825143
O 782.3220
9 7821309
9 6.365722
9 6309185
9(;;i7264ti
9C37«lt«
104007559 89157213
1(»4(H)4043 a91G330<;
I0 40<>1730 89lf;931KJ
10 39MUJII9 H91754W0
1 1^3.7;*59 10 91815*; 1 '9 o;t;9ritNil
10^3993(»03 8 9l87<>30j9 6:iU30l9
10a'W0099 8 9193708 9-6386473
10 3fi«7197 8 9i9977-''|9 038!t925
io 39H4J97 j( :i2(»,'»«:i7 :m;:i9;«75
10.3981400 8 9211895 9 0390823
10 3978506 8 92 1 7949 hi 64O02(!9
1 0-3975(; 12 922399t» ]9*>'*037 1 4
10-39727-22 H 92.3<k)43 !^fi4071.'tO
I(r:i4;(;9ni5'9 7819392
|»300,V.32 97HI7474
978l.'i5,'io
9 7813034!
Secant ' D. Cosiiu". I '
io:i(io-2a.s2
:r:Z- 10^3658574
J47y
10 3655097
10 3051022
10 3909834 8 9234;o84
103!H*»(>'.M8 8 0242120
10 3JHU004 09248 152
I0-3;h;1UI3 89254179
1 395*004 1 8 92t;0*2< 12
» 0001 786
9 6064647
96067506
90070302
9^*1073216
9 0070008
9-0078918
9 00J{lTt»&
9(J0lW(ill
9 0087454
9(*OiM)294
900!t3l.33
4t
50
61
52
63
54
55
56
57
58
59
60
' i Cosine. ll>ir
2801
2859
2850
2854
2852
'2850
2/147
2810
2813
2«40
2839
10 3955427 a r/206221
10 3:)52552]8 9272235
H»^394iMiao 8 9278245
l0 394QtIo'8!f2)M2:il
it 04 10597
9 0414031!
9*J4I7473
9 04-20908
9 0424:i42
9 (1427773
9tU3lJ0:i
!^(;434i;31
90438057
l(» 3943943 8 92:10252 l9r;44 148)
10^3941077 8 9-2'.M;249|9 0444903
10.39382Il'8 930224219 C448324
I0 39:t'».353'8 9;«m23l 9 0451743
1*^3932494:8 9314215,9 045.JlOtl
10 3'»290:W
10 3920784
10 3923932
10.3921082
I(V39l82:i5
1(^ 39 1 5.389
10 3912540
89:120194 9^0458575
8 93-26170 0-0461908
8 9332141 '9 0465400
8 9338l08'fK6468dl0
8934407090172217
8 9A»0< ►•29 9 Oi75(;24
8!l35fi!Jl(;i 9*J47902H
3475
3472
3471
3409
3407
3405
34 (;3
3401
3400
3457
3451,
3454
.3452
3450
3448
3446
3445
:i442
3441
:i43yi
I0 03,J9739
Iifn3(i027i;
I003WI8I3
io-o3*;i:{.'".(»
I0((3fil888
ioo;i(;2i20
10 0.302904
10 0363504
100304043
100304.'i83
Ioo:to5i2:r
10 0.305 (i04
|0 0:i002(K%
lofl.300747
lo()30728;t
io»;m;7832
10030H375
I003089l8i
10-0309402 1
IO-037nW)Ol
537
537
537
53H
5:ui
538
540
539
540
9 9040261: 00
!(9*;3!i724'5f)
9;«;:j91«7 fifl
9 9*k18*;50 1 57
9W;38112'56
91Mi37.'.74|55
9037036 '54
ft90:M;490 53
99<f359.')7'52
i9 9(i:v.4l7;5l
^j"9 9<i34K77 50
t*: y-96:M3;Mi:49
9963.371*5 48
641
542
In9033-253|47
;'J-|9 903271 1,40
'/;: |U9*k12108 4.1
•7*19 9031(125 .11
644
IO304(i|.')0;!»-78o7875
I0:WI44679 978059.-.3
I0 3()4I21U 9 78(^4031
7811716
9 78097;m:II(H)370551|
100371098
100371042
100372188
544
545
545
9!H;3I082 43
9-9630538I.I2
9f»629991 41
9tKi 29449 40
Ml02iUMM 39
^■*'i|9 9028358 38
103037743
I0 363427H
10.3030015
li'3027:i54
10 3023894
10 3020437
ll> 361 0981
103613527
103010075
I0 300(;<t
I0 3ti03177
10359973
103590280
10 3592844
10 3589403
I0:i585904
i|i:J(| 10 35825*27
•"■" IO3.-i79092
10 39o;>7oo>8 ii:w;i :*;« *► 0182431
lO390(;8)J7 8 9:m;7M78 9(i4*15M31
3434
:m31
.34:to
3428
:w2«i
3424
.'U22
a42i
.'m9
3417
3415
:ui3
3412
:uio
3407
3407
3104
3403
3400
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( overs.
r.i anir. Dif
io:i57.'i0.iH
I0;i572'227
lo:fc'i*iii7;i7
lo;t50.^;i09
10:i.*.01U43
I0355«ol9
io:t55:K>97
I0.^wl(J76
IOX*>4H257
10 3544840
to .'554 1425
10 3538012
10 3534000
103531190
IO;i527783
10.3524.370
lo:i,V2n972
I0 35l756;i
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Tansr.
9 7802108 l(^03727 34
U 78001841 1(H>373281
9 779820(»ilO(W7:i828
9-779'>3:i5 I0(t374370
9 77944 hi' 10 0374924
9 77!t24H4l 100375473
If779055a I0 037(A)22
»7788*rao
!) 778O703
10^037(1572
I0(»377I22
977^t»77* 1003771:72
9 7782845 10 0378223
977801(10 100378774
9 7778985 lO(W7932(i
10-0379878
10o:Ut043I
IO0:i8<t984
loo;u{l537
10 038-^091
U»0:Ut2l>4'i
lO038;i2O0
loo;ui37.j5
10 0384311
iO(Km4iW7
10 0385424
9-7777055
1»-7775I23
9 77731 91
9-777 1 2.18
!#-770y325
^^770739l
!»77'hi457
9 77o:W)2i
•^77*ll5lWJ
9 7759(;49
{(7757712
97755775 I «0iWl'''980
9-7753836' 10 0:WU>.»3II
9 7751898. 10 OlPtjnOC
i 7749958! 10 o;w7ii.Vi
9-774)tOI8J10o:{882t3
9 7740U77 H>o:t**8772
9 7744130 10 0:ut9332
9-77r-'l94 10-0389892
977402.V2 l0O3iH»452
977:10308 I0f»:wliH3
9 773*;:ie5 100391374
I 77344-20 10 039SIM
97732475 I0 0:i93606
546
548
547
547
.'148
548
.'>49
549
550
550
550
.10 1
551
552
552
553
553
653
554
554
555
9 9627812 :q
9 90272*;0 36
9020710.35
9 90'20172 :U
9 9025024 i;t3
.4 9(;25076 32
9 9(;24.V27'31
99023978130
9^9623428129
9 9(;2'2878'2a
9 90*2*2328 27
'»y(;2i777'26
9 9621220 25
9 9620(;74 24
99620122 23
HiWtniiit 22
Verse<ls.
565
666
550
557
55*1
558
558
558
559
559
560
500
5G(»
.v;l
501
663
662
t90l9<JlO
9 9018403
901 79* »9
99017355
1^9616800
&96 16246
9 9615689
l(iH:i513:{
!' 9014570
IJ 9014020
!MX!13462 II
900l2!fO4 lU
t!»0l2.341i
9-Wi 11787
9 9611228
9 !l0lO6fi;i
9<HJ10108
:iit0i);ir»48
:» ;HU»ii>87
;M)*>ia42l{
ft'>*;o7K04
I»!Mi07:H»2
Cosec. I
D.
Siitc.
60 Deg
316 24 Deg.
NATURAL SINES, &C,
Tab. y.
Sine.
•1071M124
107,5:1:1;
4o77!»i»:j
l-KKIOOi!
•iun:i:t():
4niMi677
4ii)imi:i
11 4iiM.'i:Mi
I'»l-1|I)7IM!>
I7)'in::iit
so
21
|2i
4II5U4
■<n77'.»-'
•il-Joi4.-i
4l2a7ia
4i?H;rK-.
4131044
Dil".
Covers
.^!'.';.!5»->7:n:.
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-'■.•:u!>-^:2(i'i7
.,,..,' UWI404O
.,.,-, o.'H \Ml>
" * MK»H7;n
2(m4
2(;.'>4
2t;ft:i
2(»3
A!M»;o77
6fio:(4*i:i
6«H)770
58D8I17
&IlU54«i4
Cosec. i Tung:.
_>4{.8:.;ia:ti44.wji{
2 4.'>«:;aH-jU4.v>77;i
-J4.'i37J{ll('44(;-J7l
im:>2Uu;.''> i4(;(jj:)o
2 4.iO.'itM)5j44««7-Jli
2 44U0tM;»:4473'2Wi
J-447iO.'.4 447«708
J-44.'>Jl|f;a'44fiO-JOO
2-4 4422U4l448:u;y:i
2 44>«44K'4487187
2-44hM24;44»<KJa2
243»482:i44»4178
>-4:i7!M»4-| 44Di/!7."»
2^4;t<;:t2ii:i'4oOi]7:i
;„:; .'sm>2«i 1 2 4:u7:»:m 4.j04(J72
2»j:>2
2(;ji
oj[l7t
.'iHH7,'»(tii 2r^\ 6 1 Vi, 45 1 1 (j7-j
:A8IM»6(J
4i:u::u2
4i:ii[:j!io
28|4lll«.:t8
2:/4l442tl.'i
30
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4l5222fi
41541(72
4l801tf:t
4\G2mH
41GA4&3
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417''<»*-*8
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41 8131 :f
4Ih:v».v;
4llEf;.VJ7
4 1 111 880
4U4]<^4:i21
411^71 ('t
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420244 1
42o:i(tJiu
42077 1 u
42IO:(08
r.M:i(K*4
42I«L'72
68 4220!Hlt*
.*»!» 422.t.^4l
(>0 42J<ilti:t
Cosine
28-18
2846
2045
3044
2844
2844
2843
2fM3
2842
,,,.,„ 5818887
-:j,,:.8l804i
.•:^ '!.v.i;u«:»
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3»:*!I837
5a;t7Ui2
5WM547
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r>«2!»251l
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.'>H2:«)72
&82)32»
2840
2840
283!)
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'2u:v.>
28:i8
2838
28: t8
20:17
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6800|;»!J
.'»7!i763y
i»7!l4y20
;.7;'228i
:i78U(^i2
,>787U04
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-.781728
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.'.778 IM
.-.773817
243004894ftl3l73
2-4284844 4618078
2 4280222(45221 7!>
2 42.'i;«i>2 4r»2.-.(i8:t
2 42:iJt044 4,'i2!M88
2 42224881 45:f20:i4
2 4-208y54|453820l
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2 41751152 454:i2
2 4180484 454872(1
2 4U5(i:t8 45502;tH
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2^4I142I0|4557J83
2 4(»*)882y'4.'X;0778
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2 4(m;8I32'4387«(>I
4052815
2-4<K»7520
24022247
240081)95
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1 :i;i78555
2:f!)8l387
2 3!»4820l
i'3J(31055
2 3015»:tl
.' :ji»oo828
.':MI85748
i-3870*i85
i 3855845
457132
4574o:ii>
4578367
4581K77
4585;»1>7
4581Ufl8
450243!)
45y5D82
4d98488
4G03011
4006537
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48135f)l
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2;»84O825|482084l)
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2 24427'J'i
2 2425247
2240772I
2 2;(t)02m
2^2:i7.i;3H
22;i652]WI
2 2337845
22:120433
223o:(043
^224(5878
! 2288:131
2 2251000
2223:i7li!t
218432
2 21 ;i;i 177
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2 214/545
2 2130371)
2 2113234
2 201)5112
2207MOI2
2 2rHii;t34
2 2044878
22027843
2-2oioH:n
2-|'J!):i810
2^1878871
2 i;i5otf2:*
2 1 'J 421)1)7
2 l!J28l>5)3
2 l!)01»2lO
2 1882340
2 1375510
21858801
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2 1825119
2 l«OK:i*M
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Sec.int.Vcr5. I Oil'. Conine
10U4ti:!-
I 01)47;
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I 01)50822
r 005204 4
I Ol)6;i487
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I 085831 fi
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I 0050174
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i*U8:i284
08704 71
0871858
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0878418
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101)735:1:1
100741)78
I 0078420
1 oi)77;(88
t oo7!i3i:t
lUl)UU78J
1 0»8221 1
1 )Wi:»;*.'2
I o;ui:<i 14
I 187
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18:18772
lt;42B|44
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121H)
1201
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1204
t20 4
^lit:fJ3J,3A
!>lUMU34ll37
9I(X;«37'36
2 1774020
2 1758229
21741559
2 1724011
2 I708283
2-1801877
2 1875091
2 1854(527
2-1841983
C25480
2 1G08958
I'". .,
1 ODOOKU)
1 0902305
UYJUWmn
1 oit05ni7
I n9!**i77!l
I 00;iH243
1 000971
1001 1 ;
1 iiMr2ti4i
I 100411:1
I 1005584
0001594
0902801
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OiKi52 1 !f
0!M»8428
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1211
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0!)I37(»3
Vers.
2:K(25827 4824179
2 3J{I0850 4827710
2:1705804 U;:il243 2 1592478
2:i780758;483477*''-* l'i7W»l5
2 3785tu:i|183it3l0 2 I55!*575
2 3750949,4841845 2 1543158
2 37:18075 '48 J5382 2 1 526757
•2:1721222 l'18'tl't 2 1510:178
237<»8.i1Ht If .J 17 2 1404021
2:t80l57Ji li..'..'.;i:')i 2 1477883
2:1878787 4059538
2-3*i«20I8 4883077
Secant. Cotati.,
2 I48i;i88
2 U4.'>f»);o
Tun-
12 U
1214
1215
'11216.
::::: 1217
/3*.l ,., '
0918134
I HM)8o29
t 1010004
l-|0ll4}loOtH8'V>8
110l2O57iO9l9788 '
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I-I0I50H, 0922225 ^^^
M01730rlo't2:i4 48^
1 Iiil8fi7 '
il02o:v
1 loiM-ii
I |tt2.l.<
1 1024H
9085002 ill
I-'*
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I 1028313
I in27iM(:i
I I»j;t-'!t5
I in:iM7-'f''
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.'i:)22
Cosec. Covers
122);
1229
9(K1!I3I5
h
1
1
Nine.
65 D
«-'^'
'24 Deg,
LOG. SINES, Slc.
317
Sine.
10
II
12
13
U
15
If;
17
Ms
19
21 >
21
22
23
26
»7
2n
2y
30
31
32
Xi
31
35
3«
37
30
3!1
41
42
43
4
4/>
4«
4
4ft
4ft
AO
Al
ff3
»S
54
Sj
5(i
.''7
All
(i4l
!i*ii);»3i;i3
!Miio44f;ri
:*(;ut72:»3
»f;iiuii»
Dif.
aKHJ
2H34
2lt3J
2K30
2«2/t
2fl2
2023
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IHIIlnJ.:--^:
2812
2»I0
f>«i242ii;j" :
a(ii27023* ;
9 0130833
9UIS2641
!ICl3.-.4lfi
!»«l3?iJ.-.n
OGUlUOl
I)ltl43a50
2H(I0
1 2Hf»;»
■J8'H
;27!>!»
t27U7
^'H4fi047'^,j>j
y(;lr)2234i;Ifj;
•'«'■'-"-•' 27«8
27K7
2733
2782
27811
2777
■i77-*i
CoHec.
10 3^1-1031
IO-3!h>ll!(7
10 3m»*to3.»
I(l3ft;(2707
1 U 3K8U81I2
10 3887069
i»3«H4238
1 3881 420
l0 387fl«O3
]0 387ri78M
1 3872977
iO-3«7ni«7
IO:tH«7351l
I0 38fi46,i4
io-:iiifii7:»o
crs
cds
8i»3i;7»7H
11!*37:WI9
8 M7!t7''«
8 lKtlt.>(jit!t
8!t3;il'fl8
Tntiff.
9fi4n:>83i
9-(;-iJH»23l)
Dif. Colonjy. Covers.
89409378
8 94tri2<K>
8 9421197
8 9427101
6 94330(Ht{9 0:>2:il
943889,:-
.4«,„'IO■3.'iNlf;;)!(77:^247.-.
'wil I<>'**510770 9-773<»o:io
9 (;i92(;2Mi:J::' . lo :viii7;t72 :^7728.^.M:^
9(;»9WJ3|:"; J I0 3.'io:tit77 9 772^'(i3t;
9(-J994I7 :!:!; , UKlo(M»r.)i;t !^7724(i89
'**''" 10341)7191 !»-77227ll
...,_,.. 3493(1(11 » 7720792
,33«a ■
9(1509587 ooo-fl'* 3490413 !^77I8H43
8 9397o42 9(;0(»28tJ9 ;.:',': 10
Q 9403402 9 (;.mm;i99 *;:^"; lO
9-«l.'i7yi2
y6ioo:»9i*
9 CI 03382
dill CO 104
9^103944
9 0171721
!h;i744!)o -:;■'
9 01772?),]^^ J
9eim»04i .>.,.„
90I82H0!! "ij!"
9oi«.v.7« -^.;
!hfjiii8:uii.";i!!:;
9oi9ii"3'r' I:
9 0111:1804
9- G 1 96032
90199378.;
2758
2750
754
9 02021.321.
2750
iH;204f)H4 .*;ii*
902o;o:i4
!^02l0382
27-18
2745
2744
41
9 0213127
i-0215I171|;
9 0210012.,
9 022i;i51 "i'^r
9^0224(018;-^,];
!>-G220«24 -J™
9 C22955
!) 0232287 .ti
2r,M
,2721!
2727
9 0235010
9(;2377i3
;»'02 10400 ^^L;^:,
9 0243l90j:'-J
J^C2lo91l|' ,„
9 0248029l,,^ -
9 02:>i:i4o!-i '
9 025-l(M.O|5^ 1
!* 02507721.;' ;
9 0259483 ' "^^'
Cosine Dif.
10 385^1.949
10 3850150
10-3053353
|0-3]l.'.(>551f
10 3«177(:fi
1O3H44970
10-381211(11
lo:i83940I
I (» 38300 18
nt38338:t0
I0 3831lt50
IIV 3028279
I0;i825.-.04
10 3JJ22;30
I03fll!»ii59
I03H1719I
10 -(814424
10 3811059
103008897
10 3800130
10 3003378
10 3m)0022
I0 37978W!
10 3795110
10 3792300
10 37H90I8
1 3780873
1 3784129
Ift:t78l:W(H
IO377H049
io:f7759l2
I0 377317«i
103770443
1 037077 1 3
103704:014
1(» 37022.57
103759532
l(»^375(Ut|0
9444785
8 9450072
H9J50554
8 9402433
8 9408397
89474177
948OO42
9485904
8-949170'l
9497015
9503404
!J509:iOy
89515150
9520987
89520R'2(»
8 9532048
8 9538173
8 9544294
8 9550110
8 9.-i55;i22
8 9.VM73I
H95075:t5
Secant.
foO3920!IO
10 0393201
l(M(M9:iH24
I0 0391M88
100394;*
100395510
10 0390001
„ofl-, - , ,.. I0-030fl«40
9O0I2974 :!:j^. lo3^«7020I^77l0893[lo■o;»972l2
9 0310359 :J;?Jj''t 1 3483041 9^7714912 1003977711
9 *;5 1 9742 :!:!]: ,i i o :i48o25o 9 77 \ -juu 110 0390345
23 ir/1}. I03470877i»^771l039!l0(;3;(0912
90520503 J::^" JO 3473497 9^7709<m7' 10 0399480
I '1 I
9C529B8l'oa-p 1*^347011997707134 10 04OO(M8
9 05:i3257 :^^'"i 10 :mO(;743 9-7705I8oI 100401(010
9 0530*i3i:":^l 10 :w»;3:wt!»fi 7703225 10 ami 105
9C54IHH.M r::', 10 3159990 9 77'M27I 10 0401754
9-6543375^"'' * KJ 3450025 1 9 7*'993 1 5 1 0402324
y05407J4 3^g 10 3453250 97097359 IO0402894
9 C5501 12 ...„.,' U^3449«8a'9 70!'54O2 10 04O34G5
90553477 tur, 10 :t440523 9 7''93444, IO04O4030
9 0550841 :!:....
9 050»20l|:.: *\
9«5«;3.-.o4l:f|
•^«>5oo923 ^i^;;;^
9 0570200 ..„-,.
9 0573030 1 ^^JI;
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9 0.'.OO34l u.^:
.Mr,03..:>2;^^;i
90587041
10 :i443l59 9 7091400 HV0404007
10 34:19790 9-7Gffil52Hlll>040fil 79
10 34:10430 i^7087508|lO0400753
10 34;t;J077;» 7085008, 10 ()4(M;326
10 :(429720'97fi83O48 10 0400898
D.
Cosine.
503i
503
504
504
504
5(;5
5«J5
5C0
5(>'0
5i;7
607
500
500
19007:^2 00
9 90(H;"3fJ
99000170
99(;050I2
9 900;>048
9 9004484
9!*00:i919
9 iMMrs:!^
9 9(tlt27««
9 9002222
9 9C01G55
9'«!01088
9 90(H»52O
50M
5f:9
509
670
570
671
9GA903a7
90593733
il0597"70
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10 04'I7776
10 046/1410
I0 04(UI044
100489680
1004.00315:
I f» 0490951
I0049I568|
100492225
10|)4!(266*2
10 0493000
10 0494139
100494777
100496417
10-0496066
10(U964t97
100497337
100497978
li>049mi20
Iu04:t9263
loo4;n*'»o5
I0<iri00.'i48
Hi 0501 191
6I7
616
616
617
619
618 ;
619
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!» 9.*i:W602 60
9 ;*5:i5985 59
9 95;i5369 56
95;i475l.57
9 95;J4134;56
> !*5:i;i5l5 55
030
020
620
62
622
622
622
623
623
624
624
6-24
625
626
626
626
';27
626
627
629
626
630
((29
630
631
631
631
632
63:t
632
631
031
6:i4
636
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6:17
637
637
636
6:19
636
640
6*jy
641
640
641
9 9532897
9^9532276
9531658
9^953103^1
9n5:Mi4l6
9 952J»797
9 9521*176
9 9528553
9I*5'/793I!46
9 9527306 45
9 9526685
9 9526001
9 9526437
19524613
(9524188
I 9523502
I 95229.16
19522310
M*52I683 36
9 9521055
9 9520426
f 95 1 9799
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19516541
) 9517913
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99514767
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9 950:HI4U 16
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9 9507775,14
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643
643
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9 9.>miO.'l5
9 949945J
9 949RH(>!i
Sinf
63 Deg.
32-2 27 De^.
NAYUllAL SINES, &C.
Tab. 9.
'_\ Sine.
Ui4.'i31»'.Mi:j
\\454tHU1
*j,4A4:>itim
45528;i!l
•16.'id44r(
4a:*m'38
4.'>«M;27
ll>'4.i(k'>8<)4
ll|4J(U):fll2
12
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l.'l
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17
19 45a!>oao
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'Jll45»4-J48
2.!'4.we(i:v.»
*.'3l4.'.J»!*4l.5
4 4G0Vjiia
4b7Wiii
4Ji7a&(jC
467(1153
4578739
468i:t25
4566490
4004680
4007103
4aO!)7^-l
4312325
20|4ltl41H)t*
30 4017486
31 4fi200r.fi
a2 4fiJ2titfi
:».'( 4«2.J22.'i
:u 4(i::7UiM
.Vt,4i;3<i:t}i2
:t« 4ca2ii(io
I
37'4fi'^V>i«
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40 4tf4:i2<i!t
41 4(;4r>«4.
42 4«48420
4X4(1^000
4(i:>:c.7i
4(;.'><[145
4fi.'»H7l'l
44
4 A
4(j
47:4(ii;i2!»a
4tl 4(iUHU6(;
Dit.
2o!»2
2.'i!H
25yo
25aa
25flf>
25U0
2A»8
25U8
2.'i»7
2o»7
2A87
3A8tf
25IM
2585
e^8.t
Jo84
2583
2A83
2583
2582J
2.MWI
2.JUI
2681 '
2r>Ul)<
Covers Coseo.
.V|fMHI!>.'> 2 2(12I;M1>3
a4:i7603 2 20l4;t2fi
:»4.'i4Ill2 2 2lMll77.'-i
.*i44iJ7:ii
/r4l71-U
M44;nM
2-lJlJ(y240
2l*t7«7il
2-Iltfi42l!«
2- 1 0517^3
54llf>02 2-
A43!i373 2
543fi7H4 12-
A 1 34 urn 2-
.■.43Ifi06 2-
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542G434 2
54:23847 2-
54'.M2«I 2
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Ml 3604, 2
40<M;43!»
4ti(!!K> I
4(I71''«4
46741541
4678727
4e7t»2;>«
4Rat8nv»
4f»l44.rj
4687009
4680578
4692147
4U047H;
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2380
2o79i
J578'
2678'
2j7«
2'»77
2.i77
-'■•'77
■2:r,ii
2 J 76
267fi
2675
2574
2674
2674
2:.73
2673
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2671
2671
2J'»7()
2570
25«!g
26G0
1939262
l!>2fiH08
1 ill 4370
i'JOI!l47
1889641
1877160
Iflfi4776
1 8624 1 7
I (140074
IH'J7746
1816436
I80313!i
5410020 2 179086!)
640B335'2l77rt6it6
54«5752!2 I70G34fi
a4031(I8!2-i764M3
64005S&2-I74I8U6
63S80O2 21 729093
639MS0 2-1717A06
6392838 2-1705335
6390260 2 lfi'j3IB0
6:W7«75j2Ifi8l040
63II6094 2l(>Mt»l6
63112614 21 fi6880C
6379;»:U 2 1644712
6377364 2 163263:1
6374776|21C2U670
6372196 2 1808532
6:ifi9fil8 a-1696489
6307»40 2-1584471
a* 15724 69
2-164II6I0
6360731 2 i:j:t«663
|6:tJ4l66'2 1524611
,6;15I680'2 16I2C84
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6096264
5i»Util>l9
6in26]t6
6|IK>262
6iii:i:M9
6lKVi»8
6117269
5120930
5124602
5I3B275
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5136625
6139:«>2
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I 'J62li|06
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I 116979 Ul
I U68:W37
I :i669780
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1 95277 W
I 961371 1
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l-94«.)772
Ill47i>*i6
I 9467896
61429SO 1 0443981
6146G68 1 !(43U0K:I
5364402
63618&5
6359308
63-lfl*X>4;21600772
fi:U642U2UaiiR75
6313866 2- U709U3
63)1281 2 U';.'il27
633)t7o7 21 i.*.:i2":.
6334ii;U 2 1441438
6333661 '2 I429CI5
-■■■KM', -2 I4I780B
II -J I KM.Ol.')
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61603:ttl
6164019
6 1 57 702
6161386
6irK'^04;t)
616H766
617*2441
6170129
6179818
6l8:i608
5187199
6190891
6l!l4684
519B278
6201 :)7 4
520667 1
520f)3G8
5213007
6210707
62204(;8
5224170
5227«74
6231578
6'2:i6-21U
62:18990
6242G08
6246407 1
6260 117 1
6263829
6267641
6201263
62fi4<N;9
6268685
5272402
I :i4U12(M»
1 !l402:i:i3
I 1)388481
1 U374046
1 1I3(;0H26
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I 113UI467
1 'j:io64:<i9
11)291966
liJ 278228
1<)2646I0
I !)260K19
1 !J2:t7K18
1 9223472
1920t»82l
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9196186
!)1856*W
D168!)60
l»166:i70
U 14 1796
9128230
0114601
•1101162
9087 647
9074147
9060663
9047103
19033738
I902(»2!»y
190*»6H74
I 899:M04
1 898l>lKi8
189(MIfm8
6276120 1 8963322
l7!tB39 1 «9:»JH»7l
6:i;;:iJ73
|63L'n702
'6310131
6315661
d3l2!l91
6310122
5307fi63
5306284
2 1382476
2 1370720
6287281
6291004
6J94727
2 13681*93 62PB453 I 8 11734 :m;
2 I3^I7*-?7J 6302176 1 8JI00I72
2 r* "'">6 18840924
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2-1:11--'"' ■>M.i'Mi4 I mr2047o
1M;«M)646|5:(17094i1 8HII7206
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22:12 »;•-'
2241)::,
2'206:i^
228269
221): (28
2:il59S
233269
234942
230(n6
238292
23990"!*
241648
243328
245010
21f:(i93
24m:i77
26:K>63
261760
2634X»
266130
260821
268614
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20l!H)6!
20:i603j
206302
207<W3!
:i087i(6'
2704081
2721 13
273819]
276527
277237 I
27B948f
280(MJ<»1
282:174;
284089,
2R6806
287524
289244
2909661
2926871
2944121
l09:t!H)0
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1096647
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1090197
1 100624
1101861
1103178
1 1046071
1106836.
1107106
1I081*J7
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1112494
1113828'
1116162
1 1 I64rt7
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1110170
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1123186'
1124626
1126806
1127207
1126649
11298112,
1131236)
1132680
Il3:ur26
1136270
1136017
1137964
1139312
iu(h;oi
1142011^
1143361
1144712
II4G004
1323
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1324
1326
1325
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1329
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160124
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162H31
301788 1164190
290137
2i»7"64 1
299>9:t I
30132:1 1
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308268 1
309!f!>6 1
3117:t6 1
313475 1
31621711
1566471
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1 107794 J,
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6-2 Peg.
LOG. SINES, &0.
Si
Uii
2478
2 it'0:*';o4S.i ',L{
3 ;KiJ77ii:iH
4 0WKn;J7i
i>!h(wj:i7i«L";:;!!
loi'(U:Jjl7:i
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I(>:u'i7(»;,j
lu:W2-i577
lo».ti7iriti
Vorsi'ds.j Taii^.
Dir.
Co|-.UI/»-. C'llVtT
\f\2U-2ii:U\
;» (»;Mi:f77fi
u {y.iuw2ii
u 04m-2T'i
l(i:i4l222olrH)410737
l(>:Mo:»7J4|or04iof*;M
I(i:m(>72!m) :to4-2l'Ji'H
lo:i404«27!!J042r;i:>u
io:t4()234;7i:i04'iimi.>
* 7"77^»-*
;t7««l(>2*J
:»7<>«4I4l
:»7'»ft7"^A"
!/ 7000374
9 7033488
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07IO-'K2I
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1)7101^41
f)-7II2UJ)
!»7i)7J7«ii:!!.:;lioL»;)2.vji!»
:: -"li(»'>;Mii:i7H
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•-•:i:»w;2702«;-j;
24 yWiL'iji«4 :.:"
27 !> w;.i(;7«M
2.t Ulttlli'JV.t'.i
2*nhWi4 m:.»/i
30 u (;(;440df;
31 iiGr»imH2
:i3!)-a<i:.i:t»f
24:vi
24X1
2431
242:»
242H
2420
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2424
2423
12420
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t0 33;K>0«J» 04J7;<'!'.''7l2l4*il
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10-3382743 !^(l4733mi 3 71307«H
ny'Mumuh •>047K:.7a fi 7I33«j;;
t0^3377tt.V> !)0411377I WJltVlUM
i(» 33754)4 yu4H8:M;2 y7i4m).M
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iu337od;M; !Mt4yy:i33 t)7U(;237
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l0 2H7543Hy73:MiB50
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30! u
30; »2
30y2
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t0 3353MR y053.)A2y
U'i\r,\V,H2
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3(187
30(f7
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3082
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I0 334IW;7I !^O.VI.'><142(y71740l4[;JI,j[^^
34,y«lW374yi" r; I0 334(i25l y0550J«»3y7I
35y«(;5<!i(;ni"i n!i"^'"-*«''t2 yo.v>(iUi y7i
37l!>-'i';UlOOI'24i4
io334(i25i yo55oj«»3;y 71770^14
KOI 73
10 3341414 y05GI2i]()iy7tK325l
l0 333H!»f*9 y05'M;42H!y71H«327
;it)7y
307M
3»7«
:«>75
34 ywjo;i4i5',j * !03:t:MW85 yo:.7i5«i'i y7i8y4nj '"'': I028i05y
3yy(;f;(;5«i»H:';, ,1103334172 yo'i7i;7<»i y7i;'2i7(i :r:i. 102H0752
4\.l 'J lit HiHiAH :'.' 10 3331702 yor.M|Jl33 i^7I:'.M4!( :!^;iViio2rtou.'.
41 y'i(;7o(;47
42 l^w;7:^oj4
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:i :, ia332(;y4« O03y2i»«oi072oi«yo
|240o| I
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44 !>^»;(;77(l«3 ',* 103322137 1* iX(i»232li;r> 7-''»7H27
45 iMJ'jittrj'iri'^j *i 10 3;t|y735 y 00(17445 u 72i(0{:i;j
40 yw;J^2(;(w|-.■|;;^lr>■33l733Ay0012.Vl8l!^ 7213058
47 !Hi(yt5ii(t4 "J::;, io33i403)j ytMJUooay 7217022
18 y (K;«740t|r;;; f|l033l253y y 002277-H» 722008d
10 3310111 00-^8771^7223147
yf;(;«.'nto«!.,,..iio33io
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10 28fiy23y!y 7:t:i27ii 10 051.350:
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1 'im'Mtt 4 ' y 7:^285o 110 05 1 4U 1 1
10 285!>y40 y732i;4«5,10nol5405
10 285«855'y 7324408 10 05101 ly
10 2fl5376*3 73223311 ia05l(;77;i
HV2fl50«71!>7-*20252 1005174281
10 28475SI 07318174! 1005JIM)»4
10 2844402 07310004' 10 051 8740
1 02R4 1 405 1 73 1 40 1 4 ' 1 (»5 1 03! JO
1 28383 Hi' 9 73 1 1 033 ' 1 0520053
1 2835233 :!)7;tO0852 I *> 05 2<>7n
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1^2782078
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102770;34
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1 2701504
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9 093:1
f 1(1938
9(«M3120
90!M8027
9 0952!»31
I 0957832
9741:16.50 *; " 10 2.-»80;i5« II 7l;i6Ul2 10(r576221
j»74i66:«.*;; ; J! io258:t;u;2 971:14673 Hi(>5769l7
7419624 ^;; .' 10 2580:176 7l325:i3 10 0577614
9 7422609
HMMI2730 9742.'i594
9 0!«;7((25 9 7428577
»o;»725l7 •174:11559
298,
2985
2983
2982
Mm77406
» 01(82293
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I02&7739I 97I30392 10 0578312
10 2574406 9 7 1 2It250 10 0579(»IO
10 2571423 9 7l2til08 10 0579709
""': (0256JI441 97l2:iiW5 1O058O4O8
:;.,!' 1025r;5460 97»21622 100581107
29liO
u 74:14540
u 7437520
L'otang. Dif I Tan«r, VcrsedsJ Cu»ec.
Ur256248o&7ni»fl77 lOOflflin^^?
11.3
6921
694
694
094
695
695
6!»5
J» 1M3(J2;18 26
994:15549 35
9 94348«Jl 24
9 9434172 23
*4:i3482 22
21
994:121112
9 943141
I 943072if
'94;i0028
9 9429335
t 9428643
9 9427tt49
9 9427255
9 9426661
690
iiu] I
91I4256A6
9 9425171
;;;:| 9 9424476
„JJ 9 9423779
9942:KM13
696
697
698
r»98
699
6l«»
609
790
9 9422386
'9 942I68tJ
9 94209!I0
9 9420291
!) 9419692
9 941889.1
9 94iai!l3
Sine.
61 Deg
3*26 20 Des-.
NATUlt\L SINES, &C.
Tab. 9.
.iH4«mir»
4;j.Vi7_'7
-tui>:i:i:i4
7!]i!(i,Vl!J.'i
I) if. Covers Coset".
- 'jU427:»2Do!»4W!l
2.^4 ;<
2A42
\2U
rii4i7:Jn2o.>n:u«o
.'ii:tiiiikS'io<'>7-if>ur;
A13(;U4(;2^056't!M2
oi:i410.-> 2a5612(Kl
K iwiiVM) ,7;^j|5irt|.')(;.i ;!-o."»ini7i;
Tanp.
ri54(;ji]i4
.Vi54.VU
o56U7;»P
537355 I
' '>Mt\ '•" ^^1"*'*^**^
10 4M7.1SI7 .,?j, 5I2(;4H:i :2«5I'W;i .ViJin?!'
Aiiimcu '." :A>:i'M:i •2n;i(Ui37:t|5;iH4;«>4
4tJ7ajy7 o?., 5i2Uoa ifHWuam jootHiii
4IWn3fl'».-w,'.'illHfla4 2(Uri7034i
4IW3<t74 ;p^ 511g:1JK 2047(>38y
4BB«2i2 :;'.'::" 1 i37i(a 2 04(;o7.*»n
4Bfl87'J0 .Tf ".In *'l I I2J(t 2 045:}>2fi
4U!>I2MH -'':!l! AUm7l2 2044431,i
4B'»302a;Jv::' 5iu<;i75 204:i3;jiu
2.>.«i I
4ni»6'«;i
20U»!)W(tl7
4l>OI4;tH
4I>«3!M;ii
4iWlMi'3
4iH»yo:jii
•JO 1 1. "172
4!M4l()o
4!) IWWH
2fll4!ll!)l7l
29;4tl2l7«4
o6»2C20
55!JG440
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-'':*.' f)0!»H,Vi7 2 0402l!»7 .'\(i232l!»
;?:^.' ;)fl;M;032 2 rt3!*l(i4!J Mi271'4fl
"■.*:!■- <vr:>34;»7 2o;iHni4
.t':r! jo;>o;k;2 2 03705»2
6n«n 4 28 2 o:icoo82
iil)i(aH!(.i 2 0:141)585
50K:w«2 2o:i;iyioo
c»«K0H2W 2-032iHt2«
25:i3
2,Vi3
25:W
-?*; o07H2Ur. 2 031 ((l(Wj6653a88
5(i:Mm7if
.'?(i;^t7to
Coiaoj;
1 0«4(»47rt
I »02IIIUH
I (1013751
I lIlMKtKMt
I 7i':'t"77
I 7!»7«7AI'
1 7^<it'454
I 70''>4l(i2
I 7!Ml»rt3
1 7!)2!>(;lt;
I 7!>t7:»*i2
I 7!H):)121
! 7H02U1>:»
Secant. Vers.
Oil,
I U3;',5il I2d.*i803
I I4353)l.'> 1255214
1 1437231 1 25«;(;2:>
I U3*j(i7n i^.MiOK?
M44n;r27'l2;vjIoO
1 U42771l!l2lM»Jt(J3|
lU444;30|l20227ti|
1I4^'- ■■ ■:' '•*'
1 11
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I U5LM)55|l207lM2,
1270771),
1272 IDu'
I273<;il>
1275040
^
^63aA43
A(i42378
5rr4G213
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3(» 492423« :;^jjj ,507576-4 2 O307720j*'ie''>7728
31 '4a2«7«7 or-.il '»'*■'*--<'■* 2 02!»721W rt(H',l:,UH
32 '4II2!I2!W
33'4!»3IH20
34 4!»:«:i.v»
35 4!i30fm!)
2531
25:11
25:«)
25:U)
25H0
5070702 2 02J{(;f{'i3
50(»HI7t 2 027(i453
50(hVi4I 2 02«005(i
5003111 2 0255070
2o2i» '^^^^^tiM *>24&2:»7
37|4!I4 lfl4fiL,-,,« t'058O52 20-2»4937
3»j4I»4447« 2VMt f»^*>^''24 2 02245«i*
3l)|4JM7<H>5 fJ;^ r.052J>fl5 2 0214253
40i4:M<)532 fJl:*, r»0504(iH 2 02O:t:i2!(
41 4!»V>0W>iJ';^^ 5047040 2 I»|!»3(il8
42 4»r>4567i^^2^ 5045413 2-UIU331H
43 ' '
44
41)57113
4i\4QG2UiS
40
47
40
40
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fil
52
63
54
4»040m)
4!M;72I5
4:m*i»740
4972264
4U747B7
4!*77Itlo
407nH:w
4982355
40H4877
i[4MK730,'l
67!4.'024 4l
oro,.;''»043flfl7 20l7»031
oVoI. 50 403ti r 2 t H 627 5<J
'•fV5037B:i5!2 0152404
5(i(;5-llO
56(i!)254
5fi73ll!m
5/i7i;o44
5680791
I 1453915
I 1455776
1 7880678 1 1457(>;^
I 786847.'* 1 U59504
l-78<'>('2BdjM46l371
I 7fl44l07>l I46:(23H I27(;46
1 7031943 1 lii:^KWl'l277«JI4
1 7(J19790:1 UWiJ?!) I27U303,
I 7(W)7WI 11468852 1280731!
I 7795524, 1 1470726 1282156
1 7783409 I- 1472602 l2»Ct5Hl
1 777i:to7 M474471) 1285007
1 7739218^ ri4703:>ti 1286431
I7747I41,IU7«2J9 |2H7»«-*
1 77:15076; 114fiO]2lll2B92!M
1 772:H»24|1H82006! 1290719
1 77HK)«5'll4fl:iKl*0 1292149
1 7'J:'895H;1 14H5777 I29:i5*(0
1 7('H6U43:1 1487665 1295011!
1 7674940 11489555 1296443
1 -062950 I 1491447,1207876
r7650!»72 1 1493:140 I299:vm
I 78:i9007 1 1495J35 i:t00744
I 7627053 1 14971:12 1302179
1 7015112 1 14990:10 130:iUU
1 760318311 l&00930!l30505l
ir
1 1
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1420
1427
142H
1 42r(
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143>»
1431
1431
1432
1433
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1 1:
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IliTlfM'iT
• "., !'■ , .»■ ; I,
ri7-t!*l .»7 -^»
H7377-.J2 64
»7I7R44 40
Ji7!»ui:» .11,
071 ii »"t 'n
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871O7I0 33
ii7o'.yim 54
8707H5I 33
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JI7:M!tft9 31
H7o:*a57 30
87" '
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....,, 50:i53l0i2 0l42243'J7l9:t3l
^■*"59:(2785 2 0132m»5 :p72:1I92
2624 ^"■*"*-'*",'- 012I779,.'>727054
5(m4fi3!» I 759l267M502S31|13(m41UI
56tltt48» 1 7-'>79:i«2 1 15047:14,1307926
(•1692339 1 7567470 1 1506C;i8 1309364
oti'.muX 1 75555!K>|I 1508544 1310W>-1
5700045 1 7543722:1 1510 152 1312244
5703899 I 75318(t6 ri512:u*l 1313685
5707755 I 7V:n023|l 1514272 1315126
5711612 l-7.'i08l9l 1 1516185 1316569
1 7490:171 1 15111099 13IB012
I 7484564 1 1 52001. > 1319456
1 747'i7fi« I 1521932 i:<20900
17460984 1152:1851 i:i22345
1 744'r213 11525772 13237111
,^3Jm>4=*«i,^.i«
,,■ 122
I , 21
ii^
49!»49'Jl
4997481
AOOOOOO
Cosine
2522
2522
2522
2521
2521
»4>201 67 2 00B<»9y4 ,57425 1«
5017t>45 2 0070828 574(;:m'^
fi<il5123 2 0060674 5750253
5012601 2 005^ 1532 575412*;
5Ol00Jlt» 2 lKt404O2 5757999
17437453
I 7425705
I74l3lifiy;
1 7402245
1-7300533
1 1527094 1325238
ll52!MilS 132C686
1 1531543 1328134
11533470 1:129583
11A35390 1331033
1 737»ft:i3 I 1537329 13:12483
1-7:167144 II 5:i!rj6l'i:i:i39:j4
■;"' 5*lli7559'2 0ii:iO28:i|576l87.H;l 73554*ia|l 1541195 i:i35;ififl
?" ! 5oo.'jo:i9:2o(i2oi77 57t>fi748 1 734:1803 1 154:11:10 i:i:i68:i9
50(»25l9!2(MH0O83 570*»625]l 7:«2149 1 154,V)67 13:18292
6004*000,2 00»HMMH>|5773W)3| I 7320508 1-1547005 133»74g
Coscc. Covers
2&19
Dif.
Vers. Secant. Ciitan. Tan;
8684074 1|7
14*
1441
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' ■ 'iHi:mi\.i 4 I I
J41 >
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ao7r.2oolii
«6747fi3'10
1447
1448
14411
449
afi7S3t4
S07lti(W
i4w|!2?*17
1450
«W8»C7
flW75l7
8608060
U61
1 457
Ir *
M
1454,, ' '^
Dif
Sine.
60 Deg.
29Deg.
LOO. 9tin», &c.
327
'I Sine.
||UriH.i7£Kfl
i)'ii6lt\Hii
(* fi8784-'.'i
227n
2?70
2275
■227*
2272
2271
afiB8520iJ
!»(;8(i74n7
!M»jM1!)7H
l7iiH;«;»i2:{J
I0 9««!)87a4
2l'j>-CMK12:t|
22 ;h;:io.'»47(;
2;i:i»'i:"i77i'i
25]aC0l2305
23 r>r;;>i««.ti;j
30|UPy2;t3Bd
3i £H)!)25«ViO
3:i|ft-Gy:too8o
34|a«1^3230«
3.-1 !* C!I346:SJ
37i»-fin.'»«f»8i
9«047(I.-I}
1^61>60()74
tf-a9ft32Rft
9-60d4S4)l
o-n.'t.v;7i2
4A »-»;'l.i8!»i2
47 !>';;icii;in
48 O'tiimiKaui
40tffifMI5.')4l
liO «!Mi774.S
fti:;n;:Hi;t;»47
B2,fr(Jtl72l4H
53 61)74347
S4iU(;!)7(M4ri
55»fiJ)78741
r)7l!»(i;)«3i2ii
5fl !i t;;iH.vi-j 1
5i) hi-(;!(H7."»I I
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Cosine.
Dir
Co sec.
l03U42flH
lO^'J 1 420011
10 3131)733
I0 3i374^a
I03I3.'>184
EU3I32!>I2
ro3t:mf>4i
10 3128372
I03>2(ihiri
l0 3l23H3:r
10 31 2 1:17*'
io:ini)3i2
22G7
220(i
22«4
2l'«3
5f^\^|tO 31 17031
.,.».h«3IH7;M
-^;!lH13!12.i:W
"•''''10 3110277
I (V 3 1011022
103l057**K
i&3i03ai(;
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it 0'lH22'Xi ;77437.'J20
;M>i*il7l7(; !»744i'4;m)|
*>o;*!)2('57iy744:M7*Jl
:) D'.niGirM
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2!I7!>
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:r 74.2403 . ;j7-
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ai 0745 no
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9 I0a4234
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ll0 3aa7795|iHI03fl07
"7" l03o«.'i5:K'i'.'n inraiB
--;**! 10 30113,31 79^ n i3i2(;
"rw l"-^0"IOJir!) 1117032
"iTrl '«> 'io7)(ji4:v» n2-j7:ij
223' '"^=*07'itil2l!H 127534
„.JI0310I2G6
.^;J;^10 30II<KII7
.;;;j,ii«3ort«7*''ii
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!»-lO40701|!l 7473194 .t! !:/.
9 I0455oOln 747fiIG0'^^..
9 iurion;*:» 9 7^7:»I2.'> r^Jr^
9 lo^ftjMJt 9 74H2o;m .■;;;"!:
9-lofiO(>78 9 7-»Jt-'>0''^ '
2231
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'103074380 9^1132331
103072149 &II37I2(;
]iyMi*iWHi 9 1141917
"f'r "■" ■*'M'7<i92 9 1 1 4«705
'/-' lO:iO«o4U«;!Ml5l4'II
2224
r223
10 3(K;3242 9IK16274
,^,,., |0 3fM;iOl!MHI«lO'i4
;—- I0 30.'itr7!i7 ;hi(;:>h3i
.;ofI|'*>3o.VM77 9M7(.<i,M;
-- ::iio-:w»;.43.-.H 9 1 17:1377
^, ' l«30o2Ul 9^II«0U(.-
.f.^^J 10304119269^1184 i)l2
»74«)UII3
9 7490974
97493934'
9 749(Jtt92
9^ 7499BoO
U 7.iO:2flOC
j» 7.'M>r.7f;2
9 7^H7 1 G
9 7S14fi22
9 7r)l7'i73
7 '.20.123
97^23472
'J 752t;42«
9 7''29:win
i^7•vw3U
2:m;i
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2900
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29:1*;
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29.5 1
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2:14 H I
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9 7.'.:«2.i9:;;-j
9 7.^38203-;;^:;
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9 7.'>47029',
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9 75:rJO(l»
9 7^».*"-'^''I4fi
2940
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9 7.'i«i7i«!:;:^
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2204
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10;M)2:i«;.'»3,9 12371"»4
24 1 HO7
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103012480 9l2li:.;i08
9 7rio3:»47l'
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9 7^-99794
9 7'Jo2;i«
9 7''0:.(;37
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10 30Ui:«(0;9 l27022:t| 9 7(;t<3!M
Secant. | Cover?*.! Cotiinj:.
i>ir
Cotanp;. Covers.
T)'2,'V02'4 m > 071 19^7 7
o2:/:.!t:.oi|o 71 17:132
2iV»o;ri4|'> 71 153*17
025:13547!!} 71 13240
25:rt>572o-7llloy3
02547597 9711*8945
0^2544024 9 7lO<>797
0-2541651 9-7I04(>47
O2:'3«08o!o 7102497
tH'53.'>7l0'9 7I0O340[
02:i3i*7ii,97"0Jtl95
2520773 9 7('.'M;043
<»252«800la7093Jt90
a252384o'9 7i>fM73';
0-2520875 9 7U»95rtJi
0-2517:ill|9 7'iH7J27j
2514940 9 708527 1 1
02511087 9 70831151
O^3d09O2C &7(MI09d7
0-2*06066 fr7078799l
02503108 lf707(«J4l|
^^ 2500150 9^7>'74 181
02497l94!9707232l|
O24:U2:i8,9-7"70lGO;
O240l284[y7»)(i7999i
2488;«ll9 70«5B37
24053791 9 70«nt874
02482427]97*WJI'\lO
l^247'M77ljt7"50346
2476528
2473580
0^2470032
9 7057180
9 7055015'
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97052840
0-24678m;:9 70:>(HtHl
0-2484741
2401707
2458854
2455912
2452It7 1
02450(131
9^7048513
970483*4
9 7044174
9 7942004
97039833
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447092 9 7J35 180
44415419 70.33318
2441217 97031142
()-24302 82 9 7028907
97026792I
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2432413
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24285481 9" 7020282
242:WJI719 7018084
242(Wa7l9 7015905
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(^24(l8lt78;9 7007182
240*J053 9 7iK)4!199
O2|O312!l|9 7'H)2810
0-24(>020«'9 70IM)*;3I
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0-0585315
0588018
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0-0587425
058812U
00588834
05S9A39
0-0590245
05fK)952
051*1058
0592306;
0593073
0^0593781
00594490
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701
701
701
702
703
703
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9Tt4r8l03 '
9 94 174^/2
9 9416791
9 94160941
9 94153X8
99414685
9 9413982
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58
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9 9413279
9 9412575 52
>94tl87l|oI
9 94 1 1 Kit; 60
!^941046l 49
9940973548
704
704
705
705
706
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-„,. 9 04tn)048l47
' ! 9li408342l4(i
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9 9407i;34'4d
00595199
00595909'
0596619'
00597330!
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0^05904631
0O(M>oi77
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0605893
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5 ;^9 94W!2ly43
i'79 940351ol42
-,n'l^940480I 4]
f "994 0409 ll 40
i, 994033^11 39
i\\ 9 940287o':W
i 99401959 37
i!A 9 940124836
712
9 9400333 35
I^93Im«2334
i!j9 939i»ll0 33
i J 9 939)090 32
ilj 9 9397682 31
i]*9 93969«ai:W
-,«{»-9396-25n'29
i "99395337128
:,! 1^9394821 127
i "9^9394I03[26
111 9 93933fi3|23
ijj9^93!»267l]24
-,^'9 9:J9I933'23
i;: 9 939 1 234 1 22
:^;993!«»3:3 2l
i.V! 9 938;»796 20
i.ll 99389076ll9
iff 9 9;i8fl3fi6;i8
-01 9-9387033; 17
i.M9 938<;!JU|l8
' ■i9'j;kM;i92 13
;,X!^9'!l8:>47o'U
io» 9 9384747 13
ijV9 9;i84024;l2
70. 9 9383330] 1 1
i" 19 9382576' 10
i:;'. 9 9:{81H5l| 9
LX^.l'JiKMiWii 6
ir,J^!9 93804(KI 7
i;J 19 9379674 6
I
I
I
3^8 30 Deg-.
NATURAL SINES,
&C.
Tab. y.
' Sine. Uif. Covers
llfj(l02»«9
25005037
3 5007556
ftO 10073
5015107
7 5017624
8i502UUO
9 '5022655
lo' 5025 170
It 5027685
1215030199
13 5032713
11 50;J5-J-^7
15 5037710
16 5040 >5i!
17 504_'765
18,504:)27t
19 5017788
20 5050'i*l8
21 5052809
22 50r)5.JI9
23 50)7828
24 506D33H
25,5062846
26 506?>355
27 50)»7H6:i
28 5070370
29 5072377
30 50753&4
31 5O77S90
32 5080396
33 5082901
34 5UHr)406
35,508:910
3615090414
37|50929I9
38 5095 121
39! 5097924
40l510O426
41)5102928
42,5U)54ii9
I
43 510r93li
44 5110431
45 5112831
46 5115431
47 51179311
43:5120429
495122927
50 5125425
51' 5127923
52,5130420
535132916
2519
2518
25 ly
2517
2518
2510
2517
2516
2515
2515
2515
2514
2511
2M4
2513
2512
2513
•5111
!512|
5000000
4997481
49949G3
-1992444
1989927
4987409
4984893
4982376
4979860
49773 15
4974H30
4972315
4969801
4967287
4964773
4962260
4959748
4957235
4954724
2^ »4949702
25 '4947191
^''"' 4944i;ftl
2509'^^^^ "*
2510
250S
Cosec.
2-0000000
1-9989029
1-9979870
1-9%9823
1-9959788
1*9949761
l-993975.t
1-9929752
1-9919764
Tang". Cotang'.
5773503
5777382
57812G2
5785 U4
5739027
5792912
5796797
58006H1
5804573
S4
5135413
5137908
5140404
5142891.'
5I4:>3
51478H7
5150381
Ciisine Dit
1-9909787 5808462
1-9899822 5812353
1-9&»9S69 5816245
1-9879927 5820139
I
1-9869997 5821031
1 9860030 5827930
1-9850172 58;n&28
1-9840276 58 1572(»
1-9830393 5839(127
1-9820520 5843528
I
1-9810659 5847431
1-98008(0,58513.15
1-9790972:5855241
1-9781 146'S85914H
494217211-9771331 5863056
2509
i508
.'507
2507
2507
2506
2506
2505
2505
2.504
2504
2504
2^03
2503
2.502
2502
•25U1
2501
2501
2500
2500
2499
2199
2498
2498
4939662 1-9701527 5866965
I
4937154 1-9751735 5870876
4934645 1-9741954 68747a8
4932137 1-9732186 5878702
4929630 I-9-'22427i588261G
4927123 1-9712680 5886533
4924616 1 9702944 5890450
4922110 1 9693220)5894369
4919604 l-9683507l589e289
4917099 1 967360.5 590221
491 I594ll-96(.41I4'591I6134
4912U90|l 9654435'5910U58
4909586 I 9644767 5913984
490708211 9635 no 5917910
490 15'9|1 9625464 59218.19
4902i)76|l 9615829 5925768
4809574 1-9606206 [5929699
48971)72 19596593:5933632
4894571 19586992 5937565
7320508
1 7308878
1 729/260
17285654
17274060
1-7262477
1-7250905
1 7239346
1 7227797
1-7216261
1 7204736
17l93--i22
1-7181720
17170230
1-7158751
I7I47283
1-71.35827
1-7124382
1-7112949
1 7101527
1-709(1116
1-7078717
1-7067329
1-7055953
1-7044587
1 7033233
1-7021890
1-7010559
1-6999238
1-6987929
1-6976631
1-6965344
1-6954069
1-6942804
16931550 1
Secant.
1 1547005 n:Vt
1548945
15508^7
15528;10
1554775
1556722
1558070
Vers.
131
131.- .
I344U3
1345570
1.347027
134S4SC
Dil'.|Co8ine[^
■U;5%l
I
l,.Mi._., ,. ,
15664;?0ll3"
1568436 131. .
1570394 135725-.
157-2354 135«""
1574315 13'
1576278
1578243
1580209
1582177
1.5841 46
1586118
1588091
1590C05
1592041
1594019
I3f ;
1363 111
1364577
1366041
1367512
13',-
13;'
1371 .J.,
1373392
1374863
1595999 1376336
1597980 1377809
159996311379283
1601947 1380757
4892070
4889569
4687069
488-1569
4882070
1 9577402
1 9567822
19558254
1 9548697
19539150
4879571 11-9529615
487707311-9520091
I -95 1 0577
*^- 4872077
24971
2496
2497
2495
2496
2495
2494
2491
2494
4HC9580
4867084
•J 864587
4862092
4859596
4857101
4a.5»il»7
4852113
4849619
Ver«
1-!j.501075
19491583
1-9482102
1-9472632
19163173
I 945.3725
1 9444 288
I 9434801
1-9425445
19416040
Secant. Cotaii
5U4150]
5945437
5949375
5953314
5957255
5961196
5965140
696908-1
5973030
5976978
5980926
59d4!>77
5988828
5992781
5996735
60ai>.S9 1
60O4648
6008606
I 6920308
1-6909077
1-6897856
1-6886647
1687.5449
1-6864261
1-6853085
1-684 1919
16830765
16819621
1-6808489
16797367
1-6786256
1-6775156
1-6764067
l-fi7529h8
1-6741921
1-6730864
1-67 1 98 16
1-6708782
1-6697758
t -6686744
1-6675741
I-6G64748
1 '6653766
1-6642795
Taiiff.
1603933
1605921
1607911
1609902
1611894
1615889
1615885
IB 17883
1619882
lti2lHS3
16^38h6
1625891
1627897
1629905
1 63 191 4
163.3925
■I 6.(5938
■1637953
■163y96y'14089l2
■I6419tJ7 1 110401
1382232
1383708
1385185
1386663
1388141
1389620
1391099
1392580
130:'"*"
13:i
l:V'- ,
Ki98oll9
1399993
1401477
140216.'!
14''
I41'
U7i
1471
M73
1473
1471
1474
1476
147S
1479
1479 ^
!J«{ 8607420 24;
1614007
1646028
1648051
1650076
1652102
1654130
1656160
1658191
166(1224
1662259
1664296
1666:134
1411891
1413381
141487."
141636.5
1417^57
I4I9351
1420645
14-22340
14;
M:
l4;;or.-..
1428327
USD -
U90 ~'^^ - --j
^j,,j85*S8l09 II*
1194
1494
1495
4
Cosec. Covepi Dit"
U^8
85716731 tf
Sine.
51) Ufg.
30 Deg-.
LOG. SINES, SiJli.
329
Sine
9-6989700
9-699 I8h7
9*6994073
9-*i91»&-i-lI
9-7OU0S*-^i
9700:^80;^
^ft'70O498I
B9-70CI7I58
9-70(i93;j4
10'9 70U:i08
ir9-701J)>«l
12j9-701.S8V^
is's-roisoi-j
14 1) 7020190
15!9-702iKI;»7
Ifi D-7»24,VJI
17i97()26687
]8i9-7028849
Dif
2187
2]8li
2i8.'>
2183
2181
218U
2179
2177
176
171
L'17.I
171
217U
21C9
n;;
2 1 l>li
16-1
21G2
21G2
Cosec.
19 97031011
20 9 70 (3170 :
21 9*7ll[rvl29
22 9 70t7-l8'5
23 !J7lM!Hi^|
24 9-704 1 79 J
10-3010*00
10-300.SII3
10-3005927
id;i«o:{742
10 30O15.S9
102999378
10-2997198
102995019
10 2992842
io-2y90t;«6
10 29S8492
10-2it.S(i319
1^2981148
I0-29S1978
I02H7981U
10-J977643
I0 2;/7M77
102973313
10-2971151
25 9-70J39i7
26 9 7U4rtU'J9
27 9-70l82^M
26 9 7U50397
29 9 705-^543
30 9-705468'J
31 9-7056833
32 9-7058975
33 9-701)1116
34 9-7Ufi325fi
35 9 7065394
36 9 7067531
37970r,96fi7
3tt 9-70718(11
39 97073933
40 9707fiO(i4
41 9-7078194
42 9 7080J*J3
43 9 7082450
44 970«4575
15 97n.Hr.H'J9
4(> 9 70bsH22
47 9 701t0y43
48 9 70930G3
49,9 7095182
50197097299
51 97099415
52,97I0I5-J9
53'97103642
54:& 7 105753
a71«78d3
9 7109972
9 7n2».sO
971NI8d
97116290
9 7118393
Cosine.
10 2968989
10-2966830
I0-2964C71
10 2962514
10-2960159
10-2958205
Verneds.
9 1-27022,')
9 12741)38
9 1279649
91284356
9-12y't062
91293764
9-1298464
9-1303161
9 1307855
91312547
9 1317235
91321921
9-1326605
9 1331280
9 1335964
9-1340639
91345311
9-1349981
9-1354648
97014394 .~7
9761731 lLi^=^
976202271-:,, I?
97623142
97626056
97628969
97631881
9 7634792
97637702
97640612
97643520
9-7646427
97649334
,'9 1
2914
2913
291-^
2'ill
9-1359313
91363975
9-1368634
9-1 373-290
9-1377944
0-7652*239
97555143
9-7658017
9-7600949
9 7663851
9-7666751
2910
i29l0
1290ft
' 2907
2907
2905
,2904
2904
2902
2902
290U
290tJ
Cotanp:.
10 238560(.
I U-23826MI(
192379773
10-2376858
10-2373944
10-2371031
10 2;{68n9
102365208
l(>-2;tfi229S
Coders.
9-6989700
9-69875 lii
9-6985322
9-6983132
9-6980942
9-6978750
9-6976558
9-69743G5
9-6972172
97681240
2159
2159
2157
2155
2154
2152
,,, ,.,a**''-^*6053'9-1387244
.::.: 10-2953901 9-1391889
li^29M752'9■1396532
10^2949n03'91401173i9-7695705
10-:;947457|9-1405811 9-769H596
10-1:945311 9-1410416 9-770U85
I0-2943I67191415078 9-7704373
9-7669651
9-7672550
9-7675448
9-76783441-
2149
2149
2146
2146
2144
9-138'2595 9-7684135
9-7687029
9-7689922
9-7692814
2142
141
10-2941025 9 14l9708|9-770726li
i2896
2895
2894
2S93
2892
281i I
2891
2889
2888
28-S8
-28H6
1023593b8i9-6969977
I0-2:,I564S0 9-(.'Jti77b2
l0-2353573|9-6965586
10 235066G 9-6963390
10-231:-" ■^'■" 1102
10-23 1 ;
10^231! ., 795
10 23390,1 (9-6954596
I0-23;JCli9 9-6952396
iO- 2333249 9-5950194
ra233(n 19 9 634799:1
'".945790
. ' r)943587
h'ijjin^f,;9- 6941383
Secant.
10 2318760
10-2315865
10-2:112971
10-'23 10078
9-6939178
9-6936973
9 6934766
9-6932559
r; ];. I0 293H884'91424335;9-7710I47,.,2s^'
f,\V^ 10-:^9:ta7l|9U-269CO9^771303;ti;2Si
..,,- 10-;i934fi06|9 1433581
f,\.,i 1 10-2932469 91438201
2IJ61 I
I0-2930333|9-U428I7
1029-.N199 9-1447431
I029260h7 9-1452042
10 2923936 91456651
10-2921H0fi'9-146l257
10-29l9677l'>1465S61
10-2917550 9-1470461
2134
2132
2131
--'130
2129
21-27
1-25
124
2123
2121
2120
119,
2117
2116
.114
2113
2111
nio
2109
108
2106i
2104
2103
10 29I5425[91475060
10-2913301 19-1479655
10-291 117g'9-1484-248
lfl-2909057|9-148883s
10-2906937
10-2904818
10-2902701
1 0^2900585
10*2898471
10-2896358
102894247
10-2892137
10-28900-28
102S>t7920
10-28^^5814
lO-2(iai7lO
10-2881607
Dif. Secnnt.
9-1493426
9-1493011
91502591
9-1507174
9-151 1751
9- 15 16326
9- 15-20898
9-152M67
91530034
9 1534599
9-1539161
9-154;(720
9-1548276
Covers.
97715917
97718801
97721684
9 7724566
97727447
9 7730327
9*77ai20fi
9-7736084
9 7738961
9-7741838
9-7744713
9-7747588
9-7750462
9-775:i334
9-7756206
9-7759077
97761947
9 7764816
97767685
9-7770552
P777311S
9-7776284
9-7779149
9-7782t)lJ
9-7784875
9-7787737
Coiiuip. Dif.
28.H4
28S4
2Sa3
2S82
2nS\
•2830
■J879
2878
'J877
2877
2875
2875
2874
2x72
2872
2H7I
■2871'
2S6!»
2869
2.SG7
2866
•2S6f}
2Sfi5
28(^3
2862
I0-'i'i071.s6 9-6931)352
10 23(M295iy69i'9113
10-230I404|9-6925934
10-2-298515 9-69::37.j,|
10-2295627 9-6921513
1 0-2'29-?739'9-69I 9302
111 '6!t 17090
h I 'i9 14877
10 i.o-tv.^i.;) 691-2663
10-22S1199!9-69I0449
10-2278316 9-6908233
10-2275434
10-2272553
10-2-269673
10-2266794
10-2263916
102261031
I" ■
]'>
\"
\'
lu_-.„.
10-2243794 i9-6881593
1 '»■'■' ""■ ■ ' "■' ■^'''768
li' '12
h'.. - . ■ . .''15
10 2.'J23 15 19 6872688
96906017
9-6903801
9-6901583
9-6899365
9-6897146
9-6894926
' 'iH92706
' I.H90485
' <i 88826:1
' '1886040
■J6a8:(8i7
;iO-2229448
10-2-226582
10-2-2-23716
10-2220851
U^22I7988
10-2215125
10^2212-263
Tftiiff.
0-6870460
9-6868231
9-6866002
9-1 8r>3772
9-6861541
9-6859309
9-6857076
Verseds.
la0f/24')94
100625423
10-0C2fil53
10-0626884
10-062761
10-0628;W7
100629079
10-0629811
0630544
10-0631278
10^01,32012
10-0632746
10-0633481
10-0634217
10 0634953
1(^063.1689
100636426
10-0637164
10-0637902
10-06:J8640
1 0639379
10 0610119
10 0610859
100641599
I0-O612340
10 0643082
100643823
10 0644566
10 0645309
10-0646052
10 0646796
100647541
10-0648285
1O-0649D31
10^0649777
10 0C50523
1^0051270
10-0652017
10*0rir,2765
10 0653514
100654262|
10 0055012
100655762
10^0656512
10-0657-2«3
10 0658014
10 0658766
100659518
100660271
10 0661024
10 0661778
10 06625.TJ
100663-287
10 0664043
10 0664799
10-0665555
10-0666312
100667069
100667827
10-066858S
10 0669344
Cosec
D.
C(»»iine.
730
731 ■
731
732
732
732
9-9375o0fi
19-9374577
99373847
9-9373116
'9-9372385
9-937 165.'^
9-9370921
9-9370189
9-9369456
601
59
58
57
56
55
54i
733
^Jl 9-9368722 51
734
735
736
9-936 "783
9-936:>047
9 9364311
,9-93671'83
.9-93672>l
9-9366519
736
736
737
738'
738
738
739
710
740
740
741
99363574
99362836
9-936-2098' 12
9-9361360 41
9 9360621 1 40
9-9359881 139
9 9359141,38
9-9;[5840r37
9-9337660:36
-J, 99356918|35
;]1 9 9356177 34
i'*1. 9-9355434 at
;'^ 99354691^32
yV\ 9-9353948 31
^;J- 9 9353204 '30
...19 9352459 29
;i;f 99351715:28
ij^ 99350y69 "27
lj*9^9:j50223;26
ij^ 9-9319477:25
y/^ 9-9348730,24
,,a'9-93l7983;23
7 " 9-9347235 22
1;];^ 9 9316186 21
'^^9 9345738 20
750
750
750
751
751
752
752
753
753
754
755
754
756
756
756
757
757
758
758
759
9-9344988 19
9 9344238' 18
'9-9343488 17
9-9342737 16
9 9341986 15
9-93412,'il 14
9-931IMM2 l:)
9-y3J!t"2'J 12
9-9338976 1 1
9-93:j8*22 10
99337467| 9
9 9336713
99335957
99335201
D.
9 93:14445
99333688
9-9332931
9 9332173
9-9331415
9-9330656
Sine.
59 Ue^:
i*
A
330 31 Deg. natural sines, &c.
Tab, y.
Sinf
oumoisi
5155367
515;e5!>
h\f>Q3f,\
siG-jsaii
>1G53;J3
51 6792 i
5170314
h\7-2<0i
;fI7J'i'J3
M 77782
5180-^70
5182758
518524A
518773.-?
M 9021 9
d'27lib
y5l9l
5l97r)7r.
ViOdlfil
i2(H'f;jfi
'•205130
5'J0;HI3
521W>9(
52I2J79
26i2ir.061
521 754 t
522002J
30 522498fi
52"27-IGfi
5229945
5232424
5234903
52J7381
5239859
5242336
5244613
5247290
52497fir.
5252241
5254717
5257191
5259665
5252139
5 2G 161.1
i'i 708.1
5209558
5272030
5274502
5276973
5279443
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II 798222
11800372
1-18U2523
1-1804676
I '
I
I i 3 1 I I
1 1"*13;'
risible. .
l'181763Jjt539Ub»:
1 ifll'tTtm r". M. lii
Vers. iDif.
1 541
1544
I54(
I'll'
l.>4*'
1 55 J
Cosiue' '
I 8662747 6346193
I 8654197 6350-74
1 Hf.J-.(.-.T hi?»4357
1' sl^l
1 h . . , .-'527
1862UUJ3 r.3666l4
18611590,6370703
1 -8603097 ! 6371703
18594612 6378885
l-85Sfii3S 638-2978
l-85;7fi72 6,(87073
^85(;9216 6391169
1-8550769 6395267
l-57574;9
15747352
1-57372;M
1-5727126
1-5717026
1-5706930
1-5696856
1-5C86734
1-5676722
1-5066660
1-5656625
1 5646590
1-5636564
1 t8;:uio.,|i:r.i
1-18-28 179 15)
l-l8306M:l54;.i-.
1-1812830 154893
l-I- . ;""■
I 1
1 !-
11
11^.
I1845:(.
1-184'Jll'.
Il8:.0307li5f
1 I8525O0'l5r.
I 185|694|15';
l'165t)890i15< '
155-
II
I I
I ;
I ! ■
I 1.^ ^
1-187010711575476
1-s: ... .. ■ ...
18527073 641
tj7J|l'559l'552
Cosine Oil. Vers. Sceaiit
1-8518672 6415779
I-85I0-28I 6419886
(-8501898 64-23994
1-658657J
1-5576601
1 5566639
I'84935'25 64-28l05| 1-5556685
1-8485161,6.132216
l-H4r6806J64363-2!»
1-B468460 6440441
1-8460123
18451795
1-8443476
18135166
lK4-26Hrtf,
18418574
1 8410292
18402018
I 8.193753
1 8.1 S -1498
6444560
6448678
6 152797
15546741
1 553680*
1 5526880
1-5516961
1-5507054
1-5497155
6456918 1-5497261
64610411 5477.183
6465165
6469290
6473417
6177546
64H1 676
183;7251 618',8(>8
648994 1
04941)76
Cotan.
I-.54G7510
1-5457647
1-5447792
l-5'137y'16
I ■5428] 08
1-54182M0
1 -5408460
1*5.399650
i'l878954|15fiii751
Ily8ll7llt5**3i.'i
I'l-
I :
II"-..
1-1848968
1 1
ri ■■ ■
1-19071*1 1 1 l(.U2.;22
t-J910152|l6038UI
I-19123!!
I-|Pt46i
I I9IKSH4;IL'
1 I919I32 !6h
1-1921.181 161
I l923633llG1.1294
. , .11
14 30
Tang . CoHcc |Covgr»4Uil I ^\uc,
57 Dvst
32 Deff.
LOG. SINES, &C.
338
Sine. Dif. Coscc.
0'J7^4i097, ,
3i9-7,-'isijc ;
4072:,o\?a:
•Z0\6
2m
7'971'S62I7 ,,,.,.,! 10
8;9 7258'-"J9."; J
9 9-72fiOM^)%iy
n 97264-2[>7|<';^,P
l2 9-7'-i6G-Jfi4|2Xfl5
l3'9726S269'.,„nj
14 9-7J70.73 '^""''
15 9 727JJ7f>l
16 9^ 7274 '-'78
17,9-727'.i'7S,
IS.9-727S277
19 9 728027:)!
20 9 72.H227I
21 ,9 72842*;7
22 72Hr.26O
23,9 72882:1.1
24 97290244
I
20o;j
2002
2000
i*I9'J
1998
1996
I9'(fi
I !)yj
1 9'J.t
I'jin
19»0
10J7r>790J
10-27r»''882
l0-27rj::8rj-.'
10-2751H44
102749826
IO-2747'*n
!0274:)796
743783
102741771
I027;t97'i0
10 27.17 7M
1027Jr>743
10 27.W73G
10 2731731
10-2729727
1^2727724
I0-2725722
10-2723722
10-2721 72;i
110-2719725
110-2717729
10 271573:1
10-2713740
1027 11747
lO-270y7JC
10-2707766
I 29
■ 33
25 97292234, nog
26 97294223 , "^ 10-2705777
27 9 729fi2n uZl 10-27tKCS9
28 9 7298197 uu- 10-2701K03
29 9 7300182 ™ 1(1 2<i9ySlS
30 9 731)2165 jyg^ 10-26978.15
1 9-7304148,001 1 10 269riaS2
9-7306129 nJo 10-2693871
33 9 7;»'8109 ,,j-" in26'llH91
34 9-7310087 .t-y 10"2fi!!t991.i
35 9-7312064 011110-2687036
36 9-7314040 j^^J:lO-268:.960
37 9-73 1 60 1 :. ' , g - , 1 1 0-2683985
38 9-7317989 Ini; 10-2682011
39 9-7319961 I'JLf 10-2680039
40 9732l!»32 nCA 10-267806&
Verfteds.
9 1847812
9 1852230
9 1856615
9 1860998
9186')37S
9 1869756
91874132
9 187S505
9-1832876
9-I8S7245
91891611
9 1895974
Tang
979.'>7b92
97960703
9-7961513
97966322
9^7969130
97971918
9 7974745
9 7977551
97980356
9-7933160
9 7985^64
9-798876"
9 7991569
979943711
97997170
97999970
9-8002769
9 800)567
9-8008365
8011161
8013957
HO 1 6752
80ig>46
8022340
8025133
8027925
-'""716
: ".U6
. J'.M.
Hil3y085
8041873
1974
1972
1971
41 y-73-23902 jg^^ 10-2676098
.ior..,..,-.^^« 1967 •"""^"""
42 97.J25S70
10-2674130
43 97327837,966
44 97329801 ' **
45 9733I76S
46 9-7333731
47 9-733>693
48 9-7337654
49V7339614
HM.5
19 3
1962
1961
1960
10-2672163
10-2670197
10-266a-2;i2
in-2f.f)6269
10-2f>'i4.l07
10266-2346
10-2660386
^.r .« «,io;r>ri<« ynf,a\*v ^^'wv'tau
50 9-7341572 lQ;y|l(V2fi5H428
51 g-7J4t529 iQ^fi 1<>^-'''>6*"I
52 9-7345485
53 9-7347410
54 97349393
55 9-73M34S
55 9-7353296
57 973ri5246
58 97357195
59 9-7359U2
6(' 9-73610H8
Cosine.
1955
1953
1952
1951
1950
1949
1947
1946
Dif.
I()-26545I'
10-2r»52560
10-265n607
10-2648655
10-2646; 04
10 2644751
10'26»2Sft5
lCc26408'>8
10-2638912
9 1900336,9
91904695,9
9 1 90905 19
'>I913406;9
9 19177'.8 9
9 1922107,9
9I!>26454'9-
9191"-"" "
9- 1 9:1
9 19.1 I
9-l9l;iS19 9
91948I55|9
9-1952188 9-8044661
'J-I95'i819;9-8047447
9 l96l!47|9M^^()■i1,l
9-l96547,( 9.Mo:,;lMly
9 iy(.9797|9-805f)«O3
9- 19741 18 9-8008587
919784.17 9 8061370
9 1982754 9-'5064152
9- 19H7068!'3 8066931
9-l99l38U,0-8069714;
919'I5690 9-b072494!
91999997 98075273
9-2004302 9-8078052
9 2008605 9-8080829
92012906 n-R0S160'i
9 21117204 'I -
9-2021499 ■' ■
9-2025793 'J -.'Ji.:^ .
9-2030084 19-8094707
''■•■■■ ' -T'^tSO
9-21M7-22t> y-8lU5796
9-20M506 9-8108566
9 2055783|9-8111336
9-2060058 9 8IUI0,';
9-2064.131 9-8 II r;^-
9-2068602:9-81 1'.i
Dif.
2811
2510
2809
2808
•2808
2807
2806
2805
•2804
2804
2803
2802,
2801
2800
2h00
2799
279s
279H
2796
Cotanf^
10 2042KI8
10 20.19297
l(r 2036437
10-2033678
10 2030870
10-2028062
10-2025255
1 0-2022449
la 20 19644
102010340
10-2014036
10 2011233
Cu^ cr*.
9-6721721
9fi7l9U'j
96:i7l6*'
9 6714884
96712602
9-67111319
9 6 70803 G
9-6705752
9^6703167
9-6701181
9-6698895
9-6696607
10 2006431 9-5694J19
10 200561019-6692030
i0 2flO2.s3o'9 66H97ll
10 2000030 9-P687450
101997'a31
101994433
10 1991635
1 0-1 989 -^sg
10-1986043
10 1983248
2796
2795
794
2794
^^^:]j 10 1974867
10 1972075
9-6G85159
9-6682867
96680574
9 6678-281
9-6675986
9-6673691
Si- cant
10 1930454 9 667M9
10 1977660 >-6669098
9-6666801
2791 1
■^901
.>79i)l
J79y|
101969284
1U 071 '.791
I0^07l6r»85
10 0717375
100718166
I01)7I89.>7
10 0719749
10-07-20541
100721334
100722127
100722921
10-0723715
100724510
10-0725305
100726101
10 072(;897
10 0727691
10-0728491
10-0729289
10-0730087
10 0730886-
10-0731686'
1007324S6,
1)10731286'
I0 07I40>7|
10-07.14888,
D
9 6664.502 10 0735690'
96662203 10073649ll
I tH 966494 9 6659903 1007 (7296
10-1961704 9 66'.7601'H' 0718099
10- 19609 l'.|9 66r>')10M0 0738901'
.^7yyjl0-1958l27|96652999| 10 0739708
.27Lfi|]0-l95r)339 9fl6:i0696 10 07405 13
..7u?[101952553 9-6648192 100741319
,7^,-;l0194l767 9 664'1087 10 0742125
7^1 10-1946981 9 6643781 10 074-2911
.jyiJi 10 1944197,9 6641475 10 0743739
f/^Q.J 10-1941413 9-6639168|lO-0744546
..,2N*^19''*^''*''W9'fi636S60 10 0745354 1
10 1935848 96614^52 I007461G3
10 19130 7 9 6632243 10 07469721
IOl93n286'9 66-299E2'lO-07477S2'
10-1927506 96627621 10074a'>92,
101924727,9-6625309 10 0749403'
790
790
791
791
792
792
793
793
794
794
795
795
796
796
797
797
79»
798
799
800
800
800
bOi
H)l
802
803
803
803
805
801
805
806
806
806
808
807
eos
'Osine.
41
9-926431035
9-926350734
992627U4I33
9 9-261901 32
99-J6I096.3I
9-9260292 30
9-9259487 29
9-925868] 28
9-9257875 27
9-9257069 26
9-9256261 '25
9-9255454 24
L
9-207-2S70
9-2077136
Secant. Covers. Cotjiii^. Dif,
9-81-224u^
9-8125174
2 7s I
81
J780
J77y
2779
2777
2777
T77
2774
2773
2771
■2770
2770
2769
J766
10-1921948 9-6622996 10^0750214'
101919171 |96fi20683 1^0751026'
10-1916394 96618368 10-0751839^
10-1911617 96616053 1&0752651
10-1910M1,.' 96613737 10^0751465
10-1908007 9'66n421 10 0754279
10-1905293]96609103 10-0755093'
1ft 1902.520 9-6606735 1 0-07.55908
101999747 9-66044t.6 10-0756723
10 1896975 9660'2146 10-07575.19
10-1894-204 9-6599825 10-0758356
10 1891434 9-6597504 1^0759173
10-1888664 9-6595182 10 075999o'
tn'l<^8".ft9,''^6'n':g-8 10-0760809'
■ '^ 10-0761627|
10 10 0762446;
iit\-7::i[>-i ■-Jt.Dh.-.ssi 100763266'
10 IS74826 9' .583558 la0764086
Taiiff. IVcrsc'ds.l Coscc.
ono 9-9254646 23
;, ^,9 9253^7 22
2;n;99253028 21
2 "t9-9252218 20
2ii|9-925U08 19
^Ij 9.9^30597 18
^,.,(9-9249786 17
°^: *^9'248974 16
^:; 9-9-248161 15
° -,99.M7149 U
^lj;99246535 13
IJj ;»-9245721 12
RwJ 9-9244907 11
^1. 9-9244092 10
9
8
7
6
5
4
3
2
1
l\'' 9 9243277
2J^9 9.'4-_'4C1
°; 9-9241644
^J7'9^J240a27
„,„ '99-2400 10
2Jg'9-9-239191
X 0,9-9218373
2;;" 9 9236734
'*'^"i9-923.'>914
Sine.
57Deg.
1
J
334
33 Deg.
NATL'UAL S1N£S> &C.
Tab. 9.
Sine.
U.;i446i9U
7
8
9
10
11
J.'
u
15
1 1.
i;
18
19
20
21
22
23
24
25
'27
is
;»
30
3)
36
3,
3H
39
40
4;
4:t
U
4,')
4ti
47
48
49
•U
51
5'i
:>4
iS
yj
&448830
5451269
.'>4'>3707
M56I45
54'»8:i83
^4ClO'iU
&4634r>6
5465892
.•»4683:'8
54*0763
5473 1 'JS
5475632
5478nr.G
54SU499
5482932
54H,i36*)
5467797
549022b
5492659
5495090
5497520
5499050
&502379
5504607
3507236
5509CG3
5>12t.'il
i5l4My
Dif
244U
2439
2439
2438
2438
2437
24J6
2436
2436
:^435
2435
21(4
2434
2433
243.t
2433
2432
2431
2431
2431
2430
2430
2429
2428
2429
2427
2428
2427
212/i
5519370-2^^^
Covers
4553G10
4551170
4548731
4346:293
45438 :) 5
454U17
i53fl980
4536544
4534106
4531 C72
4529237
4526802
1.V24368
4521934
4519501
4517068
151 1635
4512203
4509772
4507341
J5U4910
J50248I'
1500050
4497621
Cosec.
1 ;)J607b5
1-83525 G5
1-8344354
1 83361 r
1-SJ27959
Ih319774
I8J11599
18303432
18295274
1-8287 125
1-8278985
18270854
1-826273I
1'8-2546I7
1 -82465 1
1-623H4I6
1-8230328
18222249
1-8214179
18206 lis
18198065
1-8190021
18181985
18173958
4495193 1 8165940
44927641 1-8157930
4490337* I-8149y2y
4487909 1 8l4ly3;;66063l;i
44S)4.V2 1-8133953|6610492
44830 -G l-8l25977,6614(i73
llS0<i30|l 8118010 6613856
TunfT
649 1076
6498212
6')02350
6-.0(i49U
6510631
G5U774
651891-5
6^23064
6527211
6531360
6535511
6539663
6543817
6547972
6552)29
6556287
6560447
6564609
6568772
G572937
G577I03
6581 27 1
*>58544I
G5896I2
6593785
6597960
6602136
5521795
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5526645'^'^'
242 -)
5529069
5531492
5533915
55363-38
5538760
554118*-.'
5543603'
5546024
5548-141
5550864
5553.'8;i
5355702
5558121
5560539
'>')62956
>565373
5567790
570200
5572621
5575036
5577451
5579865
5582279
5584692
5587105
J589517
5691929
Cosine
2124
2423
2423
2423
2422
2422
2421
i2421
'2420
1 2420
2419
2119
2119
24 IH
2417
2417
2417
24l<<
2415
2415
2m
2414
(4478205
447:.730|
1-8U0052
1-81 (121 02
44733"»5:i-809416l
18086228
1 ■8078304
2414
24 n
2413
2412
2412
4470931
44li8:i08
4466085
4163662
1461240
44588)8
4456^397
4453976
4451556
4449136 1-8015213
4446717 1 8H07365
4444298 17999524
4441879 1-7991693
4439461 11-7983869
1-7976054
1 -80703 88 K'C-1^981
1-8062481
18054582
180-I6ii9l
18038809
1-8030935
I 8021070
6623040
6fi2722
''631413
6635601
1.63979-'
4437044
4434627
443221(1
4429794
4427379
4424964
4422549
1796824;
179C0449
I 7952658
1-7944876
17937102
1 7929337
17921530
1-7913831
1-7906090
1-7898357
l-7tt9i)(i33
4420135
4417721
4415308
Ml 2895
4410483
440807111 7882916
:648178
►652373
h 656570
(.660769
6664969
6669171
.673374
'1677580
668178<.
668599f.
669020,*)
6694417
66986;tO
6702845
6707061
6711^80
67)5'.00
6719721
.S723944
6728169
6732i9(i
G736624
67408 '«■!
!Co(ung
r539S650
|-5;t8H848
I -537 905 4
1-5;IG927U
1-5359494
1-5349727
1-5339969
l-53;t02l9
15120479
1-5310746
1-5301023
1-5291308
1-5281G02
1*5271904
I 526 .'2 15
1-5252.135
I 524 2-t 63
1-5233200
15223545
i -52 13999
I-5204J61
1 5194632
1-5IS501J
I-5175401H
15165796
1-5156201
t-5146614
I 5)37031.
I 5127466
1 5I179U5
I 510W52
I -5098807
1-5089271
1-5079743
I i070224
l-50f.O713
1-5051210
1-5041716
1-5032229
I -502^751
I -50 13282
1-5003821
1-4994367
Secant.
Vi-rs.
11 92363 i
I1925aS6
l-1928U2|l'.l
I- 1 930399 I ■
1-1932658 h..
11934918 1'..
1-1937181 1'.-
1613294
16I4>H7^*
1-1939446 ] 62440*2
1 194l712'l6259;l
11943'JhOl (.2758*2
1 1946251 1 1629173
11948523;1630764
1-1950796 1632157
11953072 16339501, .„.!
119.'.5350, 1635.44* !:,j J
I 1957629 ](■■-' - ' ■^'
Oil.|CV«ine
lA-
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159 1
15'"
1 \'\
1 1959911 1
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1-1964479 1641 9!i6|[?^^j»:i68074 «
I-1966767|l64:J524 ,^,,^1" ' - '-- II
I
I19f.9056 1645122
1 I97I346 164672);
11973639 164832<>
1-1975934 1649920
11978230 1651521,
1598
159'
100:
DiKi Vers. I Secant.
14984923
1-4975486
1 49G6058
4956637
M94722.i
1-49378*22
1-4928426
1-4919039
1-4909659
1-1900'288
1-4890925
1-4881570
1-4872223
1-4862884
i 435.3554
1-4844231
1-4834916
1-1980529 1653123!,
1198-2829'i' '■
)1985131 )i:
I-I9874J5 lo,:>7 M.
1 1989741 1659537
1 1992049,1661142
M994359!l66274»
1-199667' l.;i.4't-. |I
11998-
1 2001 r
IU(^
160<'
1608
1608
Ei334ftMX7
rt3T:4.t0 2C
12005937i 1670788
I-20082J8|lG72398
1-2010582 1674009'
1-20)2907
674')0S5|l-48-25610
Cotun
lOaS P4825610 l-'2
un.| Tan;r. I C
l-20l5*At4
I 2017563
1 2019894
I •202-2226
I 2024561
026899
1-2029236
1203i:.77
1-2033919
I-20362C4
12038610
1 2040958
12013308
t 2045 660
120480)4
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I-20r»2728
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2057450
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iGlOi
1611 1
1(,M
icr-
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167yj .,p
1(>80459
1682073
1683688
1683304
I68(-920
1688537
1690155
1691774
1693393
169.3013
1696634 .
1698-255 '^■'
1614
1614
Ifil.^
1616
'loll
161ft
1619
1619
16-20
1^21
osec.
1699877,
1701500;
1703)23
I70j; I-
I7"i :.'
17-1
I7i' .
I N'22
If. 2
I'.-.'"
ir.:-.
S31954
8;>U9JH5.U
S30«^g' 1 1
.S301745
S?(Kil23
■*JJ^Sl»0
Cuvere'Dif Sine.
56 Df g.
3;j Dog.
LOG. SINES, &C,
335
' I Sine. |D)f. Cosec. Versecis
9-7.'t61088
9-736.J032
3 9-/3()fi9l8
4 9-7:Jf.8s59
5 9-7370799
69*737'2737
7 9-73746751
8 9-7376611
y 9-7378.'i-l6
10 •)7;IHU-47'J
11 9-738'J41'i
12 9 73b4.'M3
in 97386273!
14 9-73h820l
15 9-73')0l29,
16 9-73yJO'>5
17 9-7393980
18 9-7395904
19 9-7307827!
20 9-7309748
21 9-7401C6S
'I'l 9-7403*>87
23 a74o:>jMr>
24 9-74u74'2i
I I
*25 9 7409337
26 9- 74 nasi
27 9 741,1164
28 9 74i:.»7S|
29 97416986
30 9-7418895
31,9^7420803
32 9-74*J'i7lO
33 9 7424(U6
34 974'Jfi520
35 9-7428423
36 9-7430325
f
37 9 743*-'226|
38 9'74.i4lL'6
.J9 97436lt24
40 9-74.i79'21
41 9 7430817
42 9-7441712
I
43 9-7.U3G0fi
44 9-7445498
45 9-7447391)
46 9 741'J28U
47 y745llci9
48,9-7453056
49'9-7454943
50 9-7456828
51 9-7458712
52 9-7460595
53 9 7462477
54,9-7464356
97466237
9-7468115
9-7469992
9-7471868
9 7473743
y-7475617
Cosine. Uif.
1944
1944
1942
1941
194U
1938
1038
1936
1 935
1933
1933
1931
1U3U
1928
19-28
1926
1925
1924
1923
1921
1020
lOlD
lOlS
1916
1916
1914
1913
1911
1911
19U9
190S
1907
1906
1904
1903
1902
1901
1900
1898
1897
1896
1895
1894
1H92
1892
1890
1889
188
1887
1885
1884
1883
1882
1881
1879
1878
1877
1876
1875
1874
10-2625325
10-2623389
102621451
111-2619521
10-2617588
1026156,»7
10-2613727
10 2611799
10-2609871
10-26U7945
10-26061*20
102604096
9 2077136
92081400
9208:)66l
92039920
9-2094177
9-2C98432
9-2102G84
9-2106934
9-2U1182
9 2115428
92 1 191.71
9 212.J912
9-2128151
9 2132388
9-2136622
9-2140854
9-2145084
9 2149311
9^2153537
Tan^r. Dif.
'102602173 9
10-2600252 9
102598332 9
10-2596413|9-
IO'i:)94495 9
10-2592579 9-
IlO 259066319
1025887499
10-258'i836 9
10 2584925 9
102583014 9
10 2581105:9
Il02579197 9
110-2577290 9
Ul2:.7.)384 9
,l0257i4MO;9
11^2571577:9
|10 2569675;9-
2157760
2161981
2166199
21 704 16
2174630
2178842
21&;w.2
21872VJ
2191464
2195668:
2199868!
2204067
2208263'
2212458',
221 6650
2220839,
2225027
2229212
9812-)174
9 8127939
9-8130704
9-8133168
981362(1
98138993
9 8141755
9 8U45I6
9-8147277
9 81.S0036
98152795
9 8155554
9-8158311
9 8161068
9-8163824
9-8166580
9 8169335
9 8172089
9 8174842
9-8177595
9 8180347
9 8U3098
9-8l8'i849
9 8 1 8y599
9 8191348
2765
27(.5
2764
2763
2762
2762
2761
2761
2759
■-759
2759
2757
2757
2756
2756
2755
2754
2753
2753
2752
2751
2751
2750
2749
2748
Cotan^.
2748
9-8194096
9-8196814 ..-.a
9 8199592' ^
9-8-2U2338
98205084
9-8207829
(102567774
10 2565S7-I
10 2563976
I0'2562O79
102560183!
|10-2')5S288'
' I
10 2556.194
10 2'>515»2
I0 25ri2f^l0
: 1
1 10 2545057
il0 2VI3l72
10 25-11288
,10^2539405
1 10-2537523
10-2535642
102533763
1& 253 1885
10 253000 -t
10-2528132
10 2526257
10 2524383
SecQnt.
9223^396
9 2-237577
92241755
9 2245932
9 2250106
9 '2254279
9 2258449
9 2262617
92283423
9-2287578
9 2-29I73I
9-2-295881
9^2100029
92304175
9 2:108319
9.2312461
923166(H
9-2320738
92324874
923290*17
9 8210574
9-8213317
9 8216060
9 8218803
9 8221545
98224286
98227026
9 8-229766
9 8212505
9-8235i44
9-8237981
9 8240719
98243455
9 8246191
9H'.MsM'.'6
.V46
2746
2745
2745
2743
2743
2743
2742
2741
2740
2740
2739
2739
2737
2738
2736
Covers.
2736
27J5
2734
2734
='^^"•-^2733
9 8259ftfl(iL-„.,
9 -^ '
9- '"
9^ ''*
9^:. -:^
9-8276241
98278969
9-8281696
98284423
9^8287149
98289*<7I
Culun:;.
2728
2727
2727,
2726,
27251
10-187482'.
10-1872061
10-1869296
10-1866532
10-1863769
1^1861007
10- 1858245
10-1855484
10-1852723
10*1849964
10-1847205
10 1844446
l(»^ 1841 689
10ia38932
10is;i(;i76
1018334-20
10-Iaill665
10-1827911
10-1825158
101822405
10-1819653
101816902
10-181 1151
10 1811401
I U- 1808652
10-1805904
10-1803156
1^1800408
10-1797662
101794916
10-1792171
10-1789426
10-1786683
10- 1 783040
101781197
10-1778455
110-1775714
10^1772974
10 1770234
10 1767495
MM 764756
lpl7620l9
10- 1 759-281
I
10-1756545
10 1753809
10!7:)107I
10 1748 UO
10 I74560fi
10^1742873
I»17401I0
10^1737408
10-1734677
101731947
1017'2!I217
10 17-26487
1(H 721759
10 1721031
10 171830^1
10 1715577
10 17128M
10 1710126
Covers.
9- 6583 fi 58
9-65N1231
9 6578903
9-6576574
9-6574245
96571914
9-6569583
9-6567251
9-6564918
9-6562585
Secant.
10 0764086
10-0764907
10-11765728
10-076G550
10-»7fi7372
100768195
10-0769018
10 0769S42
I0 0770(i66
10-0771491
821
621
8-22
9-6560250 |(t-077*2316
9-65579I5ll0-O773142i
9-65555791 10-0773968!
9 6553242
9fi5ri0904!
9 65485661
9^6546227
9 6543887
9-6541546
9 6539204
9 6536861 '
9-6534518
9 6532174
96529829
96527483
9 65 25 136
96522789
9-652tU41
9 6518092
9651!j742
9-6513391
9'6MI039'
9-6508G87
9 6506334
96503980
9^6501625
9 6499269
0-6496913 100794800
9 6494556 10 0795640
9 6492197 10 0796481
9 6489839 100797322
9 6487479 10 0798164
9-6485118 10O79JO06
1007747951
10077')62l'
100776451'
100777279
100778109
100778939'
10 0779768'
10 0780599
10 0781430
1007H2262
10 0783094
10 0783927,
10 0784760'
10 0785594
100786428'
10 0787261 1
10-0788098'
10-0788934
10 0789771
10-0790607
10 0791445
10 0792283
100793122
10 0793961
Oil J 'i'nn:;.
9^6-182757
9 6-180394
9^6478031
9 6475667
9-6473303
9-6470937;
9-6468571 '
96466204
96463H;i6
9 6161467
9 6459097
96456726
9-6454.155
9 645 1 983
9-6449610
9-6147236
9 r^444861
9-6442486
Versetls.
100799W9
1 0800692
10 0801536
Ur 0802381
100803225'
10-08040711
10-080.1917'
10^08057631
10 084>6610|
10 0807458'
10 08083061
10(1809155
10^08100<M
10 0810854
100811704
I0-08L-255J
10 0813406
10-OS14'J58
Cusec.
I
1>. Cosine.
9-9235914 60
9-9235093 &9
9-923427258
ft.„ 9-92334^)57
^*.V9y'2:J2628 56
Jn»|l^9-2;lI805 65
gj;! 9-9230982 54
nojl9-9230158'5:j
"-7 9-9229334 52
°7'9^9228,")09 5I
^:;^9-y22-'384i50
"-!:!9 9-2-26858!49
™9-9226032|48
j.5„'9 9225205|47
l^ 9 9224377 46
^riS 9 92-23549 45
2^; 9 92-22721 44
2^"i9 9221891 43
^J|9 9221062 42
^,-.19 9220232 41
2^ ;9 9219401 40
J:" 9 9218570 39
J;., 9 9217738 38
f"..-; 9 9216906 37
jj3i9-92 16073 36
g„. 19 921524035
™ 9-9214406 34
?:;7,9 92l3:i72 3J
'"='9 9212737 32
8351
836
;9 921 1902 31
a-,, 9 9211066 30
83/1 I
o^j9 92l0229 29
„^*!99209393 28
9 9-208555 2?
9 9207717 26
9 9206878 25
9^9206039 24
838
838
839
839
839
a:o
9 9'205-2OO 23
oj, 9-92043(To -22
^^ 19 920.::. 19 21
2:A!9-9202678 20
842!
842
9 9201836 19
gj3 9-9200994 18
ft,.j99200t51 17
2. .19^199308 16
844
845
8'i4
646
846
846
847
848
848
S49
849
850
850
8!}1
8j1
852
D,
99198464 15
9-9197619 14
9 9196775 13
991959-29 12
9-9195083 II
99194237 10
9 9193390 9
9-919-2542 8
9 9191694 7
9-9190845 6
9 0189996 5
9 9189146 4
9 9188-290 .3
99l874li' 2
9t865!M I
9-9185712
Stne. I
56 Deg
33G 34 Deg.
NATURAL SINES, &C
Tab. y.
10
11
I *i
13
14
15
III
17
Its
I'D
•J I
2*i
%i
'A
25
2U
'27
•IH
.'*J
:m
31
3.i
3-1
3:t
36
37
as
3y
4U
41
1
43
44
45
4(
47
41
Sine. Dil
1591929
••ri94.j40
5y67jl
:i59yu;'j
60157-2
5G03981
5606390
5C08798
5511206
^fiI3614
r>SI6021
5R 18-128
5G20834|
5623239!
5625645
5628049,,"^ i
■Mi32sr)r :1 .
•2411
i24n
2411
'2410
,2409
2409
;240&
2408
240s
.240;
2.io;
2406
2405
2406
V63526U
2403
i2403
5037663
5640066
5642467
5644}^6«t .,,,,
2403
2401
2402
5640670
.1652070
5654469
5656868
5659267
5661665
5664062
5666459
56 688.', 6
.'•671252
567.l64>i
5676043
5678437
24(»0
2399
2399
2399
2398
2397
2397
239
2396
2396
2395
•i391
2395
Covers
440S071
UU566U
1 103249
440083H
439^1428
439(i019
4393610
4391202
438S794
c
osec.
I -798391 6
1 7875208
1 7867508
I -78598 1 7
i 7852133
1-7844457
17836790
I 7829131
17821479
43S6386 1 78138^16
4383979 I 7806201
4381572 1-7798574
4379166 1-7790955
4376761 177S33-I4
4374355 1 7775741
1371951 17768146
43G9547 177G0559
1367143,1 7752980
4364740 17745409
43623371 17737845
4359H34 177.i«Si!Hi
4357533| 17722743
435,513I|I ^715204
43527.(1(1 1 7707672
43j0:i30| 17700149
Tuiip.
6 74508 5
f7493ls
6753553
6737790
67620-28
6766268
6770509
67747.')2
6778997
6783213
s74't-.'
67:>1741
6795993
■'6808321
56832 i.'5
5685619
2193
2394
.'392
2392
^692795.5^^^
56951H7L,,.,
5690403
704747'^"'**'
6 -(00246
6804501
680S758
r.8l3nl6
6s 1 7276
6821537
6825901
6h (mk;6
6si|.I.|,i
6SfH';0I
*i8i:87i
68 47143
4347930'I7C92633 085U1C
4345531 117685I2-S 6855692
4343132' 1-7677625 68599.>9
4340733 1-7670133 6864247
4338335 17662649 6868528
4335938' 17655173 6872810
4333541 1 1 7647704 6877U93
4331 144 1 7.. 40244 6881379
4328748 * 763271*1 68^5666
43L'f.3'>2 17625345 ^hsU'jS.S
4323957 1 761 7908 ■894.i4i
43J1563 17610478 6898538
Cot
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4319168' 1-7603057
4316775 1 7595642
1314381 I7f»88_'36
131 1989, 175S0837
4309597,17573446
4307205 17566063
6902832
69071:^8
6911425
6915725
6920026
6924328
4304f>13 1-755S6>7:692^63:^
5707136
5709524
57U912
714299
7166^6
5719073
238S
2388
12387
23H7
23S
572l459l|^^
5723844 03^^
2385
726-229
5728614
■» 730998 ;
■2.381
5733381
383
238,i
D.I.
1755I.L
1754:*!'
I ?■■"•
I :
ir,._..._i
17514595
1 7507273
1302423
i3O0O32
1297643
4295253
4292864
4290476
4288088
428f>70ri7499958
428331417492651
1-4825610
1-4816311
1 4807021
1 4797738
1 4788463
14779197
14769938
14760.88
14751445
1471'.'-;'-
147 :
I 47:
I 47U:i5.1
14705.350
1 46911155
1 46Hr.967
1 46777F8
1 4668616
14659452
14650296
1-4641147
I 463. '007
I 4622874
I 4613719
14604632
SecranL
12062179
1 2064547
1 2066917
1 20692S8
1 2071662
1-20740.37
12076415
Vers.
Oil
170962!'
17112.
J71287-'
1714507
1716136
17177(.fi
1719397
.[Cosine '
16 J
I6J1
IG31
I '-3 !
1-4595522
1-4586420
1-4577326
1 4568240
1 4559I6I
1 4550090
12078794
1 208U75|l
l-20!i072U|l729l-J .
I 209311'' I 7:'!^ ;,
1209:
1 2lO(^
121o:
l•21U50i*;|l'■^Ml^/
12107500 17406571
1 2109905 174-2297'
1 2ll23lJJI74/tiil«
12ll47."'-i.''-"
1-211;
119.=
1 806
Wi-li'
Ifi4*i
164i
16!
1750509 ,.,.
1752153'!'^.^
1 45410-27
14531971
) 452-2923
I 45l,{vSM
1 4504850
1 4195825
l-4486«0y
1-4477798
1 446M796
141^9801
I 4450H
14441834
42809-27
4278541
1 7485352
1747=060
1276156 I74;0776
4273771 1746.3499
1271386 1 7156-230
1260OO2|l 744-969
1^66619 17U1715
1-7434468
Secant.
6954496
6958S13
6963131
69674M
.971773
6976097
6980422
698'! 749
(i9>9it7f*
r.'l'.'SlO'j
6*97741
7002075
Cotan.
1-4432862
1423897
1 4414940
I 4Ul59yl
1 4397049
I 4388114
14379187
14370268
I 436i;j56
1-4.352451
I 4.3435.M
14334664
1-4325781
l431(i9(W;
1430-1
1 429'
1-4290.1.0
I
12I2I960
12124377
12126795 17
1-2129216 1
I 2131639 175ru:
I 2131064 175873-
1 2U';491
1-21 389201 1*
I 2141351 l"
1 2U3784'l-"
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1-2148655 17686361 '
1-2151094ll77i>""-l
121535:5 I'^
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1-2158423'I'~
1 2160870 '*■"
1-2163319,177;? J'.O
1-2165770 17^02161
1-2168.
121701
1-21731 J* w"^:.!- ■
I 2175594 1786848
12178055
165:
165i..
1-2180518
1 2182983
12185450
1-2187919
1 2190390
1-219-2864
1-2195339
1 2197«]6
178850^
1790)6^
179183(1
1793191
1795154
179r^i;
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1-4281480 l-2207746|I808480
■>»ff.
Cosec
166'.'
Covers Dif
.1-.14;
I
iMIlC, i
55 Dep^.
4
\
34 Ueg.
LOO. SINES, ^.
337
* Sine. 'Oil' Coscc. Verartls.
2 9-7-179;UiO
4 9 74S30'J9
5 9-7-li4afi7
6 <J 74Sb8J.l
7 9-7488ft95l
69-7-4g05'i2
9 97-iy24_'S
I0 9 7-194J87
n 9 74g<.U8
12 U-74y8O07
13 9-74996661
|4 975fll7.?.V
15 9-750JS;g
lR97iO.UJ4
17 9-7:»07J«7
18 9-7&U91 lU
9-75 10991
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9-75U(i91
22 9*7516.538
23 9 7518a8:»|
24 9-7&-20231'
I 1
25 9-752*2075'
26 9-7-.2J9I9
27 9-75*J5761,
28 9-75J7602
2997.2-J442
3V'9-7yn28u|
31 9-7533 us'
32 9'7J34»5l
33 975;iti7*m
34 9 7:.3^6.i4
35 9 73404.7
36 9-75422b8
371^7544119^
38 97545949
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40 9 7649dU4
41 975SU31
ri 9 7553^56
43 9-7>5508O
44 9-75*KJ'J02
45 9-755^24
46 9-7560J44
47 9-75(i2JG4
48]97564I82
19 9 75(i5 99
5()'9-75'i7nl5
51 9 7509030
52 9757.414
53 9 7573-^56
54 9 7b7^um
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1865
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1857
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333 35 Deg.
NATUR\L SINES,
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3
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7
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9
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57 976a(;»i6fi
976887M7
9769(Mli
9 7692187
Cosine. Dil
lU-2.>!t0726 y
lU2Jh'^-! "'■
10 2:i.M;
10-2.X"?". ^
10 jJ8.j.»;(.y
10-2361792 9
]0 2JS0O0s'9
10-2378225 9
10 2376444 9
10 2374663 y
102372884 9
lU 2371106 9
l023<i-)3;9 9
io-2a67:.:);i 9
lU23ii:-778 '.'
Hh2.!64(HJi •<
10 2.(62^11 -'
10^2360460 9
'l0-23r)8..89'9
10 2J.>(.920 9
10 2;i5:)151 9
]0 2:i5J381 9
10- 23516. 8 9
1023-1 !t85.l 9
10 2,148(189 9
l0^2J4(.J-26 ti
1U2>4456I <j
I0 234_'h03 9
102111043 u
l02.i39.'S'» 9
9 8-15226^
'Jrt4.iiy.*>6
9 8157614
9 S460i.lJ
9 84n3(UH
9H46:i70:>
9 84'.839(i
9R47l07:i
9847:(76u
9 8176444
9 8179127
98ltil8l0
9-8484492
262:.052 9 84S7I74
2640938 9-8497S96
2614929 9 8500575
2648899 9-8503'25;j
265-J866 9 850.59 il
26568 !2 9 85(18608
26f079.) 9-8:. 11285
2<ifi4757 9 8513961
26Gs71h9»51(;637
2*.72674 9-8M931
2676629 9-8521987
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-';::■.. . ■■int;
2»92431|y-ttJ32680
2'i9''!"' n.«-. r. t'>
270(':.
270; -J'
271 S20jy>»J4.iJ ■.')
■-7t2l40|9-854(lo:n
271:.o75 9 8bl870l
272(Hi(V>'9 8>'»l:{72
272 I'. - ■■'II
27jr • '''><
.7(17 '
' l(^'2337527'9 2713571 '9 8"»r7374
, 1 2:J3577 I 9 27 1 7 19 1 '9 8570039
I02.'J34«15 1>'275I409 9 8572704
lO 2;J3-22l.l y 27.'.5 125 9 H^^7r^r,H
10 2 iJ0i08'9 2759239 9 >■
'10 23-J8756'yj76l51 9 -
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^lii ■_■ .-J 1 -ui. ', _';,■ , .
'lu 2.i-'i7jy Vj;;-
lUiiliOOll 9 278:'..'-.„ .... >
i68S
i6ft8
26^8
2686
2<;S7
-2<i8-»
2685
J6S'i
2';8i
2683
*J68:i
26:2
•.*G82
2681
268 1
2Ht(0
2iiti0
2679
-i67H
2678
2677
2677
2676
2676
2 7..
•267..
2*74
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, 1
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26' 5
266.)
2664
Coian2".
10'i-il8265
102316520
102:M4777
102313034
10 2.111293
10 230955-
10-^107813
9-2788584 |9 85'.J066
SecanL
'J 2802 1 6/ (9-8 .07*296
9-2sy6058 9 8609954
9 3MH9947 9H612610
,2(*jU
26C0'
]'2*,5»
2656
CoviTs.l C<)tuiifr>'l)>l>
101547732
10 1515044
10 1512.156
|0-l.'i3966.S
l(H5369H2
UV 15:14295
I0-1531(ii0
CiiM»r.s.
•^6298^412
9 6235985
9629.J5ri7
9 629tl-2h
9-6-28.H(i98
96-j862(7
9-628.I8:i6
10- 152 -925 962^1403
S( cant.
10 0866355
1011867240
lO-tl368l25
10 08'i'yOli
lO08t;'JS08
10 0870785
10 0871 72
10 0872ir0
10 087344'J
10 0H74(3U
iari26-24o|9-627897o
10-15)2:1556 9-6v;7653«
10 1 520H73 9-627 il(H i 10 0875228
1 1 5 I .s ! 90 ' 'H.27 I (.(i5 ' 1 0871. 1 1 «
IO-1515508|9-6269228 10-0077009
lU 1512826 9-6266701
10 151014519 6264352
10 l:>07464'y 6261913
10 1501781196259473
10 15(»2I04 'J-62570.31
10-l499425'9 625458i»
10-0877901
10-087-711 J
100S796K'.
t0 0380'.7»
10 0881472
10 0082366
D. ' Cosine. '
845
885
886
887
10 1496747 9-6252147 10-0883261
10 I494069j9-(i249703 10 0884156
10 1491392 9 62472.58 10 0885052
I0l488715|9-6244'slj;i0 0^&5949|
10 14660:i9 9 624-2:i67<lO 0886H4'>
10-l4?t3Ji.3 g 6-23991i»!l0 088774J
9 6237471 10 08>>8W1
9 i235(J2J 10 0889540
I0-1480r.8H
10-1478013
lOi I" ■ — '■'■;■■ - ■ ...Mv M. ...
10 1
10 I . ' , : ■ - .
10-1467320 9()2;f62l9 10 0O93U0
9 622-2765 1 10 0891041
9 6220311 10 0894943
lJ-6217855 I00H95.S45
9 6215400 10 08J6749
96212943 1008976^2
9 6210485 I0 0b98556;
10-1464618
10 146 1 i»r7
10145U3O6
10U'.6(.:(5
10 1453966
10- 14 5 1 -296
10- 14 t862H 9 fl.'/^^O-ir. in 08'19461 '
10 1445»*', ,
I0-I4432''
10 14.1-2626 9 6133256 10 090 1901
10 1429961 9-6190792' 10 (»'J05810l
10 1 127296 9 6l.ya32B!looyo67l9;
10 1424632 9 hH-,860 10 Oy07l»-29
10lliiiy69 96183392 l00i(i»539
10 I4l930(i 9 6|ttu:24 10 0y094jo!
10-M16C43 9-6178455 10 09lOir.ll
inui3«isl 9-hI759*5 IOOyU'j73
■ irr>l4 IO0912I86!
I '1012 10 0'Jl.3ll99'
... : .; l*,S5l.y 100914012
10 1463339 |9 616(j096 10 0914927 1
''* '■ I - '»■'"'' *"!l'lO-09l584l'
100'J16757
: ' Iooyl7673
10 1392704 1'i-hl 56 192 iauyi8,>89|
10 U90046 96153714 I00yl950«
10•I;^^73yo '^61512^■||I0 0y•2O4•24
Tat.ir,
Vcrseii«.l i.'t)S«rc
X 2
9-9133645 60
yyi3'2760 59
9 9131875 58
y-91309S9|57
56
55
54
51
y9130l02
?SJ 9 9129215
^; 9 9128328
„^,'99l-.:7440
?2;'991265..1|52
°°,-',i9 9l2-.6l.2'5l
2; "9 9124772 50
2;"9 9l23hS2J9
«^j99l2299y8
„„„ 9 9122099 47
»;^.j 9 9121207.46
™99120315'45
J^,'9 9liy4-22,4I
2pj'9 911b528|4.I
5?^^,9-9ll7634,2
^.,., '9 9116739 41
2;^;'j99ii5dU40
2 ,9-9111943 39
2.-it9 91I405ll38
2,7 9-911315537
«;;^ 9 9112257.36
J.. „ 9 911 1359 15
«;;-^9-9ii04..o;a4
^ 9 9l0956r3-(
" 9'JlOb66r,32
y 91(7761 31
^"j 9 9106860 30
902
902
904
9(3
904
905
905
906
907
906
903
908
90U
909
910
910
911
911
912
913
913
913
915
911
916
916
916
917
918
9 910')9't9|"29
9-9105057 28
9-9104155 27
'J 9103-251 26
3910-^348 25
y 9101444 24
9-9100539 23
9 9099634 22
y-9«98728|2l
9 9097821 20
y 9096915 19
y yoyi.ou? is
y909')O99 17
y-90y4l90 16
9 9093281 15
y-9092371 14
9 9091461 1 3
y-9090550 12
I
9 9089639 1 1
9 90887 .'7 10
9-108781 4: 9
9-90669011 8
9 9085988 7
9-9085073
9 9084159
9 9083213
99082327
9-9081411
9-9080 19 1
99079576
D. S.ne.
54 Ui'ff.
340 36 Deg.
NATURAL SINES. iScC.
Tab, 9.
58SU-J0ri
WSi? >8
5884'JIU
5891 <J64
589 4JU
5899U11'
59ai.i6l
59037U
5906057
5908404
14 591 07 '.U
15 5913096;
IG :>9I544'J
59177«
l8 59iiUi;i'2
r»922476
59-J481y
59'J7I6;j
59'-W505
5931847
5934 18U
59365;i()
MI38871
59JI..*U
9 13550
y45s«'j
5948-^-^8
59JU56fi
595290.
5955241
59J757;
59.991.1
59ti*i24Ii
31
3-2
33
34
35
36
3715964584
59A6918
95925--;
5971586
5973919
5976251
5978583
5980915
5983246
598557;
5987906
599*123
5092565
5'.I94S93
59:<7^2I
5999549
600187).
U004J0::
6006 'u'S
aOOH>i54
/.01ll7y
r.oi3"»o
60 'iOl8i 1)
2353
2352
2352
2352
2351
^351
J350
2349
2.119
2.349
2.WH
J348
2347
2346
346
' Sine. Dil". Cover- Cosec
1-7006208
1-6999107
1 fiy9J61J
1 6985825
I fi979044
1-697227 1
1-6965504
1 f.95!i744
1 6951990
1 6945.M4
1 693H504
1 6931771
1122117
4119794
4117142
4115091)
4112733
41103a7
4108030
4105686
4103337
4100988
4098639
4096291
4093943
4091596 1^925045
4089250, 1-691 8326
,^,'40Sfi904'l'69n6l3
.Jj^jg 4084558 T69O4907
2315
2344
2343
40.^2213 1*6898^08
40798681 6891516
407752a 1-68&4830
.„, 4075181 16y78151
,,.; *■; 4072S37 1-6871479
"I - 4070495 1 6(<64hl4
:,^, j4U6ttl53 16s5sl55
2jJj4065Mn 16851503
2341
2340
'4063470 1 6844857
4061129 1683^*219
405H7S9 1 6831586
:,.",, 40 0450 1 6824961
.r.;,. 405J111 1681834:;
2;(3'(
2338
2338
•2337
2:J36
2336
23-i(.
2335
2.334
2331
2334
U3
233:^
2.33 :i
2332
2,131
331
2(9
2330 i
342
4051772| 16811730
4049434 16805124
4047096 1 679S525
404 J 759 16791933
404242311678.^347
4U4I1087 1 6778768
40J77il 1 16772195
4035416 16765629
403 !0.t2 I 6759070
4030748' l'675-2517
40J84l4|l 6745970
4026081' I 67394.10
402)749 1 673^897,
4t>2ni7il-672u370
40ll'0tt5 1 671985.'
4010754 'l-67133.3h
4U14423 I670682>
401.094 l-67ia328
Tmipr.
.^.^^40097.'4 I 6693833
..^^!4007j3-. 16687345!
,ij,Ti;400:>l07 16(i80864
r;|" 4002779 l-6(,743tiJ
:;i.T^ 4000451 1666792U
r*"' 3998124 1-661.1458
23:i6
232
-2326 1
32.
(24
726542'.
7269H7 I
7274310
7278767
7283218
7287671
729-2125
7296582
7301041
7305501
7309963
731442m
7318894
73-i3;lfi2
7327832
733-2303
7336777
73^11253
7345730
7350210
7354 91
7359174
73(;3r.f:o
736.-* 147
7.172<J35
7377127
73816211
7386115
7390;! 1
7395110
739961
7404113
74086 IH
741; 1-24
7417.3.1
422143
74261.55
74:11170
7435686
7440204
7414724
7 149246
7453770
7458 29^
746-2^24
7467.154
74718-^6
7176420
7430956
748.494
7490ttl3
7494575
7499119
7503665
7508212
CutBll!<:- ^OCDllt.
|3995798 I 665.00:
1399.1472 16648-»53'7512762
3991146 1-66421 107517314
.398882! 1*.63>673:7521867
3J.'('.4'J7 1 6629213 ^.'•26 t'23
'r:.tO'j8l
753.V.4I
% r,oi3:.01 ,:::,] 3J.'('.4'J7 1 6629213
■ 60i:.82r ."i:;,..l9S4l73 1 6*.2.8ly,
3981850 16016401
C-Nri!** i)il. Veis. Si'caiit. C'o*aii
3763819
3755403
3746991
37.18.591
3730 1 9.1
3721806
37134-21
•3705047
3G96678
■3688315
36799.59
■3671610
3663267
3r,5493
3646fi0
3638279
3629963
3621653
3613350
3605054
3596764
3 ■> 88181
3580-204
3571934
356307U
3555413
3517162
3538918
3530680
3522449
3514221
3506006
3197794
■3-189589
3481.39U
3473198
3465011
3456ai2
3448658
3440492
.^132331
■3424177
3416029
3^107888
3399753
33916-24
33^3502
• 375366
3 :67275
315917:
'33)107 .
33(2 84
•.«.34900
33-26822
-33 1 8750
-.331068.
3 02 .-24
.32-.M57 1
3.'86:>-2J
3.'7848.t
•3-270448
T«im
1 2^i606ao
I ■•2.16.3293
1-2365909
I 2368V^(
1-2-371146
12373768
12J76393
12379019
1-2381647
1 2184278
1 ■■23869 11
1-2389546
1-2392183
1-2.39482.3
1 2:)9746.1
1 '2400108
1240-2754
1 24U5402
1-2408052
1-2410704
I 241335:i
1 2410016
1 2413675
1
Vtrs.
1909830
191154(1
1913251
1914963
1916675
191838k
19-20101
1921815
1923530
192.5246
]\'[
1932115
19338.J4
1935554
1937274
19.38995
1940717
1942440
1944163
194581
1947611
Oil! Coftitie
1710
1711
1712
1712
1713
171.1
171 J
171-.
171.
171'
&O»ril70|4«
Mk!$8460|j«
8086749 &9
8085037 57
e<083325M
KiMlG|i55
,7,j80678<«[4;
421336,194933
1 242399911951062
12426665 1952789
1-2429313! 1 9545 1 fi
12432003: 1956 24
1 2434075 195797^
I 2^1373-19 1959701
l-2440O26| 1961431
1-2442704 1963162
1-2445385 1964893
I--244HO(i<( ly6fti'25
1 24507.54 1968358
1 24.'S3442 1970091
12456131 19718-25
1245a823|l97356u
12461518 1975295
1240421411977031
1 2406913 19757G8
1 2469614
12472317
12175022
1 -2477730
1^0440
12483152
I248.58'i.
12488583
t- 249 1302
I 249402:1
1 2496746
1 2499471
12502199
12504929
1 2507661
510396
12'iU133
2515^72
12J18.I3
19805O5
198-2-244
19839H2
1985722
1987462
1 989203
1990944
199268
1994429
199017.1
1997917
199H062
-0014<t7
-2003153
21 KU 'Oi'
2O0(. ■ 48
200* 196
2010145
'2011895
1 2i21 .■.7r2013(*l.
CoHcc. iC()VPi>i Dii
.4
^O'-iO'jj ii
80592>C1 42
■ \
9(f4eiy3«t Sh
I72.i
1721
1722
172.31
1 72-;
172 4
1 72 i
17:2.'>
172».)
1727
1727
17.S
17-2"
17:ju
1731
.-^j80^3»i>*.3M'^
173.' ~ ' '!
173,;
1^31
1731
1735
oi^jsjtty ,10
17:J5
17.16
1737
17;J7,
I73<J|
1738!
- ■ ■ :i
802r;440 23
8*i24rM'i /•
I
I
S0l'.'l9 :,l'i
«0l775!;ll3
1740
I7 4(..
1741
II .
j^i;jsii073Mjii
1744
1744
1745
1745
174*.
1747 1
1748
174^
174'.*
1750
1750
>^M»5571 II
.80i».l827|lO
8fwi2nn:; s
't'_"_.8i7 6
'M»sl*Ht 5
798hl05'
79*63-. 5
Sine.
53 Df ff.
36 Deg.
LOG. SINGS, &C.
341
' Sine.
097r,9'^l87
397697;i9fil
5;»770UAfiK
69-77W26<)l
7 9-7704332
8 9-77l>C,0*i3
y;97707;9J
109770952'i
n:9-7711219
1731
17 JO
1729
i7i;7
12,97712976 [Jj^^
13977 M702
14 '9-77 16426
15:9-77I8B0
I6|9-77I9H72
ir|9-772I.VJ3
I8!9-77233U
I9;9772S033
20 9 7726751
21 19-7728468
22 9-77:i018&
23;9-773I900
24,9-7733614
25 9':73M27
26 97737039
27,9-7738749
28 9-77 104 S9
29>7742168
30j9^774387«
3l!9-7745r»fi3
32 '9-7747288
J3 9-77H993
34i»-77S0697
35 9-7;52.J9<J
36j9-77M10]
379-7755801
38 9-7757501
t9»7759199
40 97760897
41 9776:^593
42 9-7764289
43 9 776ft9S3
U 9-7767676
45 9-7769;*fi9
46 9 7771060
17 9-7772750
4i 97774439
19 97776128
50 97777815
M 97779>01
52 9-7781186
53 9^77c*2870
54 9 7784553
55 9-7786235
'►6 977879(6
57, 9- 77 89 -196
58 9-7791275
59 9-7792953
lit* 9779463 .^
Dif.
1733
1737
17Jfi
1736
1734
1733
1731
Cosec.
102307813
10-J30fiO7'
10 2304338
10 2302602
10 J3l»086ft
Iii-2'2''9l32
10 2297399
Vtrspflp,
9 2809947
ii-2»l::834
9 2.SI772(t
9282160.1
9-282'>4Si
9-28293M
9 2833241
9-2837117
10-229:1668
10 ■J2'.I3937'9 -2840990
10-2292i07[9 2844S62
lu 2290478 9-2848732
10 22887:il|9 2852600
10-2287024 9 28:i(;4(i6
1724
1724'
1722
1721
1721 1
17l9i
1718]
1717
1717
1715
1714
1713
1712
1710
1710
1709
1708
1707
1705
1705
1704
1702
1700
1700
1698
W.91
1696
1696
1694
1691
1693
1691
1690
1689
1689
Tanp.
98H1-2610
986I.)2(;7
9-861 7'.»-.';i
9862(l.'i7e
9H(i23233
US i2.)«87
9Bti285U
9 8631 1 9'
98633848
9 8636'>0O
!J8i3'Jl52
9-8641803
9-H»i444'il
lfr-2285293 92860330 9 8 47IOj
10 22S3^74 9-2864192 9 8619755
Ilh22.i1 850 9-2868053 9 8652404
10 2280128 9 2871911 9-665 j(»53
10 2278407 9 287r-.768;9 8657702
10 2276686 9 28;96-22|9 86.i0i50
10 227496719 28H3475 9*8662997
t02273249!9 2887326'9 8665644
102271532 9 2891 175 98668291
10 2269815|9-289'>022|9-8670937
10-2268100. 9-2>*9s867l?-Nfl7358;i
I0-2'266386I9- 290:71 r9-8676228
10 2264673|9-2906552 9 8678873 .,,. .
10-2262961,9 2910392 9 8681517 "
1687
1686
1685
1584
1683
lf382
1681
16S0
1679
1678
1677
i
2643
2644
2612
-'6 13'
26121
2'i-l 1
2ii41
2r,40l
2b40
2'40
2639
2fi38
2(>38
J6:i<i{
26(71
-0(71
2636
2636
2636
9 ^>i .790 9 H734302l^,I.*'i^
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10 0987979
12:8856
1226228
1223600
122U973
1218346
1215719
1213093
1210 467
1 207842
120521 S
1.02593
1199969
1197346
1194723
1192100
1189478
118 68 '16
118423'.
1181614
n78993!9 59")2539 10 0994706
n76373!9 5949987 100995.69
1 17 754'9 5947434 IOO'.W i63-i
U7U34I9 5944881 lOO'ta7-97
1168510,9 59.2326 10 0998562
1165897 ,9 5939770 10 0;»99528
1163279 9-59 17214 101(1110494
11.^06 -2 9.59.34656 10 1001461
1 1 ■ .8044 9-5932098 10 10{)2428
II ■>5l28!9 5929538 10 HH1.3396
J 152811 '9 5926978 10 1004.364
115U195 9 5924417 10 1005.333
9 6000849
9-,i9y8314
9 '*995779
9 59932 13
9 5990706
95988168
9-5985629
I
9-5933089
9-5980549
9 59781H)7
9-59754;>l
9 ,)972921
9 5970376
9 5967831 10 88938
9 .'.965285 100989898
9 5962737 10 0990858
9 5960189 10 0991819
9 5957640 10)>99278l
959r)5090 10099.1743
2614
llO
261
2i
2613
2612
2612
2612
2.11
26 1
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2', 10
2609
2609
2609 ^
2609 *"
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.605 IS
200.I \l
1147580
1 1 4496 .S
in 2350
n397.;6
ll.i7122
9 5921854 10 1006:103
95919291 M IH07273
9 5916727 10 1(K)82J4
9 5914162 in IU09216
95911596 10 1010188
,.10
IJ3 10 ll34508iy590J029 10 lOllitiO
U31895 9 5906461 10 1012133
1129282 9 59(»3.-.93 10 IOI3107
1126670 9 5901323 10 1014081
]\j^,i>: .i-.^.t47-,2 10 1015056
H21 i^l 101016032
111-- ' :'.US 10 1017008
O. Cosine. 1 '
1116225
1113614
IIUOOI
1 108395
JI0:>7h6
1103177
1100.568
1097960
109-.
\0'2.
10901 .J
1087532
10819-26
1082121
1079715
1077110
1074506
1071902
9-58)l034 10I017915
9588H460 10 101h962
y.58858HS 10-10199 40
UJrt8 M3S 10 1020918
9 5880731 10 1021897
9:ih7ril53 10 102.'877
9 5875-.73 10
9.^872993 10
■ -1112 10
- !0 10
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9 58G266:i 10
9 5M60078 10
9 ■'8'.7492 10
9:.8'>4905 10
9 585231s' 10
9 5849729 10
9. '.847 1 39 10
Dif Tanff.
102 857
10-218 8
1^2.1919
102'iMOl
1 01:7 784
1028767
I02;751
1030735
10 11720
1032706
10.33692
1034 .79
Versed*. Coseo.
95 »
9.S3
953
95 4
95.
955
956
t90-2.l4a6
9 9022514
9 902i.'iHl
9 9020628
9 9')l9r)74
9 'JO 18719
9 9017764
-.- 9 '016808
pfH 9 9015852
ly, 9 90 1 48 >5
;?' 9 013938
^;;,, 9 9012980
g?5 9 9012021
960
960
961
962
9.2
963
963
964
964
965
966
966
9 90 n 062
9 9010102
9-9009142
9 900S181
9 9007219
9 9006257
9 900') 294
:t 9004331
9 900.1367
9 9002403
9 9U0I4.J8
9 9000172
96;
967
968
968
9 8999 ')06
9 899 .539
98 97.')72
9 8 '91,604
g-,. 9 89956.1fi
J*J9 8Jj4667
9 899J697
J^V;9?^9'i2727
,,-^98991756
u-Z 9 -990784
.7.3 U 898 812
^y • 9 8988849
-,,9 8587867
^' ■* 9 898 .893
9 8985 .M 9
9 8914944
\ib*JS .968
9 8982992
974
97,
976
976
977
977
978
978
979
980
98U
981
981
982
983
9:i3
984
984
995
986
986
987
9 8982015
9 8 (1 1038
9 8980060
9 8'.i79>H2
9 8^78103
9^977123
9 8I76I43
9 8975162
gS97.l8l
9 8973199
9 897-2216
9 8971233
9 8970249
9 p9692'.5
9 8968280
9 89 <729 t
9 n966,)0^
9 896.321
D. I Sifif.
02 Ucr;.
314
38 Deg.
NATIJKAL SINES, &C,
Tab. y.
Sine.
hTsgcTs
61:>8907
26161198
3 6163-189
4^61 5780
516168069
6 6170359
6172648
r.l74D;tG
6177^2-1
fiir'JaU
fil8i:ys
niS40S4
6186370
01H8655
(il'JOKtg
61'-»55«7
6107790
620007.1
6iOiJ5!i
6i!0463f)
6:»06917
6'^9l9H
6:^11-178
62I37&7
6i'I6036
62lH;n4
6225146
6227423
622t6i(8
62:11974
62^*4248
6'2;J(i522
B23o796
6241069
n_43:iJ2
624.'t6 1 -J
112478-5
(1250156
G2J2427
625.1696
625(>9l)h
62^9235
fi2 1503
626:i77l
ti2<i003H
6268305
'i2705;i
.2728 )7
6275102
'i27736(i
r)2796J)
6281894
62^4157
2»C420
6 2^1 (J iH2
6-;9094
6293204
Dif. Cover*
2282
•2281
22hl
22'<1
228U
2279
•2279
2278
227(5
227.i
J27ti
2^77
2275
2276
2274
2274
2^7 1
2^73
22731
r272i
2i'71|
227 1 1
2271
2269
2270
1^269
J2fi(*
226«
2267
2267
«66
J266
26i
26i
2265
2263
263
.'263
261
2261
Dii:
373V243
3783964
378 1 fig.
377 MOH
3777 13U
377485*
3772577
3770302
3768026
37fi:i75J
371.3178
3761204
3758931
37J665a
:i7'u:iHt\
3/V2115
J7VJ^44
3747573
3715304
374303.1
374076-
37:18497
3736229
3733962
373H;95
37^9429
727163
372489M
37^2634
37203C9
3718106
37I5S-U
J13i84i
371I3IH
3709057
3701.796
C
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Tang.
I 6242G92 7812856
1 6236648
! 623060!)
I 6224576
7« 1 75 ii
7^22229
782t)9l9
1 ii2H549 7<n6Il
1 62I2'v.:8 78i630i
16206513 7841002
1-6200501 7^45700
I 6194500 7850400
1-618850; 7855103
I 6ly25in 7.S5980H
1 6176524 7864515
I 6170544 7869224
1-6164569 7871935
1-6158600 7.'^78';49
I 6152637 7883364
1-6U66S0 7s«H082
1-6140728 7S9280-'
I 6134783 7897524
I 6128S43 7902'248
16122908 7906975
16116980 7911703
16111057 7916434
16105140 792H*i7
1 699922ft 7925902
1 60933. M
1 60 •57423
1 6081528
1 6U75640
1 6069757
I -6063879
1-6058009
1 6052142
1 60i6281
160104-26
I f;034'i77
1-60:8734
7930640
7935379
7940121
7. M 1865
7949611
17954359
17959110
7963862
7968617
7973374
7978134
798-2895
CtilatiiJ.
I 279941ti
1-27917*5
I 278407*1
1 2776419
I 27.8765
1-2761116
1275^73
12745&3:i
1 •27.38204
1 '2730578
1 272-2957
I-27I53I2
12707733
1 2700130
1 269-2532
1 268 19 10
t 267735.1
1-2669772
1 L66.'196
1 265 1626
1 26l70fi2
1 2639:>a3
1 263195U
I 2624402
l-i") 16860
1-26093Z3
I 2601792
1 2594-267
125^1)747
I 2579232
1-2.W172.J
12564219
Secant.
Vers.
1 25567
1-2549229
I 2541742
12534260
1 25-26784
1 6022896 7DS7659' 1*2519313
I 6017064'7992.|25 l2511Hi8
I (i0112.i7 7997193 1'2504388
I 60O54 1 ti HOO 1 963; 1 2496933
1 5999()00 '501167 H. 1 24894^4
I 5993790, HOIlJll 1 24S:040
1 5387986
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I 5976394
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1 51164824
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8025849
8030632
80354 IM
1 5959048 IM)4(I206
15953276 8044997
1 5947511 •04;»790
i 594I7'1I8054.84
|-5!l3:i99f; 80-9 82
I593U247
1 5924501
t 5918766
I 591 t033
1 5907306
I 5901584
15895668
15890157
Sr{afii. Cotaii.
S061181
80689S3
s07.K'^7
807^593
80-13401
8088212
809(025
8097840
Thii;
I 2690182
1 J "■■ '
I
1 -.,..>:,...
1 2701737
I 2704:3:
127075-29
1-2710429
1-2713331
I 2716235
1 2719142
1 27220:>2
1 272496:1
1 2727877
1-2730794
I 273(712
I 2736634
1 27 9557
12742184
1 2745412
I 2748343
I 2751276
1 2754212
I 2757151
1 2760091
12763(134
1-2745980
1-27689-2S
1277187^
1 2774831
1-2777787
1 278074 1
1 27,:*3705
12786667
I 2789632
1 2792600
1 2795570
12798543
I -^HO 1 5 1 -.
12H0! 'If)
1 2»(l747"i
I-.;il0457
1 -2811441'
ers.
Oil
i?n98y2 ,~.
21,
t''j:y
21.30660] I -ji:[7o6j350 .W
51
21324 45l
2134211
2136037
2137835
J 139633
2UI4J1
179G
1 79'.
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211-
21 t
■*:^^*'*'iUI^*^*^'»
1-2916430
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1-2822112
1 28-25407
l-282»ilMl
1 2^U401
2834406
2837411
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2S43428
2S46410
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2S52472
2S5519^
28:.8". 14
2861539
2864 ■>66
'2867. '»96
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2157648
2159453
21 6 12 '.y
2163065
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217J9l»
2175730
2177541
2179.354
218M 7
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.'184795
2186610
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2190.'43
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219.3577
J 195696
a 37
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1813
l**l-'l'" I.. -■ .
1814
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l9,6|7-rM90?3
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1817- I
1817 '- 'I
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1819'
2197515 ,„.>[J 7*024^ 17
2199335 ■ 7-00 ,h5 14
J201I55 " 15' 15
.202976 . 114
2--'04798 I
20.620
084J3
-^210267
2212091
221 916
215742
•2217569
2219396
•221 223
22f05l
-22-24880
2-22 -710
22285 to
1824
IK.'I
I>27
I8;i7
1830
1830
7/924311 6
(.'(tsec. Co^Hr** Otf
:?'
.)9,
777.1-0
7773290
7771460
Sine.
51 Dftr.
I
I
I
^
38 Dep.
LOG. SINES, &C.
345
Sine.
9-7893420
9^7B950:f6
9-789«fiM
3]9 7898'2'i6
4!97»9!)«»0
5'97yuuy3
6l9-79t)^lV4
7 9-7904715
89-7906325
9f979079.it
U 9-79 11148
12979I27M
13 9-7914359
U|9 7915963
15»'79175G6
;6l97'Jl9WiB
17 9-79J07(i9
18J97U22369
19»?92^W68
20|!>- 7925566
21,9 7927163
2'297928760
23>79a03.^:>
^4|9 7931949
259793354.1
26 &-79:tf.13S
27 »-79367J7
28'y7y38317
-i9'97y39907
30 9-7941496
31 197943083
32 9 7944671'
33 9794 ;'J56
34 !>7947?S41
35!979494'^5
36 9^7951005
I
Dif. Coflec. Verseds. Tan^. Dif.
9-7952590
9-7954171
9-7955751
9 7957330
9-7958909
42'979604B6
I
43 9-7962062
44'979fi3638
45 9796 J2t 2
46 y-79H(;7Kfi
47 9-796S359
4S9796993U
49'9797I501
50 9 7973071
51 9797464U
52 9797620H
53 9 7977775
54 97979341
55 9-7980'JO';
56 9-798247U
57 97984034
fl-79s5596
97987158
9-7988718
1616
1616
1614
1614
1613
1611
1611
1610
1608
1608
1C07
16U6
16U5;
1604
lf;03
1602
ItiOl
1600
1J99
1598
1597
I
1595:
10-2106580
102104964
102ID334S
102101734
10-2100120
10 2098507
102096896
lo-^ogft-js:.
10209.367'.
lojoifjo*;?
lO2(»90459
102088852
10 2087246
1 02085641
102084037
10 208245'!
10-2090832
10 2079231
10-2077631
1 0-2076032
9-326313S,
9^326f)806,
9-327047:i
9 3274137
932778(K)
9 3*281461
9-32S5121
9-8928098
9-8930702
9-8933306
9 89.ri909
9-8918511
9 8941114
9-8943715
9-32H877S 9-89Jfi317
9-329-i4.34 9 8948918
9;t2!){;os9 9-8951.1!',*
9329974i;9895ill9
9 330339i;|9 8y5fi7l9
9-33070ir9 89J93ll»
93310^8'* 9 8961918
9 3314334 9 89fi4517
9-3317978 9-8967116
9-3t2I6.'0 989f.97l4
9:«2fi26t
93328900
9:1332537
102074434 9-3336172
\Iqj 10-2072837 19-3339806
''^"10 2071240!9 .X343438
IVij 10-206964 5 :9-33470r,fi
j^^|1020;8051 9.33.0697
,-qo 1 102066457 9335 132 1
""110-2064865 9 33'.7g49
?Qni)0'-«'*^^273;9. 3361572
1590
1589
1587
1S87
1586
1585
1584
020*^1683,9336519-1
102060093
9-3:»688l4
lU-2058504 9-3372432
'10 2056917 9- 1376049 ]9-900364r)
10-J0f);')3.t0 9-3379 64^9 901 1237
y-897-2312
9S9749I0
9 8977507
9 8980104
9-8982700
9-8985296
9-8987892
9 8990487
9 8993082
98995677
9 8998-271
990tfTi865
9-9003459
9-9006052
lO20'>3744 933H3-2r^
10-2052159 9 33Sfi8Ky
..ajlO 2050575 93390J99
^^2*02048992 93394107
9 9013830
9 9016422
9901901.1
9-9&2l6(l4
KO
1581
1580
1579
1579
1577
1576
1576
1-^74
1574
1573
1571
1571
1570
1569
1568
1567
1566
1565
K)64
1564
1562
1562
1560
102047410 9.3397714 9-90241fl5
lU-2045829 9-3401319 9 90-26786
JO'2044249 9-3404922 99029376
10-2042670|9 3408524 9-!»0319'JS
I0 2U41091 9 3JI2124'!l9n34;.5'.
10-2(i39514|9-3415722 9 9037144
lU-2U3793«t9-34193l9
l(»-2»Mi64l
1U-203007U
Kri028l99
ro-20'26'l-29
io-2025;v;u
lO-202.3;92
I0'2022'22;'t
10-202O6.i9
10 2019094
10-2017530
I0 20r.9fi6
1020144114
IO201-2-S42
102011282
1342-2913
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93 13,I6kS
9 343727'.
93440863
9 3444U8
9 344^031
9 3451612
034 >5 192
93458770
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9 3419495
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9^90M>08'>
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9 9068188
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9'J(t7.3357
9
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9 90836112,
2604
2604
260
2(K)2
260:j
2601
2601
260 1
26011
2G00
2600
•2599
2599
•:^599
259H
-'598
259H
2597
2597
2596
2596
259
2595
2595
259
2594
2594
2594
2.)93
2593
J 59'.
2593
25V2
25'»1
2VJ1
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25^9
2589
25&M
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25S7
25Ht4
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2586
25S6
2*iB6
•2.VS5
!5«5
2'.84
fiS4
- 1
I
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nn?.
Col „
10-1071902
1 01 069298
101066694
10- 1 or. 4091
1OI06148Q
IOI0'>8866
10-1056285
tO10i3683
IOH):iloS2
TO 1048481
1O1045.H81
101043281
10-1040681
10-1038082
10] 035483
1 01032884
101030-286
10 1 027688
101025090
101022493
10-1019836
101017300
I0I014704
1O10I21DS
101009513
Covers.
101006918 9-578-2085
101004323 9-5779470
9 5847139
95844549
9 5841957
9 6839364
9.^83677l
9 5834176
9-5831581
9 58-289S5
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9-5-!2n90
9-58l85i89
9-5815988
9-5813386
9 5810:83
9-5808179
95S0.5574
9-58029(;M
9 5800361^
9-5797753
9 5795144
9-5792534
9-5789923
9-578731 1
9-5784698
10-1001729
100999135
10-09965 1
10 0993948
100991.(55
10 09-<N763
IO09.HM70
1O09H357H
1 00980967
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10 0960267
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9-5776854
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9-577 1C20
9 5769001
9 5766382
9-5763761
95761139
9-5758517
9 5755893
9-5753269
9-5750613
9 5748017
9-5745390
9574-2761
957401.32
9-5737S02
9-5734870
9 573-2238
9 57'296ii5
101195250319 5726970
10 11949915 9 57^4335
10 0y473'2S|9 5721699
10094l741i9 57190';2
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1 093956919 57 1 3784
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10 0934397,9 5708503
10 0931812:9 5705861
10092922719 5703218
10 ()9*2fi643 19 5700573
10 0924059 9-5697928
10 0921475, 95(;9-)JM2
I0 0918891.9 5692(>.i5
1U09163O8I9. 5689987
StrcanL D. Cosine.
01034679
O10J56';6
10.16654
1037642
01038^31
01039621
01040611
01041602
O 104.591
0104358'!
01044578
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01046565
0- 1047560
1018555
0-1049550
1950547
01 05 1 543
01052541
01053539
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01055537
01056536
01057537
01058538
01059539
1060542
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01062548
O 1063552
01 064556
01065551
1066567
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1070596
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1073625
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1076658
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9 8846775
9 884S717
9-88446 '19
9 884.1599
9 884 2540
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I
1
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i
350
41 Deg.
NATURAL SINES, &C.
Tab, y.
Sine. Di(- Covers
«5ti0r>90
656-^785
«564980
6567174
6r>69?fi7
6571360
6573752
iia5
JI'J5
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'i")84706
ri580083
5591271
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2190
2139
21881
2I&8I
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1437215
343'»U20
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3428J40
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342l0^fi
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669131)6
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CoHiiii' Dif.I Vers.
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869286;
8697976
8703087
8708200
8713316
8718435
1 524-'531
I V. 237433
1 52323:19
1 5227250
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I 52"lH76 873380ii
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1-518670-^ 8749201
1-5181661 8754338
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1-5151477 8785*215
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1-5141452 87y55-is
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1-5131446 HS05y.5.i
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1-5116472 ^821357
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1-5106511 8831707
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I-508I690 8857i3n
1-5076739 8862822
1-5071 7il3 8^680I7
l'5066'i52 887.1215
1-5061915 8878415
1-5056982 8883619
1-5052054 M8S.S325
150J7131 8891033
l-50i22U'8H99-244
l--5037-297|890l4ii8
1-5032387 8909675
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1 50-27481
1-5022580
l-5ul7(i8'i
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1-5007903
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1 4998141
1-4993-267
1 4988:197
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1 4973813
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1-4964113
I 4959270
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1 4914765
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1 1490176
M 48342
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11449762
1-1443011
1 1436326
1 14J96I5
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1-1409508
1- 14028 15
I »39i;i26
1- 13894 11
I-I38276I
I 1376036
J t.l694l4
I 1362747
I 135^085
1 1349427
11342773
11336 124
1- 1329 179
11322839
1-1316203
J 1309571
1 IJ02944
I i 9'i32I
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1 128.3088
11. 7^473
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11 -203271
M 256674
1-I23QU8I
1-1*24.1193
1 I2;i909
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1171305
1164768
1158235
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112)635
1119127
1112624
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1-3250130 ::452:>04
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2508516
2510143
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14 J2
1441
1440
1439
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1434
1433
1433
1431
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1430
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1429
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14211
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9-82:i972l
9-823113*1
9-8232555
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10 1827666
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10 181 8972
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10 I. si 0308
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10-180.VJ8H
10^1804550
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10 1795937
10 1794504
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10 1790-' 12
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10 1785927
10 1784500
10 1783074
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10 177SS02
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10-1774537
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10-1767145
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111 1764014
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9-389680G
9-3900184
9-39035 'U
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9-3910309
9 3913682
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10 0551831 9
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Secant. D.l Cosine. '
2544
2544
2514
2544
2544
J54.I
2543
J 5 43
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25 13
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2'i43
25 12
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NATURAL SINKS, C
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3250534
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3246243
3244098
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3239810
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2112
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2137
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3229099
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2130
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3203453
320l:tt9
319lMh;
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3194922
3192791
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1-I9-14;6")
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1-4925488
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1-4906280
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,17359002 23
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1971
17347 1731 17
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36389941266270ljj;^i5;|733r'iM|ij
3i.4;704r^<>70f.l'.'
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3651078j2674571
3654770'2 76551
36:.«1 4 267H53J
3i62l62 2680iU
3665y : ' :-^'
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1980
1982
732 1 4i.7
[y^',;7:{l9486
198
19*4
i»sec. I iiviTs l>i(
7317 Of
7315521
731 *5:i7
Sine.
47 iJe^,
i
42 Deff.
LOG. SINES, &C
353
1 9 82565I2
3 9 8259314
7 9 8264910
8 9 8.-nr>.'io7
y 9 a'jr./'ut
10 9tt-69l»98
n;9 8-i70493
]2|9-8*^'I887
I I3'9-8V73*79
I l4,9-8274fi71
L ||6'9 827CU63
■B||9■82^74^3
r T> 9 8-75^843
^ ]6|9-d28(>'i31
199828lfil9
iiO 9 s2»3006
21 9 8284393
22 9 8285778
23 9 8287163
24 9 82S6M7
25 9-82899.10
26 9H29!3rj
27 9-8292(ly4
28 9 8J9407')
'»*j 9 8jy:>454
3U9Si9&833:
3]'9'829e212
32 9 8299589
33 9 83U0966:
34 9 K3U2342
35 9^3037 1 7
3C 9 8305091
37 9 830G464
38 9 8307837
.-{9 9 8309209
4ll9S3IO:i80
41 9 83n9riO
42 9 831332U
43 !)8ai4Gti8
4 4 9ya|()0*i6
.is 9 8317123
4fi 9-8;n8789
47 9-8.('20l55
[48 9-8321519
'49 9 8322883
50 9-8 I24^4G
51 9 832.'<609
52 9 H326970
53 9-8328331
54 9^8329691
5598331050
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57 !)N.j3,(7(",r.
5rtj9s33:»l::2
rj99W3t;-17S
*it) hi m:i378:13
Dif.
-osec.
Cosine,
1403
1401
1401
IJOl
i:ju9
l.'iQ.S
1398
1397
1396
I3yrj
1395
1394
1392
1392
1392
1390
M90
1388
1388
1387
I3>7
1385
1385
1384
138:)
133 J
138.'
I3HI
137!!
1379
1379|
13771
l;<77
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1374!
137 J
1373
1372
1*71
1370
1370
13'B
1366
1367
I3(i6
1366
1364
1364
1361
1363'
1361
I3f^l
1350
13^9 j
13^81
l.ir>S
I35fi
1355
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10 174'1891
10 1741488
10 1742087
101740686
10 1739285
10 17.t7S8ri
10 173G488;
I0 173'>090
19-1733693
10 173-2297
ID i73oyo-J
10 17:^9507
iO-1728113
101726721
10 1725329
10 1723937
Hi- 172^547
10 1721157
101719769
101718181
1017161*94
101715507
101714222
Ifrl7128:t7
10-1711453
101710070'
10 1708688
10 1707306
1 01 705925
10 1704546
1017031C7
I0I70I788
10- 1 70(14 II
10-1699031
lol6'J7(.5y
lOIfi9G2S3
10-1694909
10-1693536
101692163
1 0-1 6^0791
10-1689420
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10-1606660;
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10-1681-^11
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10^1678481
10-1677I17
101675754
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10^1673030
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10 ir,.,'
10 1663522
IO-lMi2167
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9l09(-HH3
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9 4103-162
9-4Kk;750
9 4110036
i/4l 13321
9-4116604
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99544374
9 9546915
9 9549455
99551995
9955453a
9 9557075
9-9559615
94119885 995fi2154
94 12:11(16 '.)•»-' ;'■:;
94I-6445'''
94l297'22'y' . . -
9 413299819 9572311
9 4130273 9-957485U
94139546 99577;»89
9-4142818 9-9'79927
9-4l4ti08e 9
9 4M9357
9 4l5-i625
9-4155891
Dif.
254!
2540
254(1
25-10 1
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2539
2539
100455626
10-0453085
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1004-26150,
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9 5165287
9-51624.36
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10-1290403
10-1291542
10l2y-2fi81
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10 I2'MV(.|
10- 1296 102
10-1297344
10-1298387
101299530
10 1300G74
10-1301818
101302963
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jJ42i^-8703898!54
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"■*•' 9 8700470;51
9 4159156
94162419
9 4165681
9 41fi8942
9-4 1 72201
9-4175459
9-959006U
9-9592fil8
9-9595155
99597(193
9-9fi0023ti
9-y6027(i7
9-9G05305
9-4178715 9 9'-«07842
9-4181970 9-9GI037>*
9 4185-223 9 9(; 1-29 15
9-4I8HJ75 9yr.|5)52
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9-4lU4975|'J'9C2052.
9-4198223 9-9(523061
9 4201471) 9'" ■•'. -
9 42047i5'*»
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9-4211-201
9-4214442
, 10D4'22611
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9-5148168,10^1308699
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9-514'.M53 10^1319998
9-5l39ig4| 10 1312149
9ril36734,lO 1313;JOO
9-M33872 10 13U452
95l3)0a9!l0-131nG04
9-5128146 10-1316758
9 4217681
9-4220920
9 4224156
94227392
9-4230626
9-423 JB5S
9y'..U-2U-l
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9-9638275
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9 4261. 1
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9'427»5-*i .J ju > i,Mj>F
9 427575gI9-9683893I
9 428StiOl
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Covers.
9 9(.ynr26
9 9(i96 5.19
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2536
2537
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25.Jfi
2.V'Jr
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10-0387085
10-0304548
101)382012
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10-0376939
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10-0366796
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9-5125281
95122415
9-5119548
9-5116679
9-5113810
9-5110940
9^5108068
9 5105195
9-M0-J3.il
9-6099446
9-5096570
9-5093693
9 5090SI4
9-5087934
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101317912
10-1319066
10-13'2t)221
10-1321377
10-1322534
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10-1324849
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10-1327167
10-1328:127
10-1329488
10-1330649
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)!.;« 9 870845c:
1138
1139
9-8707319
9^8699326
9 8698182
19-8697037
9-8695891
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9-8692449
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9-8689002
9-8ri8785l'4t)
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1169
1169
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9-8656531 13
9 8655362 12
9-8654192' 11
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9-8649504
9-6648331
9 86471S6
98645981
9-8644S06
9-8613629
9-8(>-12452
J 8641275
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47 1)^
1i A
I
4
354 43Deg.
NATURAL SINES, &C.
Tab. 9.
Sine.
68*21237
6428489
Dif.
21 '^7
2i2f;
212G
Covers
JIBUDK)
3177*39
3175763
3173037
317 1. ■) II
6a30613^j*^i3169:J87
«83a73i*^jgt3iti7.^62
6834S61
6ai698-l
'ia.t9l07
iyj(if<4r-':'9
1 1 tiS^.'M.'iO
12
8816866647
83
24
2S
2(.
27
2H
30
31
3'i
33
3-i
3i
3<i
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38
39
4U
41
42
4:«
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4.S
4f.
49
S<»
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52
53
Gft4547I
6847591]
'ltt4!*7 1 1 1
ti8rilrl30
68ri391H
*i»56066
r.af>8i8i
13165139
.31 6301 G
3ir,089J
3I3S771
13156650
'3151529
J3 152409
3150289
314B170
!314f.05:
,3143934
,3141816
B868701
587087.1
0872988
(i87M01
6877213
()879325
(iH8U35
r>88354fl
2123
2 1 2;*
21'Ji'
2121
2121
2VI0
2120
21 19
2118
2118
2118
2nc
2116
21161
2115
2tu;
2114'
21131
..1]3'3127012
S .,1 I12-18y9
n '3122787
J J;3120C75
; ^,3118565
^'i.i,3n6454
13139700
3137584
31354G&
3133353
3131239
3129125
fi8a.>f,55jj,jQl3l 14345
2108
fi887765li!I,!P 3112215
rt8H!J8r3
lOS
107
3110127
3 1 080 1 9
3105911
310380&
6S98;i02
*:uoo.|07
fiU0ZM2
(•904617
69r)6721
6908824
3101698
3099593
3097488
; 309 5383
13093279
I'3091176
2105
I'^IOS
2105
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i2103
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, ,13089073
'';'308t.9:i
'.M>... I.; 13084869
i;y 172.32
69193J2
<192U3-J
6923531
6925630
69277^8
6929825
t. 93 1 92 J
MIdMOlS
55 8836U4
56 6938368
&7S>40»H
S8G848S88
66 6»46S8«
2101
3100
2100
2099
20''' •
^097
2096
;20l»6
8085
9885
30827(;8
308066s
3078568
(ii-f. \,-.(t
306807S
3065882
Cosec.
4662792
46382-iO
4653652
40490^9
4644529
4'i3997J
4635422
4630875
4626331
4621792
4617257
4612726
4608198
4603675
4599156
4594641
45901J0
4585623
4581120
Tanp:
9325151
93.30591
933C034
9341479
9346 9ii
9352380
9357834
9363292
936S753
9374216
9379683
93H5I53
9.1906^5
9396101
9401579
9407061
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1-4576821 9429017
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4558666
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9 ;5 10211
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1-45^19712 9462042
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4531852
9467556
9473074
9478595
94S4I19
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9063886
3061781
30S8686t1
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4518498
4514055
4 ri 096 1 6
4505181
4500749
I-452294619495176
9500709
950C245
9511784
9517326
9522971
l-07-.i30H7
I 0717435
J 07111 H7
I 0704943
1 0698702
10692466
10686233
1-0680004
10673779
I 0667558
10661341
1-0655128
10648918
1-0642713
1-0636511
1-0630313
1-06/4119
10617929
I 0611 742
10605560
I or)99J91
10593206
10587035
105SOSB7
10574704
10568544
1-05623SS
1-0556235
10550087
10543942
10537801
I Dif. Cosine! '
1-3699315
l-370.-^p--^
I-;f7(ir:
I-37U1,.. ,
1-3714266
1-3718011
1-3721760
I -37255 1 2
1-3729268
13733026
1-3736788
1-3740553
1-3741
1374
1375.
1-375^
1-375"..
1-3763210
1-3766998
1-3770789
1-3774583
1-3778380
1-3782181
1-3785985
2700365
270832-1
27I0J14
2712305
2714-297
2716290
2718284
2720278
2722272
I •189
■.<*
'9
1991
1991
1991
729969S
7297646
729S&7 SI
7293668fS0
7291677 49
7289686 4«
1902!
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19<
1 9-'
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4496322 952S4-20
4-191893 9533971
4487478
4483063
4478651
4474243
9539526
9545D83
9550644
9556208
4469839 9561774
4465439 95t.r344
446l('r' '■'■-■:■':
445*.' . i
44522'.-,- .-.l:J
4447878 y5b9653
1-0531664 l-37'^9792 2748?:-
10525531
1-0519401
1-0513275
4443497
41.39120
4434748
4430,179
4426013
442)652
44ir295
4412941
44aS59a
4404246
4399904
4.)95565
Coftiue'Dif. Vci>. I Secant.
9595241
9600829
9606421
9612016
9617614
9623215
9628819
9034427
9640037
Culan.
1-0507153
10501034
10494920
1-0488809
10482702
1-0476598
10470493
10464402
1 04.'.8310
104.S2221
! 0146136
I iil4n(>5
1 043397
1 0427904
10421833
10415767
10409704
10403645
10397589
10391538
1-0385489
1037844811
o3;9m Mm
1 *'w:
^*''g-
I 3805053! 2
1'3808877''.'-
1-381^
1-381'
1-3821'
1382;
l-382>
13831
1-3835734,.:'
1-3839584 'j;
1-3843437 2;:-.. ■
1 3817294 27783:.
1 38M n3 ■27803-^
1-3855017 278339-
l-385*^^'<t
1-.3862-
1-386'
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1387.
l-38r,'- -
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'388*'
-U3l If
^671 IB
63^14
*«15 13
■■iAj!
796n-88»
5383 t-SSO
L<M<C. *
^
4<> LW,
43 Deff.
LOG. bINES, &C,
355
' I Sine. |Dif.
9-ji:*.i7833
1 9 8339188
3!^8.M1894;
5 9 bJ4-;-^97;
fi,9 834:.948!
Its?
13J3
1353
1352
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l.-fil
1340
7'99.%I7297|,.,„I
1*148
8 9^634864^:
9|9-R349994
10 9-8351341
ll|9-tt.*r.2r,89
r2 9S354033
13,98355378
14|9 8356722-
15|'J-93ft806«i
I6i9-e.359408
17|D-83(>0750
18 9-8362091
19 983*i3431
20 9 83G4771
2119-8366109
2298;J67447
23!9-S-3«8784
2419-8370121
25 9 8371456
26'98372791
2798374125
28i98375458
29 9 8376790
30.98378122
3119 8379453
3219-8380783
33; 9-8382 II 2
3419-8383441
9-83847^9
98386096
9*8387422
9*188747
9-8.i9y072
9 83^)1396
9-8392719
9 83940-11
I
J 347
1347
1345
1343
1344
1344
1342
1342
\:Ul
1340
1340
1338
1338
1337
1337
1335
133S
1334
1333
1332
1332
1331
1330
1329
1329
1328
1327
1326
1325
1325
1324
132:1
1322,
1322
1321
Co«ec. IVerseds.
IO-lfiK2T67i9-429!HO'J
10-1610812 9-42yr»l)ri
10- 1 659459 9 4298::2l>
UHI658I06 9-43UI424
1^1656754 9-4301(i-26
10-Ki55403i9 43o73-'7
10-1654052 9-4311U27
10-1652703 9-4314225
10-1651354!943l;422
10 l'i50UOGi9 4320617
10-1648659 9 4323811
10-1647312
10- 1 645967
101644622
10-1643278
110-1641934
i 10- 1 640392
10 1639250
101637909
10 1636569
10-1635229
101633891
101632553
101631216
10-1629879
101628544
10 16272U9
10- 1 625875
10-1624542
1016-23210
|10 1621878
jlO 1620547
101619217
1 10 1617888
10-1616559
101615-231
10 1613904
101612578
10 1611253
10 16099-28
jiO'l60.StiO'l
I0l6072al
101605059
liMfi04637
10l(i03ai6
43 9 8305363
44[9'8396684 , ,o,,,
9-8398004 ^t" 11^1601996
83')*(32:3 ,J^ 101600677
8-84)10642 I::;yiiai59n3.'i8
4819-8401959 J3J^|l0-159804l
10-1590724
■":! 10- 1595407
^ ^lOl5iW092
^^101592777
^JJ lOl^'JHoJ
[^1210 1590150
49 9-8403276
50 9Sl(»s593
51 9-841)5908
52 9 8407223
53 98iOS537
54l9'8 109850
943271M)4
9-4330196
9-4333386
9-4336574
94339762
9 434-2948
9-4346133
9 4349316
9 4353498
9-4355678
94358858
9- 4362036
9-4365212
9-4368387
94371561
9-4374734
9-4377905
9 438107
94334-243
9-4387411
9-4390576
94393741
!J-4396904
9-4400066
y-4403227
94406386
94409544
9-44 1 2700
9-4415855
9-4419009
944221G2
9-4425313
9 4428463
94431611
9 4431758
y U37tMl4
'J 4441049
9 444-1192
94447334
9 4450175
9 4453614
94456752
94463024
TnnfT.
9-9696559
9^699091
99701624
9970415
99706689
9-y7oy22i
9-971 1754
9-9714286
9-9716818
y-97iy3r.lt
9-9721882
9 9724413
9-972b945
99729477
9 9732008
9-9734539
9 9737071
9 9739602
9 9742133
99744664
9 9747195
9 9749726
99752257
99754787
9-9757318
9-9:
9 97
9-97674-iu
997i)997U
99772500
99775030
9 9777560
9-9780090
9 9782620
9 9785149
9 9787679
9^9790209
9-9792733
9 .f795-268
99797797
9-9800326
9 980l'856
Dif.
2532
2533
2533
2532
2532
2533
2532
2532
■J 532
2532
2531
2532
2532
2531
2531
2532
2531
2531
2531
2531
-^531
2531
2530
2531
2531
Cotnnp.
10 0303441
100300909
IIU0298376
11^0295843
'100293311
10 0290770
10 0-288246
10 0285714
10 0^283182
10-0280*i5U
10 0278118
10-0275587
10-0273055
10 0270523
10 0267992
100265161
100262929
100*260308
10 0257867
Covers.
950:M294
9 5021388
95018480
95015572
9 5012663
95009752
9-5006840
95003927
9-5001013
9-499 S098
3-49!(5IS2
9-4992264
94989345
9-4986425
9-49ft3504
9-4980582
9 497765S
9-4974734
3-4971805
Secant.
100255336 9-4968881
1 0-0252805 [9-4965953
9 980538:
-...,1
2530
2530
2530
25;J0
2530
2530
2529
2530
2530
2529
2530
25-29
25-29
2530
25-0
!25'^4
1U-0250-J71
IU-024;74I
1O0J45213
I U 0242682
10 0240151
10 0237621
1U0-J350TI
10 0-' ^
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9 4963024
',»-49(ill093
94957162
9-4954229
94951295
94918360
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■ ' IJ4S6
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9 9807314:.';,-
9 98104431-^,4
9 98129721--^
9 9818030 ^j55
99820559
9 9823087
9 9825616.,.,^
9 9^2^145™
25-2**
2528
y 9835730 2..og
2528
2529
9 9S30673
9 9333202
9-44661.58
9 1; '^' 1
9 i
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'l44;8l>8l|9 9H-i5844
9 44S I aU8 9 9848372
100231970
ia022-2440
10-02 I9'J 10
IU021738O
100214.851
1O02I2321
10 0209791
10 0207262
100204732
lU 0202203
10 0199674
100197144
100194615
10U1920K«
100189557
1001S70-28
10U184499
1U0181970
10 0179441
100176913
10 0174384
100171855
10-01693^
100166798
I0-01M270 9-4862726
9-4933667
9 49307-24
9 4927781
9 4921836
9-4921891
9491S944
94915996
9 4913046
94910096
9 4907144
9490-1191
9 4901237
^14-^96282
9-4a9'.326
9 4892368
9' 4m.S!U09
9 48Si_i4,iy
9-4883488
94880525
94877562
9 4874.97
9-48716.*!
9 48''8i>(>l
9-4865696
Covers.! Cotaii^-
25-J'J
2528
Dif.
1001
1001
:h3
■sio
'S3G
160
Tang, |Verseds.
10 1358725
10-1359904
10 1361083
10-1362263
10 136.3443
10 1364624
10 1365806
10 13669S9
101368172
10131,9356
10 1370540
10-1371726
101372912
10-1374098
10^ 1375286
10-1376474
191377662
10 1378852
101380042
101381233
10 1382124
10l38t6!7
10 1384810
10- 1386003
101387197
10-1388392
101339548
10 1390785
101391982
101393179
1& 1394378
101395577
101396777
10 1397978
10*13^'9!'"
10 UL'!
lO'Uu)
10-1402787
10Ul>3*H)I
)0-l405l96
i014')(i40I
I0-U07MI7
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10-1410022
11} 1 111230
I I) I J I
10 141 1.~ .'
10 14160711
IOI417282I
I0l4l8495i
10 1419708
101420922
10 14-22137;
10^1423352!
10.1424568
10 1425785'
10 14270021
I a 1428-2-' I
10 U29439I
ll>l430659|
D.
1179
1179
1180
1180
1181
1182
1183
1183
1184
1184
1186
1186
1186
1 188
1188
1188'
1190
1190
1191
1191
1193
1193
1193
1194
1195
1196
1197
1197
1197
1199
1199
1-200
1201
l-JOl
Cosine.
9 8641275
9 8640096
9 8638917
9 8637737
98636557
9 8635376
98634194
9-863391 1
9 8631828
9 8630644
9 86-29460
9-8(i2e274
98627088
98625902
9-8624714
9-86-23526
9 86-22338
9 8621148
98619958
98618767
9 8617576
986 1 6383139
98615190
98613997
98612803
I20J
1205
1-205
9 8611608
9-8610412
98609215 33
9 8608UI8 32
9 8606321:31
9860562230
9 8604423 29
9-8603223I28
9-860J02-2'27
8600821 26
85996 19 25
85984t6|24
98597213123
98596009 '22
98594804 21
19 8593599120
I !^l9 8592393119
•207
1208
I*i08
1-209
12i-'
1211
1213
1213
1214
1215
1215
1216
1217
1217
1219
1218
1220
9859118618
Cosec. D.
98689978
9-a588770
^- ' --.F.l
:''l
:..':. :141
98583929
9 8582718
9 8581505
98580292
98579078
9 8577863
9 8576648
98575432
9 85742 15
9 8572998
9 8571779
9 85705r,i
9 856934 1
Sine.
40 DekT.
2 A 2
356
44 Deg.
NATURAL SINES, &C.
Tub. 9.
It
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
-M
'I'l
U3
24
25
26
27
28
^9
3(1
3t
3.'
34
3S
36
37
38
3!)
40
41
42
43
44
A'.y
X(.
\7
AH
49
50
51
5y
5J
54
6946584
694S67G
69J0767
69 '12858
6954949
6957039
6959128
6961217
6963305
6965392
6967479
6969565
6971651
6973736
6975821
69779(15
6979988
698-i07I
6984153
6986234
6988315
6990396
992476
6^94555
6996633
6998711
7000789
7002866
;oo7oi«
7009093
7011167
70 13241
7t»153|4
U'JJ53l
7023601
7025672
02774 1
029sn
031879
7033947
7036014
703>i08l
7(140147
ro42'.>l3
UU*J7H
7UJ6342
7048-JOfi
i)J04fili
7 05 .'5:3 J
054594
U56fi55
7058716
060776
06 283 i
7064894
iH'if.951
7i>ti901l
707106SJ
2092
209 J
2001
2091
2090
2089
2089
2088
2087
2087
2086
2086
2085
2085
20S4
2083
■J0&3
■.'082
2081
2081
2081
2080
2079
2078
2078
2078 . '
Sine. |Dif. Covers
30534 16
3051321
304!t2.J3
30471 12
3045051
3042961
3040872
Cosec.
3038783
3036695
3034^108
3032;"»21
3030435
3028349
3026264
30-J4179
iO2J095
3020012
3017929
3015817
3013766
3011 C85
3009G04
3007524
3005445
3003367
3001289
2077
207 G
2076
!2075
2074
2074
2999211
291*7134
2995058
2992982
2990907
2988833
2073 ^^^*'^-'^
.,(',! 2984686
-'* '.'982613
207
2072
; 2980541
|2070 '^^^^^
L,7, 2976399
IS,r;2''74J28
207(1 * — ^
ir^^ 2970189
^™2966053
20671
2067
206fi
12963986
;96VJ19
2066
20 S5
2064
20'i4
'! 2959853
2053
2(tr)J
2062
2061
2061
2060
2059
059
lorg
20 "tH
05/
2957787
2955722
2953fi58
2951594
2949531
2947468
2945405
2943345
2941284
2939224
2*»37I65
2935 1(»6
2933047
'J 2930!)S'J
'2928U32
Co'.iiK* Dil". Vers.
■4395565
■439123
-438fi9(lll
■43M2574
■43782 il
•4373932
■4369616
4165305
■4360997
4356693
4352393
4348097
■4343805
4339516
4335231
4330450
432(;672
4322399
4318129
4313663
4309600
4305342
4301087
4296836
4292588
4288345
4284105
4279868
4275036
4271407
4267182
426-2961
4258743
42545-39
4-250319
4246112
4241909
4237710
4233514
4->293->3
4225134
4220950
4216769
4212'»92
4208418
4*204248
4200082
4195920
4191761
4187605
418.M51
4I7'J306
4175161
41710-20
4166883
4162749
4158619
4154493
4150370
4l4ri251
4142U6
Secant.
Tanp. Colanj».
9656888
9662511
9r.68l37
9673767
9679399
9f)85035
9690674
9696316
9701962
9707610
9713262
9718917
97*J4575
9730236
9735901
9741569
9747210
9752914
9758591
9764272
9769956
977:.643
1 035:i303
l-ft349277
10343254
10337-235
1 0331220
1-0325208
1-0319199
10313195
10307194
10301196
1-0295203
I 0289212
I 02S3226
10277243
10271253
I 0265287
10*259315
1 U2'>:)346
10247381
1-0241419
1 0*235461
1 0-229506
978l3,i:j;i(t-223555
9787027 1 0217608
9792724 1-021 1664
Secnn* I V*.ra JDif. Ctisin
9798424
9S04127
98(»9833
9815543
9821*256
9826973
9832692
9838415
9844141
9849871
9855G03
9861339
9867079
987*2821
9S7S567
98»4316
9890069
9895825
9901584
9907346
9913112
9918381
10205723
10199786
101938531
1018792;(!
101819971
10176074
10170155
I 01642;J9
10158326
I 01 524 1«
10146512
101406101
10134712
101*28817
I 01229*25'
101170381
101I1I53
10105272
1 0099394'
100915*20
I00a7f.49
IO091782
1-39(JI'
I3905;>,,
1-3909453
1 3913366
I«9172R3
13921-203
13925127
13929051
1-3932'.'-
1 39J'."
1 3y4o-
I 3941 :
1-39 W7V
1-3952688
1-3956639
1 -3960593
1-39645 M
1-3968512
1-3972177
l-397644i
13980416
1-3984 91
1398836'.»
13992:151
1-3996336
14000J25
14004317
1-4008313
1-4012312
1-4016315
I-40-20321
2021 ,
7 1 9 5396 60
•281064' •-
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1-4024330
1-4028343
1-4032360
1-4036380 287
1 4040403 2^
14044430 38
2R3292-J
20-29I; "
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283495 1 1
283698 1
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28->1204|o"i!
28532 181 ;«t^;..
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7I67078]47
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715&y-27 4^
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2861382
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10T582287
10 1580979
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10 157M366
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76
75
2.5t;r9
2 9389
2-9785
30091
I DisL3.
2-57 1'J
3^^
1
26242
3-7. - . i
2-6765
37157 334^711
2-6862
3-7048
33578
2-7280
3-6568
3 4100
27786
35967
34733
■2-8-28 1
3&355
3 5355
Ul.
Dep.
Ul
L 4
Dift
L6.
6|
H
H
4
^B
^^^^^^%
^H
360 LENGTHS OF CIRCULAR ARCS. Tab. 11.
1 ^H
D
Arc
D<
? Arc
De| Arc |
' Arr
|/'|Arc
^M
^^^v
1
■017453 i
6
1 0646508
12
2111S484I
1 2909
1 4a
1
^H
^^^^^^^^
2
-0349000
6-
I 10821041
12:
.'21-293017
2 5818 !
2 97
3 2 ^m
^^^^^^^L
3
-0523%'i9
6;
J 1 0995374
12
1 2- 1467550
3 8727 1
3 145
3 2 ^M
^^^^^^H
4
•0698 13i
6^
1 11170107
12^
21642083
4 1163e
1
1 194
5 4 ^H
^^^^^^^H
S
-087-^665
6:
11 344640
12'i
■21816616
5 1454^
S 242
^^^^^^^H
C
•I0-(7I9H
66jM5l9l73
121
2- 199 11 19
6 17453
S 291
6 5
^^^^^1
^^^^^^^H
7
■1221730
67' II 693706
127
2-2I'i56y2
7 20362
7( 339
7 fi
^^^H
^^^^^^^H
6
-1396263
65
11868-239
12fi
2-2340214
8 23271
S, 388
8 6
^^^1
^^^^^^H
9
1570796
6S
l-204'2772
129
•2-2514747
9 •26180
9 436
9 7
^^H
^^^^^^H
]0
•I7453-29
70
1-2217305
no
2-268l«80
10 29089
10 485
10 8
^^H
^^^^^H
11
■1919862
71
12391838
131
2-2863ai3
11 31998
'11
533
111 9
^^1
^^^^^^H
12
■2094395
72{ 1-2566371
132
23038346
12 34907
m
582
12110
^^H
^^^^^^^H
la
•22G89U'8
73
12740904
133
2-3212879
13 37815 |13 fiaO
13 11
^^^H
^^^^^^^H
u
■2443461
74
1-2915436
L14
23387412
14 40724 14 679
14|ll
^^^1
^^^^^^^H
15
•2617994
75
1-3089969
13a
2-3r>6 19451
15 43633 15 727
15 12
^^^M
^^^^^^^V
16
•2792527
76
13264502
136
2373(i478'
16 46542
,16
776
16 13
^^^1
^^^^^^^H*
17
•2967060
77
1-3439035
137
23911011'
17 49451
17
824
17114
^^^1
^^^^^^H
18
•3141593
78
1-3613568
138
^■4085544
8 52360
18
873
18 15
^^H
^^^^^^^B
19
•3316126
79
13788I0I
139
2-4260077 1
9 55269
19
92!
!9 15
^^^1
^^^^^^^^^1
20
•3490659
80
13962634
140
2-44346 JO ^
JO 58178
20
970
20 16
^^H
21
■3665191
81
1-4137167
141
24609142 S
l\ 61087
•2ri018
21 17
^^H
^^^^^^H
22
■3839724
82
1-4311700
142
24783675 i
i2 63995
22 1067
■22 18
^^H
^^^^^^^H
23
■40 1 42 1 7
83 1-4486233
143
24958-208 ■-
3 66904
23 1)15
23 19
^^^H
^^^^^^^H
24
•4188790
84 1 46fi0766
144
25132741 ■.
A 6981 t
|24<I164
24 19
^^^H
^^^^^^^H
2*.
■4363323
85 1-4835299
145
2^5307274 k
5 72722
•25 1212
25 20
^^^1
^^^^H
■4:.37sr.6
Hf, I-5im9832
146
25481807 *i
6 75631
26 1*261
*2G 21
^^^H
^^^^H
■4712389
87 1-5184364
147
2-5656340 2
7 78540
|27 1309
27 -22
^^^1
^^^^^^H
28
•4886922
88 1-5358897
148
25830873 '2
A 81449
•28
13.571
28;23
^^H
^^^^^^^H
29
•5061455
89
1-5533430
149
■2-600-)406 2
9 84358
29
14061
29 23
^^^1
^^^^^H
30
5235998
90
l-57079f>3
150
26179939 3
87266
,30
1454
30 24
^ ^^
^^^^^H
31
•5410521
91
1-5882496
ISI
2 6354472 3
1 90175
31
1503
31 25
M
^^^^^^^H
32
•558'i054
92 l-fi0570'2y
15-2
2-6529005 3
2 93094
32
155!
32 26
^^^M
^^^^^^^H
33
•5759587
93 1 6231562
153
2C703n38 3
3 95993
S3
1599
33 27
^^^M
^^^^^^^^
34
•59:mi9
94
1-6406095
154
2-687a070 3
4 98902 34
1618
34 27
^^^M
^^^^^
35
-6108652
95
1-6580628
155
27052603! 3
5 101811
35
1697
35 28
^^^H
^^^^^^^
3B
•62y3IS5
96
1-6755161
156
2 7-227136' 3
6 104720
36
1745
JG 29
^^^1
^^^^^^^H
37
•645771 S
97
1-6929694
157
2 7401669 3
7 107629
37
1794
37 30
^^^H
^^^^^^^H
38
■6GH22:il
98
I 71042*27
158
2 7576202 3
8 U0538
38
1842
38 31
^^^1
^^^^^^^H
39
•6806784
99
17278760
159
27750735 3
9 113446
39
1891
39 32
^^^H
^^^^^H
40
•6931317
100 I 7453293
160
27925-2G8' 4
1
1 16355
40
1939
40 32
^^H
^^^^^H
41
■7155850
101 1 7627325
161
2 8099801 4
I 1 19264
41
1988
41 33
^^H
^^^^^^^H
42
■7330383
102 1-7802358
162
2-8274334' 4
2 12-2173
42
2036
42 34
^^^H
^^^^^^^H
43
•7J()4916
103 1 7976S9I
1G3
i844a867i 4
3 125082
43
2085
13 35
^^^H
^^^^^^^H
44
•7679449
104 1'81514'24
164
2-8623400. 4
4 127991
44
2133
14 36
^^^1
^^^^l^v
45
■7853982
105
18325957
165
28797933 4
5 I3O900
45
2182
15 36
^^H
^^^^^^
46
-8028515
106
18500490
166
2-8972466 4
6 1333U9
46
2230
16 37
^^^H
^^^H
47
•8203047
107
1-8675023
167
2 9140999 4
7 136717
47
■2279
17 3S^
^^^H
^^^H
43
■8.177580
108
18849556
168
2-9321531 4
8 139t;
18 39
^^^1
^^^H
49
•8'>521 13
109
1-90-24089
169
29496064 4
9 142-
19 40
^^^1
^^HkJ
50
-8726646
no
lgi986*>i
170
29670597 5
14544-i .>i/|
-'4i4
^0 40
^^H
^^^^Hi
51
■8001179
111
I 937 J 1 55
171
2-9845130 5
1 148353
61
2473 .
&1 41
^^H
^^^^^^^ft
62
•9075712
112
19547688
172
30919663 5
2 151262
52
2521 i
^2 42
^^^M
^^^^^^1
S3
•9250245
113
1 9722220
173
10l9419(i ;5
3 I54I7I
53
2570
i3 43
^^H
^^^^^^^H
54
■9424778
114
10896753
174
3-0363729 5
4 157030
54
2618 .
^44
^^^1
^^^^^^^H
55
•9599311
115
2 0071286
175
30543262 |5
'.159959
55
2666 i
>5 44
^^^1
^^^^^^^H
56
•977.1844
116
20245819
176
30717795 5
6 16-2397
56
2715
>6 4&
^^^H
^^^^^^H
57
•9948377
117
20420352
177
3 0892328 5
7 165806
57
2763 !
^7 46
^^H
^^^^^^^H
38
1-0122910
118
20:.94885
178
3l0r,(i8S| 5
8 168715
-'•8
2812 .
>S47
^^^H
^^^^^^^B
59
10297443
tl9
20709418
179
31241394 5
9 171624
59
2860 ,
i9 48
^^^H
^H
60
1>
1-0471976
Arc
120
20943951
180
De
3-14159*27 6
174533
60
2909
Aic
SO 4a
""a
H
De
Arc
AfC
Arc
^^^v
^1
p
J
^
^^^"
J
Tab. 12. COMMON and hyp. logarithms. 361
■
CL
HYP. LO.
CL
HYP. LO.
CL
HYP. LO.
CL
HYP. LO.
•01
•02302585
■26
■59^67212
•51
I1743I840
•76
1-7 1996467
^^^1
■02
•04605170
■27
•62169798
•52
MU734425
•77
I77*299«i2
^^^H
■03
■orm77y*
■29
■64472383
■53
1220371110
■78
179601637
^^^^1
■04
•09l'ID310
■29
■66774908
•54
1-24339-195
•79
18I9(M'222
^^^H
05
■11512!) i5
■JO
•69077553
•55
1-26642IH0
■80
184206807
^^^H
•06
■USISSII
■31
•71.180138
■'.6
l-2>94i76:i'
■81
l865(i9.J'J3
^^^1
•07
liillSOSr.
■32
•7368 J723
■57
I3l2l73.i0
■82
1-8881 19:8
^^^H
•08
■1842Uti81
•33
•759S5.109
58
l-:J354y935
•83
19lll45'i3
^^^^1
•09
20723266
34
•78-2H7893
■:i9
1 3-8 .2520
•84
193417148
^^^H
•10
■23025S5I
3J
■80590478
■60
1-38 155106
■85
19571973J
^^1
■11
25:t2fl4.H.
•36
•82893063
61
1-J04'i769l
•86
1 98022318
^^1
•12
27631021
•37
-85195618
•62
1-42760276
■87
200 24DOI
^^^H
•13
*2«f9 13600
•39
•»74'-8234
■rtil
145062861
'88
2 02627488
^^^H
•14
32236191
•39
•89800--19
64
147 165446
•h9
2 019.:ut)7l
^^^1
•l-i
34'i3S77
■40
•921U3404
■6:>
I49'i68031|
90
2U72326.'.S
^^H
•IB
•36S41I«2
•41
•9U05 it)9
■66
1 51970616
-91
2 0'*535.*43
^^^1
•17
3914.1947
42
■96708574
■67
15427 1201
•92
2 1 1 r.37S2y
^^^1
•18
■41446-132
•43
■990111^9
68
15 57578**
■93
2-11110414
^^^H
■19
43749117
•44
101313744
■69
1 58878371
94
•2 164121199
^^^1
•20
4605 1 7u.
•45
103616329
■70
161180957
95
2la7J55H4
^^H
•21
-4B.3:>42fl7
■4'i 105918914
•71
163183542
■96
2 21048169
^^H
•2'i
•M)f>56»72
•47 108^21499
•72
H.5786I27
■97
2'2.U5U754
^^^H
•23
5-'9j94'.7
-48 < 1-10521084
■73
1 6803^712
•98
225653339
^^^H
•24
•552620*2
•49 |112y2fif'70
■74
1 70391297
■99
2 279559^.' 4
^^^H
^B
■'25
■37564627
•50 1115129255
•75 l-7i6y3»B2 1 00
230i58509
■
Tub. 13. — A TABLE of Uumbs. Bhowinjf Ihe Dvfrrcvs,
^^^ 4^
Minutes, and Seconria, ihat every Point and Quar*er-[)uint
^^^^
of the Cumpuss iiiukes with the Meridian.
Nunli.
Piiu^r
D * *r
Pl>.4r
SiMlJl.
1
1
2 48 45
1
^^^^^^^H
2
5 37 30
2
^^^^^^H
3
8 26 IS
3
^H
NbE
NbW
I
1 1
1 2
1 • 3
11 15
14 3 45
16 52 311
19 41 15
1
1 1
1 2
1 9
.S b B
SbW
^B
NNB
NNW
2
2 1
2 2
2 3
22 30
'25 18 45
28 7 30
30 50 15
2
2 1
2 2
2 3
SSB
ssw
^^^^^^^B
NEbN
NW b N
3
33 -45
3
SBbS
SWbS
^^^^^^^^^
3 1
36 33 45 3 1
^^^^^^^^^
3 2 39 22 30
3 2
^^^^^^^^B
3 3
42 11 15
3 3
^H
NE
NW
4
4 1
4 2
4 3
45
47 48 45
50 37 3U
53 26 15
4
4 1
4 2
4 3
S .
sw
'
^^^H
NCbB
NWbW
5
5 1
56 15
59 3 45
5 n
5 1
SEbK
SWbW
^^^^^^^^1
5 2 61 52 30
5 2
^^^^^^^1
5 3|64 41 15
5 3
^^H
KNK
WNW
6 67 30
6 1:70 18 45
6 2*73 7 30
6
6 1
6 2
t:sE
W9W
^^^^^^^^K
6 3
75 56 15
C 3
^H
SbN
WbN
7
7 I
7 2
7 3
78 45
81 33 45
A4 22 30
87 11 15
7
7 I
7 2
7 3
Eb&
WbS
1
Cart
Wait
a
90
9
Kui
Wert
362
TAllLE XIV.
k
Equivaljent ExpRBflsioNs FOR SiN. A. Cob. a, and Tav. a.
VALU8S OP SIN. A>
FOHMULA. . . . COS. A tail. A«
COS, A
cot A*
V(l -COS.* a).
1 1
or
^(I + col,' a) cosec. A
tan. A
^(1 +laa'A)
2 sin. ^ A COS. J^ A.
I — COS. 2 A
x/-
10.
u.
13.
U.
16-
16.
17.
18.
19.
2 tan, i A
I + tan. "Ja'
2
cot, i A + tan. J A *
1
cot. A + tan. J A *
2 sin." (45*' + i a) - 1.
1 - 2 sin.« (45° - J a).
l-tan.M45° - Ja)
1 + ian.*(45°-4A)'
tan. (45° + i a) - Ian. (45°
4
tan. (45° + i a) + tan. (45° - J a>
sin. (60° + a) - sin. (60° - a).
VALDS8 OV COS. A*
Sin. A
tan. A
sin. A col. A.
^(1 _ BJn.'A).
1 1
^- - " , or .
^(1 + tan." A) sec. a
cot. A
^'(l +COt.-A)
i A — sin.* i A.
1 — 2 sin.* J A.
2 COS.* J A - 1.
24. y/
1 H- COS. 2 A
25.
20.
27.
28.
1 - tan.« i A
1 + lan.^JA'
coL J A — tan. ^
cuL ^ A 4- tan. ^ a
1 + tan. A tan. ^ a
tan. (45' + i a) + coL (45° + i a) "
29, 2 COS. (45° 4- i a) cos. (45° -^ J a).
30. COS. (00° + a) + COS. (60° - *>
VALUES OP TAN. A.
31.
32.
5111. A
COS. A
cot. A
^'VC^.-O-
34.
sin. A
^(1 -sin.* A)'
35.
^(l - COS.* a)
• COS. A
36.
2 tan. i A
1 -tan.'iA*
37.
2 cot 4 A
COt,» J A - I ■
38.
2
cot. jl A - tan. ^ A
39.
COL A — 2 cot 2 A.
40,
1 — cos. 2 A
sin. 2 A
41.
sin. 2 A
1 + cos. 2 A '
42.
/ 1 - cos. 2 A
V 1 + COS, 2 a'
43.
Un. (45« + i A) - tan. (45° - J a)
TABLE XV.
363
TOUMVIM RILATITI TO TWO ArC8 OR AnOLSB.
1. Bin. (a -f b) = sin. a cos. b + cos. k sin. e.
8. sin. (a. — b) = ain. k cos. B ~ cos. k sin. b.
8* COS. (a + b) = COS. A COB. B - BID. A Btn. B.
4. COS. (a -«- b) =: COS. A COS. B + Sin. A sin. b.
5. tan. (a + b) =
6.
tan. A + tan. b
1 — tan. A tan. i
- - tan. A — tan b
tan. (a — b) =: ; — :
^ ^ 1 + tan. A tan. B
P 7.
8.
COS. (45'
±B)=)
+ B)=r
V2
(sin. (45^ d: b) ^\ COS. b ± sin. b
< . , ,
tan. (45'' ± b) = -— ,
'^ 1 :^ tan. b
1 ± sin. B
9. tan.«(45°±iB> =
l^sin. H
10.
11.
19.
18.
sin. (a+b) _ tan. A+tan. b ^ cot. a+cot. a
sin. (a- b) ^ tan. a— tan. b"" cot. b— cot. a'
COS. (a + b) _ cot. B— tan. a cot. a— tan. b
cos. (a-'-b) "cot. B+tan.A " cot. a -t- tan. b*
Hin. a + sin. b tan. ^ (a + b)
sin. A — sin. b "" tan. JKa — b)'
cos. b 4" cos, A _ cot. J (a + b)
COS. B — COS. A tan. J (a — b) '
14. sin. A COS. B =r ^ sin. (a + B) 4- ^ sin. (A ~ b).
15. COS. A sin. B =: ^ sin. (a 4- b) — i^ sin. (a — b).
16. sin. A sin. B = j^cos. (a-^ b) — i^cos. (a+b).
17. cos. A cos. B = i^COS, (a + B) + J COS. (a ^ b).
18. sin. A + sin.B = 2sin. ^(a+b)cos.^(a-«-b).
19. cob. a + COS. B = 2 COS.* ^ (a + b)co8. Hk'^ b).
sin. (a + b)
20. tan. A + tan. b = ^ .
COS. A COS. B
sin. (a + b)
cot. A + cot B = , T '
sill. A sin. b
sin. A— sin. b = 2 sin. ^(a*-b)cos. ^(a + b)
cos. 8 — cos. a = 2 sin. ^ (a— b) sin. ( (a + b)<
21.
22.
23.
24. tan. a
29. cot. b ~ cot A =
sin. (a — b)
tan. b= ^
cos. A COS. B
^^ sin. (a — b)
sin. A. sin. B
26.
27.
2S.
29.
{sin." A — sin.' b =: ) . , v • / . ■*.
COS.* B-CO.." A =1 ""• (* - ») »""• (* + »)
COS.* A — sin." B = COS. (a — b) cos. (a + b)
tan.. A - t.„.. B = 'jMA^»).in.(A + B)
COS." A COS.* B
, « sin. (a — b) sin. (a + b)
cot." B — '•Ot* A = > ....
sin.' A sin.' B
DIPFEReNCBS OP TRIOONOMETRICAL LINES.
80. A sin. B = 2 sin. } A b cos. (b + ^ A b).
Si. — A COS. b = 2 sin. i^ s sin. (b + j^ A b).
sin. A B
89. A tan. b =:
83. — A cot. b =
COS. B COS (b + a b) '
sin. A B
sin. B sin. (b + A b) *
»^- { - A ("cJo b] = } "»• ^ - »»■ <2 B + ^ »)•
- ^ COS.* B COS." (b + A b)
-W. A(cot.',) = ''"t"-°'r.AV^ -
aio." B Bin.' (a + A b)
DirFEBENTIALS OF TBIOONOMBTBICaL LINKS.
37. d sin. b = d b cos. b.
38. — d COS. B = d B sin, b.
dB
3&. d tan. B =:
40. — d cot B =
COB.'B
dB
sin.' B
^••{-d(:!:i:*S =}'''" •■■"•»-••'•
42. d (tan.* b) =r
2 d B tan. b
43.-d (cot* B) s
2 d B cot ■
ain.*»
364
TABLE XVI
AitfA.LVTiCAL Formulas, fok solving all the casf.!> or a Rkctilineab T&i<
ANOLR ABC, OF WHICH THREE PARTS ARC KNOWN,
1. Formula . .,
TALU» or AB.
nc sin, o
ftlO, 1
10.
II.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2],
22.
23.
24.
25.
26.
127.
CUS. ■ -^ klu. Ji COL Q
•
AC
co«. A i- liii, A. cut. c*
00 COS. B 4- Hc sill, a col. a.
AC cn«. A -f- AC sin. a col. b.
^(bc" + AC* — 2 bo X AC COS. c).
■c COS. B i \/C*c' — Bc" jtin.' u).
AC CO«. A ± V("°* ~ «^ «"" *)'
TAtoBt or AC.
AB sm. ■
Rill.
BC sir. a
sin. A
AB
COS. A + «in. A coL »*
BC
COS. c + sin, o cot, ■'
AB COS. A -f- AB sin, A COt. O.
BC C0«. C + BC »i0. cot. A.
^(bC* -|- AB* — 2 bo X AB cos. ■).
AB cos. A jt V("** ~ *■* *'■*' *)-
BC COS. O i V(*^ ~ ^ •'"•' ^)-
vALOKs or BC.
AC sm. A
Bin. B.
AS iiin. M
siki. c
AO
COB. Y + MB. OOL A
AB
cos. a + SID. D cci, A
AC cos. - AC sin. c. cot. a.
AB cot. B 4- AB l^n. 8 COt. C.
iJ{Alf -f Ac' -• 2 AB X AC CO*. A ),
AO COS. C i V(*"* " *^ *'°' *-'}•
AB CO*. « i V("^ — *■' ""•' '0-
vALOis or un, A.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
AB
BC sin. B
sin. (b + c).
tin. u cu». c 'f' CDB. a bIb. c
BC Mil. C
Vt.t-« +
AC* -
7b' -
■ 2»c X
Mil. a
AC
COB. Cj
V(«=* +
- 2bc X
AS
COS. a)'
v/'-
CO*, c
b' + AC"
2ab X
AC
ac»\«
••in. c (ac
±^
-
AL* .IU.«
ci
■0«. D
AH
■in. a (ab «
±^*.^
—
ab' Bin.*
^;.
AO
VALfll ttr cot. A.
± ^JAxf - BC* slr>« c)
AB
± ^(ac' - BC* sin.* a)
AO
- COS. (• f c).
Bin. B sm. c — cos, a c<»». c.
AC — ac coi. c
>^(^BC" + Ai:^ - 2 BC X AC CO*, c) '
AB — Br COS. a
^(SC* 4. A«" -^ 2aO X Afl COB. ■) *
AH* + AC* — BC*
2ab
y *f
AC
sin*
r ^ cm. 11
^f(
ab'
—
AC*
sin.*
«)
\a
"
AS
kin.i
■ ^COS. B
V(
*L«
—
Al^
»itt.*
•)
AO
*
VALOU 0» TAS. A.
46
ao «o.
± ^(A,i - Bc« sin.* c) •
47.
43.
ic sin. a
- Un. (0 + c).
49,
t«n. a •!• Un. c
Un. B tAP. c — 1 '
50.
BC «in. c
*C — BC COA.
Kl
BC am. a
AB — itc co«. a
52.
53.
54.
AC cm. c :fc ^(ab^ - AC* ain.* c)
AO sin. c ^ eol. c ^(ab* — ac* •in." J)'
AB COS. B ::fc ^(aO* -• AB* SJH .'a)
AB sin, B qp C OL B ^(aC* — AB^ m^TTj
4
4
d
TABLE XVI. CONTINUED.
365
55. FoBHULl
TALUKI OF 11 H. B.
AC sin. A
I
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
bS.
G9.
70.
71.
72.
73.
74.
AC am. s
AB
MD. (a -t- c).
lin. A coi. c ^ CM. A. sin. o.
AC lin. A
^(aB* + AC* ^ 2 AB X AO COS. a)
4C sin. c
^(BC* + A<;' ~ 2 bC X AC CM. C)
V'-
COS. J
k:» r ab'-
AC^V.
Sbc X a»
r
. A»' sin.
'0
C(M. C
bc
sin. e (bo
±v*-'-
Hc' tm.
^c)
TALVM or COS. B.
J: V(BC< -^ AC* lin.^ A)
K
± VfAi^ - AcSin.'c)
■^ ^^— ^^^^ ^
A«
— COS. (a + c).
siD. A fin. c — co«. a cm. c.
AB — AC COf. A
^C*"* + AC* — 2 AB X AO CUB. *) "
Bf — AC Cn«. C
^(BC" -|- AC* -- J BC X AO COS. C_> *
SC' + AB* — ac"
*1»C X AB
AB <(in ■ A ^ COT. A \^(l»C* — AB* 510." a)
»C
»c sin,' c Ip coH. c ^(ab* — bc* «b.* c)
VAtt'RI or TA?(. B.
AO 4111. A
± ^(flc* - Ac' sin* a) ■
AC fin. c
75. — Uo. (a + o).
tan. A + Ufi. c
76.
?7.
78.
tin. A tBti. c — 1
AO tin, A
AB — AC CO«. A
AC tin. a
BC — AC CtH. C
-*- V \«C» + AB* - AC*/
AB CO«. A i ^{lic' - Ab' WD.' a)
BO.
AB Mil. A ^ coU A ^ (mt* — AB* tin.' a)
BC CO*, r ^ ^(j«B* — BC* lin * c)
Bff AJn. ^ ^ cot c ^(a0* — M* lin.* oV
VALDKt or SIM. C.
B3.
AO
BC
84. lio. (a + ■).
83. BIO. A cot. B + COS. A tin. B.
86. ~ tl^l .
i^(BC* + AB* — '£UC y AB COS. B)
p- AW li". A
' ^(ab*+ AC* - 2ab > AC «».a)*
sin, B (»C COB. B :t ^At* — BC* »(n,* b)
D9* ' - ■ -. ■.
90.
91.
92.
tin. A (ac C0«. a i ^Bf* — A(" »|||* »)
BC
VAMisi or CUB. C.
± ^(At* — Ai^ Sio.* b)
AC
± ^(bc« - A9* tin.* *)
93. — COS. (a + b).
04. ttn. A SID. B — COS. A COS. B.
_, BC — AS cot. B
E> J.
97.
98.
V(BC* + AB* -
AC —
2bc X
AB cot. A
AB CCS. b) '
VfAB ■ + AC* -
B7* + AC* - AB*
2 AB X AO COB. a)
B ^(AC* - BC* tin."
'2 so X AC
BC tin.* B ^ ciis
•)
AC tin.* a!^! cos.
AO
A V(»C*
- AC* tin.* A)
BO
TALOCI or TAN. C.
AB bill, B
± Vt*<^- Al.»»io.*B)*
AB "in. A
100.
101. . .
± Vt •»*^* - *»' »'"•* a)
102. - un. (» + b).
103. '"•*+'«"•»
104.
105.
(so. A tsn. B — 1
AB tin. H
BC — AB COS. a '
AB sin. A
AC — AB cot. A *
BO cot. n ^ ^t AC* — BO* tin.* »)
107.
108.
BC tin. B Z^ col. B ^f AC* — BC* tin.* b)'
AC m». A i %'(*C* — AC* tin.* a)
AC nn. A Zp col. a ^(bc* — ac' tin.* a)'
366
TABLE XVII.
Analytical Expressions in reference to a Spherical Trianolk ABC.
1. Formula. . . . sin. a =
sin. Bc sin. b
sin. BC sin. G
sin. ab
2. sin. A =
3. siu. B =
4. sin. B =
5. sin. c 1=
I 6. sin. c =
7. COS. A =
sin. AC
sin. AC sin.
A
sin. BC
sin. AC sin.
C
sin. AB
sin. AB sin.
B
sin. AC
ftin. AH sin.
A
sm. EC
COS. BC — COS. AB COS. AC
sm. AB sm. AC
8. COS. A ^ COS. BC sin. b sin. c — cos. b cos. c.
COS. AC — cos. BC COS. AB
9. COS- B ^
sin. BC sm. AB
10. COS. B ^ COS. AC sin. a sin. c -• coa. a cos. c.
COS. AB — COS. BC COS. AC
11. COS. c ^
sm. BC sin. AC
12. COS. c =: COS. ab sin. a sin. b — cos. a cos. b
sin. B
13. tan. A =
14. tan. A =
15. tan. B =
16. tan. b:=
17. tan. c =
18. tan. c =:
sm. AB cut. BC — cos. AB COS. B
sm. c
sm. AC cot. BC — COS. AC COS. c
sin. c
sin. BC cot. AC — COS. bc cos. c
sin. A
sm. AB cot. AC •— COS. AB COS. A
sin. A
sin. AC cot. AB — COS. AC COS. A
sin. B
sin. BC cot. AB — COS. BC COS. B
19.
sin.
Sin AB Sin.
BC !S
A
Hin. c
20.
sin.
sin. AC sin.
A
sin. B
21.
sin.
sin. BC sin.
B
sin. A
22.
sin.
sin. AB sin.
B
siu. c
23.
sin.
sin. AC sin.
AB r~
C
Sin. B
9i
din
sin. BC sin.
C
25. COS. BC =
sin. A
COS. A + COS. B COS. C
sm. B sin. c
26 eo8.Bc =r cos.A6in.ABsin. AC + cos. abcos.ac.
COS. B + cos. A COft. C {
sin. A sin. c * '
28. COS. AC =: cos. B sin. BC sin.AB+cos. bccos.ab.
1
COS. C -f cos. A COS. B I
27. COS. AC =
29. COS. AB =-
sin. A Sin. B
80. COS. AB = cos sin. bc sin. ac + cos. bc cos. ac.
31.
tan.
sin. AB
BC !^
Sin.
B cot. A + COS,
B COS.
AB
82.
tan.
sin. AC
Sin.
C cot A + COS.
c cos.
AC
33.
Un.
sin. BC
sin.
C cot. B + COS.
c cos.
BC
34
Un
sin. AB
AC — .
sm.
A cot. B + COS.
A cos.
AB
35.
tan
sin. AC
sin
A cot. C + COS.
A cos.
AC
QA
Ian
sin. BC
sin. B cut c + cos. B cos. bc
In workinf; by lop^nritbms it is oOen necessary to transform tliese expressions by the in^nh
duction of a subsidiary arc or angle. Tbus, in theorem 26, find a dependent anp:1e. s, by 'b*
expression tan. s = cos. a ton. ab. Substitute for cos. a, in theor. 25, its value in this, it nil'
, /cor. ACcoi». fl-|- sin. Acsin.»\
become cos. bc =: cos. ab cos. ac + tan, s cos. ab sm. ac = cos. abI ■ 1
\ cos. 8 /
COS. AB cos r AC ~~ S^
"* — '— . The latter expression Is evidently logarithmic ; and the trBBsfoRn**
COS. s
tion is equivalent to dividing the triangle into two right-angled triangles, by letting^ fall a per
pendiculai*.
I
TABLES XVIII. XIX.
367
8
I B
< <
^ II - •
\W "51
II II
>^
' .§ i
II .= p
H H ^
^ • ft ** I ^ fi -tf
+ f «
% V U
^ d II II
I I
A.
I
2 -
O
a eg
P 1
^i
•* H »4
II
N
+
Of
ei
c
3
i
3
^
^ <
■ ^ «• '
O c
3 £
I*
V
O
a.
a
II V
)
H
a,
f
X
II 11
w
d 11
5 H
9. *:
S 2
a
+
V
£
bfi
at
04 •*•
II II ".
09 ■<
z :: II
^ H
B a
=^ w
IN '^
"* i
II II
n -4
X
£t « H
O
o
■ft. a. X
I
w e, I <
fi^i
B B
'5S 'S
i I
II II
H H
(N X
X «■**
P CM
I •^' - £ E
-Si t-
I "
« A
5 ^.
be
^ K I) II
• H H H
O P
p a
^
B >>
.2 -5.
5+ I
S
It
K
-a
.9
a
w
•g . S g g ^ »
^ S . U «l « c u
C "J "«*- I, 11 M • •
= ^- g g I' II II K e
^ s II II s s 8 • :;
z Ili.<^2 8|j|,
r? ills o £ s 5
X
^ f »n « »^ 00 ct o -*
;i
ll5 5f|SJ.|^
Oil — ^SO** <
|l|if I = -
|l-|-^fcll|lil
a e P lI.E 'S'c •<
■- :^ = _- S E e 5
5
I
:
ar w * ••
368
TABLE XX.
Numbers often ubkd in Calculations, with thbib Looakituus.
[ For thccircmnftrcntx 0/ a circle to diameter unity, to 25 decimaf ptacetf and itt Ivgaritkm to 20 ptactn^
tec p. xxiii.]
Circumference ofa circle, to diameter 1
Surface of a sphere to diameter 1
A rea of a circle to mdius 1
Area of a circle to diameter I
Capacity of a sphere to diameter 1
Capnjity ofa sphere to radius 1
3- 14 159. &c., nearly = \J {Z\miV2^), nearly =
V(97 409089). nearly = V(3060-2), nearly =
V(961-39), nearly — V(9488-53), arc equal
to radius
Arc equal to radius, expressed in seconds
Length of 1 degree
sin I"
sin 2"
sin. 8"
Number whose Hyper, log*, is := 1
Modulus of the common logarithms
Complement to tlie same
12 hours, expressed in seconds
Complement to the same
24 hours, expressed in seconds
Complement to the same
360 degrees, expressed in seconds
Compression of the earth = yj^
Sidereal revolution of the earth, in days
Tropical revolution of ditto
Sidereal year, in seconds
Tropical year, in seconds
Passage of a comet, perihelion distance 1, from
perihelion to extremity of latus-rectum
Log. k, (Gauss. Theor. M. c. c. I.) k
k in seconds, (Gauss. Theor. M. c. c. 6.) . . . . .
Sidereal lime into mean solar lime
French loises into inttr^s")
feet into metres J
^^— toisca into English feet
' feet into English feet
metre into English feet
millimetres into English inches
} =
3141&926
•7853982
•5235988
4- 1887902
206264 "-8
•01745329
•00000465
•00000970
•00001454
27182818
•43429448
2-3025851
43200
00002315
864U0
•00001157
129G0OO
0033333
36525638
365-24226
31558150"
31556929"
109'»-6I545
00172021
3548"' 1876
^ ..,
at 61" 3
j^
{ ::::
o
Centcs. degrees of quadrant into sexages degrees
minutes of do. into minutes
seconds of do. into seconds
LofariUuac
4971499
98950S99
9 7189980
0-6220S66
l*758122fl
53144-251
8 2418773
4*6w55749
4 9S66049
5 1626961
0434-2945
9 6377843
0-3622157
46354S37
5 3645163
4 9365137
5 0634863
61 126U50
7 52-28787
2-5625978
2 5625910
7 4991116
7-4990947
2 039S718
8 2355!il4
35500065
9-99Sei26
02S98200
9 5116687
8058372
0(J276860
51599-29
85951741
9-9542425
1732393S
3-510M5O
The arithmelioal complements of tliet^e lust 10 logarithms will senre to convert mean
solar time into sidereal t:m^, metres into toifw^s, &c., English feet into toitM», &c..
ami the sexagcslnial divisions of vl\c L\vvAdratit into the centesimal divisions.
4