Mathematical Tables: Containing the Common, Hyperbolic, and Logistic Logarithms, Also Sines ...

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MATHEMATICAL TABLES;

CONTAINING THE

COMMON, HYPERBOLIC, AND LOGISTIC

LOGARITHMS, JDr. John S. Billing

U. 8. Army,

ALSO

SINES, TANGENTS, SECANTS, AND VERSED SINES,

BOTH NATURAL AND LOGARITHMIC.

TOGETHER WITH

SEVERAL OTHER TABLES

USEFUL IN

MATHEMATICAL CALCULATlQJdS: .

ALSO

THE COMPLETE DESCRIPTION AND USE OF

BY

CHARLES BUTTON, LL.D. F.R.S. &c.

LATE PROFESSOR OF MATHEMATICS IN THE ROYAL MILITARY ACADEMY.

THE SEVENTH EDITION.
WITH SEVEN ADDITIONAL TABLES OF TRIGONOMETRICAL FORMULAE.

BY

OLINTHUS GREGORY. LL.D.

Pro/euor of MeUkematics in the Royal Military Academy ; Vice-President of the Attronomical
Society of London ; Honorary Member of the Cambritlge Philotophicai Society,

the Institution of Civil EnffineerSj 8fC,

LONDON :

PBXNTBD FOR LONGMAN, RKKS, ORME, AND CO. ; BALDWIN AND CRADOCK ; J. RICHARDSON ;
J. G. AND K. RIVINOTON ; J. BOOKBR ; HAMILTON AND CO. ; J. DUNCAN ; WIIITTAKKK
AND CO. ; SHERWOOD AND CO. ; PARBURY AND CO. ; J. 80UTER ; SIMPKIN AND MAR.SUALL ;
J. WICK STEED ; T. BVMPUS ; G. MACKIK ; AND HOl'LSTON AND SON: AND FOR J. PAKKKR;
OXFORD; AND J. AND J. J. DEIGUTON, CAMBRIDGE.

1834.

^i

• • ••

• • • • •
•• •• •

• • • ••

• • • •

• •- • •• •

»• •

• •

• ••
•• •

• •- •

• T • • •

••-•. • ••• ••.• •

• - -• •••• •

. :. •••••..

• •••. •• •
.• • • •

• •

LONDONt

rKINTFD BY WILLIAM CIOWK8,
Dtik* Su«»t, Liunbeib.

CONTENTS.

9 *

$ #

I.— INTRODUCTION.

Description and use of logarithmic table.'t ix

Definition and notation ib.

Properties of logarithms x

Construction of logarithms xi

Description and use of these tables xiii

Of the large table ib.

Logarithmical arithmetic xvii

Of the table to 20 places xxi

Of the hyperbolic logarithms xxvi

Of the logistic logarithms xxvii

Of the log. sines and tangents to every second xxviii

Of the general table of log. sines, tani^ents, &c xxx

Theorems for the construction of t<iblcs, and surd expressions for the

sines . ^xxxvii

Trigonometrical rules .'J ,' ^j'

The cases of plane triangles resolved by logarithms . . • / J/ '1*^ * ,

The same by natural sines, &c ':ilviii ; .; »'

The cases of spherical triangles resolved by logarithms ^Us. >' *.*

Use of the versed sines /, /U •» .

Of the traverse table .^ *. IsVii.V/;^.

Of Mcrcator's sailing •' / » T^'**. *' /

Of the lengths of circular arcs /^ /..*^xii»«^ *., »' .'

Of cum paring the common and hyp. logs '* 'If^'i''*" <>^ *'

II.— TABLES.

Table

I — T/>earithins from 1 to 108000 1

2.— Logarithms, &c. to 20 places 202

3._Id. with differences 213

4, — Numbers to logarithms to 20 places 216

5 & 6. — Hyperbolic logarithms 219

7. — Logistic logarithms -. . 230

8. — Sines and tangents to seconds -^237

9. — Natural and logarithmic sines, tangents, secants, and versed sines 268

lO.— Traverse table 35?

1 1 . — Length of arcs 360

12. — ^Tablo to change common and hyperbolic logarithms from one to

the other 361

13. — Points of the compass ib.

14.— Equivalent expressions for sin. .A, cos. A, tan. A . . . . 362

15. — Formulsp for two arcs 363

16.— Formule for the solution of a plane triangle 364

17. — ^Analytical expressions, spherical triangle 366

18. — Formulae for quadratics and cubics 367

19. — Formulae useful in astronomy ib.

20. — Useful numbers and their logarithms 368

CORRRCTION OF ERRORS IN THE SIXTH EDITION OF THESE TABLES.

[As many persons in Public Institutions and Private Seminaries, where this
seventh edition will be introduced, have purchased and will probably continue
to use the sixth edition ; they are requested to correct their copies, to agree
with the Logarithms, Sines, Tangents, &c. specified below.]

• • •

Logarithms :—
Log. of 647 should be S109043

10070 0030295

10989 0409582

11003 0415111

11230 0503798

33071 5194474

49523 6948069

67999 8325025

75843 8799155

77649 8901359

^,17438 8917493

, :'V<pj910 9205929

»^ : Irfi^fe-Jarrfe page, No. 3330 should be 8330.

*' Co& oVB9S92 should be 9211244

9222686
9246462

/ •/ :.^ •. .\5;r)42' 9710067

\ V»», oV88S92 should be 9i

. ••/.••/. .:y36ia', 9i

••/• //••*.. ^071 V 9i

• ••• •• •

I* •

94688 9762949

94750 9765792

95339 9792706

104891 02073823

105879 02480983

In the Logarithms to 20 places: —

Log. of 554 should be 9 in the 19th place.

627 75 ..... 6 & 7th pi.

644 5 6th pi.

756 20 13 & 14th pi.

762 9 12th pi.

In the Differences of Logs, to 20 places : —

Log.of 101028, the Istdiff. should be42987,&c.

00004, the 2d 53025,&c.

00021, the 2d 530458,&c.

Hyp. Log. of 837 should be 6*7298241.

L(>gi'«tic Log. under 17 opp. 57 should be 5241
• *«. ••.• tSv ... 0«5 « « • • • . • « o/U<5

.••• •*•. Ow ... 01 a....... Ot/4/

■ .•• •*•• OO ... DU . . ... ... OOv7/

Nat. and Log. Sines, Tang, &c. : —

Log. sin. 0^23' 19" should Iks 7 8313893

Log.tan. 47 48 81431820

Log. sin. 1 9 8 2429396

Log. vers. 6 36 7-8213324

Log. co»ec. 10 6 10*7560528

Log. ver?. 12 59 84076380

Nat.cosec. 13 4 44231224

Nat. sin. 14 6 -2436150

Ug. sin. 15 60 94403381

Nat. coveis. 19 51 •6604411

Nat. versin. 20 7 0610057

NaL COS. 20 7 -9389943

Nat. sin. 22 42 -3859060

Nat. covers. 24 6 -5910695

Log. cot. 26 8 10-3092578

Log. covers. 26 42 9- 7409001

Nat. covers. 27 10 -54341 96

Nat. cosec. 27 26 21705335

Nat. covers. 35 17 -4223798

Nat. Un. 35 35 7154898

Nat. cos. 37 2 -7982853

Nat. cos. 37 35 -7924671

Log. sec. 38 3 101037642

Nat. cosec. 39 7 1-5850334

Nat. covers. 39 8 3688728

Nat. cosec. 39 19 1-5782680

Nat cot. 39 45 1-2023693

Nat. vers. 39 57 -2333949

Nat cot 40 40 11639763

Nat Un. 40 56 -8672460

Nat. cot 40 5& 11530754

Log. COS. 41 44 9-8728849

Nat sec. 42 9 1-3488168

Nat Un. 42 45 -9243905

Nat versin. 42 59 -2684479

Table Diff. Lat and Departure :—

Dist. 3. deg. 14 should be 2-9169.

Tab. 12. Common and Hyp. Logs : —
Against c. l. 09 should be Hyp. Log. -20723'^6G.

Pr^ John S. BUlin^s^

PREFACE.

Thb very ample introduction, prefixed to the following collection of
Mathematical Tables, supersedes the necessity of using many words
here by way of preface, and leaves little more to be mentioned than
the necessity and occasion of this work, with some account 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 fifth or last edition. / t^iHdiQg, as
well from the report of others, as from my own experience* that' tttogfe
editions (to say nothing of the very improper alteration iij'the form^
of the table of sines, tangents, and secants in the last ^f1th^jT.)V/iere
so very incorrectly printed, the errors being multiplJed -'6&ypnd *all
tolerable bounds, and no dependence to be placed on thettf lor aav
thing of real practice, I was led to undertake the painful office or
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 profits of the book would not enable him fully to
reward my pains.

I 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 others of the most perfect
works of the same kind, as Briggs's, Vlacq's, Gardiner's quarto book,
&c. ; by which means 1 detected many errors in each of them, which
had not before been discovered ; and of these, between twenty and
thirty were in the two editions of Gardiner's quarto work, printed at
London in 1742, and at Avignon in 1770. But, besides detecting
many previously unknown errors in the said third edition of Sherwin,
which was no more than was expected, I discovered, with 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 PREFACE.

beginning and end of the table ; though Mr. Gardiner, the editor of
that edition, had made the table correct in that respect in his own
quarto work before mentioned, which was also printed in the same
year, 1742, with the said third edition of Sherwin ! The errors from
this cause, in that third edition, amounted to several thousands ; and
they have continued to run through all the editions of Sherwin ever
since that time ! But they are here corrected. Nor has less attention
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 everj' proof-sheet.

But in giving this edition to the world, I was not satisfied with

barely making it correct. I was aware that the materials themselves

might be much improved; and I have accordingly enlarge^!, or

otherwise greatly amended them, in various respects. Among the

imprq¥«T]ft^s of the old materials may be reckoned the following : —

. nanbclyvi^n*^"^ l^rg^ ^Me of logarithms, the proportional parts, near

^, .••.^*-:the'*begii(l5ing, are more conveniently arranged, being now all placed

./,*•;••/••* ^ iivwi*.3jinid opening of the book where their corresponding differences

•* •***,\oiiifri»^tf^, logarithms to sixty-one figures are brought to their

**^.gr(Jpe(:ptaice*in the book, and more conveniently disposed all in one

**•• *p*ftge ; the large table of sines, tangents, and secants, is more com-

* modiously arranged, and rendered more distinct and convenient for

use ; the natural sines, 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 differences, in both, set between the two columns to

which each of them answers ; and the versed sines here introduced

into their proper place in the same pages with the 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

important 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

persons the most experienced in these matters.

The improvements in the tables, by the introduction of new
matter, are both great and numerous. The tables numbered 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 differences, in the pages of natural sines, &c., are now

PREFACE. VU

first introduced : as are also the tables of hyperbolic and logistic
logarithms ; the logarithmic sines and tangents for every second, in
the 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., — the uses and exemplifications of
he whole being very amply detailed.

Royal Mil Acad. fVoolwicfi,
February^ 1785.

*i>* In 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 mistake take out the three constant
figures next above the said line. 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 0, 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. These improvements,
besides that of new and better formed figures now introduced, and
other attentions, contribute to render this edition of the tables more
convenient and correct than either of the former ones.

December, 1800. C. H.

In this fl/lh edition several of the tables have been n\uch enlarged
and improved, and some new ones introduced. 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 table of Hyperbolic Loga-
rithms is introduced afler the old one.

London, May, 1811.

The seventh edition is now presented to the public with still, farther
improvements. In onler to reduce the price, the Historical Intro-
duction, which occupied 124 pages, is omitted. The impartial,
interesting, and valuable information, contained in that Introduction,

VllI PREFACE.

is now to be found in Dr. Hutton'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. The
tables of logarithms to 61 places^ with their difierences, 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 appreciated by the readers- of
Cagnolif Collet, Borda, Ursin, &c. : but are, as yet, by no means
so well known to £nglish compute]^ as they ought to be, notwith-
standing the exhibition of tables nearly similar, by Mr. F. BaUy, 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 particulars have been transferred
into this part from the Historical Introduction just mentioned ; and
a page^ exhibiting the surd values of the sines of arcs to every third
degree in the quadrant. These, with the decimal values of the prin-
cipal surds, as ^, ^5, ^(5 + V^)> &c-» arranged in immediate
connection with them, will often 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 Hutton's Mathematical
Tables the reputation, for accuracy and extensive utility, which they
have maintained for nearly half a centur)'.

OLINTHUS GREGORY.

Royal Mil. Acad. fVoolwich,
March, 1830.

DESCRIPTION AND USE

OF

LOGARITHMIC TABLES.

Thus
or
or

1

2

3

4

1

2

4

8

16

1

2

3

4

1

3

9

27

81

1

2

3

4

The Definition and' Notation of Logarithms,

LoGiiRiTHMS may be considered the indices or arithmetical series of
numbers, adapted to the terms of a geometrical series, in such sort that
corresponds to 1, or is the index of it, in the geometricals.

5, &c. indices or logarithms;
32, &c. geometric progression.
5, &c. indices or logarithms.
243, &c. geometric series.
5, &c. indices or logarithms.
10, 100, 1000, 10000, 100000, &c. geometric series.
Where the same indices serve equally for any geometric series ; 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, or 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 geometrical series,
and receive their proportional logarithms, whether integers or decimals.

Or, the logarithm of any number is the index of that power of some other
number, which is equal to the given number. So, if n be =: r", then the
logarithm of n is Tt, which may be either positive or negative, and r any
number whatever, according to the different systems of logarithms. When
N is 1, then n = 0, whatever the value of r is ; and consequently the logarithm
of 1 is always in every system of logarithms. When n is =: 1, then n is
= r : consequently r. is always the number whose logarithm is 1, in eveiy
system. When r is = 2*718281828459, &c., the indices are the hyperbolic
logparithms, such as in our 5th table : so that n is the hyperbolic log^ithm of
(2*718, &c)". But in the common logarithms, 9* is = 10 ; so that the
common logarithm of any number (10") is (n) the index of that power of 10
which is equal to the said number. So 1000, being the 3d power of 10,

has 3 for its logarithm ; and if 50 be := 10 , then is 1.69897 the common
logarithm of 50. And hence it follows, that this decuple series of terms

10* . 10*, 10«. 10\ 10«. 10"^, 10"^, 10"*, 10"^,
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 '69S97 as before : also the
number '05, falling between the terms '1 and '01, its logarithm will

X DESCRIPTION AND USE

fall between •- 1 and — 2, and is indeed — - 2 + '69897. Tlic index is
also called the characteristic of the log^arithms, and is always an inte^r
either positive or negative, or else := ; and it shows what place is occupied
by the first significant figure of the given number, either above or below the
place of unit«, being in the former case -f- or positive, in the latter — or
negative.

When the characteristic of a logarithm is negative, the sign — is commonly
set over it, to distinguish it from the decimal part, which being the logarithm
found in the tables is always positive: so — 2 -f- '69897, or the logarithm of
'05, is written thus 2'69897. But on some occasions it is convenient to
reduce the whole expression to a negative form ; which is done by making
the characteristic figure less by 1, and taking the arithmetical complement of
the decimal, that is, beginning at the lefl hand, subtract each figure from 9,
except the last significant figure, which subtract from 10 ; so shall the re-
mainders form the logarithm entirely negative. Thus the logarithm of *05,
which is 2-69897, or - 2 + '69897, is also expressed by — 1*30103, which
is wholly negative. It is also sometimes thought more convenient to express
such logarithms wholly as positive, namely, by only joining to the tabular
decimal the complement of the index to 10 : in which way the above loga-
rithm 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 logarithm 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 . so the
arithmetical complement

of 1 '69897 f and of 2*698971 where the index — 2, being negative, is added
is 8-30103 "t is 11-301033 to 9, and makes 11.

Tht Properties of Logarithms.

From the definition of logarithms, either as being the indices of a series of
geometricals, or as the indices of the powers of the same root, it follows, that
the multiplication of the numbers will answer to the addition of their loga-
rithms ; the division of numbers, to the subtraction of their logarithms; the
raising of powers, to the multiplying the logarithm of the root by the index
nf 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: —

1st. L. a6 or a X 6 is = L. a + l. b
L. 18 or 3 X 6 is = L. 3 -f l. 6
L. 5 X 9 X 73 is = L. 5 + L. 9 -f- L. 73

2d. L. a -4- 6 is = L. o — L. 6

L. 18-f- 6 is= L. 18 - L. 6

L. 79 X 5 ^ 9 is = L. 79 -f L. 5 — L 9
L. i or 1 -i- 2 is = L. 1 - L. 2 = — L. 2 = - I.. 2

L. or 1 -T- W IS = — L. 71.

7t

oj-ji' - ml ^ "*.m

3d. L. r"is = 71 L. r; L. r" or l. 1/ ^ is = — l. r; l. r" is = — l. r.

71 II

1 3

L 2* is = 6 L. 2; l. 2» or l. V 2 is = i l. 2 ; l. 2» is = | l. 2.

Thus, any number and its reciprocal have the same logarithm, but with
contrar)' signs ; and the sum of the logarithms of any number and its com-
plement, is equal to 0.

OF LOGARITHMIC TABLES.

XI

To construct Logarithms,
It is shown in my History of Logarithms^ that the logarithm of — is =r

Of

— X : — I : + — : H 7 &c., where 2 is the sum and x the difierence

fw z ^ S:^ 52* 72^

of a and 6; al.so m = 2*302585092994, &c., the hyp. logarithm of 10.

l*herefore if a and b be any two numbers differing only by unity, so that j* or

2

6 — a may be = 1 ; then shall the logarithm of 6 be = l. a + — x :

m

— f- ^t + ^^ ^* Which gives this rule in words at length: call z the

2 «f2 *iZ

sum of any number (whose logarithm is sought) and the number next less
by unity ; divide -8685889638, &c. (or 2 -h 23025, &c.) by 2, and reserve
the quotient: divide the reserved quotient by the square of 2, and re-
serve this quotient : divide this last quotient also by the square of 2, and
again reserve this quotient : and thus proceed continually, dividing the last
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 1, 3, 5, 7, 9, 11. &c., as long as
division can be made: that is, divide the first reserved quotient by 1, the 2d
by 8, the 3d by 5, the 4th by 7, &c. Add all these last quotients together,
then the sum will be the logarithm of 6 -4- a; 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.

Eiample 1. To find the Log. of 2,
Here the next less number is 1, and 2 -f 1 r= 3 =2. whose square is 9. Then

3) -868598964

9) -289529654

9) 32169962

9) 3574440

9) 397160

9) 44129

9) 4903

9) 545

9) 61

1) -289529654

3) 32169962

5) 3574440

7) 397160

9) 44129

11) 4903

13) 545

15) 61

289529654
10723321
714888
56737
4903
446
42
4

Log. 4 -301029995

Add Log. 1. ... -000000000

Log. of 2 -301029995

Example 2. To find the Log. ofS,

Here the next less number is 2, and 2 + 3 = 5 = '?, whose square is 25, to
divide by which always multiply by -04. Then

>.

5 )

•868588964

1) •

173717793 (173717793

25)

•173717793

3)

6948712 ( 2316237

25)

6948712

5)

277948 ( 55590

25)

277948

7)

11118 ( 1588

25)

y 11118

9)

448 ( 50

25)

445

"9 y^

11)

IS ( 2

18

Log.

I -176091260

Log.
Los:.

2 add.... -301029995

3 -477121255

xii DESCRIPTION AND USE

Then, because the sum of the logarithms of numbers gives the logarithm
of their product, and the difference of the logarithms gives the logarithm of
the quotient of the numbers, from the above two logarithms, and the loga-
rithm of 10 which is I, we may raise a gpreat many other logarithms, thus :

Example 3.

Because 2x2 = 4, therefore to L. 2. . . * 301029995 J

acfd L. 2 -301029995^

sum is L. 4 '602059991^

Example 4.

Rocause 2x3 = 6, therefore to L. 2 -301029995

addL. 3 -477121255

sum is L. 6 778151250

Example 5.

Because 2* = 8, therefore L. 2 -301029995f

mult, by 3 3 \

gives L. 8 -903089987

Example 6.

Because 3« = 9, therefore L. 3 477121254^^^

mult, by 2 2

gives L. 9 -954242509

Example 7.

Because l^ = 5, therefore from L. 10.. 1-000000000

teke L. 2 -301029995J

leaves L. 5 • 698970004^

Example 8.

Because 12 = 3 X 4, therefore to L. 3 477121255

addL. 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, &c. ; and then using composition and
division, we may easily find as many logarithms as we please, or may speedily
examine any logarithm in the table.

See, farther, the History of Logarithms, in my Tcacts, vol. i. 8vo.

xiji

THE DESCRIPTION AND USE OF THE TABLES.

The following collection consists of various tables, in the following order^
viz. 1. A large table of logarithms to 7 places of figures ; 2. A table for find-
ing logarithms and numbers to 20 places ; 3. Logarithms to 20 places, with
their 1st, 2d, and 3d differences ; 4. Another table of logarithms to 20
places, with their 1st, 2d, and 3d differences ; 5. Hyperbolic logarithms ;
6. Logistic logarithms; 7. Logarithmic sines and tangents to every second
of the first 2 degprees ; 8. Natural and logarithmic sines, tangents, secants,
and versed sines, with their differences 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 and quarter 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 useful
trigonometricul formulae, &c. Of each of which in their order.

Of the 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 logariUim to any number, and the number to any
logarithm, to 7 places of figures. This table consists of two parts ; the first
contains, in 4 pages, the first 1 000 numbers, with their corresponding loga-
rithms in adjacent columns ; the second contains all the 108000 numbers and
their logarithms, with the differences and proportional parts, disposed as
follows : in the first column of each page are the first 4 figures of the num-
bers, and along the top and bottom of the columns is the 5th figure, in which
columns are placed all the logarithms,* the first 3 figures of each logarithm
being at the beginning of the lines in the first column of logarithms, signed
at the top and bottom, and the other 4 figures in the remaining columns.
Sometimes the first three figures of the logarithms are found in the line next
below the number, viz. when the fourth figures have changed from 9's to O's,
in which case, a bar is placed over the first ciphers in the whole of that line
to catch the eye, thus 0. Afler the 10 columns of logarithms stands their
column of differences, signed D ; and lastly, after that, the column of pro-
portional parts, signed Pro. Pts., showing what proportional part of each
difference corresponds to 1,2, 3, &c., the whole difference answering to 10 ;
or showing the -j^, -j*jj, -^q, &c., of tlie differences.

Note, The logarithms in these columns are 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 denomination,
have the same decimal logarithm, and these differ only 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 denomination, or lefl-hand figure, of the natural number, from
the units place. So that, if the natural number consist of only one place of
integers, the index of its log. will be : if of 2, 3, 4, 5, &c., the index of its
logarithm will be respectively 1, 2, 3, 4, &c., being 1 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 a decimal, and
its first significant figure be in the place of primes, 2ds, 3ds, 4th8, &c., the

index of its logarithm will be respectively T, 2, 3, 4, &c. ; or the figure which
expresses the distance of the first place of the natural number from the

XIV

DESCRIPTION AND USE

Number

Logtr. 1

•2651

3 •423409"

265 1

2-4234097

26-51

1-4234097

2-651

0-4234097

•2651

1 -4234097

•02651

2-4234097 ;

002651

3 4234097

units place, but with a negative sign, as the number is below the place of
units, the sign being written above the index instead of before it, as that part
only of the logarithms is to be considered as negative, the decimal part of it
being always affirmative. And in the arithmetical operations of addition
and subtraction with logarithms, the negative indexes will have tlie contrary
eff*ect to that of the decimal part of the logarithm, viz. when the logarithm is
to be added, the figure of the negative index must be subtracted, et vice versa
Hence, if 4234097 be the tabular or decimal part
of the logarithm belonging to the figures 2651,
without any regard to their particular denomi-
nations ; then according as they are 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 how far its
first figure on the left hand is from the units
place ; so when a logarithm 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 more than that of the index when positive, or
by setting the first significant figure in that decimal place, 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 consisting of S figures.

Find the number in the column of numbers in one of the first 4 pages of
the table, and immediately on the right of it is its logarithm sought. So the
Ingarithm of 72 is 1-8573325, and the logarithm of 3*33 is 0*5224442. when
the proper index is supplied. .

2. To find the Logarithm of a Number consisting of A Places,

In the first column (signed N) in some one of the pag^s 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 2254 is 3*3529539, and
Uiat 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 5th figure at the top 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 logarithm are the first 3 common figures of
the 2d column (signed 0), and the last 4 figures are on the same line, but in
the column signed with the 5th figure of the g^ven number. So the loga-
rithm of 23204 is 4-3655629, and that of 74640 is 287297 16, and tliat of
•083178 is 2-9200085.

NotCf When the last four figrures of the logarithm begin with a cipher, or
any figure less than the last four in the 2d column begins with, then the first
3 common figures are those in the next lower line : so, in the last example,
the first 3 common figures are 920, and not 919. This is indicated by the
bar over tlie first cipher in 0085, as already explained.

OF THE TABLES. xv

4. To find the Logarithm of a Number of 6 Places.

Find the logarithm of the first five figures by the last article and take the
diflerence between that logarithm and the next following logarithm, of (which
is the same thing) find the difference nearest opposite in the last column but
one, signed D; then under that difference in the last column (of proportional
parts) and against the 6th figure of the given number, is the part to be added
to the logarithm before found for the first 5 figures, the sum being the loga-
rithm sought. So to find the logarithm of 3409*26 : the logarithm of 34092,
the first 5 figures, being 5326525, and the common difference 127, under
which and against 6 in the last column is 76, which being added to tho
former logarithm, and the proper index prefixed, i. e. 3 for 4 places of
whole numbers, we have 3*9926601 for the whole logarithm required.

5. To find the Logarithm 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 logarithm of the 7th 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.

Thus, to find the logarithm of 3*409264. The
several parts being taken out according to the Numb. Logar.

rule, and placed as in the margin, the sum gives 34092 . . 5326525
the whole logarithm sought. ^a ' ^t\

NotCy In the same way we might take out the : ?L

proporUonal part of an 8th figure, dividing iU 3-409264 . 0-5326606
tabular part by 100, or setting it two places farther

to the right hand than the first logarithm. Or the whole proportional paM
for any number of figures above five, may be found at once, by multiplying
the common tabular difference of the logarithms, found as ' ^27

before, by all the figures afler the 5th, cutting off from the 64

pro luct as many figures as we multiply by, and adding the "508

rest to the logarithm of the first 5 figures before found. 762

So in the last example above, having found the common 81,26

difference 127, multiplying it by 64 the last two figures, 5326525
cutting off two, add the rest to the logarithm of the first 5, 0*5326606
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

34092 5326525

6 76

4 .5,1

D ....••.. 1,02

34092648 7 • 5326607

648

1016
508
762

827296
5326525

7 '5326607 the same as the other.

6. To find the Logarithm of a Vulgar Fraction, or of a Mixt Number.

Either reduce the vulgar fraction to a decimal, and find its logarithm as
above. Or else (having reduced the mixt number to an improper fraction),

xvi DESCRIPTION AND USE

subtract the logarithm of the denominator from the logarithm of the nume
rator, and the remainder will be the logarithm of the fraction sought.

Example 1.

To find the log. of -/y or • 1875.

From log of 3 0-4771213

Take log. of 16 1 -2041200

Rem. log. of ^y or • 1875 1-2730013

Example 2.

To find the log. of 13 J or f .

From log. of 55 1-7403627

Take log. of 4 06020600

Leaves log. of^ or 13-75 1 • 1383027

7. To find the Natural Number atuwering to any given Logarilhnu

Find the first 3 figures, next afler the index of the giren logarithm, in the
second column, signed 0, and the other 4 figures on the same line in one of
the nine following columns ; if the figures of the logarithm be thus found
exactly, then on the same line in the first column are the first four figures of
the natural number, and the 5th is at the top or bottom of that column
in which the last four figures of the log. were found. So to find the number
answering to the logarithm 2*5890108. In p. 63 I find the first three
figures 589, and in column 6 of the line above are found the other four -0108
(because 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 the first four figures 388*1, and 6 at the top of the column,
making in all 388-16 for the numbet sought ; having placed the decimal
point so as to make three integers, being 1 more than 2 the index cf the
given logarithm.

But if the given logarithm be not found exactly in the table, subtract the
next less tabular logarithm from it, and look for the remainder in the pro-
portional parts under the difference between the two tabular logarithms next
less and greater than the given logarithm, and against it, or the part next
less, is a 6th figure to be annexed to the five figures before found. And if
the remainder be not found exactly in the proportional parts, subtract the
next less part from it, and annex a cipher to this 2d remainder, then against
the nearest proportional part (either greater or less) is a 7th figure to be
annexed to the six before found. And that figure will be the nearest to the
truth in that place, either too much or too little.

Example,

To find the number answering to the logarithm 1-2335678
The next less tab. log. is the log. of 17122, viz. 2335545

Ist rem. 133

5 for the part 127

The difference is 254 J
Lie of pro. pts. gives J

and the table of pro. pts. ffives ) ^ . ^jl rem. 60

2 for the part 51

feo that the number sought is 17- 12252, making two integers for the index 1.

OF THE TABLES. xvij

Or the 6th and 7th figures may be found without the table of proportional
parts, by dividing the first remainder by the tabular dif-
ference, annexing* one cipher to the dividend for each ' 127 o
figure to be found. So, in the last example, the re- — —r-
mainder 133, with two ciphers annexed, being divided ^^g
by the tabular difference 254, as in the margin, the
quotient gives 52 for the 6th and 7th figures, the same as before. In like
manner may be found the numbers to the following logarithms.

Logar. 1-2345678 1 3-7343003 1 1 092 1406
Numb. 1716200 15-423758^^1236348

2-3720468
•02355303

4-6123004
40954-39

3-2946809
1970-974 .

OF LOGARITHMICAL ARITHMETIC.

I. Multiplication by Logarithms,

Add together the logarithms of all the factors ; then the sum is 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 logarithms.

And that the difference between the affirmative and negative indices, is to
be taken for the index to the logarithm of the product.

Example 1.

To multiply 23- 14 by 5062.

23-14 its log. is 13643634

5062 its log. is 07043221

Product 117-1347 20686855

Example 2.

To multiply 2581926 by 3457291.

' 2-581926 its log. is 041 19438

3-457291 0-5387359

Product 8-92647 0*9506797

Example 3.

To multiply 3902, and 597-16, and 0314728 all together.

3 902 its log. is 05912873

597-16 2-7760907

•0314728 2-4979353

Product 73*33533 1 8653133

The S cancels the 2, and the 1 to carry from the decimals is set down.

Example 4.
To maltiply 3-586 and 21046, and 08372, and 00294, all together.

^ 3-586 its log. is 05546103

2-1046 3231696

0-8372 1-9228292

0294 2-4683473

Product -1857618 12689564

Here tlie 2 to carry cancels the 2, and there remains the I to set down.

b

xvUi DESCRIPTION AND USE

II. Diviiion by Logarithms.

From the logarithm of the dividend, subtract the logarithm of the divisor ;
the remainder is a logarithm, whose corresponding number will be the
quotient required. .

But first observe to change the sign of the index of the logarithm of the
divisor, viz. from negative to affirmative, or from affirmative to negative ;
then take the sum of the indices if they be of the same kind, or their difference
when of different kinds, with the sign 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
logaritlim, add it to the index of the logarithm of the divisor when that index
is affirmative, but subtract it when negative ; 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*3831509

Divisor 4567 3*6596310

Quotient 5290782 - 0-7235199

Ejpample 2,

To divide 37* 149 by 523*76.

Divid. 37149 its log ^ 1*569947

Divis. 523-76 2*7191323

Quot 07092752 2*8508148 ' 5 : ^ - ^

Example 3.

To divide 06314 by 007241.

Divid. 06314 its log «-8003046 ^ - : ^ "' ' *

Divis. 007241 3*8597985 -. r > . -

Quot. 8-719792 0*9405061 " ^' - ^ ^ - ^

Here I carried from the decimals to the 3 makes it beeome S, which taken
from the other §, leaves remaining. *

Example 4.

To divide 7438 by 12*9476.

Divid. -7438 its log. 1*8714562

Divis. 1*2*9476 1*1121893

Quot. -05744694 S7592669

Here the 1 taken from the I makes it become S to set down.

III. The Rule of Three, or Proportion,

Add the logarithms of the 2d and 3d terms together, and from their sum
subtract the logarithm of the 1st, by the foregoing niles ; the remainder will
be the logarithm of the 4th term required.

Or in any compound proportion whatever, add together the logarithms of

ff

k

OP THE TABLES. idx

M the terms that are to be multiplied, and from that sum take the sum of the
others; the remainder will be the logarithm of the term sought.

But instead qf subtracting any logarithm, we may add its complement, and
the result will be tlie same. By the complement is meant the logarithm of
the leciprocal of the given number, or the remainder by taking the given
log^thm from or from 10, changing the radix from to 10 ; the easiest
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 must 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 1.

To find a 4th proportional to 7234, and 2.519, and 357*4862. .

As 72-34 . comp. log 8*1406215

To 2-519 0-4012282

So 357-4862 25532592

To 12 44827 10951089

Example 2.

To find a 3d proportional to 12796 and 3247 18.

As 12-796 , comp. log 8*8929258

To 3 24718 0-5115064

So 3-24718 0-5115064

To -8240216 19159386

Example 3.

/ To find a number in proportion to '379145 as '85132 is to '0649.

A? -0649 . comp. log 111877553

to -85132 I 9300928

. So;-379145 1-5738054

To 4-973401 06966535

f

««^ Example 4.

what will be the in-

A ^Tf the inter/itf (lf;100/. for a year or 365 days be 45/.,
^/^tctest of 279-2af^* ij^days ?

• r '.'•V*'ftlOO\ , r 80000000

•:'^J.'^5r<^">P- >^& {7-4377071

•• •; rrt.* r279-25 2-4459932

• * fc7 1^74 2 4377506

. SW4^5 0-6532125

* Ife '9^53296 0-9746634

•

*

. *",t4V. Involution^ or Raising of Powers,

Multiply tB^pfllga^thm of the number given by the proposed index of the
power, and thij^oduct will be the logarithm of he power sought

Note, In mulfcplying a logarithm with a negat ve index by any affirmative
number, the product will be negative. — But whai is to be carried from the

b 2

'H

« DESCRIPTION AND USE

decimal part of the logarithm will be affirmative.— llierefiire the diffemee _
will be the iDdex of the product ; and it is to be accounted of the same kind
with the greater

Example I,
To find the 2d power of 2-5791.

Root 3-5791 iti log 0-4114682

index 2

Power 6-651756 0-8239364

Example 2.

To find the cube or3-07l46. '

Root 3-07146 its log 0-4873449

Power 28-97575 - 1 4620347 v",'

Example 3. ^'.' ^

To find the 4th power of 09163; .(/^:";.

Root -09163 its log, S-9620377 ^ ''-irij

Power 0000704938 5-8481508 * . '7;'.

Here 4 times the n^ative index being 8, and 3 carried, oo, the difference' -
5 is the index of the product. ' '

Example 4. ' ,

To find the 365th power of 1:00.4^, •-■• ■ ; .^"V;

Root 1-0045 itf log. 000^94SSk-- -.>■•":

index '* JpS ; .. ■•..'■ .

Power 5-148888 o'Tjlgrai." ■ ...■ •

V, EvolKtim, or Extraction t>f It^glt^\i ..

Divide tne ogarithm of the power, or given numC^'^ jj^tWiyleti'.and the ^
quotient will be the logarithm of Ihe root required. ,^ ,'■ , ' -.■ ,'.

Note, When the index of the logarithm is ue^aliv^. ^i^ tt^'^lfisor is nol ,,
exactly contained in it without a remainder, increase-X^U^lcn' a nunfber ^S..'
will make it exactly divisible; and carry Uic unJtkj'Ma'dw^, [f.<i*so tafiny ■
tens, to the left-hand place of the decimal part of the hjganlbin-^ thcaj.divida •'
the results by the index of the root ■'•*.'•.•'•»" '•

•.■.-Kh?.

Example 1. . .'*•*?' '■■'- '

Tofinu the square root of 365-" •'^^Ca i' ■ " -

Power 365 2 ) 2-5622929 -if^ ■

Root 19-10498 l-281I4(!i' - ; .' -

m^

OF THE TABLES. xw

Example 2.

To find the cube root of 12345.

Power 12345 3 ) 40914911

Root 2311162 13638304

Example 3.

To find the 10th root of 2.

Power 2 10 ) 03010300

Root 1071773 00301030

Example 4.

To find the 365th root of 1 04 5.

Power 1045 365 ) 00191 163

Root 1-000121 00000524

Example 5.

To find the square root of '093.

Power 093 2)2-9684829 l|^-f^^^s

Root -304959 14842415 ^TaV^/^

Here the divisor 2 is contained exactly once iu 2 the negative index, there-
fore the index of the quotient is I.

Example 6.
To find the cube root of '00048,
Power 00048 3 ) 46812412 ^ - •^] '- / z- ^/ /^

Root 07829735 28937471 . - ..

Here the divisor 3 not being exactly contained in 4, augment it by 2, to
make it become 6, in which the divisor is contained just 2 times ; and the 2
borrowed being carried to the other figures 6, dc., makes 2*6812412, which
diTided by 3 gives '8937471.

». •■

-!^

OP THE TABLES FOR LOGARITHMS TO TWENTY PLACES.

Thbsb are tables 2d, 3d, and 4th. Of these, table 2 contains all numbers
firom 1 to 1000, and all uneven numbers from 1000 to 1161; with their
logarithms to twenty places ; table 3 contains all numbers from 101000 to
101139, with their logarithms to twenty places, and the 1st, 2d, and 3d dif-
ferences of those logarithms : and table 4 contains all logarithms regularly
from 00001 to 00139, with their corresponch'ng 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 logarithm to any other number, and the
number to any other logarithm, to twenty places of figures.

(I.) Tojind the Logarithms to given Numbers.

Casb 1. If the given number b be found in any of these three tables ;.
then its logarithm b is in the line even with it

■>

uii DESCRIPTION AND USE

Case 2. If b is known to be the 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 figures of a given number 6', be
found in table 3 ; let a' be an integer, a' its logarithm ; h the remaining
figures of 6' ; x the complement of 6 to d' or I ; d', d", d'", the IsU 2d, Sd
difi^erences of the logarithms in the same line with a' ; / = ^ d"' X

jf -j- 1 4- d" : Then b' the logarithm of the number 6' will be

(d' X 5) + a' to 12^

(J X d'' -f- d' X J) + a' to 17 > places of figures nearly.

(J xf + d' X J) + a' to 20 3

Example I.

GHven the number 6' = 01010,26227,6351, to find b' its logarithm nearly
to twelve places.

Here a' = I0I026 a' = 00443,31579,747

J = 2276351 J d'. . .. + 9 785,618-

d' = 429881746 b' = 200443,4 1365,365 -

Example 2.

.Given 6' = 001010,26227,63509,6-26, to find b' ite log. nearly to 17

places. Hereo'zr 101026.

J = 0-22763,509626 ; j: = 0*772365 ; d' = 42988,174579 ; d" = 425510.

Now ixD" 16432,45

d' 42988,17457,86

jxp" -f D ^ 42988,33890,31

J a? d" + d' X J 9785,65466,42

a' 0443,31579,74695,33

And (J J d" + d' X J) + a', or b' 200443,4 1365,40 161,75

Example 3.

Given 1/ = 001010,26227.63509,62573.17345, to find b' its log. nearly
to 20 places. a' = 101026.

8 =: 0-22763,50962,573173; x = 077236,490374; .r + 1 = 1*772365 ;
D' = 42988,17457,86301 ; d" = 42550,96343 ; d'" = 84236.

Now i d'" X X + 1 49766

d" 4 2550,96343

/ 42551,46109

ixf 16432,62757

d' ^ 4298 8,1745 7,86301

ixf+ d' 42988,33890,49058

ix/+D''x5 9785,65466,45604

a' 00448,31579,74695,32791

And b' 5,00443,41365,40161,78395

Case 4. If the number 6 do not come under one of the preceding cases :
put a for the first five figures of b ; n for 101, the least, or some one, of the

numbers in table 3 ; then — or — = a is to be had in tabic 2, with a its

OF THE TABLES. xxiii

b
logarithm ; lei 6' =: — or 6a, and a' the first six sigpnificant figures of 6'

(found in table 3) be an integer, and a' its logarithm ; put B for the remain-
ing figures of b* ; x the complement of h to d! ; d', d", e'", the 1st, 2d, 8d

differences of the logarithms in the same line with a' ; /*= J d'" X x + 1 + d".
Then a the logarithm of the number 6 will be

^ X « + V ± A = b' ± A to 12"^

1^ J d" + i/ X 5 + a' i A — b' i A to 17 > places of figuren nearly.

^xf + d' X a + a' ± a = b' ± a to 20 j

Example,

Given h' = 3-14159,26535,89793,23846,26434, to find b to twenty places.

Here a = 31415 Let a = — = 311.

n

Then 6' = — =r 001010,15840,95144,02970,57 ; a' = lOlOl^.
a

I =: 84095,14402,97057; x =. 0.15904,85.597; jj + 1 = 1-15905;

d' =: 42992,855 74,0633 7 ; d" = 42560.23099; d"' = 84263.

Now ^ d"' X Jp + 1 32555

d" 42560,23099

/ 42560.5565 4

i x/ 3384,59761

d' 42992,85574,063137

^xf+ D^ 42992,88958,66098

i x/ -h d' X « 36154,93242,03919

a' 00438,58681,74054,30961

A 49276,03890,26837,50555

And B 0-49714,98726,94133,85435

»

Or let a = ~ = 3 216 = 0536 x 6.

a

Then ft' = 6a = 1010336,19739,44775,0549; a' = 101033.
I = 0-61973,94477,50549 ; x =r 038026,055225 ; x + 1 = 1 38026 ;
1/ = 42985,1961 8,8076 0; d" = 42545.06747 : d"' = 84219.

Now 4 d'" Xx+1 38748

d" 42545,06747

/ 42545,45495

i x/ 8089,17910

d' 4^ 985,19618,80760

^x/4- p' 42985,27707,98670

Jx/+ d' X ^ 26639,67187,88811

a' 00446,32488,03359,61854

b' 100446,59127,70547,50665

a 0- 5073 1,60400.764 13,65230

b =: «' - A 0-49714,98726.94133.85435

(II.) To find the Number f to given Logarithm*.

Case I. When the logarithm b is found in any of these three tables ; then
its number 6 is in the line even with it.

xxiT DESCRIPTION AND USE

Case 2. If the first five fibres (omitting the index) of a given logarithm
b', be between 00432 and 00492 : take them as an integer, and put a' ard
a' for the logarithms, in table 3, next less and greater than b^, aS and d their
numbers ; let d' (= c' — a') and d" be the 1st and 2d differences in the line

with a'; a =b'- A';d'=(c'-a'=)l;x = 5^^:i^; a= -— ^ ;j :

then A' = a' 4" ^» nearly true to 17 places of figures.

Example,

Given the logarithm b' = 5,00446,59127,70547,507

to find 6' its number. a'= 5,00446,32488,03359,6 19

tf's: 101033 A = 0-26639.67187,888

6 0-61973,944776 D^ = : 42985,19618,808

6' = 101033-61973,944776 !> - A = 01 6345,52430,920

X = 0-38026
d" = 000000,42545
i X d" = 00000,08089,1
d' + J X d" = 0-42985,27707,9

But when any other logarithm b is given, subduct '004321 from the first
six figures of b : call the remainder r, and let a be the logarithm in table 2,
next less than a, or next greater than the complement of a, and a its number :
then b' = B — A, or b' = 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/ ;

or if b' = B + A, then 6 = — .

a

Casr 3. If a', the first five figures (omitting the index) of a given loga-
rithm b', be found in table 4 : let a' be its number ; and put a' as an integer,
and Zi the remaining figures of B^ and x the complement of A to d' ; cf ,
d'\ d'"y the 1st, 2d, 3d difierences of the numbers in the same line with a! ;

y r= d'' — ^ d'" X X -f- I • ^hen the number h', whose logarithm is b', will be

(^ X A) + a' to 12^ ,

(d' — J X f/" X A ) + a' to 17 > places of figures nearly.

(dT^fxY X A) + a' to 20 j

Example,

Given the logarithm b' = 000006,9331 1,3771 1,69929, to find 6' its num-
ber to 20 places. Here a' = 00006.

A = 0-93311,37711,69929 ; x = 006688.622883 ; x + 1 = 1066886 ;
(T = 23029,29742,21293 ; d"= 53027,.02746 ; d'" . = 1 22100.

Now i d!" X x+ 1 43422

d" 53027, 52746

/ 53027.09324

ix/ 1773.39115

d' 23029,29742. 21293

d' -ix/ 23029.27968,821 78

d'-Jx/x A 21488,93801,72000

a' 10001,38164,64943.57474

And 6' 100015,96535,87452,9474

OF THE TABLES. xxr

Case 4. If the logarithm b do not come under one of the preceding^ cases.
Put A for the logarithm in table 2, next less than b, or next greater than the
complement of b, and a its number; let b' = b — a, or b' = b -|- a ; and A^
the first five fi<rures of b', may be had in table 4, with d its number ; put a'
as an integer, and let A be the remaining figures of b' ; x the complement of
A to u'; d\ d'\ d"'\ the 1st, 2d, 3d differences of the numbers in the same

line with a' ; /= d" — ^ d'" x x -|- 1 : then the number 6', whose logarithm
is b', will be

d' X A + a' X a = o^ to 11

rf'-ixrf'XA +

<f— ix/ X A + a

a' Xa = a^'toll^

a! X a = o^' to 16 > places of figures nearly.

a' X « = ah' to 19 3

Example,

Given b = 4*46372,61 172,07184,15204, to find 6 iU number.
Let A = 1-46239,79978,98956,08733. a = 29.

b' = B - a = M)0132,81 193,08228,06471. a'= 00132

A = 0-81193,08228,06471 ; x = 18806,91772 ; x + 1 = M8807 ;
if = 23096,20835,34589 ; d" = 53181,59733 ;cr" =1-22457.

Now ^ d"' X X + 1 48496

a' 53181,59733

/ 53181,11237

i x/ 5000,86402

(f 23096,20835,34589

d' - IjXf 23096,15834,4818 7

(t - i x/ X A 18752,48284,85771

of 10030,44036,01963,96855

b' 10030,62788,50248,82626

b=i ab' 000029,08882,08665,72 1 59,61 54

Or, given b =:T-4 6372,6 1172,07184,15204, to find b.

Ji€t A = 2-53655,84425,71530,1 1205. a = 344.

b' = B + a = T00028,45597.78714.-26409. V = 00028.

A = 0-45597,78714,26409 ; x = 0-54402.21286; x+ 1 = 1-54402;
d' = 23040,966-29,91521 ; d" =: 53054.39634 ; cf" = 122163;

Now id"^ X x + 1 6-2874

<f ' 53054,39634

/ 53053,76760

ix/ 14431,21179

if 2 3040,96629,91521

if - j^ x/ 23040,82198,70342

if-ix/xA loSoej 0496, 55627

a' 10006,4 4931,7 0511,6728 1

y 1 0006, 55437,8 1 008^22909

hss" 000029,08882,08665,721 59,616

wri DESCRIPTION AND USE

OF THE TABLE OF HYPERBOLIC LOGARITHMS.

This is table 5^ in pages 219 — 223, which contain the series of numbers
1-01, 1-02, 1-03, &c., to 1000, with their hyperbolic logarithms to seven
places of figures. They are so called because they square the asymptotic
spaces of the right-angled hyperbola ; and they are very useful in finding
fluents, and the sums of infinite series. The table, as well as the following
rules, were first given at the end of Simpson's fluxions, but they were ren-
dered much more correct in the French edition of Gardinei^s tables, printed
at Avignon in 1770, being very incorrect in the last figure in Simpson's book.
But both those books are very erroneous in the example for finding loga-
rithms by the table.

I. IVhen the given Number is between 1 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 logarithm of 3*45678

3-45339 ) 00678 (0019633

1-2383742

log. 1-2403375

Here the next less number is 3*45, and its logarithm 1*2383742, the re-
mainder or dividend '00678, 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 345678.

2. IFhen the given Number exceeds 10.

Find the logarithm of the number as above, supposing all the figures afler
the first to be decimals, then to that logarithm add 23025851, or 4*6051702,
or 6*9077553, &c., according as the given number contains 2, or 3, or 4, &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 within the limits of the table.

Example.

To find the hyperbolic logarithm of 345*678.

1-2403375
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 1-2403375, to which adding 46051702
the hyperbolic logarithm of 100, the sum is 5-8455077 the hyperbolic loga-
rithm required of 345-678.

OF THE TABLES. sxni

Note, The hyperbolic lognrithm of any number may be also found from
Brig^s's logarithms, viz. multiplying Briggs*8 logarithm of the same number
by the hyperbolic logarithm uf 10, viz.

Multiplying by 2-30258,50929,94045,f8401,79914,

Or dividing by ite reciprocal . •43429,44819,03251.82765,11289.

Note 2. There is also now added a supplementary table of Hyperbolic
Logarithms (Tab. 6.) of numbers from 1 to 1200.

OP THE LOGISTIC LOGARITHMS.

These are in table 7, pages 230 — 235, which contain the logistic logarithm
of every second as far as tlie first 88' or 5280^'.

The logistic logarithm of any number of -seconds is the difference between
the logarithm of 3600'' and the logarithm of that number of seconds.

The chief use of the table of logistic logarithms is 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 logarithms, putting the
logarithm where its complement should be^ and the contrary.

1. To find the Logistic Logarithm of any Number of Minutes and Seconds^

within the Limits of the Table.

At the top of the table find 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 to be
taken as if they were minutes, and the minutes of an hour as if they were
seconds.

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 given ; then in the same column, even witli the difference on the left*
hand 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 its half, third, &c., and multiply the 4th term by 2, 3, &c.

The logistic logarithms in this table are all affirmative, as well above as
below 60^ ; but the index of those above 60^ is — 1 ; below 60^ down to 6',
the index is ; and below 6' the indices (being either 1,2, or 3) are ex-
pressed in the table.

XXVUl

DESCRIPTION AND USE

Examples.

As 60'
To 46' 12"
So 8 7

k>. log.

00000

.. 0-1135

. . 0-8688

As 60'
To 78' 27"
So 13 53

To 18 9

As 78' 27"
To 60
So 18 9

To 13 53

As 24'» . .
To 46' 1 1"
So 8^ 7

To 15' 37"

As 46' 11"
To24»*
So 15' 37"

ToS** r

• «

• •

• ■

CO.

• a
. .

• a

CO.

a a

• •

• •

CO.

• •

• •

lo. log.

00000
1-8836
0-6357

As 60'
To 1531
So 40' 12"

To 1 179

As 40' 1-2"
To 1179
So 60' 0"

To 1531

As 24'* , a
To 76' 34"
So 13" 53'

To 44' 17"

As 76' 34"

So 44' 17"
To 13'* 53^

• •
• •

a •
. a

CO.

• •

• •

• •

CO.

• •

• •

• •

CO.

• •

• •

lo. log:
0-0000
0-8713
0-1135

To 6 15

.. 9823

0-5193

0-4848

As 46' 12"
To 60
So 6 15

CO. 1-8865
. . 0000
. . 0-9823

0-1164
0000
0-5193

1*8865
0-4848
0000

To 8 7

. . 0-8688

0-6357

0-3713

As 60'
To 4721
So 37' 28"

CO. 00000
. . 1-8823
. . 0-2045

. 1-6021
01137
0-8688

. 1-6021
1-8941
0-6357

To 2948

, . 0-0868

0-5846

1-6863
0-3979
0-5846

1319

As 4721 ..
To 60' 0"
So 2948

CO. 01177
. . 00000
. . 00868

01059
0-3979
0-1319

To 37' 28"

. . 0-2045

0-8688

0635V

The logistic logarithms may be used in tri^nometrical operations, whea
two of the terms are small arcs, with the logarithmic sines or tangents of
other arcs ; observing, that instead of the logarithmic sine or tangent, to
take the complement of their logistic logarithm ; and th^ contrary.

But this may be as readily and more naturally done by the logarithmic
sines and tangents themselves of such small arcs, as taken from the next
followixtg table of sines and tangents for every second of the first 2^ or 120^.

OF THE LOGARITHMIC SINES AND TANGENTS TO EVERY

SECOND.

Table 8, pages 238 — 267, contains the log. sines and tangents for every
single second of the first 2 degrees of the quadrant ; the sines being placed
on the lefl-hand pages, and the tangents ^on the right. The degrees and
minutes are placed at the top of the columns, and the seconds on the lefl-
hand side of each page, the logarithmic sine or tangent being found in the
common angle of meeting. So of 1° 52' 54" the log. sine is 8-5163420, and
the log. tangent 8*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 ascending on the right-hand side
of the pages. So the cosine of 88^ 7' 6" is 85163420, and its cotangent
85165762.

OF THE TABLES xxix

When it is required to find the sine or tangent, &c. tu 3ds, &c, or any
other fractional part of a second, subtract the tabular sine or tangent of the
complete seconds 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.

Example.

To find the log. sine of 1° 52' 54" 25'" or 1° 52^ 54" f J or ^.

1° 52' 54" sine 8-5163420
1 52 55 .. 8-5164061

dif. 641
5

12)3205

pro. part. 267
1° 52' 54" 8-5163420

1° 52' 54" 25'" 8-5163687

Here the sine of \° 52' 54" taken from the next leaves 641, which multi-
plied by 5 and divided by 12, or multiplied by 25 and divided by 60, gives
267 the pro. part ; this aidded to the first sine gives that which was required.

On the contrary, if a sine or tangent be given, to find the corresponding
arc ; take the difference between it and the next less tabular number, and the
difference between the next less and greater tabular 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 numerator by 60, and dividing by the denominator.

Example.

To find the arc whose sine is 8*5163900.

l"" 52' 55" 8-5164061

1 52 54 8-5163420

1 52 54 45'" 8-5163900

diff: ... 480
diff: ... 641

Finding the number is between the sines of 1^ 52' 55" and 1^ 52' 54", take
the differences between the sines as in the margin, and the differences give
If^ for the fraction of a second, or if nearly, which abbreviates to f " = 45"^;
and therefore the arc sought is 1° 52' 54" 45'".

MThere the 1st differences of the sines and tang^ents alter much, as near the
beginning of the table, the 2d, 3d, &c. differences may be taken in, and then
the logarithmic sine or tangent will be expressed by this series, viz. : —

Q = A -j-xiZ-j- J?.— ^D''-f-jr.— — . — r— d'" &c., or nearly a -{- (i>' — i d") * »

^ « 3

where a is the next less tabular logarithm, d', d", d'", &c., the 1st, 2d, 3d, &c.»
differences of the tabular logarithms, and x the fractional part of the arc over
the complete seconds.

d'

14453
14404
14357

d"

XXX DESCRIPTION AND USE

Example,

To find the log. tangent of 5' 1" 12''^ 24"" or 5' V ^ or 5' 1'' 206.

Taner.
5'0" .. 71626964
5 1 .. 7-1641417
5 2 . . 71655821
5 3 .. 71670178

Here a = 71641417 ; x = ^% ; d' = 14404 ; and the mean 2d diff. d"

=: - 48. Hence a 71641417

xd' 2977

X. — - — d" 4

-49
-47

Therefore the tangent of b' I" 12'" 24'"' 71644398

And on the other hand, when the sine or tangent is given, and falls near
the beginning of the table, from the same series we may find x the fractional
part of a second. For suppose it be required to find the arc whose tangent
is 71644398. This falling between the Ungents of 5' 1" and 5' 2", take the
differences, &c., as above, and the series gives 7*1644398 = 71641417

^ J.D' -j. J. . i^ d" ; or 2981 = 14404* - 24 (jr« - x), or - 24jt« +

14428* = 2981 ; which gives x = '2067" nearly = 12"' 24"". Therefore

the arc required is 5' 1" 12'" 24"". Or rather the approximate value a + d'

\ Q - A 2981 2981

— Ad' . Of = q, gives x = r~r/= i^j/.^ . o^ = i.^^^ - = 2067, the

^ ^ d' - in" 14404+24 14428

same as before.

OP THE LARGE TABLE OP NATURAL AND LOGARITHMIC
SINES, TANGENTS. SECANTS, AND VERSED SINES.

Table 9, page 268 — 357, contains all the sines^ tangents, secants, and
versed sines, both natural and logarithmic, to every minute of the quadrant,
the degrees at top, and minutes descending down the left-hand side as far as
45^, or the middle of the quadrant, and from thence returning with the de-
grees at the bottom, and the minutes ascending by the right-hand side to 90^,
or the other half of the quadrant, 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, cotangents, &c., being on the same line with the
minutes, and in the columns signed with their respective names, at top when
the degrees are at top, but at the bottom when the degrees are at the bottom.
The natural sines, tangents, &c., are placed all together on the left-hand
pages, and the logarithmic ones all together, facing them, on the right-hand
pages. Also in the naturals there are two columns of the common differ-
ences, and in the logarithmic 3 columns of common differences, each column
of differences being placed between the two columns of numb^s having the
same differences ; so that these differences serve for both their right-hand
and lefl-hand adjacent columns : also each differential number is set 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 that the sum of the decimal tigures of any
two such numbers is always ] integer, with in each place of decimals

OF THE TABLES. xxxi

All this will be evident by inspecting one page of each sort, as well as the
method of taking out the sine, &c.^ to any degrees and complete minutes.
It is, however, to be observed, that in all the log. sines, tangents, &c., and
in such of the natural as have any significant figure for their index or
characteristic, the indices are expressed in the table, 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 for their integer or index,
both the index and decimal separating point are omitted ; and wherever this
is the case, it is to be understood that all the f^ures in such columns are
decimals, wanting before them only the separating point and index 0.

The sine, tangent, or secant of any arc, has the same value, or is expressed
by the same number, as the sine, tangent, or secant of the supplement of
that arc ; for which reason the tables are carried only to a qusidrant 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, for 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^,
proceed thus : in the natural versed sines, to radius add the natural cosine,
the sum will be the natural versed sine ; and in the log. versed sines, add
0*3010300 to twice the log. sine of half the arc, the sum, abating radius
10*0000000, will be the log. versed sine required.

1. Given any Arc ; tojind its Sine, Cosine^ Tangent , Sfc.

Seek the degprees at the top or bottom, and the minutes respectively on
the left or right ; then on the same line with these is the sine, &c. each in its
proper column, the title being at 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, take the difference between the tabular sines, &c.
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 minutes ; so
shall the sum or remainder be the sine, &c. required.

Note^ The proportional part is found thus, as 1 ' is to 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 that 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
better so to do, by dividing the numerator of the firaction by the denominator,
or by dividing the sexagesimal by 60.

Example 1.

To find the natural sine of 1^ 48' 28'^ 12"'.

In the column of difference between the natural sines of 1** 48' and 1** 49
is the difference 2907 ; and 28" 12'" being = 28 2" = '47' ; therefore as

1 : 2907 :: -47 : the pro. part + 1366
to which add sin. 1° 48' ... 0314108

makes sin. of 1** 48' 28" 12'" 031 5474

xxxii DESCRIPTION AND USB

■

Example 2.

To find the natural tangent of 8** 9' 10" 24"'.

8° K/Ung. 1435084

8 9 1432115

diff. 2969

1 : 2969 :: (10'' 24'^'=) 17'^ : + 515
8°9' 1432115

8° 9' 10" 24'" 1432630

Example 3.
Tf) find the natural coversed sine of 4*^ 6' 5'' 40'".

1 . 2902 (teb. dif.) : : ^\y = 1 » 974

5" 40" : pro part / ^'^

4° 6' covers 9285026

4° 6' 5" 40'" 9284752

Example 4.

To find the logarithmic cosine of CP 8' 42".

1 : 136 Uab. dif.) :: •?'= 42'': pr. pt. - 95
6^ 8' cosine 99975069

6» 8' 42" 1^9974974

Example 5.

To find the log. sec. of 7° 12' 50".

J : 160 (ub. dif) ! I ^' = 50" : pr. pt + 133
7'* 12' secant 100034381

7° 12' 50" 100034514

Example 6.

To find the logarithm cotangent of 39** 4' 12" 20'".

1 ; 2581 (tab. dif.) I : -205 = \ .«,
12" 20'" : pro. part ...J ^**^

89° 4' cotan 100905978

390 4/ 12" 20"' 100905447

The foregoing method of finding the proportional part of the tabular dif-
ference, to be added or subfracted, by one single proportion, is only true
when those differences are nearly equal, and may do for all except for the
tangents and secants of large arcs near the end of the quadrant in the natural
sines, &c., and in the log. •ines, &c., except the sines and versed sines of
small arcs, the tangents of both large and small arcs, and the secants of lai^e
arcs. And when much accuracy is required, these excepted parts may be

jr - 1
found by the series used in the last article, viz. Q = a + JPd' + <r • —5 — d"

J? — 1 « — 2

4- « . — 5 — . — 3 — !>'" &c. or = A + (d' — Jd") . X nearly ; where a is the

tabular number for the degrees and minutes, d', d", d'", &c., the 1st, 2d, 3d,
&c. tabular differences, and x the fractional part over the complete minutes.

OF THE TABLES. Mxiii

&c. ; 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 tangents of
small arcs, they may also be found, perhaps easier, from their corresponding
natural ones, viz. find the natural sine, versed sine, or tangent of tht^ given
small arc, and then find the log. of such natural number by the 1st or large
table of logarithms, whicli will be the log. sine, &c. required. And the lo^.
tangent and secant of large arcs vrill be also found by taking the difference
between 20 and their log. cotangent and 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 the corresponding number.

Example 1.

To find the log. sine of 1° 48' 28" 12'".

The natural sine, found in Ex. 1. above, is '0315474 ; and the log. of this
is 8*4989636, which is the log. sine required.

Example 2.

To find the log. versin. of 1° 48' 28" 12'".

1° 48' nat. vers 0004934

1 : 92 tab. dif. 1 1 'AT = 28" 12'" : + 43

r 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 0416210

1 : 2914 tab. dif : : 56' = 33" 36"' : + 1632

2° 23' 33" 36'" nat. tan. . . 0417842
Its log. 2 23 33 36 log, tang. 8-6210121

Example 4.

To find the iog. tang, 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° 11' 31" 48'".

lU complement is 1® 48' 28" 12'"

Its log. sine in Ex. 1 is 8*4989636

Which taken from •. 20*0000000

Leaves log. sec. 88° 1 1' 31" 48'" 11*5010364

c

XXXIV

DESCRIPTION AND USE

Example 6.
To find the nat. sec. of 88® U' 31'' 48^'.

89** 11'
88 12
88 13
88 14

nat. sec.
31-544246
31-836225
32-133663
32-436713

291979
297438
303050

5459
5612

jytif

153

Hence a = 31544246; d' = 291979; d" = 5459; and W'^ = 153;
j=i •53' = 31"48'"; j:.^!^ =- 12455; * . ^-^ ""i— = •06125.^^6;:'.

Then a 31544246

X D

X - 1

Jf

154748
-680

X - I j: — 2

jn

9.5,^'ri.-)«^S'-

31-698323

In the 6th example^ the natural secant is found by the differential series to
be 31*698324. But by taking: the number to the logarithm of it, as found in
the 5th example, it is 31-698329 ; the difference may be owing to the log^.
not being far enough continued. But this method by the series seems to be,
in many instances, more troublesome than finding the secant by dividing 1
by the cosine.

2. Given any Sine, Tangent, Sfc. to find, its Arc,

Take the difference between the next less and greater tabular number of
the same kind^ and the difference between the given number and said next
less or next greater tabular number, according as the g^veu number is a sine,
tangent, &c., or a cosine, cotangent, &c., noting its degrees and minutes ;
then the two differences will be the terms of a vulgar fraction of a minute, to
be added to those minutes, to 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 denominator ; or brought to sexagesi-
mals, by multiplying by 60, &c. Also, where the tabular diff*erences are
printed, the subtraction of the less tabular number from the greater is saved.

^ Example 1.

To find the arc to the natural sine *0315474.

Ans 1<^ 48' 28" 12'" . . . 0315474

Subtr 1 48^ next less . . . 0314108

1366
60

Tab. difference 2907 ) 81960 ( 28"

5814

, 23820
23256

564
60

2907 ) 33840 ( 12'"

OF THE TABLES. xxxv

Example 2.

To find the arc to natural tang. '1432630.

Next grreatpr 1435084

Answer 8** 9' 10" 24'" 1432630

Next less, subt. fr. each 1432115

5T5
60

Tab. difference 2969 ) 30900 ( 10"

29690

1210
60

72600 ( 24'"
5938

13220

Example 3.

To find the arc to logarithm cosine 9'9974974.

6° 8' 9-9975069

Answer 6° 8' 42" 99974974

95

60

Tab. difference 136 ) 5700

544

260

Example 4.

To find the arc to logarithm cot. 10-0905447.

3904' 100905979

Answer 39® 4' 12'' 20'" 10090544 7

53T
60

Tab. difference 2581 ) 3186*6 ( 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 be 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, also 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
m 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-
tnral 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 DESCRIPTION AND USE

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 secant 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 proposed
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 500000000.

200000000
Given 500000000 its log. 116989700

•02 8-3010300

•0197830 nat. tan. of 1° 8'

2170
60

2910) 130200 (44"
1164

1380
1164

216

60

12960 (44'"
1164

1320

Hence from 90° O' 0" 0'"

Take the comp 1 8 44 44

Leaves arc required 8S 51 15 16

Example 2.

To find the arc to natural secant 31*6983333.

200000000
Given 31 698^ its log 11-5010365

•0315474 8*4989635

•0314108 nat. sine of T 48'

1366
60

2907) 81960 (26"
5814

23820
23256

564
60

33840 (12'"
2907

4770

Hence from 90° 0' 0" 0'"

Take the comp 1 48 28 12

Leaves arc required 88 11 31 48

i

OF THE TABLES. xxxvii

The following: rules in reference to the sines and tangents of small arcs,
«|riven by Dr. Maskelyne, in his introduction to Taylor s Logarithms, will
oflen be useful : —

1. To find the sine. To the logarithm of the arc reduced into seconds,
w*th the decimal annexed, add the constant quantity 4*6855749, and from the
sum subtract one-third of the arithmetical complement of the log. cosine, the
remainder will be the log. sine of the given arc.

2. To find the 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. To find the arc from the sine. To the given log. sine of a small arc
5*3144251, add ^ of arith. comp. of the log. cosine: subtract 10 from the
index of the sum, the remainder will be the log. of the number of seconds and
decimals in the arc sought.

4. To find the arcfrofn the tangent. To the log. tangent add 5'3144251,
and from the sum subtract^ of the arith. comp. of log. cosine: take 10 frum
the index, and there will remain the logarithm of the number of seconds and
decimals of a second in the g^iven arc.

%* See, also. Dr. Maskelyne*s remarks, before the directions for the use
of the Traverse Table.

On the Construction of these Tables,

The computation of tables of sines, tangents, secants, &c. is evidently a
work of great labour ; but, considerable as it doubtless is, it has been much
diminished by the employment of various trigonometrical theorems, 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 of the diameter of a circle is equal to the sum of
the squares of the chord of an arc, and of the chord of its supplement to a
semicircle.

2. The rectangle under the two diagonals of any quadrilateral inscribed in
a circle, is equal to the sum of the two rectann;les under the opposite sides.

3. I'he sum of the squares of the sine and cosine (often called the sine
of the complement), is eiiual to the square of the radius

4. The difference between the sines of two arcs that are equally distant
from 60 degrees, or j 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.

5. The sum of the cosine and versed sine is equal 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 verged
sine of double the arc.

8. A mean proportional, between the versed sine and half the radius, is
equal to the 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 chords to the chord of thrice the arc.

11. As the chord of an arc is to the sum of the chords of twice and thrice
the arc, so is the difference of those chords to the chord of five times the arc.

12. And in general, as the chord of an arc is to the simi of the chords o.
n times and /i -f- 1 times the arc, so is the difference of those chords to the
chord of 2 71 4- i times the arc.

XXXVIU

DESCRIPTION AND USE

13. The sine of the sum of two arcs is equal to the sum of the products
of the sine of each multiplied by the eosine of the other, and divided by the
radius.

14. The sine of the difference of two arcs is equal to the difference of the
said two products divided by radius.

15. The cosine of the sum of two arcs is equal to the difference between
the products of their sines and of their cosines, divided by radius.

16. The cosine of the difference of two arcs is equal to the sum of the said
products divided by radius.

17. A small arc is equal to its chord or sine, nearly.

18. As cosine is to sine, so is radius to tangent.

19. Radius is a mean proportional between the tangent and cotangent.

20. Half the difference between the tangent and cotangent of an arc is
equal to the tangent of the difference between the arc and its complement.^
Or, the sum arising from the 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 the said half complement.

21. The 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 the secant and cosine. Or»
as cosine is to radius, so is radius to secant.

23. Radius is a mean proportional between the sine 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 difference between an arc
and its complement is equal to the tangent of the said difference added to the
tangent of the less arc.

25. The 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 difference and 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 method is this : the 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 to be added ; inscribe

HI, IK, KL, LM, MN, NO, OP, &c., cach equal to the radius ab ; and to the
opposite sides draw the perpendiculars be, hq, ir, ks, lt, mv, nx, ov, &c. ;
so shall the angle a be the common difference of the angles iuq, ikh, eli,
L3rK, &c. ; their sines hq, ir, ks, &c. ; and their cosines iq, kr, ls, &c.
Now let any one of them, lmk, be given, then the rest will be thus found : —
Draw Ta and Kb perpendicular to sv and mv ; now because of the equiangular
triangles abe, TLa, Kwb, alt, amv, &c., it will be ab : ak 1 1 kt : sa
(= J LV + i Ls) : : LT : Ta (= 4 MV + i KS,) and AB : BE ! : LT I i.a
(= i LS - i Lv) : : KT (= i km) : J Mb (= J mv - i KS.) llence are'givcn

OF THE TABLES. xxxix

the sunes and cosines rs, my, ls, lv. And the method of continuing the
progressions is evident. Namely,

as AB : 2ae : : -f "-^ : mt + MX :: mx : nv + nv. &c.

(^mv:nx -f- lt :: NX : oy + mv, &c.

^ o Clv : NX — lt : : MX : oy — my, &c

or AB : 2be :: < «

I^my: mt — MX :: nx : ny — ny, &c.

And on the other hand, ab : 2ae : : ls : kt + kr, &c.

Therefore put ab = 1, and make be x lt = La, ab x kt = sa, sa — La := ly,

2ae X ly — tm = MX, &c.

The sense of these general theorems is this, that if P be any one among a
series of angles in arithmetical progpression, the angle d being their common
difference, then as radius or

1 . 4 COS. a . . -^^.^ p . g.^ (p ^ rf) _^ sin, (P - d)

1 • 2 «;n d" S^^^' ^ ' ^**"' (^ + <0 - sin. (P - d)
1 . 4 sm. a . ^^.^ p . ^^^ (P ^. d) « COS. (P - cQ

where the 4th terms of these proportions are the sums or differences of the
sines or cosines of the two angles next less and greater than any angle P in
the series ; and therefore subtracting 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 same manner are all the rest
to be found. This method, it is evident, is equally applicable whether the
common difference d, or angle a, be eqmd to one term of (he series or not :
when it is one of the terms, then the whole series of sines and cosines becomes
thus, viz. as 1 : 2 cos. d : :

sin. d : sin. id : : sm. id : sio. d 4. sin. 3d : : sin. 3d i sm. 9(1 + nn.id:: sin. id : stn. 34 4- sin. 5tf. &e.
*con.tf : 1+oos.M: : COS. 2<f: 00s. d •{•COS. S(i:*ooiw 3rf*cos.Stf 4.00s. M •cos.tf 00s. ad -I* cos. 5d, &e.

27. The following values of the natural sme for every third degree in the
quadrant, have greatly contributed to facilitate the computations : —

sin. 0° = *

sin. 30= HV(5 + V5)-f V»^+Vf-V(i5 + 3V5)-Vl-VM

sin. 6^ = i [V (30 - 6^5) - 1 - Jb]

sin. 9<^ = i[VI+VJ -V(5-V5)]
sin. 12^ = i [^3 + V (1^ -I- 2 ^5) - ^Ib]

sin. 15<^ = i[V|-VJl
sin. 18° = 1 [^/5 - 1]

sin. 21^ = J [7(15 - 3^5) H- ^(5 " V^) + ^/^ + Vi - ^^^ - Vfl
sin. 24° = i [V1& + 73 - V (1<> - 2 75)]
sin. 27° = 1 Wib + J5) + S - V*l
sin. 30° = I

sin. 33° = J [7(15 + 375) + 7¥ + 71 - V(5 + V^) - Vi - Vil

sin. 360 = ^ 7 (10 - 2 75)

8in.39°=:i[7(5~75)4.7V+7| + 7i + 7.i«7(l5-375)l

sin. 42°= J LI + V (30 -1-6 75) - 75]

sin. 45° = 7J

sin. 48° = i [715 + 7 (10 + 2 75) - 73]

sin. 51° = i [7 (15 - 375) + 7(5 - 75) + 7^ + 71 - 7f - 7i]

sin. 54° = i [75 -f 1]

xl DESCRIPTION AND USE

sill. 57° = i [V (15+3^5) + V (5 + 75) + V! + Vi - V*/ - -^i]

sin. 60° = ^ V3

sin. 630 = i [V (5 + ^5) + Vf - Vi]

sin. 66° = ^ [1 +7 (30 - 6 V5) + ^5]

sin. 69° = i [^(15 - 3^3) + ^V +4i + 7i + 7J - V (5 - V^)]

sin. 72°= :}V (1^ + 2 75)

sin. 75° = i yj + 7i]

sin. 78° = H\/^ + V (3^ + 5 ^5) - I]

sin. 81° = i [>s/f + VJ + V (5 - V5)]
sin. 84° = i [y/lb + V3 + V (10 - 2 ^5)]

sin. 87° = i [(^5 + ^5) + V (1^ + 3 V^) + ^^ + Vi - ^/i - V?l
sin, 90° = 1

V3 = 1-7320508076 V4 = 1-5811388301

V 5 = 2-2360679775 W = 2-7386127875

^15 = 3-8729833462 J (^ + ^5) = 26899940479

^1 = 0-7071067812 ^ (5 - ^5) = 1-6625077511

^1 = 1-2-247448714 ^(10 -f 2 ^^5) = 3*8042260652

^/(10 - 2^5) = 2-3511410092

V (15 + 3 ^5) = 4-65920636-29

V (15 - 3!^5) = 2 8795478929
^ (30 + 6iy5) = 6-5891128284

V (30 - 6^5) = 40722956836

28. The natnial sines, tangents, secants, &c., being computed by means
of these and otlier convenient theorems, are arranged in order on the letl-
hnnd pages of table 9 ; and the logarithmic sines, tangents, secants, &c.,
belonging to the same degrees and minutes respectively, stai\d on the oppo-
site right-hand pages. They are, of course, easily ascertained by coniputing,
one by one, the logarithms of the sines, tangents, &c., to which thev belong.
Thus, 9-3836752,* the log. sine of 14°, is simply the log. of 2419219, the
natural sine of 14°; 9*39677.11, the log. tangent of 14° is the logarithm of
'2493280, the natural tangent of 14°; and su on.

29. But, all this may indeed be accomplished with much greater facility.
For, since sin. -J- cos. = tan. ; tan. : rad. ::*ra<l. : cot. ; sin. : rad. :: rad. :
cosec. ; cos. : pad. :: rad. : sec; wemay, after having found the logarithmic
sines and cosines ; or, in other words, all the sines, minute by minute, &c to
90° proceed thus : —

From 10 -f- sin. take cos. there remains tan.
From 20 take tan., there remains cot
From 20 take 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
index of the sum, the remainder is the log. versiu.

Add -3010300 to twice the log. sin. of half the comp. of the arc, and take
lO from the index of the sum, the remainder is the log. coversin.

xn

TRIGONOMETRICAL RULES.

1. In a ri^ht-lined triangle, whose sides areA, b, c, and their opposite
angles, a, 6, c ; having given any three of these, of whi<ih 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 l for a logarithm, and l' its arithmetical
complement. Then

Case 1 . When three sides a, b, c, are given.

Tlieci
And

Put prr^.A + B-j-cor semiperimeter.

* V A X B

/ 1 / P X (P ~ C)

s'. * c = r 1 / .

* V A X B

L. S. i C = J . (l. P — A + L. P — B + l' A + l' b).

l' S. J C = J (l. P + L. P — C -f- l' A + l' b).

C t* y k* "^ i- C*

Note, When a = b, then s. i c =: — x -r-. And s' i c = r 4 / * — .

A 2 ** V A*

Case 2. Given two sides a, b, and their included angle c.

A ~ B

Put 8= 90°— Jc, and t d= , j X t. s; thenars + d ; and 6= s - d.

And

= v/(

A + B
4 A B X S« J C

rr

+ r^^

Or in logarithms, putting l. q = 2 l. (a — b), and l. r = l. 2 a 4- l. 2 e +
2l. 8. Jc - 20,

then L. c r= i L. (q + h).

If the angle c be right, or = 90® ; then t. a rr — r ; t. 6 = — r;

B a

r r i

c = A, or = — 7 B, or =: V A« + B«.

s. a

s. b

If A = b; then ar= 6 = 90° - Jc, and c = ^^ X 2 a.

r

Case 3. When a side and its opposite angle are among the terms given.

8. a s. 6 8. c
found.

luen =: — r = — ; from which equations any term wanted may be

xlii

TRIGONOMETRICAL RULES.

When an angle, as a, is 90°, and a and c are given.
Then
And

B = ^(a* — cO = V(a + c) X (a — c).

L. B = ^ (l. A -{- C + L. A — C).

Note, When two sides a, b, and an angle a opposite to one of them^ are
given ; if A be less than b, then 6, c, c, have each two values ; otherwise
only one value.

II. — ^In a spheric triangle, whose three sides are a, b, c, and their opposite
angles, a, 6, c ; any three of these six terms being given, to find the rest.

Case 1. Given the three sides a, b, c.

Calling 2 p the perim. or p = J (a + b + c).

s. (p — a) X s. (p - b)

Then
And

. J c = r 4 /-

V S. A X S. B

S. A X S. B

L. S. J C = J (l. 8. P — A + L 8. P — B + l's. A + l' S. B).

L. S' C = J (l. 8. P + L. S. P — C + l's. a + l's. b).

And the same for the other angles.

Case 2. Given the three angles.

Put 2 ^ = o + 6 + c.

V 8. a

Then
And

8

X s. 6

V s. a X s. 6

L. s. J c = J (l. s'^ + l. s'p — c + l' s. a -f i«' s. h).

L. s' J c = J (l. s' ^ - a + L. s' p — 6 + l' 8. a + l' 8. 6).
And the same for the other sides.

Note, The sign > signifies greater than, and < less than ; also -^ the
difference.

Case 3. Given a, b, and included 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,

like or unlike c as M is > or < b. Or let s' J. a + b : s' ^. a -*- b : : t' J c :

t. M, which is > or < 90°, as a + b is > or < 180°, and s. J. a + b : s.

A-^B::t'Jc:tN, > 90°, then a = m + n ; and 6 = m — N.

Again, let r : s' c : : t. a : t. m, like or unlike a as c is > or < than 90® ;
and N = B '^ M. Then s' m : s' n : : s' a : s' c, like or unlike n as c is > or
< 90°. Or,

A X «. B X 8« J C

;. Jc= y/-

rr

+ s* J. A •-- B.

TRIGONOMETRICAL RULES. icMu

la logarithms, put l. q zz 2 l. s. i^ a •«- b ; and l. r = l. s. a + l. s. b +
2 L. «. J c - 20 ; then l. s. J c = J l. (q + a).

Case 4. Given a, 6, and included side c.

First, let r : s' c : : t « : t' m, like or unlike a as c is > or < 90° ; also
n z=: b ^ nu Then s' n : s' m : : t c : t. a, like or unlike n as a is > or <

90°. Or, let s' J. a+ b: s' i. a ^b : : t. i c : t. m, > or < 90° as a + A

is > or < 180^; and s. Ja + 6 : s. ^a^ b : : t. J c : t. n, > 90°; then
A = M ± N ; and b = h ::p n.

Again, let r : s' c : : t. a : t' m, like or unlike a as c is > or < 90° ; and
71 = b-^m: then s. m : s. n : : s' a : s' c, like or unlike a as m is > or < 6

Case 5. Given a, b, and an opposite angle a.

1st. s. A : s. a : : s. b : s. 6, > or < 90°.

2dly. Let r : s' b : : i,a : i' m, like or unlike b as is > or < 90° ; and
t. A : t B : : s'm : s' 7t, like or unlike a as a is > or < 90° ; then cz^m-jo n,
two values also.

3dly. Let r : s' a : : t. b : t. m, like or unlike b as a is > or < 90° ; and
s'b : s' A : : s' M : s' N, like 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 b : also c is = m ± n, and c = m ifi n, as b is like or un-
like a.

Case 6. Given a, 6, and an opposite side a.

1st. 8. a : s. A. : : 8. 6 : s. 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. M : 8. N, > or < 90° ; then c = ii* ± n, as a is like or un-
like b.

3dly. Let r : s' a : : t. 6 : t' m, like or unlike 6 as a > or < 90° ; and
s' 6 : s' a : : 8. m ; 8. n, > or <90° ; then c = fii±7i,asais like or unlike 6.

But if A be equal t) b, or to its supplement, or between b and its supple-
ment; then B is unlike 6, and only the less values of n, n, are possible.

Note^ When two sides a, b, and their opposite angles a, 6, are known ; the
third side c, and its opposite angle c, are readily found thus : —

8. 4 (a -^ 6) : s. J. (a -f 6) : : t. J (a -^ b) : t. i c.
s. i- (a -^ b) : s. J. (a -f- b) : : t. ^. (a •^ 6) : t. | c.

III. In a right-angled spheric triangle, where h is the hypotenuse, or
side opposite the right angle, b, p, the other two sides, and 6, p, their oppo-
site angles ; any two of these iive terms being given, to find the rest ; the
cases, with their solutions, are as in the following table.

The same table Will also serve for the quadrantal triangle, or that which
has one side =: 90°, h being the angle opposite to that side, B, p, the other
two angles, and b, p^ their opposite sides ; observing, instead of u to take its

x)iv

TRIGONOMETRICAL RULES.

supplement ; or else mutually chang^ing the terms like and unlike for each
other where h is concerned, and its real value is taken.

Case

1

Given

H

B

H

6

B

6

B
P

B

P

b

Req'

6
P

B
P

P

H

P

P

H
h

P

H
h

P

H
B

P

SOLUTION «.

s. H : r : : s.b : 8.6, and is like b

r : t'.H : : t.B : s'.pl , > or <
s'.b : r : : s'.h : s.p J like b

90^ as H is like or un-

r : s.H :: s.6 : s.b, like 6

r : s'.6 : : t.H : t.p "> , > or < 90° as h is like or un-

r rs'.H:; t.6 : t'.pj like A

i.w • F • » S«B • S*H 1 t_ ^^ ^^ ^>rvn

- * « ^t L I » «?ach > or < 90° :

r : t.B : : i\b : s.p >* '^ ^ '

I ^ t L I true

i.B : r : : s .6 : s.p J

both values

I

r : t'.B : : s'.p : t'.H, > or < 90° as b is like or unlike p
r : s'.b : : s.^ : s\b, like b
r : s.b : : tp : t.p, like p

r : s'.b : : s'.p : s'.h, > or < 90° as b is like or unlike p
r : s.p : : t'.B : t'.6, like b *
r : S.B : : t' p : V,p» like p

r : t'.6 : : i',p : s'.h, > or < 90° as b is like or unlike;?
s.p : r : : s*,b : s'.b, like 6
8.6 : r : : s',p : s'.p, like p

The following Propositions and Remarks, concerning Spherical Triangles,
(selected and communicated by the Rev. Nevil Maskelyne, D.D., Astro-
nomer Royal, F.R.S.) will also render the calculation of them perspicuous,

and free from ambiguity : —

«

*' 1. A spherical triangle is equilateral, isoscelar, or scalene, according as
it has its three angles all equal, or two of them equal, or all three unequal ;
and vice versa.

** 2. The 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; (he three
sides will be, accordingly, all less than 90°, or equal to 90°, or greater than
90° ; and vice versa,

" 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, df,
PE, forming by their intersections a new spherical
triangle def ; each side of the new triangle will be
the supplement of the angle at its pole ; and each
angle of the same triangle, will be the supplement
of the side opposite to it in the triangle a b c.

««

•«

TRIGONOMETRICAL RULES.

zlv

*^ 6. In any triangle ▲ b c, or a 6 c, ri^ht anizled
in A, 1st, The angles at the hypotenuse are always of
the same kind as their opposite sides ; 2dly, The
hypotenuse is less or greater than a quadrant ac-
cordinir as the sides including the right angle are 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,
rice versd, 1st, The sides including the right angle, are always of the same
kind as their 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°, if the 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 quadrants, may
be known from the following tables: —

ARC =:

Sin..
Tan. .
Sec. .
Cos. .
Cot..
Cosec.

0"

90°

180°

270°

360«

R

- R

■

GO

— 00

R

CD

- R

— CD

R

R

- R

R

QD

— CD

. QD

CD

R

— OD

- R

CD

The character oo denotes infinity.

The changes of signs are these: —

13th.
14th
15th
16th.

1st.

5th.

9th

2d.

6th.

10th.

3d.

7th.

11th.

4th.

8th.

12th.

am.

COS. tan. cot. tec.

+ + -f- +

- -h -f -

-»--- +

xlvi

THE CASES OF PLANE TRIANGLES RESOLVED BY

LOGARITHMS.

In this and the following solutions of spherical triangles, it is to be observed,
that when we say the sine, tangent, &c. we mean the logarithmic sine, tan-
gent, &c. as fbund by the table.

C

A B 1>

Prop. I. — Having the angles^ and one side ; to find either of the other sides.

Add the logarithm of the given side to the sine of the angle opposite to
the side required, and from the sum subtract the sine of the angle opposed
to the given side ; the remainder will be the logarithm of the side required.

Example. In the triangle b c d, having the angle c d b 90°, c b d 51° 56',
BCD 38° 4' and the side b d 197*3 ; to find the side c d.

2-2951271 log. of 197-3
9-8961369 sin. of 51° 56'

12-1912640 sum
. 9-7899880 sin. of 38° 4'

2-4012760 log. 251-9278 c d req.

Or you may add the complement of the sine of the angle opposed to the
given side, to the two other logarithms, the sum (abating radius) is the loga-
rithm of the side required ; as shown in art. 3 of Log. Arith. And it is to
be observed, that the complements of the sines in the table are to be found in
the columns of the cosecants : for (passing over the first unit) the cosecants
of the same arcs are the complements of the same sines. AJso the comple-
ments of the tangents are the cotangents.

Example, The sine of 38° 4' being 97899880, the cosecant uf 38^ 4' is
10;2100120, which (omitting the first unit) is the complement of the said
sine.

0-21001-20 CO. ofsin. 38°4'
2-2951271 log. of 197 3
9-8961369 sin. of 51° 56'

2-401-2760 log. 251-9278, as before.

But if one side and the angles of a right-angled 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, to the logarithm
of the given side^ the sum (abating radius) is the logarithm of the side re-
quired.

10-1061489 tan. 5P 56'
2-2951271 log. of 1973

2-401-2760 log. 251-9278 as before.

OF RIGHT-LINED TRIANGLES. xlvii

Prop. II. — Having two sides, and an angle opposite to one of them ; to Jind
** the other two angles, and the third side.

Add the sine of the angle g^ven to the logarithm of the side adjoining that
angle, and from the sum subtract the logarithm of the side opposite to that
angle, or add its arithmetical comp. the remainder or sum will be the sine of
the angle opposite to the adjoining side.

Example. In the triangle abc, having tlie side ac 800, bc 320, and the
angle abc 12S° 4' ; to find the angles bag, acb, and the side ab.

7 0969 100 ar. com. log. 800
2-5051500 log. of 320
9S96I869 sin. 128^ 4'

9-4981969 sin. 18° 21' bag.

Having bag and abg the angle acb is their supplement to 180^, viz.
38° 35' ; and you may find the side ab by the first proposition.

Prop. III. — Having two sides and the angle between them ; to find 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 firom the sum subtract the logarithm of the greater side, or
add its arith. comp. : the remainder or sum will be the tangent of the angle
opposed to the less side.

Example. In the triangle bgo, having the side be 197*3, and gd 251*9;
to find the angles bcd, gbd, and the side gb.

7*5987728 ar. com. log. 251*9
12-2951271 rad. + log. 197*3

9-8938989 ton. 38° 4' bgd.

But if the angle included be oblique, add the logarithm of the difference of
the given sides to the tong^nt of half the sum of the unknown angles, and
firom the sum subtract the logarithm of the sum of the given sides, or add its
complement ; the remainder or sum will be the tongent of half their dif-
ference.

Example. In the triangle abc, having the side ab 562, bc 320, and the
angle abc 128° 4^; to find the angles bag, acb, and the side ac.

The sum of the given sides is 882, and the difference 242, the half sum of
the unknown angles is 25° 58'.

70545314 com. log. 882
2-3838154 log. of 242
9-6875402 tong. 25° 58'

9 1258870 tang. 7 37

25 58

Angle acb 33 35 sum.

Angle GAB 18 21 dif.

These 7° 37' being added to 25° 58' the half-sum of the angles unknown,
3 sum is 33° 35' for the greater angle acb ; and the same 7° 37' being sub-
cted from 25° 5S', the remainder is 18° 21' for the lesser angle cab. Lastly,

)winir the angles, and two sides, the third side may be found by the first

position.

xlviu OF RIGHT-LINED TRIANGLES.

Prop. IV. — Having the three sides ; to find any angle.

Add the three sides tof^ether, and take half the sum, and the diflTerences
betwixt the half-sum and each side : then add the complements of the loga-
rithms of the half-sum, and of the difference 'between the half-sum and the
side opposite to the angle sought, to the logarithms of the diflTerences 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 ab 562, ac 800, and ac
320 ; to find the angle abc.

AC = 800
4B = 562
BC = 320

sum 1682

H = 841 CO. 7 0752040

H - AC = 41 CO. 8-3872161
H — AB = 279.. 2-4456042

H — BC == 521.. 2-7168377

^ sum 84 1 = H sum 206248620

Tang, of 64° 2' = i sum 10-3124310
Whose double 128° 4' is the angle 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 will 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 exannple already given. The sine of 128^ 4', or of
its supplement 51"^ 56', is -7872939. Hence

800 : 320 : : 1 : -4 : : '7872939 ; ?

-4

nat. sin 18° 21' + = -31491756

Here we have only to consult the table twice ; while in the logarithmic
method it must be done /bur times.

Again, for Prop. III. Suppose there are given ac = 450, bc rr 540, and
angle c =: 80°; to find ab. By formula 7, Table 16, we have ab = V(*^*
-f AC* — 2 BG. AC cos. c) = Vt540« -|- 450« - 2 . 540 . 450 . 1736482) = 90
V(6*+ 5* - 60x 1736482) = 90^(61 - 10-418892) = 90 ^50581108 =
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 heights and distances may be readily solved
by means of the natural tangents and secants ; the base X tan. angle at base,
giving the vertical altitude, and base X sec. angle at base, giving the sloping
or hypotenusal distance.

xhx,

THE CASES OP SPHERICAL TRIANGLES RESOLVED BY

LOGARITHMS.

The resolution of spherical triangles is to be performed by the table of
sines, tangents, and secants ; which we shall show by the 28 propositions
following; whereof 16 are of right-angled, and 12 are of oblique triangles ;
and first,

Of right-angled Triangles.

B

Prop. 1 . — Having the legs ; to find the hypotenuse.

Add the cosine of one leg, to the cosine of the other leg ; the sum (abating
radius) is the cosine of the hypotenuse required.

ErampU In the right-angled triangle abc, having ac 27® 54', and bc 11®
W ; to find AB the hypotenuse.

9*9911927 cosin. 11° 30'
9-9463371 cosin. 27 54

9*9875298 cosin. 30 ab req.

■ ■■■■» ' ■

Paor. II. — Having the two legs; to find either of the angles.

Add the sine of the leg next the angle sought, to the cotangent of the other
leg : the sum (abating radius) is the cotangent of the angle required.

Example, In the right-angled triangle abc, having ac 27° 54', and bc 1 1°
30' ; to find the angle bag.

9-6701807 sin. next leg 27° 54'
10-6915374 cot, opp. leg 1 1 30

10-3617181 cotan. bag 23 30

Prop. III. — Having the hypotenuse^ and one of the angles ; to find the other

angle.

Add the cosine of the hypotenuse to the tangent of the angle g^ven ; the
sum (abating radius) is the cotangent of the angle required.

Example, In the right-angled triangle abc, having the hypotenuse ab 80®,
Slid the angle abc 69° 22' ; to find the angle bag.

9-9375306 cosin. hyp. ab 30° 00'
10-424189 6 tang, abc . . . 69 22

103617202 cotan. bag . . 23 30

^EOP. IV. — Having the hypotenuse^ and one of the angles ; to find the leg next

the given angle.

Add the tangent of the hypotenuse to the cosine of the angle given ; the
«um (abating radius) is the tangent of the leg required.

d

1 THE RESOLUTION OF

Example. In the right-angled triangle abc, having the hypotenuse ab 30^,
and the angle arc 69° 22' ; to find the leg bc.

9-7614393 tang. hyp. ab 30<>00'
9-5470 18S cosin. abc . . 69 22

93084581 tang, bc 11 30

Prop. V. — Having the hypotenuse, and one of the angles ; to find the leg

opposed to the given angle.

Add the sine of the hypotenuse to the sine, of the angle given ; the sum
(abating radius) is the sine of the leg required.

Example, In the right-angled triangle abc, having the hypotenuse ab 30^
and the angle bac 23° 30^ ; to find the leg bc.

9-6989700 sin. hyp. ab. . 30° 00'
9*6006997 sin. bac 23 30

9-2996697 sin. bc 11 30

Prop. VI. — Having one of the legs, and the angle next U; to find the

hypotenuse.

Add the cotangent of the given leg to the cosine of the given angle ; the
sum (abating radius) is the cotangent of the hypotenuse required.

Example, In the right-angled triangle abc, having the leg ac 27° 54' and
the angle bac 23° 30^ ; to find the hypotenuse ab.

10-2761563 cot. ac 27° 54'

9 9623977 cos. bag ... 23 30

10-2385540 cot. hyp. ab. . 30 00

Prop. Wh'^Having one of the legs, and the angle next it; to find the other

leg.

Add the sine of the leg given to the tangent of the angle given ; the sum
(abating radius) is the tangent of the leg required.

Example, In the right-angled triangle abc, having the leg ac 27° 54', and
the angle bac 23° 30^ ; to find the leg bc.

9-6701807 sin. ac. . 27° 54'
9-6383019 tan. bac 23 30

9-3084826 tan. bc. . 11 30

Prop. VIII. — Having one of the legs, and the angle next to it; to find the

other angle.

Add the cosine of the 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 bc IP 30', and
the angle abc 69® 22' ; to find the angle bac.

9-9911927 cos. bc 11° 30
9-9712084 sin. abc 69 22

9*9624011 COS. BAC 23 30

SPHERICAL TRIANGLES. li

P«op. IX. — Having one of the legs, and the angle opposite to it ; to find the

hypotenuse.

Add the radius to the sine of the given leg, and from the sum subtract the
sine of the given angle, or add its cosecant ; the remainder or sum is the
sine of the hypotenuse required.

Example, In the right-angled triangle abc, having the leg bc 11° 3(y, and
the angle bac 2S° SCV ; to find the hypotenuse ab.

9-2996553 sin. BC ITSC
0-3993003 cos. bag 23 30

9-6989556 sin. ab 30 required.

Pbop. X.— Having one of the legs, and the angle opposite 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.

Example, In the right-angled triangle abc, having the leg bc 1 1° 30', and
the angle bac 23° 30' ; to find the leg ac.

9-3084626 tang, bc 1 1° 30'
10-3616981 cot. BAC 23 30

9-6701607 sin. ac 27 54

Prop. XI. — Having one of the legs, and the angle opposite 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 angle abc.

9-9623977 cos. bac 23° 30'
0-0088073 sec. bc 1 1 30

9 9712050 sin. abc 69 22

Prop. XII. — Having one of the legs^ and the hypotenuse ; to find the angle '

next the given leg.

Add the tangent of the given leg to the cotangent of the hypotenuse, the
sum (abating radius) is the cosine 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 bac.

9 7238436 tan. ac 27° 54'
10-2385606 cot. ab 30 00

9 9624042 cosi. bac 23 30

Prop. XIII. — Having one of the legs, and the hypotenuse; to find the angle

opposite to the given leg.

Add the radius to the sine of the given leg, and from the sum subtract the
sine of the hypotenuse, or add its cosecant ; the remainder or sum will be
the sine of the angle required.

d2

lii THE RESOLUTION OF

Example. In the right-angled triangle abc, having the leg bc 1 1° 3(y, and
the hypotenuse ab 30°; to find the angle bac.

9-2996553 sin. leg bc 1^30'
0*3010300 cosec. hyp. ab 30 00

96 006853 sine of bac 23 30
Prop. XIV. — Having one of the legs, and the hypotenwe ; to find the other

Add the radius to the cosine of the hypotenuse, and from the sum subtract
the cosine of the given leg, or add its secant; the remainder or sum is the
cosine of the leg required.

Example, In the right-angled triangle abc, having the leg bc 11^30', and
the hypotenuse ab 30° ; to find the leg ac.

9-9375306 cosin. ab 80° 00^
00088073 sec. bc 1 1 30

99463379 cosin. ac 27 54

Prop. XV. — Having the angles ; to find the hypotenuse.

Add the cotangent of one oblique angle to the cotangent of the other oblique
angle; the sum (abating radius) is the cosine of the hypotenuse required.

Example. In the right-angled triangle abc, having the angle bac 23° 80'.
and the angle abc S9° 22' ; to find the hypotenuse ab.

0-3616981 cot. bag 23° 30^
9-57.58104 COL abc 69 22

^^9375085 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 angle, 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 of the leg opposite to the angle whose co-
sine was taken.

Example. In the right-angled triangle abc, having the angle bac 23° 30^,
and the angle abc 69° 22' ; to find the leg bc

9-9623977 cosin. bac 23° 30'
0-02879 16 cosec. abc 69 22

9.9911893 cosin. bc 11 30

Of Oblique Triangles.

Prop. XVII. — Having the three sides ; to find any of the angles.

Add the three sides together, and take half the sum ; also the difference
l»«tween the half-suin and tlie side opposite to the angle sought. Then add

SPHERICAL TRIANGLES. liii

the cosccantR, or the complements of the sines, of the other sides, to the sines
of the half-sum and of the said difference; half the sum of these four loga-
rithms is the cosine of half the angle required.

Krample, In the triangle szp, having the side zs 40**, ps 70^, and pz
38° 30' ; to find the angle zps.

PS = 70° C
PZ =r 38 30
zs = 40

Sum 148 30

j^ sum 74 15

zs = 40

Diif. 34 15

cosec. 00270142

cosec. 0-2058505

sin. ^sum 9*9833805
sin. dif. 9 7503579

2) 1 9-9666031

cos.l 5° 47' 9-9833015
zps31 34 required.

Prop. XVIII. — Having the three angles ; to find any of the sides.

Let the angles be changed into sides, taking the supplement of one of
them ; then the operation will be the same as in the former proposition.

Prop. XIX. — Having two angles, and a side opposite to one of them; to find

the side opposed to the other angle.

Add the sine of the side gfiven to the sine of the angle opposite to the side
required, and from the sum subtract the sine of the angle opposite to the side
given, or add its cosecant ; the remainder or sum will be the sine of the side
required.

Example. In the triangle szp. having the angle szp 130° 8' 12", spz
sr 34' 26'', and the side zs 40° ; to find the side Ps.

9-8080675 sin. zs 40° 0' 0"
9.88382941 .

850/ "'"••"
0-28088581

1165 / ^*- *»*^

9-9729842 sin. ps rtqd. 70

See page Ixi following.

Prop. XX. — Having ttoo angles, and a side opposite to one of them ; to find

the side beiuxen the angles given.

Let a perpendicular fall from the angle unknown, on its opposite side ;
then add the cosine of the given angle next the given side, to the tangent of
the given side ; the sum (abating radius) 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 falU.

And the second arc, comprehended between the 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
the sine of the second arc.

The sum or difference of these two arcs will be the side required.

Example, In the triangle szp, having the angle zps 31° 34' 26", zsp
30° 28' 12", and the side pz 38° 30' ; to Bnd the side sp.

993037811 f31°35' ."

440 1 ^^-^^^ i . -34
9-9006052 tan. pz 38 30

9-8310273 tan. pr Ist arc 34 7 30

liv THE RESOLUTION OF

9-74886981

932 f ""* ^'^

9-7884529 1 ,

1227 J ^»- 2iPs

0-23014041

23131 "°^"^

97679103 sin. sr 2d arc 35 52 30

add PR 1st arc 34 7 80

sum is sp 70

See page Ixi following.

But when the perpendicular falls out of the triangle, the difference of the
two arcs will be the side required.

Prop. XXI. — Having two angles, and a nde opposite to one of them; tojind

the third angle.

Let a perpendicular fall from the angle unknown, on its opposite side:
then add the cosine of the given side to the tangent of the adjacent angle;
the sum (abating radius) is the cotangent of the first angle to be found,
comprehended by the given side and the perpendicular.

And the second angle, comprehended by the perpendicular and the side
unknown, is to be found thus : add the sine of the angle found to the cosine
of the given angle opposite to the g^ven side, and from the sum subtract the
cosine of the other angle given, or add its secant ; the remainder or sum will
be the sine of the second angle.

The sum or difference of these two angles will be the angle required.

Example. In the triangle szp, having the angle zps 31*^ 34^ 26'\ ssp
30^ 28' 12^ and the side pz 38^ 30^ ; to find the angle szp.

9-8935444 cosin. pz 38° 30' 0"
9-78845291 , f31 34 .

1227/ ^"^-^^^ 1 . . 26

9-6821200 cot

. 1st < PZR 64

18

50

9-95476191
507/

sin.

PZR

/64

18

•

50

9-93539481
594/

cos.

ZSP

fso

29

48

006954431
336 j

sec.

ZPS

{':

34

•

26

9-9598447 sin. 2d < szr 65 44 21
then add 1st < pzr 64 18 50

tlie sura is SZP 130 3 11

See page Ixi following.

But when the perpendicular falls out of the triangle, the difference uf the
two angles will be the angle required.

Prop. XXII. — Having two sides, and the angle between them ; tojind either

of the other angles.

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 angle required ; the sum (abating radius) is the
tangent of the first arc, comprehended between the given angle and the seg-
ment of the g^ven side where the perpendicular falls.

SPHERICAL TRIANGLES. It

And the second arc is the difference of that side and the first are, being
comprehended between the same segment and the angle required.

Now add the sine of the first arc to the tangent of the g^ven angle, and
from the sum subtract the sine of the second arc, or add its cosecant; the
remainder or sum will be the tangent of the angle required.

Example. In the triangle szp, having the side pz 38° 30', ps 70^, and the
angle zps 31° 34' 26'^; to find the angle zsp.

9-93037811 f31°34' ."

44o| ^^''°- "^ i . . 26
9*9006052 tang, pz 38 30

9-8310273 tan. pr, Ist arc 34 7 30
taken from ps 70

leaves s a, 2d arc 35 52 30

{34 7
. . 30

1227 f ^*"ff- ^'•^ \ ^! ^^ 26

9-74886981

932

9-7884529

1227

0-2320011

873 f «>sec.sR ^ ^ ^30

r35 53 .
\ . -30

9-7696270 tan. zps req. 30 28 12
See page Ixi following.

To find both the unknown angles. *

Add together the cosecant, or the complement of the sine, of half the sum
of the given sides, the sine of half 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 cosine, of half the
sum of the given sides, the cosine of half their difference, and the cotangrent
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
iaif-sum, and you will have the lesser angle required, the same as in the
former operation.

PS =r

J»Z =

70° 0'
38 30

Sum
IDiff.

108 30
31 30

-^ Sum
^Diff.

54 15
15 45

<ZPS
^<ZP8

-81 34 26"
= 15 47 13

Cosec. i sum 009067 19
Sin. j^ diff. 9-4336746
Cot. i ZPS 10-5486352

T. 49°47'30" 100729817

Sec. i sum 02334015

Cosin. i diff. 99833805
Cot. i ZPS 10*5486352

T. 80° 15' 42" 10-7654172

Half sum of angles required is 80° 15' 42"

Half the difference is 4 9 47 30

The greater angle szp is 130 3 12

The lesser angle zsp is, as before 30 28 12

X^ROP. XXIII. — Having two sides, and the angle between them ; to find the

third side.

Let a perpendicular fall from either of the angles unknown, on its opposite
vnde: then add the cosine of the given angle to the tangent of the side from
"Whose end the perpendicular is let fall ; the sum (abating radius) is the tan-

g:ent of the first arc, comprehended between the given angle and the segment

of the side where the perpendicular falls.

Ivi THE RESOLUTION OF

And the second arc is the difference of that side and the first arc, being*
comprehended between the same segment and the end of the side required.

Now add the cosine of the second arc to the cosine of the side from whose
end the perpendicular falls, and from the sum subtract the cosine of the first
arc found, or add its secant ; the remainder or sum will be the cosine of the
8id«3 lequifffd.

Example. In the triangle szp, havins^ the side pz 38° 30', ps 70°, and the
angle zps 31° 34^ 26^' ; to find the side'zs.

9-93037811 r31°35' /'

440 1 ^^^^"•^'•^ t . -34
9-900 6052 tang, pa 38 30
9-8310273 tan. pr, 1st arc 34 7 30

taken from ps 70
leaves sr, 2d arc 35 52 30

9-90859881 ^ ;„ „„ f 35 53 .
457/ ^^"*"-" 1 . -30
9-8935444 cosin. pz 38 30
008202361 „„ f34 7 .
428/ *""• '^ 1 . . 30

1*8842553 cosin. zs req. 40
See page Ixi following.

Prop. XXIV. — Having two sides, and the angle opposite to one of them; to

find the angle opposed to the other side.

Add the sine of the angle given 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 remainder or sum will be the sine
of the angle required.

Example. In the triangle szp, having the side ps 70°, zs 40°» and the angle
8ZP 130° 3' 12'' ; to find the angle zps.

9-8838294') . f49°56' /'

Q3Q|sm.sup.szp| 4g

9 8080675 sin. zs 40

0-0270142 cosec. Ps 70

9-7189961 sin. zps req. 31 34 26
See page Ixi following.

Prop. XXV. — Having two sidex, and the angle opposite to one of them ; to

find the third side.

Let a perpendicular full 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 that angle ; the sum (abating radius) is the tangent of the
first arc, comprehended between the given angle and the segment of the side
where the perpendicular falls.

Now the 2d arc, comprehended between the same segment, and the end
of the side required, is to 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 cosine of the other given side, or add its secant ; the remainder or
sum will be the cosine of the second arc.

The sum or difference of these two arcs will he the side required.

(7811 f31°35' ."

440 1 ^^^-^^'^ 1.^34

SPHERICAL TRIANGLES. Ivii

Example. In the triangle szp, having the side pz 38^ 30\ sz 4(1°, and the
angle spz 31*^ 34' 26" ; to find the side ps.

9-930378 n
440 J
99006052 tan. pz 38 30

9*8310273 tang, pr, 1st arc 34 7 30

9*8842540 cosin. sz 40
01064556 sec pz 38 30

9*9086432 cosin. sr, 2d arc 35 52 30
add PR, 1st arc 34 7 30

gives PS req. 70

See page l&i following.

But when the perpendicular falls out of the triangle, the difference of the
two arcs will be the side required.

Prop. XXVI. — Having iux> sides^ and the angle opposite to one of them ; to

find the angle bettoeen them.

Let a perpendicular fall from the angle between the sides given, on ita
opposite side : then add the cosine of the given side next the given angle, to
the tangent of that angle ; the sum (abating radius) is the cotangent of the
first 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
^iven side, is to be found thus : add the cosine of the first angle found to the
tangent of the given side next the angle given, and from the sum subtract the
tangent of the other given side, or add its cotangent ; the remainder or sum
will be the cosine of the second angle to be found.

The sum or the difference of the first and second angles will be the angle
required.

Example, In the triangle szp, having the side pz 38° 30', sz 40^, and the
angle spz 31° 34' 26'^; to find the angle szp.

9 89S5444 cosm. pz 38° 30' 0"

9*78845291^ szp -f ^^ ^^ •

1227 / ^°g*8ZP -[ . . 26

9*682 1200 cotan.PZR,lst< 64 18 50

9-6368859 1 f 64 19 .

43^1 cosm. pza | _j-

9*9006052 tang, pz 38 30
00761865 cotan. sz 40

9-6137213 cosin. szr, 2d < 65 44 22
add PZR, 1st < 64 18 50

gives szp, req. 130 3 12
See page Ixi following.

Wiii TUE RESOLUTION OF

Prop. XXVII. — Having two angUi, and the side between them ; tojlnd either

of the other sides.

Let a perpendicular fall from the given angle, which is next the side re-
quired, upon its opposite side : then add the cosine of the given side to the
tangent of the given angle opposite to the side required ; the sum (abating
radius) is the cotangent of the first angle to be found, comprehended by the
g^ven fiide and the perpendicular.

And the second angle is the difierence between the first and the given
angle next the required side, being comprehended by the perpendicular and
that side.

Now add the cosine of the first angle found to the tangent of the side
gWen, 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 SV 34' 26", szp
130^ 3' 12", and the side pz 38"" 30' ; to find the side sz.

9-8935444 cosin. pz 38° 30' 0"
9-78845291 , „ J 31 34 .

1227 1 ^"^- '^^ 1 . . 26

9-6821200 cot. pzr, 1st < 64 18 50
taken from szp 130 3 12

leaves szr, 2d < 65 44 22

9-6368859T . „.^ r64 19 .
43^1 cosm. PZR I _j^

9*9006052 tang, pz 38 30

0-38617501 „^ ^^„ ('65 44 .

1028 J ^^'^^ \ . .22

9*9238126 tan. sz req. 40

See page Ixi following.

Tojind both the unknown sides.

Add together the cosecant, or the complement of the sine, of half the sum
of the angles given, the sine of half their difference, and the tangent of half
the given side ; the sum (abating radius) is the tangent of half the dif*
Terence of the sides required.

Add also together tlic secant, or tlie complement of the cosine, of half the
sum of the given angles, the cosine of half their difference, and the tangent
of half the given side : the sum (abating radius) is the tangent of half the
num of the sides required.

Then add half the difierence of the sides required to their half-sum, and
you will have the greater side: and subtract the half-difference from the
half-sum, and you will have the lesser side required, the same as in the
former operation.

Cosec. } sum 00056062
Sin. i diff: 9-8793527
Tang, i Pz 9-5430936

SZP 130°
SPZ 31

3^
34

12'
26

Sum 161
Biffl 98

37

28

38
46

i Sum 80
4 Diff: 49

48
14

49
23

Sec. ^ sum 0*7968360

Cosin. i diff: 9*8148437

Tang, of 15° 94280525

Tang, i PZ 9*5430936

Tang, of 55° 101547733

Half sum of the sides required is 55°

Half their difference is 15

PZ 38 30 jThe greater side sp is 70

i PZ 19 15 Lesser side SZ is, as before 40

SPHERICAL TRlANOL£a lis

Prop. XXVIII. — Havijig two angles^ and the side between them ; to find the

third angle.

Let a perpendicular fell from either of the angles given, upon its opposite
side: then add the cosine of the side given to the tangent of the given
angle, from which the perpendicular does not fall ; the sum (abating radius)
is the cotangent of the first angle, comprehended by the g^ven side and tha
perpendicular.

And the second angle is the difference 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 add the sine of the second angle to the cosine of that given angle
firom which the perpendicular did not fall, and from the sum subtract the siue
of the first angle found, or add its cosecant ; the remainder or sum will be
the cosine of the angle required.

Example, In the triangle szp, having the angle szp 130^ ^ 12^ spi
3P 84' 26^ and the side pz 38^ 30' ; to find the angle psz.

9*8935444 cosin. pz 3S°3<y 0"
9-78845291 , f 31 34 .

1227 / ^°er. 8^=^ I . . 26

9-6821200 cot pzr, 1st < 64 18 50
taken from szp 130312

leaves sza, 2d < 65 44 22

004517731 r64 19 .

101 j c^««.pzr| _j^

9-9303781 i rsi 35 .

440]- <^o«'«-«" \ , -84

9-95982461 . ^^ J 65 44 .

209 j " *""• "* \ • • 22

9-9354550 cosin. psz req. 30 28

See page Ui following.

^^ THE RESOLUTION OF

FOR THE USE OF THE VERSED SINES MAY BE ALSO
ADDED THE FOLLOWING PROPOSITIONS.

. Prop. I. — Having tu» sides of a spheric triangle^ with the angle between

them ; to find the third side.

Add together the log. versed sine of the contaiued angle, and the log. sines
of the two sides ; the sum (abating twice the radius) is the logarithm of a
number to be found, which added to the natural versed sine of the diOerence
of the two given sides, the sum will be the natural versed sine of the third
side sought

Or when the contained angle is above 90^, add the log. versed sine of its
supplement, and the log. sines of the two sides together ; the sum (abating
twice the radius) is the logarithm of a number to be found, and subtracted
from the natural versed sine of the sum of the two given sides, the remainder
will be the natural versed sine of the third side sought.

Example 1 . In the tHangle szp, having the side pz 38° 30', Ps 70°, and the
angle zps 31° 34' 26" ; to find the side zs.

91703625 log. ver. sine zsp 31° 34' 26"
9-7941496 log. sine of pz 38 30
9-9729858 log. sine of ps 70

8-9374970 log. of the numb. 865960
Nat vers. diff. sides 31° 30' 1473598

Nat vers, zs 40° 2339558

Example 2. In the triangle szp, having the side pz 38° 30', zs 40°, and the
angle szp 130° 3' 12"; to find the side ps.
The angle vzp is the supplement of szp.

9-5520590 log. vers, vzp 49° 56' 48'^
9-7941496 log. sin. pz 38 30
9-8080675 log. sin. zs 40

9-1542761 log. of the num. 1426514
Nat vers, sum sides 78° 30' 80063 2 1

Nat vers, ps 70° 6579807

This proposition may be very useful in finding the distances of places od
the earth, whose longitudes and latitudes are Inown ; the distances of stars,
whose declinations and right ascensions, or longitudes and latitudes, are
known ; and consequently the altitudes, or common altitude of two stars, or
two altitudes of the sun, and time between the observations, or difference of
azimuth, being taken, the latitude of the place may readily be found.

Prop. II. — Having two angles of a spheric triangle^ and the side between

them ; to find the 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 will be the supplement of
the third angle. But if one of the given angles exceed 90°, take its supple-
ment, and the result will be the third angle.

SPHERICAL TRIANGLES. m

The following remarks and directions, for rendering the proportional part of
a logarithm always additive, and for using c + t, c — U &c., for s or c, &c.
in the foregoing propositions 20, 21, 22, 23, 25, 26, 27, 28, were cummu-
nicated by the Rev. Nevil Maskelyne, D.D. astronomer royal, and F.R.S..
the fourth case having been invented by him many years since, and de-
livered to the computers of the Nautical £phemeri8. as precepts necessary
iQ 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,
owing to the logarithms not being carried tp a greater number of places in
the table, as will sufficiently appear from the logarithmic differences 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 differences
of the log. sines of small arcs, or cosines of large ones, will sometimes affect
the accuracy of the result of the second part of the operation, unless the first
arc be found to a small part of a minute or second : to prevent such error,
and render the computation easier^ putting t, t', 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 s use c + t

23 arc is near 90°, for— c use t — s

25 arc is near 90°, for c use s — t

26 angle is near 90°, for c use s -|- t'

27 angle is near 90°, for c use s -f t'

28 angle is very small, for— s use t' — c.

This obviates the necessity of fmding the first arc to a very minute exactness,
which otherwise would be necessary in taking out the sine or cosine of the
same arc in the second part of the work.

Where the foregoing precepts direct to subtract a sine or cosine, it will be
readier in practice to add a cosecant or secant ; and where they direct to sub-
tract a tangent (which is done in Prop. 26), it will be readier to add a cotan-
gent. This method being used, if it be required to find the logarithmic sines,
&C to the exactness of a second, and the logarithm is increasing (as irf the
sines, tangents, and secants), write down the logarithm for the degree and
minute without the seconds ; and also write down the proportional part for
the seconds ; but if the logarithm is decreasing (as in the cosines, cotangents,
and cosecant*), write down tlie logarithm for the next greater minute, and
also write down the proportional part for the complement of the seconds to
^ ; and proceed in like manner with every logarithmic sine, cosine, &c. used
mn the work ; the sum of all the logarithms (abating one or two radii or tens
in the index, according as 2 or 3 logarithmic sines, &c. are used in the part
of the work in question) will be the logarithmic sine, cosine, tangent, or co-
tangent required.

EiampU 1 . To find the log. sine of 34° 17' 24".

Here log. sine of 34° 17' 97507287

And as 60 : 24 or as 10 : 4 : : 1853 : . . 741

9-7508028

In USE OF THE

Example 2. To find the log. cos. of bb"" 42' 36''.

Locr. COS. of 55^ 43' 9*7507287

60 : 24 (60 - 36), or 10 : 4 : : 195 3; .. 741

9-7508028

Example 3. In the triangle pls, given

p = 20° 30' 48"
PS = 85 3 40
PL = 89 10

to find L8 by Prop. 23 ;
SD being perp. pl.

p 20^31' .'^ COS. .. 9-9715404

. .-12 95

PS 85 8 . tan.. . 11 0624350') cos. found by taking \ ^ oo^n^ois
. . 40 9814 J tang, from sine J »*^349686

PD 84 43 43 tan.. . 11 0349663 110349663

PL 89 10 cosec. PD 84° 44' ." 100018374

LD 4 26 17 — 17 .. 33

cosin. LD 4 27 ... 9 9986888
— 43 . . 70

cosin. Ls 20 53 24 . . 99704714

Here to avoid the trouble of finding the proportional part for the large
logarithm difference of the cosine of ps, that posine is found by subtracting
the tangent of it (already found) from the sine, which is easily found, because
the differences are small : and, for the 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 differs most from 90°, over or under.

OF THE TRAVBRSE TABLE.

This traverse table, or table of difference of latitude and departure, in pttg€6
158, 159, is so contrived, as to have the whole in one view, and is so plualy
titled as to want little or no explanation.

The distances 1, 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 if the
distance consists of two significant figures, the difference of latitude, and the
departure, is each to be taken out at twice ; and if of three figures, at thrice.

The chief design of this table is for the ready and exact working of tra-
verses ; but it may also be applied to the solution of the several cases of
plain sailing, and to some other uses

Prop. I. — Having the course and distance^ iojind the difference of latitude

and departure.

Seek the course on the lefl-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 the
distance, is found both the difference of latitude and the departure.

Example 1. A ship sails ssw | w 37 miles ; the difference of latitude and
the departure are required.

Find the course 2f points on the lefl-hand side of each page, and even
with it in the double columns signed 3 and 7, the two figures of the distance

TRAVERSE TABLE.

the diflerence of latitude for 30 is 25* 732, and for 7 is 6*004, tlie sud
31*736 for the whole difference of latitude ; and the departure for 3C
15*423, and for 7 is 3*599, the sum is 19022 for the whole departure. Th

Dist. J)iff. Lat. Dep.

30 .... 25*732 .. 15*423 *

7 6004 . . 3*599

37 miles 31*736

19*0*22

Example 2. A ship sails se 49^ 148 miles ; the difference of latitude and
the departure arc required.

Find the course 49 degrees on the right-hand side of each page, and even
with it in the double columns signed 10, 4, and 8, the difference of latitude
at 100 miles is 65*606, at 40 is 26*242, and at 8 is 5*248 ; the sum is 97096
for the whole difference of latitude. And the departure at 100 miles is 75*471,
Ikt 40 U 30-188, and at 8 is 6*038; the sum is 111*697 for the whole de-
parture. Thus,

Dist. Diff. Lnt Dep.

100 65*606 . . 75*471

40 26*242 .. 30*188

8 5*248 . . 6*038

148 miles "97 096 111*697

Pbop. n. — Having 9everal courses and distances ; to find the difference of

laUtude and the departure.

Make a table in the following manner, and put therein each course and
distance ; then find the difference of latitude and departure to each course by
the preceding, and place them in the proper column ; the difference of the
sums of the northings and southings is the whole difference of latitude ; and
the difference of the sums of the eastings and westings is the whole departure.

Example. A ship from the latititde of 50^ north sails according to the
courses and distances set in the traverse, table ; the differences of latitude and
Iho departure are found at the bottom.

THE TRAVERSE TABLE.

1

Courses.

Dist

Diff. of Lat.

Departure.

Miles.

North.

Soalb.

East

Wert.

SSE^E
SE^E
SbWf W

S48° W
N58°W
S40°W

79
86

108

112

70

84

6*101

69*671

54557

101*687

74*942

64*348

37-241
66*479

36*384
83*231
69*734
53*994

6*101

365*205
6101

103*720

243343
103*720

Diff la. 359104

Depart. 139*623

is proposition may be applied in the surveying of large tracts of land,
ouDty, &c. and was made use of by Mr. Norwood in measuring the

Ixiv USE OF THE TRAVERSE TABLE.

distance from York to London, as the road led him, observing the several
bearings by his circumferentor, and finding by such a table his several differ-
ences of latitude and departure, by which he obtained the distance between
the parallels of London and York, pretty near the truth, so long ago as the
year 1635 ; as may be seen in his Seaman's Practice,

Also in plotting the survey of a county thus taken, the circuit station-lines,
though consisting of many hundreds, may be reduced to a few for the first
closing, and the like for the intermediates of each line first plotted, by which
every station may perhaps be more truly placed than by any other method :
the distances in the table may be 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.

Pbop. III. — Having the difference of latitude, and the departure ; to find

the coune and distance.

Seek the given difference of latitude and departure, taken together, in their
columns, or the nearest numbers to them ; and the course is even therewith
at the side, and the distance at the top and bottom : but if the given difference
of latitude and departure cannot be found nearly, take j^, ^, &c. part, or any
equal multiple of them that can be found ; then the course is even with them
at 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 miles w ; the course and distance are required.

In the double column over 9, even with 49^ at the right-hand side, is found
together the given difference of latitude and departure ; therefore the course
is 49^ sw, and the distance 90 miles.

Example 2. Given the diff*erence of latitude 30 miles n, and the departure
Id miles E ; the course and distance arc required.

Here the given difference of latitude and departure, or any numbers near
them, are not to be found together in the table ; therefore taking ^ or the
double of each, the course is found to be 31^ ne, and the distance 35 miles.

Note. A table computed to every mile in the distance up to 100 miles
would more readily solve this example.

Prop. IV. — Having the departure and middle latitude ; to find the difference
of longitude, according to the m^hod first given by W. Jones, Esq. F.R.S.

Seek the given departure, or the next less number in the columns signed
lat even with the middle given latitude found among (he courses, and at the
top and bottom (signed 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' n, 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 70921 ; therefore 90 miles is the difference of longitude sought.

Example 2. Being yesterday noon in latitude 46° 25' n, and this day at
noon in 47° 35' n, so that the middle latitude is 47° n, and the departure ia
foun-l 112'53 miles w; required the difference of lonn;itude.

In the column signed lat. over 10 at the bottom, even with 47 at the right-
hand side, is 6*8200 ; therefore subducting 68 200 from 1 1253, the remainder
is 44*33 ; then over 6 is 40920, and 40*92 subducted from 44*33 leaves 3*41^

OF MERCATORS SAILING. IxT

which is found over 5 ; therefore the difference of longitude is 165 miles
west.

If the middle latitude he not an even degree, hut have odd minutes ; find
the difference of longitude, for the even degrees next less and greater, and
add a proportional part of the difference between the two results to the lesser ;
the sum will be the difference of longitude sought.

Suppose the middle latitude in the last example had been 47° 20' n ; then,
after 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 166 miles west.

Note. Though 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 as easy, and very expeditious.

Prop. V. — Having the latitudes and the longitudes of two places, to find 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 with the difference of latitude
and departure, find their bearing or course and distance by the third.

Example, Let the Lizard be given in the latitude of 49° SCK n, and U^ 21'
w longitude, and Cape Ortegal in the latitude of 44° KV n, and 70° 43' w
longitude ; to find the bearing and 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 is
96*844 miles w, for the departure ; and the bearing, or course, answering to
340 miles difference of latitude, with 96*844 departure, is found about 16°
sw ; and the distance about 354 miles.

OF MERCATOR'S SAILING.

The uses of the table of meridional parts are fully supplied by the table of
logarithmic tangents, as is demonstrated in N'* 219 of the Philosophical
Transactions, It is there proved, 1st. That the meridional line, or scale of
Mercator's Chart, is a scale of the log. tangents of the half-complements of
the latitude. 2dly. That such log. tangents of Mr. Briggs's form, are a scale 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.

Hecce it follows, that the difference of the log. tangents of the half comple-
ments of the latitudes, is to the differt.ice of longitude a ship makes in sailing
on any rumb firom the one latitude to the other, as the tangent of 51° 38' 9"
(whose logarithm is 10*1015104) to the tangent of the angle of the rumb or
course with the meridian ; so that :

I. If two latitudes, and the difference of longitude, be given, the course and
distance are readily determined by this rule.

Take, by help of the tables, the difference of 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 *
the sum (abating 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

e

Ixvi OF MERCATORS SAILING.

reduced to minutes, the sum (abating radius) shall be the logarithm of the
distance in minutes.

Example, Given the Lizard to be in latitude 49^ 55' n, Barbadoes in 13^
W N, and their difference of longitude 53^ 00' or 3 ISC w ; to find the course
and distance.

1 r !«♦ J Barbadoes 38° 25' 1. tan. 98993082 1. 3180' = 3*5024271
* \ Lizard 20 2^ 1. tan. 95620477 const, log. 101015104

diff. 3372*605 its co. log. 6 4720346
Log. tang, of the course 49*^ 59' 10" sw 100759721

Log. sec. of the course 49 59 10 10-1918067

Log. of 2205' diff. of the latitudes 3*3434086

Log. of 3429*378 distance of Barbadoes from the Lizard 3*5352153

II. If two latitudes and the course be g^ven, the difference of longitude is
obtained with tlie same ease : for as the tangent of 51° 38' 9" is to the tangent
of the course, so is the difference of the log. tangents of the half-complements
of the latitudes, to the difference of longitude sought Therefore, to the
complement of the constant log. 10*1015104, add the log. of the difference of
the log. tangents 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 difference
of longitude in minutes.

Example. Given the latitudes 49° 55' and 13° 10', and course 49° 59' 10";
to find the diflference of longitude.

Lat. 13° 10' its i CO. lat. 38° 25' 1. tan. 9*8993082

Lat. 49 55 20 2^ 1. tan. 9*5620477 co. const log. 9*8984896

diff. 3372*605 its log. 3*5279654

Log. tang, of the course 49° 59' 10" 10*0759721

Log. of 3180' = 53° for diff. of longitude 3*5024271

By this rule, having two good observations of the latitude, and the course
duly steered, the reckoning of a ship's way is best ascertained, especially if
you sail near the meridian.

III. If the latitude departed from, the course steered, and distance sailed,
be given; to find the ship's latitude, and difference of longitude.

First, the latitude is obtained 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, the sum or remainder is the present latitude * then having the
two latitudes and the course, the difference of longitude is found by the second.

Example. Having sailed from the Lizard, in lat. 49° 55' n, on a course
49° 59' 10" south-westerly 3429*378 miles: rec^uired what longitude and
latitude the ship is found in.

Log. of 3429*378 the distance sailed 3*5352153

Log. cosine of 49° 59' 10" the course 9*8081933

Log. of 2205', or 36° 45' diff. of the latitudes 3*3434086

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
found 3372*605, and the further process in nothing differing from the second
rule» by which the difference of longitude will be found 53° 00'.

CIRCULAR ARCS. Lxvii

Thus the dead reckoning by the log. line, and daily account of a ship*s way,
are duly kept, and the trouble very little more than by plain sailing.

These are all the cases that occur in practice ; the rest, which are mostly
speculative, are either easily reducible to these, or else not to be performed
by logarithms, and therefore come not at present under our cognizance.

But it is to be noted, that both the complements of the latitudes are to be
estimated from the same pole of the world ; which may be from either ; and
therefore if one latitude be n, and the other s, to have their complements,
you must add 90^ to one of them, and subtract the other from 90°, and then
the operation will be the same as in the preceding cases.

Example. Given St Jago, one of the Cape-de-Verd Islands, in the lati-
tude of 14° 56' 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.

inolf fSt.Jago 52° 28'. 1. tan. 101144965 1.1812' 3-2581582
^co. lai. -^ St Helena 37 7^. 1. tan. 98790845 const, log. 101015104

2354-120 its co. log. 66281714

Log. tang, of the course 44° 11' 53" sb 99878400

Log. sec of the course 44 11 53 101445200

Log. of 1841' diff. of the latitudes 3^650538

Log. of 2567-875 distance of St Helena from St. Jago 34095738

Or if it be thought easier, when one latitude is n, and the other s, you may
add 90° to each of them, the sum of the log. tangents of their halves (abating
twice the radius) will be the same as the difference of the log. tangents of the
former. For an example, take the same latitudes as in the preceding.

Tu OAO I fl4°56'= 104°56'1 ., , ,^ r52°28' 1. tan. 101144965
Then 90^ + 1 15 45 ^ 105 45 j" ''^ ^""^^ i 52 52^ 1. tan. 1012091 55

The sum (abating twice the radius) equal to the former distance. . 2354 120

Also, when both latitudes are of the same name, that is both n or both s,
you may add 90° to each of them, the difference of the log. tangents of half
these sums will be the same as of the log tangents of half the complements
of those latitudes.

TABLE FOR THE LENGTHS OF CIRCULAR ARCS.

"This is Table 11, and constitutes page 360. It contains the lengths of every
single degree up to 180, and of every minute, second, and third, each up to
CO. The form of it is obvious ; the length of each degree, minute, second,
c)r third, immediately following it on the same line in the next column. And
Xhe two following examples will show the use of the table.

ExampU 1. To find the length of an arc of 57° 17' 44" 48'".
Take out from their respective columns the lengths answering to each of
t.he8e numbers singly, and add them all together, thus :

57° 9948377

17' 49451

44" 2133

48"' 39

the sum or 1*0000000 is the whole length,
and is equal to the radius ; that is, the length of an arc of 57° 17' 44" 48'" is
equal to the radius of the circle.

Example 2. To find the degrees, minutes, &c. in the arc 1, which is equal
to the radius.

ixviu COMMON AND HYP. LOGS.

Subtract from it the next less tabular arc, and from the remainder the next
less again, and so on till nothing remain ; and opposite to the several r um-
bers subtracted, will be the degree, minutes, &c. ; thus :

Given length 1-0000000

bT" 0-9948377

51623
17' 49451

2172
44" 2133

48'" 39

So that the arc, which is equal to the radius, contains 57° 17' 44" 48"'.

TABLE FOR COMPARING HYP. AND COMMON LOGS.

This is Table 12, and is the upper part of page 361. It contains the
hyperbolic log^. answering to the first 100 common logs, and is very useful
for speedily changing the one into the other.

Example 1. To find the hyp. log. answering to the common log. 0*9542425.

Beginning at the lefl-hand, and dividing the given number into periods of
two figures each, including the index, take out the hyp. log. to each period,
omitting two figures at the 2d period, four at the 3rd, and six at the 4th ;
then add them all together, thus :

com. log. hyp. log.

09 20723266

54 1243396

24 5526

25 58

0-9542425 2-1972246 answer.

Example 2. To find the common log. answering to the hyp. log. 2* 1972246.
Subtract continually each next less tabular hyp. log. from the g^ven num-
ber, and from the remainders ; and the several common logarithms answer-
ing to these tabular hyp. log^. joined together, will be the com. log. required,
thus :

hyp. log.

given 2-1972246

09 2-0723266

1248980
54 1243396

5584
24 5526

58
25 58

0-9542425 answer.

The remaining tables are oflen useful in trigonometrical investigations, as
well as in different researches in the higher mathematics ; but they require
no particular explanation.

TABLE I.

CONTAINING

THE LOGARITHMS OF ALL NUMBERS

From 1 to 108000.

u

.>

Ximih

r« 1

l.> lOir, ulkI

L

«;A»iin»is N. 100 L. 00;

llH>irL.'j;rs.»i|l, IlHlioi'S.

_'-«!

N.I \.^%.

150| 1760913

N.
200

3010300

I

Koummod

bl 1-707571)2

lOO; 0000000

'I

0-30 10300

53 1-7160033

101

0043214

151 1789769

201

3031961

.1

0477I^13

53 1-7242759

102

0086002

152 1818436

202

3053514

4

0602i)(iOO

54 1-7323938

103

0128372

153' 1846914

203

3074960

a

0-69S9700

55 1-7403027

104

0170333

154

1875207

204

3096302

6

0-778 !r.l3

56 1-7481^^0

105

0211893

155

1903317

205

311753B

7

0-8450980

57 l-73r,s-|9

106:0253059

156

1931246

206

3138672

8

0-i)03U900

58 1-763 IL'MI

107 0293833

157

1958997

207

3159703

'J

0-9542425

S9 l-7708;V_'O

108

0334238

158

1986571

208

3160633

10

l-OUOOOOO

60 1-7781513

109

0374265

159

2013971

209

3201463

11

10413937

6ll 1-7853-398

110

0413927

160

2041200

210

3222193

1-2

1 ■079181-2

63 179-23917

111

0453-230

161

2068259

211

3242625

13

1- 1139434

63, 1-7993405

112

04U2180

162

2095150

312

3263359

14

1 1481280

64 1-8061800

113

0530784

163

2121676

213

3283796

i:i

1 17009 13

65,18129134

114

0569049

164 2148438

214

3304 138

16

1-2041200

66 1-8195439

115

0606978

165'2174S39

215

3324385

17

l-23044By

67,18260748

116

0044580

166 2201081

216

334453S

IS

1-255-2725

68 1 8325069

117

0681859

167 2227165

217

3364597

19

1-2787536

69, 1-8388491

US

0718820

168 2253093

218

3384565

•iX\

1-3010300

70| 1-8450980

119

0755470

169^2278867

219

3404441

21

1-3322193

7l' 1-8512563

120

0791812

170 2304489'! 220

3424227

22

1-34 -24227

72 1-8573325

121

0827854

17ll232996! |221

3443923

23

1-3617278

73. 1-8633229

122

0863598

172 2355284 222

3463530

S4

1-3802112

74 1 869-2317

123

0899051

173; 23804611! 223

S483049

2:)

1 ■3979 101)

754-8750613

124

0934217

174 2405492 1224

1502480

•m

1-4U0733

76 I880S136

125

0969100

175; 2430380 1 225

3521825

■11

1 4313C3B

77 1-8861907

126 1003705

176 2455I27J 226

3541084

^S

1-4471580

78!i-8920!)K:

127 1036037

177 2479733:1227

3560259

an

1-46-23980

79 1 8976:n 1

128 1072100

178 2504-200li228

3579348

:nj

1-4771213

80|I-9030!11IO

129 1105S97

179.2528530j!22»

3598355

-Tl

1-4913617

81 1-9084 '-50

130 1139434

180 2552725, 230

361787S

3-2

l-.i05l50(P

82:1-9138139

iSl 1172713

181 2576786:1231

3636130

;i3

1-5185139

83;1-9I907SI

132 1205739

182 26007I4|i232

3654880

:il

l-53l47b9

64; 1-9242793

133 1238516

183 2624511'i233

3673559

:)j

1 5440680

6511-9294189

134,1271046

184 2648176 234

3692159

»R

I 55630-25

86 1 93149S5

135 1303338

185 2671717

235

3710679

ST

15682017

8711-9395193

136 1335389

186 2695129

236

3729120

;is

1-5707836

88 19444827

IS7 1367206

187 27184.16

237

3747483

3y

1-5910646

89 1-9493900

138'"I398791

168 2741578

238

3765770

.10

1-6020600

90 1-9542425

139; 1430148

169 2764618

239

3783979

41

1-6127^39

91 1-9590414

14o'l4612SO

190 2787536

240

3802112

4d

1-6232493

■Si 1-9637878

14lll492191

191 2810334

241

3820170

43

1-G3346S5

93, 1 9684829

142 1522883

192 2^33012

242

3838154

44

16434527

94! 1-9731279

143 1553360

193 2655573

243

3S56063

45

16532125

95

I-97i7:;:i6

144 1563625

194 2878017

244

387389S

4G

1-6627578

96

1-98-22712

145J 1613680

195 2900346

245

3891 661

47

1-0T20979

97

1-9S677I7

146, 1043599

196 2922 61

246

3909351

4S

1-6812412

!is |'!l!ll-226I

14711673173

197,2944662

247

3926970

4fl

16901961

99 I-D:)r)(i352

14S! 1702617

198 2966652

248

3944517

r><)

l-69»9700

lilO,-3-Oi;ilOOOO

149 1731663

199 2968531

249

3961993

N

IxJfJ.

_N.! Lng.

N.! Log.

N I Uff.

N.

w-

N. -2.30 L. 39
N.

250

2:a

2.V2
253!

254J

235;

256

257

258

259

260
261
262
263
264

265

3M79400
3996737
4014005
4031205
4048337

4065402
4082400
4099331
4116L97
4132998

4149733
4166405
4183013
4199557
4216039

4232459

266 4248816
267i 4265113
26S' 4281348
2C}J 4297523

27 o! 4313638
•i7 1 ! 432.7693
272} 43 15689
273:4361626
2741 4377506

275! 4393327
276 4409091
2771 4424798

27814440448

279 4456042

280 4471580
281 ! 44H7063
282 j 4502491
283.4517864

284

285
286
287

288
289

•290
291
292
293
•294

295
•296
297
•298
299

"N.

4533183

4548449
4563660
4:>78819|
459.^925'
4608978

4623980
46389301
4653829J
4668676;
4683473

4698220
4712917!
47275641
474-21 03
4756712

N.

300
301
302
303
304

305
306
307
308
309

310
311
312
313
314

4771213
4785665
4800069
4814426
4828736

4842998
4857214
4871384
4885507
4899585

4913617
4927604
4941546
4955443
4969-296

OF NUMHFUS.

N.| Log".

350 5440680

351 5453071

352 5465427

353 5477747

354 5490033

315 4983106
316:4996871
317j 5010593
318 5024271
31915037907

320
321
322

5051500
5065050
5078559

3-23^092025
324^5105450

325| 51 18834

326 5132176

327 5145478

328 5158738
329' 5171959

330 5185139
33l'5l9S280
332' 52 1138 1
333' 5224442
334; 5-237465

335' 525044 S

336 5-263393|

337 5-276-29f)j
33s'5-2S9107l
339 '5301997

310:5314789
311; 53^27544
342 5340^26I
3i3!535-i:Ml
344:5365584

345 5378191
3 16! 5390761
3 17 1 5403295
3 18; 5415792
349:54-28-251

N.

Locr.

355

5502284

356 5514500
357; 5526682

358 5538830

359 5550944|

36o' 5563025'
361 1 5575072
362 1 5587086;
363 5599066
364' 5611014'

365* 5622929
^66 5634811
367; 5646661
368 5658478
369' 5670264

370, 5682017
37 1 ' 5693739

372 i 57054-29

373 5717088

374 57-28716

375 5740313

376 5751878
377| 57634 14
378' 5774918
379' 5786392

380 15797836
381 ! 5809250"
382 58-2063 l.|
3S3 5831988;

384 5843312

385*5854607
386 5865873

357 5877110

385 5888317
389 5899490

390' 5910646
39i;59217(>S!

392:593286 1 1
393 :y.)r3:)'2(y
394;5!)54yri.i

395 59659T1

396 597ri952
397j 5987905
39S 5998H31
399 6009729

N".

400
401
402
403
404

405
406
407
408
409

60-20600
6031444
6042-261
6053050
6063814

607455

6085260

6095944

6106602

6117233

QJ|455 6580114
456 6589648
457! 6599 162

458 6608655

459 6618127

410 61-27839
41l!6138418

412 6148972

413 6159501

414 6170003

415 6180481
416' 6190933
417J 6-201361

418 6211763

419 62-22140

420
421

6-232493
6242821

I^<r.

4-227)553125
4-23 6-263404

424 6273659

425 6283889

426 6-294096
427-6304279
428' 6314438
4-29J 6324573

430 6334685
43 r 6344773

432 6354837

433 6364879

434 6374897

I

435' 6384893

436 6394865

437 6404814

438 6414741

439 61-24615

410 6434527

441 64443S6

442 6454223

443 6464037

444 6473830

445' 6483600
446 6493349
447j 6503075
448 6512780
149 65-22463

N.

I OiT,

N.

3_

Locr.

450 653-21-25
45l| 654 1765
45-2 -6551384
453 6560982
454:6570559

460
461
462
463
464

6627578
6637009
6646420
6655810
6665180

465 6674530

466 6683859

467 6693169

468 6702459

469 67117-28

470
471

47-2^
473
474

475
476
477
478
479

480
481
482
483

484

485
486
487
488
489

490
491
492
493
494

495
496
497
498
499

NT

6720979
6730209
67394-20
6748611
6757783

6766936
6776070
6785184
6794279
6803355

681-2412
6821451
6830470
683947 1
6848454

6857417
6866363
6875290
6884 ] 98
6893089

6901961
6910815
6919651
6928469
6937269

6946052
6954817
6963564
6972293
6981005

Loot.

u2

LOGARITHMS

N. 500 L. G9

N.

Log.

500 6989700

501 6998377
502=7007037
503'70156S0
504 i 7024305

505
506
507
508
509

510
511
512
513
514

515
516
517
518
519

7032914
7041505
7050080
7058637
7067178

7075702
7084209
7092700
7101174
7109631

7118072
7126497
7134905
7143298
7151674

520 7160033
52117168377

522

7176705

523 7185017

524

7193313

525 7201593

526
527
528
529

7209857
7218106
7226339
7234557

530 7242759
531 1 7250945
53217259116
533' 7267272
534| 72754 13

535' 7283538
536:7291648

537 7299743

538 .73078'23

539 7315888

540
541
542
543
544

545
546
547

548
549

LN:

7323938
7331973
7339993
7347998
73559S9

7363965
7371926
7379873
7387806
7395723

Loot.

N.

550
551
552
553
554

Log".

7403627
7411516
7419391
7427251
7435098

555 7442930

556 7450748

557 7458552
5581 7466342
559| 74741 18

560; 7481880
56117489629
562' 7497363
563; 7505084
564i 7512791

565
566
567
568
569

570
571
572
573
574

575
576
577

578
579

580
581
582
583
584

585
586

587
588
589

590
591
592
593
594

595
596
597
598
599

7520484
7528164
7535831
7543483
75511231

75587491

7566361

7573960;

7581546

75S9119

7596678
7604225
7611758
7619278
7626786

7634280
7641761
7649230
7656686
7664128

7671559
7678976
7686381
7693773
7701153

7708520
7715875
7723217
7730547
7737864

7745170
7752463
7759743
7767012
7774268

N.l

Loot.

N.

600
601
602
603
604

605
606
607
608
609

610
611
612
613
614

1^)2:.

7781513
7788745
7795965
7803173
7810369

7817554
7824726
7831887
7839036
7846173

7853298
7860412
7867514
7874605
7881684

615 7888751

616 7895807

617 7902852
618' 7909885
619| 7916906

620 7923917
62117930916
622 7937904
623' 7944880
624:7951846

625- 795S800
626* 7965743
62717972675
628)7979596
629. 7986506

630' 7993405

631 8000294

632 8007171

633 8014037

634 j 8020S93

635: 8027737

636 8034571

637 8041394

638 8048207

639 8055009

640
641
642

8061800
8068580
8075350

643 8082110

644

8088859

645 8095597

646
647
648
649

8102325
8109043
8115750
8122447

N.

650
651
652
653
654

655
656
657
658
659

660
661
662
663
664

.OCT.

8129134
8135810
8142476
8149132
8155777

8162413
8169038
8175654
8182259

8188854

8195439
8202015
8208580
8215135
8221681

665 8228216

666 8234742

667
668

8241 258
8247765

Locr.

669.8254261

670' 8260748
671:8267225
672 8273693
673^8280151
674,8286599

675! 8293038
676 8299467
677 '8305887
678- 8312297

679 8318698

680 8325089

681 8331471
682' 8337844
683 8344207
684^8350561

685. 8356906
686 8363241
687,8369567
688 8375884
68918382192

690' 8388491
691 1 8394780
69218401061
693-8407332
694 1 84 13595

695 8419848
696^8426092

697
698
699

N.

8432328
8438554
8444772

Log.

N.

700
701
702
703
704

705
706
707
708
709

710
711
712
713
714

715
716
717
718
719

720
721
722
723

Log-

8450980
8457180
8463371
8469553
8475727

8481 S9 I
8488047
8494194
8500333
8506462

8512583
8518696
8524800
8530895
8536982

8543060
8549130
8555192
8561244
8567289

8573325
8579353
8585372
8591383

72418597386

72518603380
72618609366
727| 861 5344
728' 8621314
72918627275

730 6633229

731 8639174

732 8645111

733 8651040
734 1 8656961

735 8662873

736 8668778

737 8674675
738;86S0564
73918686444

740
741
742
743

6692317
6698 182
8704039
6709888

744 8715729

745
746
747
748
749

N.

8721563
8727388
8733206
8739016
6744818

Log.

N. 750 L. 87

OF NUMBERS.

— 1
O

N.

U}g.

N.

800

Log.

N.

850

Log-

N.

900

Log.

N.

950

Log.

9777236

750

8750613

9030900

9294189

9542425

751

8756399

801

9036325

851

9299296

901

9547248

951

9781805

752

8762178

802

9041744

852

9304396

902

9552065

952

9786369

753

8767950

803 9047155

853

9309490

903

9556878

953

9790929

754

8773713

804

9052560

854

9314579

904

9561684

954

9795484

755

8779470

805

9057959

855

9319661

905

9566486

955

9800034

756

8785218

806

9063350

856

9324738

906

9571282

956

9804579

757

8790959

807

9068735

857

93-29808

907

9576073

957

9809119

758

8796692

808 9074114

858

9334873

908

9580858

958

9813655

759

8802418

809 9079485

859

9339932

909

9585639

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9818186

1

760

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810 9084850

860

9344985

910

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960

98-22712 •

761

8813847

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861

9350032

911

9595184

961

9827234

762

8819550

812.9095560

862

9355073

912

9599948

962

9831751

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9360108

913

9604708

963

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764

8830934

814

9106244

864

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765

8836614

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915

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9380191

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967

9854265

768

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818

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868

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9628427

968

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769 8859263

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9132839

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9390198

919

9633155

969

9863238

770 8864907

820

9138139

870

9395193

920

9637878

970

9867717

771 8870544

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9143432

871

9400182

921

9642596

971

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772,8876173

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9148718

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9405165

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9410142

923

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774 8887410

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9159272

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924

9656720

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9164539

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9439889

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8920946

830

9190781

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9444827

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8932068

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9201233

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932

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783

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9484130

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9513375

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9289077

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9537597

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9772662

999

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9995655

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25
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28
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1030
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55
56
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58
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55
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57
58
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61
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4383

7532

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3823
6966
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6379
9512
2643
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8898

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5144
8264
1381
4497

7610
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3829
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4138
7280
0419
3557

6692
9.S25
2956
6084
9211

2335
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7921
1031
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8

9

5911

6232

9124

9446

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2657

5545

5866

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1133

1452

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5119

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187
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14 LocAiiiTiiMs N. 14000 L. J40|

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9029

9338

9648

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1246

1553

1859

2166

2472

2779

3085

3392

17

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4005

4311

4618

4924

5231

5537

5843

6150

6456

306 305

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6762

7U69

7375

7691

7987

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8600

8906

9212

9518

1 ; 31 31

19

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0130

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0742

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5272

5578

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0217

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1133

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1532049

2354

2659

2964

3270

3375

3980

4185

4490

4795

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5100

5405

5710

6015

0320

6625

6929

7234

7539

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9 276;S!S

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2109

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3022

3327

3631

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5153

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5761

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2754

3056

3359

3061

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5172

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6079

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311

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0910

1212

1513

1813

2117

2418

2720

3022

3323

1440

3625

3927

4228

4530

4831

5133

5434

5736

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8 94S

341

41

6640

6941

7243

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300

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2964

3265

3566

3867

4168

4469

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5070

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5973

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6374

6875

7175

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9681

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7086

7386

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7686

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8585

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9185

9485

9785

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8 240 239
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49

N.

1610634

0984

1283
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1583
3

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4

2182
5

2482

2781
7

3081

3380

Diffw.

N. 14500 L. 101

N.

OV NIJMBKHS.

1450. 1613680

5L
52
53
54

55
56
57

58
59

1460
61
62
63
64

65
66
67
68
69

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71
72
73
74

75

6674

9666

1622656

5644

8630

1631614

4596

7575

1640553

3529
6502
9474
1652443
5411

8376

1661340

4301

7261

1670218

3173
6127
9078
1682027
4975

1

7920

76 16908641

77 3805'

78 6744

79 9682

1480
81
82

83
84

85
86
87
88
89

1490
91
92
93
94

3980
6973
9965
2955
5943

8928
1912
4894
7873
0851

3826
6799
9771
2740
5707

8673
1686
4597
7556
0514

3469
6422
9373
2322
5269

8215J
1158

y

4279; 4578
7273 7572

1702617
5551
8482

1711412
4339

7265
1720188
3110
6029
8947

1731863
4776
76S8

1740598
3506

95 6412

96 9316
971 1752218
98 5118

8016

f)264
3254
624 L

9227
2210
5192
8171
1148

4123
7097
0068
3037
6004

8969
1932
4893

7H52!
0809

3764
6717
9668
2617
5564

8509
1452
4393
7332
0269

2911' 3204
584416137
877519068

4099 j
7038|
9975

1704; 1997
4632:4924

755717849
04SO'O773

3402
6321
9239

3()94
6613
9530

2154 2446
5068' 5359
797918270
0889,1180
379714087

6702 6993
9606 9S97
2508 2798
5408 5098
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1 i

0563
3553
6540

9525
2508
5490
8469
1446

4421
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(1365
3334
6301

9265
2228

5189
8148
1105

4060
7012
9963
2912
5859

8803
1746
4687
7620
0563

3497
6430
9361
2290
5217

8142
1065
39S6
6905
9822

2737
5050
8561
1471
437S

7283
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3088

8885

3

4878
7871
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9824
2807
5788
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4718
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4355
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6723
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5177
8170
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3105
6086
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5016
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3927
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2821
5781
8740
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4650
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9392
2335
5275
8213
1150

4084
7017
9947
2876
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8727
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4570
7488
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3320
6233
9143
2052
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5477
8470
1460
4449
7436

(1420
3403
6384
9362
2339

5313
8285
1256
4224
7190

0155
3117
6077
9035
1991

4946
7898
0848
3796
6742

5610
8582
1553
4521
7487

5451
3413
6373
9331
2287

5241
8193
1143
4091
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9686' 998 1
26-29 2923

7574 1 7864
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9175! 9465

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5569
8507
1443

4377
7310
5240
3168
6095

9019
1941
4S62

7780
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3611
6524
9434
2343
5250

8155
1057
3958
6857
9754

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5863
S801
1737

4671
7603
5533
3461
6387

9311
2233
5 1 54
8072
5988

3903
6815
9725
2634
5540

8445
T348
4248
7147
5044

5908
8880
1850
4817
7783

5747
3709
6669
9627
2582

5536
8488
T438
4386
7331

(1275
3217
6157
9094
2030

4964
7896
5826
3754
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9604
2526
5446
8364
1280

4194
7106
5016
2925
5831

8735
1638
4538
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9177
2146
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1043

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6965
9922

2878

5831
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7626

5569
3511
6450
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8189 i
1119
4046
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9896
2818
5737
8655
1571

4485 1
7397 1
5307 1
3215:
6121

9026
1928
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7727
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296

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59
89
118
148
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173
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DifTer.

IG

LOGAHITHMS

N. 150rjO L. 17G

N.

1500
01
02
03
04

05
06
07
08
09

1510
11
12
13
14

15
16
17
18
19

1520
21
22
23
24

25
26
27

28
29

1530
31
32
33
34

35
36
37

38
39

1540
41
42
43
44

45
46

47
48
49

1760913
3807
6699
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1772478

5365
8250
1781133
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4096
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0168
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5942
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1792645
5518
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4126
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5422
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3912
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2932 3219
5805, 6092
8676 8963
1546 1832

4413
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3004
5864

4700
7565
5428
3290
6150

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1578! 1863
4432:4717
7284 7569
5135' 5420

2983
5830
8675
1518
4359

7198
5036
2871
5705
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1367
4195
7021
9840
2668

5489
8308
1125
3941
6754

9566
2376
5184
7990
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3268
6114
6959
1802
4643

7462
5319
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5988
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4478
7304
5128
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5771
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1407
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2657
5465
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3

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1781

2071

4675

4964

7567

7856

5457

5745

3345

3633

6231

6519

9115

9403

1997

2285

4877

5165

7756

8043

5632

5920

3507

3794

6380

6667

9250

9537

2119

2406

4986

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8138

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3862

6435

6721

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9579

2149

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5002

5288

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5704

5989

3553

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6399

6684

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2080

2370

4927

5211

7766

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5603

5886

3438

3721

6271

6555

9103

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1932

2215

4760

5043

7586

7869

5410

5693

3233

3515

6053

6335

8872

9154

1689

1970

4504

4785

7317

7598

5128

5409

2938

3218

5745

6026

8551

8832

1355

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3

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6

2360
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2649
5543
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1323
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7096
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2861
5741
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1495
4369
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5111
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5559 5846
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6838
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2498
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5975
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6617
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2252
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5690
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6307
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4288
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2781
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5971
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2939
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8723
1612
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7385
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3149
6029
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3228
6121
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5070
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5435 5721
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6143 6429
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1737
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8102
5972
3840

6706
9570
2432
5292
8150

1007
3861
6714
9565
3414

5261
8106
5949
3791
6630

946S
2304
5138
7970
5801

3629
6456
9281
S104
4925

7745
5562
3378
6192
9004

1814
4622
7429
5234
3037

Differ.

*W0

29
68

87
IIG
145
174
203
232
261

289

29
58

«7
116
145
173
202
231
260

9

2881287

284

57
86
114
142
170
199

227
256

283

28

67
86
113
142
170
198

266

2821281

28

66

85
113
141
169

197
228

264|2 S3

Differ.

66
84
112
141
169
197

I

N. 15500 L. 190

OF NUMBERS.

17

N.

1550
51
52
53
54

55
56
57

58
59

1560
61
62
63
64

65
.66
67
68
69

1570
71
72
73

1903317
6118
8917

1911715
4510

7304
1920096
2886
5675
8461

1931246
4029
6810
9590

1942367

5143
7918
1950690
3461
62*29

8997

1961762

4525

7287

1

74 1970047

2806
5562
8317
1981070
3821

6571
9319
1992065
4809
7552

2000293
3032
5769
8505

2011239

3971
6702
9431
2022158
4883

7607

2030329

3049

5768

8485

3597
6398
9197
1994
4790

7583
0375
3165
5953

8740

1524
4307
7088
9868
2645

54*21
8195
0967
3738
6506

9273
2038
4802
7563
0323

3081
5838
8592
1345
4096

6846
9593
2339
5083
7826

0567
3306
6043

8778
1512

4244
6975
9703
2430
5156

7879
0601
3321
6040
9756

I

3877
6678
9477
2274
5069

7862
0654
3444
6232
9018

1803
4585
7366
0145
2923

5698
8472
1244
4014
6783

9550
2315
5078
7839
0599

3357
6113

8868
1620
4371

7121
9868
2614
5358
8100

0841
3579
6317
9052
1786

4517
7248
9976
2703
5428

8151
0873
3593
6311
9028

4157
6958
9757
2553
5348

8142
0933
3723
6511
9297

2081
4864
7644
0423
3200

5976
8749
1521
4291
7060

9826
2591
5354
8115

0875

3633
6389

4438
7238
0036
2833
5628

8421
1212
4002
6789
9575

2359
5142
7922
0701
3478

6253
9027
1798
4568
7336

0103
2867
5630
8391
1151

3908
6664

9143-9418
1896j2171
4646 4921

7395
0143
2888
5632
8374

1115
3853

7670
0417
3163
5906
8648

1389
4127

6590,6864
9325 9599
2059.2332

4791' 5064
752117794
0249 0522

2976
5700

8424
1145
3865
6583

3248
5973

8696
1417
4137
6855

9299 9571

3

4718
7518
0316
3113
5907

8700
1491
4281
7068
9854

2638
5420
8200
0979
3756

6531
9304
2075
4845
7613

0379
3144
5907
8667
1427

4184
6940
9694
2446
5196

7945
0692
3437
6181
8922

1662
4401
7137
9872
2605

5337
8066
0794
3521
6245

8968
1689
4409
7126
9842

4998
7798
0596
3392
6187

8979
1770
4559
7347
0132

2916
5698
8478
1257
4033

6808
9581
2353
5122
7890

0656
3420
6183
8943
1702

4460
7215
9969
2721
5471

8220
0967
3712
6455
9197

1936
4674
7411
0146
2879

5610
8339
1067
3793
6518

9240
1961
4681
7398
0114

5278
8078
0876
3672
6466

9259
2049
4838
7625
0411

3194
5976
8756
1534
4311

7086
9858
2630
5399
8167

0932
3697
6459
9219
1978

4735
7491
0244
2996
5746

8495
1241
3986
6729
9471

2210
4948
7684
0419
3152

5883
8612
1340
4066
6790

9512
2233
4952
7670

5558
8357
1155
3951
ff745

9538
2328
5117
7904
0689

3473
6254
9034
1812

4588

7363
0136
2907
5676
8443

1209
3973
6735
9495
2254

5011
7766
0520
3271
6021

8769
1516
4260
7003
9745

2484
5222
7958
0692
3425

6156
8885
1612
4338
7062

9785
2505
5224
7941

9

038510657
8

5838
8637
1435
4231
7025

9817
2607
5396
8183
0968

3751
6532
9312
2090
4866

7640
0413
3184
5953

8720

1485
4249
7011
9771
2530

5287
8042
0795
3546
6296

9044
1790
4535
7278
0019

2758
5496
8231
0966
3698

6429
9158
1885
4611
7335

0057
2777
5496
8213
0928

Differ.

280

28

m

84
112
140
168
ItfG
224
252

279

28
56
84
112
140
167
195
223
251

278 '277

28
56
83
HI
139
167
195
222
250

28
55
83
111
139
166
194
222
249

1276

28
55
83
110
5;i:i8
6,166
7|193

8221
91248 248

276

28
55
83
110
138
165
193
220

1

2

3|

4

5

6

7
8
9

274 273

27
55
82
HO
137
164
192
219
247

27

55

82

109

137

1164

191

218

246

272,271
27

27

54

82

109

136

163

54

81

108

13d

163

lOOjlOO

218 217
245 244

Differ

18 LOGARITHMS N. 160(X> L. 204[

N.

1

2

3

4

2557

2528

3099

8

3371

9
3642

DiflVr. (

16D0

204120(

1471

1743

2014

2285

272 371 1

01

3913

4185

4456

4727

4998

5269

5541

5812

6063

6354

T

27

27

02

6625

6896

7167

74 3S

7709

7981

h-2b\

9522

8793

9064

■

M

"

03

9335

9606

9877

6148

6419

6690

0960

!231

1502

1773

■

lOftlOB
136|l36|

04

2052044

2314

2585

2856

3127

3397

3668

3939

4209

4480

I

05

4750

5021

5292

5562

5833

6103

6374

6644

6915

7185

t

)«3

163
190
217
244

06

7455

7726

7996; 8267

H537

8807

9078

9348

9613

9889

i

07

2060159

0429

06991 0969

1240

1510

1780

2050

2320

2590

»«■

08

2860

3131

3401

3071

3941

4211

4481

475)

5021

5291

09

5560

5830

6100

6370

6640

6910

7180

7449

7719

7989

1610

8259

8529

8798

9068

9339

9607

9877

0147

6416

6686

a-ornro

11

2070955

1225

1495

1764

2034

2303

2573

2842

3112

3381

Tp3

27
fl4

12

3650

3920

4189

4459

4728

4997

5267

5536

5605

6074

19

6344

6618

6882

7151

7421

7690

7959

9228

8497

8766

3 81

81

14

9035

9304

9573

9K42

0111

0380

0649

0918

1187

1456

6 13S
ftl63

lOS
135
161

19

20817S5

1994

2263

2532

2801

3070

3338

3607

3876

4145

16

4414

4682

4951

5220

54S8

5757

6026

6294

6563

6832

im

IBS

17

7100

7369

7637

7906

HI74

8443

8711

8980

9248

9517

S«3

216

18

9785

0054

0322

nwii

6859
3541

1127
3810

1395

4078

1664
4346

1932
4614

8200

4882

B42

19

2092468

2737

3006 3273

1620

&150

5416

5686

5954

6222

6490

6758

7026

7294

7562

21

7830

8098

8366

8634

H902

9170

9437

9705

9973

0241

_

2CS

m

22

2100508

0776

1044

1312

1579

1847

2115

2382

2650

2918

I

27

27

23

3185

3453

3720

3988

4255

4523

4790

5058

5325

5593

2
3

W

107

24

5860

6126

6395

6662

6930

7197

7464

7732

7999

8266

lo;

35

8534

8801

9068

9335

9603

9870

0137

0404

0671

6938

!>

1.14

26

2111205

1472

1740

21)117

2274

2541

2808

3075

3342

3609

^

JU

107

27

3876

4142

4409

4fi76

4943

5210

5477

5744

6010

6277

B

28
29

6544
9211

6811
9477

7078
9744

7344
fHill

7611
6277

7B7B
0544

8144
0810

8411
T077

8678
1343

8944
1610

!»

241

240

1630

2121876

^142

2409

2675

2942

3208

3474

3741

4007

4273

31

4540

4806

5072

5338

5605

5S71

6137

6403

6669

6935

32

7202

7468

7734

8000

8266

8532

8798

9064

9330

9596

17^

27
6.1

33

9862

6128

5394

OCfiO

<"|926

1191

1457

1T23

1989

^255

2

.'>3

34

2132521

2786

3052

331 S

3584

3849

4115

4381

4646

4912

3

«0

80

35

5178

5443

5709

5974

6240

6505

6771

703'?

7302

7568

4

I0«
133
ICO

lOG
133
l&U

36

7833

8098

8364

8629

8895

9160

9425

9691

9956

0221

6

37

2U04S7

0752

1017

1283

1548

1813

2078

2343

2609

2874

7

186

186

38

3139

3404

3669

3934

4199

4464

4730

4995

5260

5525

a 213

812

39

5790

6055

6319

65H4

6849

7114

7379

7644

7909

8174

9 33!l

239

1640

8438

8703

8968

9233

9498

9762

6027

6292

0556

0S21

41

2151086

1350

1615

18S0

2144

2409

2673

2938

3203

3407

42

3733

3996

4260

4625

47H9

5054

5319

5583

5847

6111

204

263

43

6376

6640

6904

7169

7433

7697

79C1

8226

8490

8754

26

36

44

9018

9282

9546

9S11

0075

0339

6603

0867

1 131

T395

A3

7»

63
79

45

2161659

1923

2187

2451

2715

2979

3243

3507

3771

4034

100

lOS

46

4298

4562

4826

5090

5354

5617

5881

6145

6409

6672

132

132

47

6936

7200

7463

7727

7991

8254

8518

H781

9045

9309

158
186

158
184
210
237

4A

9572

9S36

0U99

0363

6026

6890

1153

1416

1680

1943

49

N.

2172207

2470

2733

2997

3260

3523
5

3786
IT

4050
7

4313
8

4576
9

I

1

2

3

~4~

Differ. 1

N. 16500 L. 217

I

OF NUMBERS.

19

NL

1650
51
52
531
54

55
56
57

58
59

1660
61
62
63
64

65
66
67

68
69

1670
71
72
73
74

75
76
77
78
79

1680
81
82
83
84

85
86
87
88
.89

1690
91
92
93
94

95
96
97
98
99

N.

2174839
7471

2180100
2729
5355

7980
2190603
3225
5845
8464

2201081
3696
6310
8922

2211533

4142
6750
9356
2221960
4563

7165
9764
2232363
4959
7555

224014S
2740
5331
7920

2250507

3093
5677
8260
2260S41
3421

5999

5103
7734
0363
2991
5618

8242
0866
3487
6107
8726

1342
3958
6571
9184
1794

4403
7011
9617
2221

4824

•

7425
0024
2622
5219
7814

0407
2999
5590

8178
0766

3351
5935
8518
1099
3679

6257

2 I 3

8576 8833

2271151
3724
6296

8867

2281436

4004

1408
3982
6554

9124
1693
4260

65X0i^26
9(34 9390

2291697
4258
6818
9377

2301934

1953
4515
7074
9633
2189

1

53661 5629
7997i 8260
0626 0889
3254 3517
5880' 6143

8505, 8767
1128 1390
3749,4011
6369: 6631
8987 9249

1604' 1866
4219! 4481
6833 7094
9445 9706
2055. 2316

4925
7532
ol38
2741
5344

7945
5544
3142
5738
8333

0926
3517
6107
8696
1283

3868
6452
9034
1615
4194

6772
9348
1923
4496
7068

9638
2206
4774
7339
9903

2466
5027
7586
0144
2701

4664
7271
9877
2481

5084

7685
0284
2882
5479
8073

0667
3258
5849
8437
1024

3610
6194
8776
1357
3937

6515
9091
1666
4239
6811

9381
19S0
4517
7083
9647

2209
4771
7330
9888
2445

3

5892
8523
1152
3779
6405

9030
1652
4273
6893
9511

2127
4742
7355
9967
2577

5186
7793
0398
3002
5604

8205
0804
3402
5998
8592

1185
3777
6366
8955
1541

4127
6710
9293
1873
4452

7030
9606
2180
4753
7325

9895
2463
5030
7596
0159

2722
5283
7842
0400
2956

2389
5003
7617
0228
2838

5446
8053
0658
3262
5864

8465
1064
3661
6257

8852

1444
4036
6625
9213

1800

4385
6969
9551
2131
4710

7288
9863
2438
5011
7582

0152
2720
5287
7852
0416

2978
5539
8098
0656
3212

6418
9049
1677
4305
6930

9554
2177
4797
7417
0034

2650
5265

7878
(1489
3099

5707
8314
0919
3522
6124

8725
1324
3921
6517
9111

1704
4295
6884
9472
2059

4644
7227
9809
2389
4968

7545
0121
2695
5268
7839

0409
2977
5543
8108
0672

3234
5795
8354
0911
3467

8

5 6

6682
9312
1940
4567
7193

9816
2439
5059
7678
0296

2912
5526
8139
0750
3360

5968
8574
1179
3783
6334

8985
1583
4181
6776
9370

1963
4554
7143
9731
2317

4902
7485
0067
2647
5226

7803
0378
2953
5525
8096

0666
3233
5800
8365
0928

3490
6051
8609
1167
3723

9

6945
9575
2203
4830
7455

0079
2701
5321
7940
0558

3173

5788
8400
1011
3621

6229

8835
1440
4043
6645

9245
1843
4440
7036
9630

2222
4813
7402
9990
2576

5160
7743
0325
2905
5484

8060
0636
3210
5782
8353

0922
3490
6057
8621
1185

3746
6307
8865
1423
3978

8

7208
9838
2466
5092
7718

0341
2963
5583
8202
0819

3435
6049
8661
1272

3882

6489
9095
1700
4303
6905

9505
2103
4700
7-295
9889

2481
5072
7661
0248
2834

5419
8002
0583
3163

5741

8318
0893
3467
6039
8610

1179
3747
6313

8878
1441

4002
6562
9121
1678
4234

Differ.

2«4 26»

20
63
79
105
132
168
184
210
237

28
53

79
106
132
158
185
2U
288

262

9

258

28
52

77
103
120
155
181
208
0|232

257

Si
51

77
103
129
154
180
208
231

9

258

255

28
51

77
102
128
153
179

28
51

77
102
128
154
179
205*204
230*230

Differ.

c 2

20

U ir.A K

ITHM

s N. 171)00 L. 230j

N.

1

■2

3

4

5

(i

1'

S

9

U.lte,.

1700

2304489

4745

5000

5256

5511

5766

6022

6277

6532

6788

01

7043

7298

7554

7809

S064

8320

8575

8830

90S5

9340

02

9596

9851

0106

6361

6616

6871

1126

1381

1636

1891

03

2312146

2401

2656

2911

3166

3421

3676

3931

-tlS6

4441.

04

4696

4951

5206

5460

5715

5970

6225

6480

6734

6989

256

3551

05

7244

7499

7753

8009

8263

8517

8772

9026

9281

9536

1 2S

"m;

06

9790

6045

6299

6354

0808

1063

1317

1572

1826

«081

3 77

4 103

77

103

07

2322335

2590

2944

3098

3353

3607

3661

4116

4370

4624

08

4879

5133

5387

5641

5896

6150

6404

6659

6912

7166

a I3H

138

09

7421

7675

7929

8183

9437

6691

8945

9199

9453

9707

C 164

7 17a

153

179

1710

9961

6215

0469

6723

6977

1231

1485

1738

1992

J246

11

2332500

2754

3008

3262

3515

3769

4023

4277

4530

4784

9 230

230

12

503S

5291

5545

5799

6052

6306

6559

6813

7067

7320

IS

7574

7827

8081

8334

8588

8841

9095

9348

9601

9855

14

2340108

0362

0615

0869

1122

1375

1628

1991

2135

2368

Vj

2641

2894

3148

3401

3654

3907

4160

4414

4667

4920

1

16

5173

5426

5679

5932

6185

6438

6691

6944

7197

7450

t1

3 SI

35
51

17

7703

7956

8209

9462

8715

8967

9220

9473

9726

9979

18

2350232

0484

0737

0990

1243

1495

1748

2001

2253

2506

3 7fi

7«

19

2759

3011

3264

3517

3769

4022

4274

4527

4779

5032

4 103

5 137

6 133

101

127

152

1720

5284

5537

5789

6042

6294

6547

6799

7052

7304

7556

21

7809

8061

8313

8566

8819

9070

9323

9575

9627

0079

7 178

177

23

2360331

0584

0S36

1098

1340

1692

1844

2097

2349

2601

8 203

303

23
24

2653

S105

3609

6128

3S61
6380

4113
6632

4365

4617

4869

5121
7639

91229

228

5373

5625

5876

6864

7136

7387

25

7891

8143

8394

8646

8896

9150

9401

9653

9905

6156

26

2370408

0660

0911

1163

1414

1666

1917

2169

2420

2672

252 251

27

2923

3175

3426

3678

3929

4181

4432

4693

4935

5186

T 25 25

28

5437

5689

5940

6191

6443

6694

6945

7196

7448

7699

2 50' CO

29

7950

8201

8452

8703

8955

9206

9457

9706

9959

0210

3 78 76
1 101 UH>
5 I2S 126

1730

2380461

0712

0963

1214

1465

1716

1967

2216

2469

2720

31

2971

3222

3472

3723

3974

4225

4476

4727

4977

5328

II 15i 151

32

3479

5730

5980

6231

6482

6732

69S3

7234

7484

7735

7 176 17C

8 202 201

9 227 22«

33

7986
2390491

8236

0741

8487
0992

8737
1242

8988
1493

9238
1743

9469
1993

9739
2244

9990
2494

6240
2744

34

35

2995

3245

3495

3746

3996

4246

4496

4747

4997

5247

36

5497

5747

5998

6248

6498

6748

6998

7246

7498

7748

37

7998

8248

8498

8748

6998

9246

9499

9748

9999

0248

38

2400498

0748

0997

1247

1497

1747

1997

2247

2496

2746

350

249

39

2996

3246

3495

3745

3995

4244

4494

4744

4993

5243

1 25

-B

1740

5492

5742

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6241

6491

6740

6990

7239

7489

7738

3 75

4 100

M
75

ion

41

7988

8237

8487

8736

6985

9235

9464

9734

9983

0232

42

2410482

0731

0980

1229

1479

1728

1977

2226

2476

2725

5 125

125

43

2974

3223

3472

3721

3970

4220

4469

4718

4967

5216

SIM

U!l

44

5465

5714

5963

6212

6461

6710

6959

7208

7457

7705

7 175

174
199

46
AC)

7954
2420442

8203
0691

9452
O940

8701
1189

8950
1437

9199

1686

9447
1935

9696
2183

9945
2432

6194

2680

sl^

824

47

2929

3178

3426

3675

3923

4172

4420

4669

4917

5166

48

5414

5663

5911

6160

6408

6656

6905

7153

7401

7650

49

7898

8146

8395

8643

8891

9139
5

9388
6

9636

7

9884

01 32
9

N.

1

2

3

4

ItiffeK

N. 17300 L. 243

N."

1750
51
52
53
54

53
5G
57

58
59

1760
61
62
63
64

65
6fi
67
68
69

1770
71
72
73
74

75
76

77
78
79

1780
81
82
83

84

85
86
87
88
89

1790
91
92
93
94

95
96
97
98
99

N.

2430380
2861
5341
7819

2440296

2771
5245
7718
2450189
2658

5127
7594
2460059
2523
4986

7447

9907

2472365

4823

7278

9733
2482186
4637
7087
9536

2491984
4430
6874
9318

2501759

4200
6639
9077
2511513
3949

6382
8815
2521246
3675
6103

8530
2530956
3380
5803
8224

2540645
3063
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7897

2550S12

1

0629
3109
5589
8067
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3019
5492
7965
0436
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5373
7840
0306
2769
5232

7693
6153
2611
5068
7524

9978
2431
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7332
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2228
4674
7119
9562

2004

4444
6883
9321
1757
4192

6625
9058
1489
3918
6346

8773
1198
3622
6045
8466

0886
3305
5722

8138
0553

1

2

OF NUMBERS.

"T4"

0877|
3357 j
5837
8315
079 Ij

3266
5740
8212
0683
3152

1373

1125
3605 3853'
6085 6332

5620

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0552
3016

5478

7939
0399
2857
5314
7769

5223
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5127
7577
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8562
1039

3514
5987
8459
0930
3399

5867
8333
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3262
5724

8185
5645
3103
5559
8015

'o469
2921
5372
7822
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2473
4919,
7363,
9806
2248

4688
7127
9564
2001
4435

6869
9301
1732
4161
6589

9016
1441
3865
6287
8709

1128
,3547
5964
8380
0794

2718
5163
7607
0050
2492

4932
7371
9808
2244
4679

8810
1286

3761
6234
8706
1177
3646

6114
8580
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3508
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8431
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5714 J
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5515;

2962 !

5408.
7852
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2488

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7112 7355
9544 9787
1975 2218
4404 4647
6832 7074

9258 9501

1683 1926

4107 4349.

6529 6772 ,

8951 9193.
i !
1370 1612

3789 4030 ;

6206 6447 i

8621 8863

1036 1277

1621
4101
6580
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4008
6482
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1424
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6360
8826
1291
3755
6217

8677
1136
3594
6051
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5959
3412
5862
8312
0760

3207
5652
8096
0539

2980

5420
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5295
2731
5166

7599
5030
2461
4889
7317

9743
2168
4592
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1854
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9104
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5

6

1869
4349
6828
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1781

4256
6729
9200
1671
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6607
9073
1538
4001
6463

8923
1382
3840
6296
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1205
3657
6107
8557
1005

3451
5897
8340
5783
3224

5664
8102
5539
2975
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5273
2703
5132
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9986
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4834
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2096
4514
6931
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6

2117
4597
7076
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2029

4503
6976
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1918
4386

6854
9320
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4247
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9169
1628
4086
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1450
3902
6352
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1249

3696
6141

8585
1027
3468

5908
8346
5783
3218
5652

8085
5516
2946
5375

7802

5228
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5076
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9919

2338
4756
7172
9587
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8

7

2365
4845
7324
9801
2276

4750
7223
9695
2165
4633

7100
9566
2030
44931
6955

9415
1874
4331
6787
9242

1695
4147
6597
9047
1494

3941
6385
8829
1271
3712

6151
8590
1026
3462
5896

8328
5759
3189
5618

8045

5471
2895
5318
7740
0161

2580
4997
7414
98-29
2242

9

8

2613
5093
7571
5048
2524

4998
7470
9942
2411
4880

7347
9813
2277
4740
7201

9661
gl20
4577
7033
9487

1940
4392
6842
9291
1739

4185
6630
9073
1515
3956

63^

8833
1270
3705
6139

8571
1002
3432
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8288

0713
3138
5561

79821
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2822
5239
7655
5070
2484

'3

u

5

•7
8
9

246

25

49

74

98

123

148

172

197
221

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25
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172
196
221

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243

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171
195
220

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194

219

1242 241

24|
48
73
97

24
48
72
96

121,121
.,145 145
7 169 169
8,194 193
9I218 217

Differ.

22

LOGARITHMS . N. 18000 L. 255

N- 1 1

2

3

4

5

6

7

8

9

D

Pro.

1800 2552725.2966

3208

3449

3690

8931

4172

4414

4655

4896

240

01 5137

5378

5619

5860

6102

6843

6584

6825

7066

7307

241

1

24

02 7548

7789

8030

8271

8512

8753

8994

9235

9475

9716

2
3

4

48

72
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03 9957

0198

5439

0680

0921

1161

1402

1643

1884

2125

04 2562365

2606

2847

3087

8828

3569

8810

4050

4291

4581

6

120

05 4772

5013

5253

5494

5784

5975

6215

6456

6696

6987

6

7
8

144
184

06 7177

7418

7658

7899

8189

8380

8620

8860

9101

9841

192

07 9582

9822

0062

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0543

0783

1023

1264

1504

1744

9

216

08 2571984

2224

2465

2705

2945

8185

3425

3665

8905

4146

289

I 24

09 4386

4626

4866

5106

5846

5586

5826

6066

6806

6546

240

ISIO 6786

7026

7266

7506

7745

7985

8225

8465

8705

8945

2

48

11 9185

9424

9664

9904

0144

0383

0628

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1108

1848

3
4

6

72

96
120

12 2581582

1822

2061

2301

2541

2780

8020

3259

8499

8788

13, 8978

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4457

4697

4936

5176

5415

5655

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6138

6

143

14

6873

6612

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7091

7330

7570

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8048

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7

187

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9963 0202

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17. 3549

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4505

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4983

5222

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. 18| 5939

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7133

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6437

6675

6914

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23 7867

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8820

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9-296

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8

190

24 2610248

0486

0725

0963

1201

1439

1677

1915

2153

2391

288

214

25 2629

2867

3105

3843

3580

8818

4056

4294

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4770

287

26 5008

5246

5483

5721

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6107 6435

6672

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27 7385

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3
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71
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9999

0237

0475

0712

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1

1425

1662

1900

29 2622137

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3324 1 3562

3799

4036

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119

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4748

4986

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5460

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7

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31

6883

7121

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8069 8306

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190

32

9255

9492

9729

9966

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0440 0677

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1151

1388

9

21S

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2631625

1862

2098

2335

2572

2809 3046

3283

3520

3757

287

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34

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4230

4467

4704

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5177 5414

5651

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7544 7780

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7470

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8650

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9358 9594

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1010

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2189

2425

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2896

3132

3368

3604

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4075 4311

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5725

5960

6196

6431 6667

6903

7138

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44

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7845

8080

8316

8551

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9022

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N. 18500 L. 267

OF NUMBERS.

23

N.

1850
51
52
53
54

55
56
57

58
59

I860
61
62
63
64

65
66
67
68
69

1870
71
72
73
74

75
76

77
78
79

2671717
4064
6410

8754
2681097

1

1952
4299
6644
8989
1332

3439 3673

5780

8119

2690457

2794

5129
7464
9797
2702129
4459

6788
9116
2711443
3769
6093

8416
2720738
3058
5378
7696

2730013
2328
4643
6956
9268

1880 2741578

81
82
83

84

85
86
87
88
89

1890
91
92
93
94

95
96
97
98
99

1 N.

3888

6196

8503

2750809

3114

5417

7719

2760020

6014
8353
0691

3028

5363
7697
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2362
4692

7021
9349
1676
4001
6325

8648
0970
3290
5610
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0244
2560
4874
7187
9499

1809
4119
6427
8734
1039

3344
5647
7949
0250

2320! 2549

4618 4848
6915|7145
9211:9441

2771506
3800

6092
8383
2780673
2962
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1736
4029

6321
8612
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3191
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5596
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3023
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2271
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3805
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9

3830
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7230
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4388

6686
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1277
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8154
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5021
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9

D

234

233

Pro.

234
23

47
70
94

117
140
164

187
211

I
2
3
4
5
6

7

8
9

233

232

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70

93

117

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210

232

231

23
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229

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8 184
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7 160

8 183
U2(Hi

^:^*

24

•logarithms N. 19000 L. 278!

N.

1900

1
7765

2

7993

3

8222

4

8450

5 6 7

8679(8907 9136

8

9364

9

9593

D

Pro.

228

2787536

01

9821

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0735

0963 1192 1420

1648

1877

1

23

02

2792105

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3247 3475 8703

3931

4160

2

3
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5529 5757. 5985

6213

6441

04

6669* 6898

7126

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8038 8266

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5

114

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9634

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6

7

8

137
160
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1457

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3507

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4190

4418

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4873 5101

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5556

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08

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7832

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09

8059

8287

8514

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1243

1470

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2152

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45

11

2607

2834

3061

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3516

3743

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4425

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12

4879

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5883

5560

5787

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6242, 6469

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6923

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5

13

7150

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7604 7831

8058

8285

8512 8739

8966

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6

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159

15

2821688

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2368

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3048

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8
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204

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7127

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18

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46

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2107 2334

1

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1920

3012

3238

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3917

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4821

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/

4

90
113
136
158

21

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22

7534

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7986 8212

8438

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7

23

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6245 0470

0696

0922

1148 1373

1599

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8

181

24

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2276

2502 2728

2953

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3405 3630

3856

4082

9

203

25

4307

4533

4759 4984

5210

5435

5661

5886

6112

6837

225

26

6563

6788

7014 7239

7465

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7916 8141

8366

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23

27

8817

9043

92689493

9719

9944

0169 0394

0620

0845

2

45

28

2851070

1296

1521 1746

1971

2196

2422 2647

2872

3097

3

A

68

29

3322

3547

3773 3998

•

4223

4448

4673 4898

5123

5848

6'll3

1930

5573

5798

6023 6248

6473

6698

6923

7148

7373

7598

225

C135

7 158

8 180

31

7823

8048

8273 8497

8722

8947

9172

9397

9622

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32

2860071

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0521 0746

0970

1195

1420

1644

1869

2094

9 203

33

2319

2543

2768 2993

3217

3442

3666

3891

4116

4340

34

4565

4789

5014 5238

1

5463

5687

5912

6136

6361

6585

224

1 nalk

35

6810

7034

7259 7483

7707

7932

8156

8381

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2

22

45

36

9054

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9502 9726

9951

0175

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37

2871296

1520

1745 1969

2193

2417

2641

2865

3090

3314

4

90

38

3538

3762

3986 4210

4434

4658

4882

5106

5330

5554

224

5

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112
134

157

39

5778

6002

6226 6450

6674

6898

7122

7346

7570

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7

1940

8017

8241

8465 8689

8913

9136

9360

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8

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179

41

2880255

0479

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1374

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42

2492

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2939 3163

3387

3610

3834

4057

4281

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43

4728

4952

5175 5399

5622

5845

6069

6292

6516

6739

1

22

44

6963

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7409 7633

7856

8079

8303

8526

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2
3

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67

45

9196

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9643 9866

0089

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4

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2891428

1652

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112
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3660

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4106 4329

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9

1)

0'20l

N.

1

It8.

N. 19500 L. 290

1

OF NUMBERS.

25

1950
51
52
53
54

55
56
57

58
59

1950
61
62
63
64

65
66
67
68
69

1970
71
72
73
74

75
76

77
78
79

1980
81

82
83
84

85
86
87
88
89

1990
91
92
93
94

95
96
97
98
99

N.

2900346
2573
4798
7022
9246

2911468
3689
5908
8127

2920344

2561
4776
6990
9203
2931415

3626
5835
8044
2940251
2457

4662
6866
9069
2951271
3471

5671

7869

2960067

2263

4458

6652
8845
2971037
3227
5417

7605
9792
2981979
4164
6348

8531
2990713
2893
5073
7252

94*29
3001605
378 1
5055
8128

0569
2795
5021
7245
9468

1690
3911
6130
8349
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7211
9424
1636

3847
6056
8264
0472
2678

4883
7087
9289
1491
3691

5891
8089
0286
2482
4677

6871
9064
1256
3446
5636

7824
6011
2197
4382
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5291
7469

9647
1823
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6172
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1

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3018
5243
7467
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1912
4133
6352

8570
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3004
5219
7433
9645
1857

4068
6277
8485
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5103
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6111
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2702
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7091
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1475
3665
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8043
0230
2416
4601
6785

8967
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4216
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4

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3240 3463 II

5466

5688

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7912

9912

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7875

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0726 0945

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3686 3908
5910 6133
8134 8356
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2578 2800
4799 5020
7018 7240
9236 9458
1453 1674

3668

5883
8097
0309
2520

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6940
9147
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5764
7968
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6105
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6770 6990

8968
1165
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4979
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3727
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4637
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1170
3346
5520
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4576
6800
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3466
5686
7905
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2339

4554
6769
8982
1194
3405

5614
7823
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2237
4442

6646
8849
1051
3251
5451

7650
9847
2043
4238
6433

8626
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3008
5198
7386

9574
1760
3945
6129
8313

0494
2675
4855
7034
9211

1388
3563
5737
7911
0083

D

222

221

9

220

219

218

Pro.

222

22
44

07
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133
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178
200

221

22
44

06

88

111

133

155

177

199

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22

44
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132
151

170
198

219

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197

218

1 22

2 44
3- 65
4; 87

5 109

6 131
7,163
8|174
9(196

VMk,

26

LOGARITHMS

N. 20000 L. 301

N.

1
0517

2000

3010300

01

2471

2688

02

4641

4858

03

6809

7026

04

8977

9194

05

3021144

1360

06

3309

3526

07

5474

5690

08

7637

7853

09

9799

0016

2010

3031961

2177

11

4121

4337

12

6280

6496

13

8438

8653

14

3640595

0810

15

2751

2966

16

4905

5121

17

7059

7274

18

9212

9427

19

3051363

1578

2020

3514

3729

21

5663

5878

22

7812

8026

23

9959

5174

24

3062105

2320

25

4250

4465

26

6394

6609

27

8537

8752

28

3070680

0894

29

2820

3035

2030

4960

5174

31

7099

7313

32

9237

9451

33

3081374

1587

34

3509

3723

35

5644

5858

36

7778

7991

37

9910

0123

38

3092042

2255

39

4172

4385

2040

6302

6515

41

8430

8643

42

3100557

0770

43

2684

2896

44

4809

5021

45

6933

7145

4C

9056

9269

47

3111178

1391

48

3300

3512

49

5420

5632
1

N.

2

0734
2905
5075
7243
9411

1577
8742
5906
8070
0232

2393
4553
6711
8869
1026

3182
5336
7490
9642
1793

3944
6093
8241
0388
2534

4679
6823
8966
1108
3249

5388
7527
9664
1801
3936

6071
8204
5337
2468
4598

6727
8856
0983
3109
5234

7358
9481
1603
3724
5813

2

0951
3122
5-291
7460
9627

1794
3959
6123
8286
0448*

2609
4769
6927
9085
1242

3397
5552
7705
9857
2008

4159
6308
8456
5603
2749

4894
7037
9180
1322
3463

5602
7741
9878
2015
4150

62A4
8418
0550
2681
4811

6940
9068
1195
3321
5446

7570
9693
1815
3936
6055

"3~

4

5

1168

1386

3339

8556

5508

5725

7677

7893

9844

0061

2010

2227

4175

4392

6339

6556

8502

8718

0664

0680

2825

3041

1984

5200

71,43

7359

9301

9516

1457

1673

3613

3828

5767

5982

7920

8135

0072

0288

2224

2439

4374

4589

6523

6737

8671

8885

0817

1032

2963

3178

5108

5322

7252

7466

9394

9609

1536

1750

3677

3891

5816

6030

7954

8168

5092

0306

2228

2442

4363

4577

6498

6711

8631

8844

5763

0976

2894

3107

5024

5237

7153

7366

9281

9494

1408

1621

3534

3746

5659

5871

7783

7995

9905

0117

2027

2239

4148

4360

6267

6479

4

5

6

8

1603 1820 2037

3773 3990; 4207

5942

8110

0277

2443
4608
6772
B935
1096

3257
5416
7575
9732

18S8

4043
6198
8351
0503
2654

4803
6952
9100
1247
3392

6159 6376
832*/ j 8544
0494.0711

2660
4825
6988
9151
1312|

3473
5632
7790
9948
2104

4259
6418

2876
5041
7204
9367
1528

3689
5848
8006
0163
2319

4474
6628

8566 8781
0718 0933

2869

5018
7167
9315
1461
8607

5537 5751
7680| 7895
9823 0087
1964' 2178
4105 4319

6244
8382
0519
2655
4790

6924
9057
1189
3320
5450

6458
8596
0733
2869
5004

7138
9271
1402
3533
5663

7579 7792
9707 9919
1833 2046
3959 4171

6084

8207
0330
2451
4572
6691

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28

LOGARITHMS

N. 21000 L. 322

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05
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07
08
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11
12
13
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15
16
17

18
19

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21
22
23
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25
26
27

28
29

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31
32
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35
36
37
38
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N. 21500 L. 332 of numbers.

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30

LOGAK1THM8

N. 22000 L. 342

N.

2200 3424227

01 6200

02 8173

03 3430145

04 2116

05 4086

06 6055

07 8023

08 9991

09 3441957

2210 3923

1 1 5887

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13 9814

14 3451776

15 3737

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19 3461573

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24 3471348

25 3300

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29 3481101

2230
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2775
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44 3510229

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46
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3933
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1964

3921

5877
7831
9785
1738

3691
5642
7592
9542
1490

3243 3438
5190, 5385
7136,7331
9082 9276
1026' 1220

2970 3164
4912 5106
6854 7048
8795 8989
0735 0929

3

2674
4612
6550

8486
0422

4819
6792
8765
0736
2707

4677
6646
8614
0581
2547

4512
6477
8440
0403
2365

4325
6285
8245
0203
2160

4117
6072
8027
9981
1984

3886
5837

7787
9737
1685

3633

5580
7526
9471
1415

3358
&301
7242
9183
1123

3016
6990
8962
0933
2904

4874
6842
8810
0777
2743

4709
6678
8636
0599
2561

4522
6481
8440
0399
2856

4312
6268
8222
0176
2129

4081
6032
7982
9931
1880

3828
5774
7720
9665
1609

3552
5495
7436
9377
1317

2868 3062 3256
4806 5000| 5194
6743 6937:7131
8680 887419067

0616 0809

2357 2550
4*291 4484
6*224 6417
8156 8349'
0088 0*281 :

1 I 2

2744
4678
6611
8543
0474

1003

2937
4871
6804
8786
0667

5

6

5214 5411
7187 7384
9159 9356
1131 1328

3101

3298

5071 5268
7039 7236
9007 9204
0974; 1171
2940 3137

4905| 5102
6869 {7066
8833 9029

0795
2757

4718
6677
8636
0594
2551

4508
6463
8418
0371
2824

4276
6227

8177
0126
2075

■ 4022

15969

7915

9860

1804

'3747
5689

i7630
9571
1511

1 3449

5387

7325

9261

1 1196

3131
5064
6997
89*29
^60

5

u991
2953

4914
6873
8832
0790
2747

4703
6659
8613
0567
2519

4471
6422
8372
0321
2270

4217
6164
8109
0054
1998

3941

5883
7825
9765
1705

3643
5581
7518
9454
1390

3324
5258
7190
9122
1058

5608
7581
9554
1525
3495

5464
7433
9401
1367
3333

5298
7262
9225
1188
3149

5110
7069
9028
0986
2943

4899
6854
8808
0762
2715

4666
6617
8567
0516
2464

4412
6358
8304
0248
2192

4135
6077
8019
9959
1898

3837
5775
7712
9648
1583

3517
5451
7363
9315
1*246

5806 6003
7779 7976
9751 9948
1722 1919
8692 8889

5661
7680
9597
1564
8530

5495
7459
9422
1384
8345

5306
7265
9224
1182
3138

5094
7050
9004
0957
2910

4861
6812
8762
0711
2659

4606
6558
8498
0443
2387

4330
6*272
8213
0158
2092

4031
5969
7905
9841
1777

3711
5644
7577
9508
1439

9

5858
7827
9794
1761
8726

5691
7655
9618
1580
8541

5502
7461
9420
1377
8384

5290
7245
9199
1153
3105

5056
7007
8957
0906
2854

4801
6747
8698
0637
2581

4524
6466
8407
0347
2286

4*225
6162
8099
0035
1970

3904
5887
7770
9701
1682

9

D

197

196

195

194

198

D

Pro.

198

80
40
50

7»

90

no

130
158
178

197
1

3

4
6
8

7
8
9

79

118
138
158

177

196
SO

59

78

98
118
137
157
17c

195
1

21

3
4
5
6 117

50
78

137
156
178

194

19

58
78
97

no

136
155
91175

Pit.

N. 5

Si5UU I

i. ;552

OF NUMBERS.

N.

I
2018

2
2211

3
24U4

4

2597

5

2790

6

7

3176

2250

3521825

2983

51

3755

3948

4141

4334

4527

4720

4912

5105

52

5684

5877

6070

6262

6455

6648

6841

7034

53

7612

7805

7997

8190

8383

8576

8768

8961

54

9539

9732

9924

5117

D310

5502

5695

5888

55

3531465

1658

1851-

2043

2236

2428

2621

2813

56

3891

3583

8776

3968

4161

4353

4546

4738

57

5316

5508

5700

5893

6085

6278

6470

6662

58

7239

7432

7624

7816

8009

8201

8393

8596

59

9162

9355

9547

9739

9931

5123

5316

5508

2260

3541084

1277

1469

1661

1853

2045

2237

2429

61

8006

8198

3390

3582

3774

3966

4158

4350

62

4926

5118

5310

5502

5694

5886

6078

6270

68

6846

7037

7229

7421

7613

7805

7997

8189

64

8764

8956

9148

9340

9531

9723

9915

5107

6b

8550682

0874

1066

1257

1449

1641

1832

2024

66

2599

2791

2982

3174

3366

3557

3749

3940

67

4515

4707

4898

5090

5281

5473

5664

5856

6d

6431

6622

6813

7005

7196

7388

7579

7771

69

8345

8536

8728

8919

9111

9302

9493

9685

2270

3560259

0450

0641

0832

1024

1215

1406

1598

71

2171

2363

2554

2745

2936

3127

3319

3510

72

4083

4274

4466

4657

4848

5039

5230

5421

73

5994

6185

6376

6568

6759

6950

7141

7332

74

7^05

8096

8287

8478

8668

8859

9050

9241

75

9814

6005

6196

0387

5578

5768

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1150

76

8571728

1913

2104

2*295

2486

2677

2867

3058

77

3630

3821

4012

4202

4393

4584

4775

4965

78

5587

5728

5918

6109

6300

6490

6681

6872

79

7443

7684

7824

8015

8205

8396

8586

8777

2280

9848

9539

9729

9920

5110

5301

5491

5682

81

3581253

1443

1634

1824

2014

2205

2395

2585

82

8156

3347

3537

3727

3918

4108

4298

4488

88

5069

5249

5440

5630

5820

6010

6200

6391

84

6961

7151

7341

7531

7722

7912

8102

8292

85

8862

9052

9242

9432

9622

9812

5002

5192

86

8590762

0952

1142

1332

1522

1712

1902

2092

87

2662

2852

3041

3231

3421

3611

3801

3991

88

4560

4750

4940

5130

5319

5509

5699

5889

89

6458

6648

6837

7027

7217

7406

7596

7786

2290

8355

8544

8734

8924

9113

9303

9493

9682

91

3600251

0440

0630

0820

1009

1199

1388

1578

92

2146

2336

2525

2715

2904

3093

3283

3472

93

- 4041

4230

4419

4609

4798

4987

5177

5366

94

5934

6123

6313

6502

6691

6881

7070

7259

95

7827

8016

8205

8395

8584

8773

8962

9151

96

9719

9908

0097

0286

0475

(1664

5854

1043

97

3611610

1799

1988

2177

2366

2555

2744

2933

98

3500

8689

8878

4067

4256

4445

4634

4823

99

N.

5390

5579

5768

5956

3

6145
4

6334
5

6528

6712

1

2

1 6

1 7

31

3369
5298
7226
9154
1080

3006
4931
6855

8778
5700J

2621
4542
6462
8381
5299

2216
4132
6048
7962
9876

1789
3701
5612
7523
9432

1341
3249
5156
7062
8967

5872
2776
4679
6581
8482

5382
2282
4181
6078
7976

9872
1767
3662
5555

7448

9341
1232
3122
5012
6901

9

3562
5491
7419
9346
1273

3198
5123

7047
8970
5892

2814
4734
6654
8572
5490

2407
4324
6239
8154
5067

1980
3892
5803
7714
9623

1532
3440
5347
7258
9)58

1062
2966
4869
6771
8672

5572
2472
4370
6268
8165

5061
1957
3851
5745
7638

9530
1421
3311
5201
7090

9

191

190

189

1)

Pro.

193

193

1

19

2

39

3

68

4

77

6

97

G116

7 ISfi

H 154

9 174

192

192

19
38
68

77
9«
116
134
164
173

191

1
2
3
4

6
G

7
8
9

19

38

67

7tf

96

116

134

163

172'

190

1
2
3

4
6
6

7
8

19

38

67

76
96

114

133

162

171

189

1
2
3

4
6

19
3»

67
76
9J^

I)

6,113

7 132

8 161

9 170

Pit.

32

LOGARITHMS N. 23000 L. 361

N.

2300

I
7467

2

76t>d

3

7'845

4

8034

5
8222

6
8411

7

8600

8 1 y

8789 8977

D ivo.

3617278

01

9166

9355

9544

9732

9921

0110

0298

0487

0676 0865

■ ^^^^

02

3621053

1242

1430

1619

1808

1996

2185

2374

2562 2751

•

189

1 . « ^«.

03

2939

3128

3317

3505

3694

3882

4071

4259

4448 4636

J

9

04

4825

5013

5202

5390

5579

5767

5956

6144

6332 6521

2

3

67

05

6709

6898

7086

7275

7463

7651

7840

8028

8216 8405

4

76

06

8593

8781

8970

9158

9346

9535

9723

9911 0099 0288 1

o

95
113

07

3630476

0664

0852

1041

1229

1417

1605

1794

1982 2170.

7

132

08

2358

2546

2734

2923

3111

3299

3487

3675 3863 4051 |

8

151

09

4239

4427

4615

4804

4992

5180

5368

5556

5744 5932

188 ?

170

2310

6120

6308

6496

6684

6872

7060

7248

7436

7624 7812

11

7999

8187

8375

8563

8751

8939

9127

9315

9503 9690

12

9878

0066

0254

0442

0630

0817

T005

1193

1381 1569

188

13

3641756

1944

2132

2320

2507

2695

2883

3070

3258 3446

1
2
3

19
38
50

14

3634

3821

4009

4197

4384

4572

4759

4947

5135 5322

15

5510

5698

5885

6073

6260

6448

6635

6823

7010 7198

4

7«

16

7386

7573

7761

7948

8136

8323

8511

8698

8885 9073

6

94
113
13t!

17

9260

9448

9635

9823

0010

0197

0385

0572

0760 0947

18

3651134

1322

1509

1696

1884

2071

2258

2446

2633 2820

'8

150

19

3007

3195

3382

3569

3757

3944

4131

4318

4505 4693

1

01

169

1

2320

4880

5067

5254

5441

5629

5816

6003

6190

6377 6564

21

6751

6939

7126

7313

7500

7687

7874

8061

8248 8435

22

8622

8809

8996

9183

9370

9557

9744

9931

0118 0305

187

187

23

3660492

0679

0866

1053

1240

1427

1614

1801

1987,2174

1

19

24

2361

2548

2735

2922

3109

3296

3482

3669

385614043

1

2
3

37

56

25

4230

4416

4603

4790

4977

5163

5350

5537

5724 5910

4

75

26

6097

6284

6471

6657

6844

7031

7217

7404

7 59 l| 7777

5
6

7

a

94
112
131

27

7964

8150

8337

8524

8710

8897

9083

9270

9457 9643

28

9830

0016

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0389

0576

0762

0949

1135

1322; 1508

150

29

3671695

1881

2068

2254

2441

2627

2814

3000

3186:3373

9

168

2330

3559

3746! 3932

4118

4305

4491

4677

4864

6050 5236

31

5423

5609

5795

5982

6168

6354

6540

6727

6913

7099

32

7285

7472

7658

7844

8030

8217

8403

8589

8775 8961

186

33

9147

9334

9520

9706

9892

0078

0264

0450

0636 0822

1

19

34

3681009

1195

1381

1567

1753

1939

2125

2311

2497

2683

186

2

37

35

2869

3055

3241

3427

3613

3799

3985

4171

4357

4542

4

74

36

4728

4914

5100

5286

5472

5658

5844

6030

6215 6401

6

9S

37

6587

6773

6959

7145

7330

7516

7702

7888

8074 8259

6

7

a

lis

130
149

38

8445

8631

8817

9002

9188

9374

9559

9745

9931

0117

39

3690302

0488

0674

0859

1045

1230

1416

1602

1787

1973

187

2340

2159

2344

2530

2715

2901

3086

3272

3458

3643

3829

41

4014

4200

4385

4571

4756

4942

5127

5313

5498

5683

42

5869

6054

6240

6425

6611

6796

6981

7167

7352

7538

185

43

7723

7908

8094

8279

8464

8650

8835

9020

9205

9391

1

19

44

9576

9761

9947

0132

0317

0502

0688

0873

1058

1243

2
3

4

37
66
74

45

3701428

1614

1799

1984

2169

2354

2540

2725

2910

3095

46

3280

3465

3650

3835

4020

4206

4391

4576

4761

4946

.^a ■ V %

47

5131

5316

5501

5686

5871

6056

6241

6426

6611

6796

185

6 111
7130
8 148

48

6981

7166

7351

7536

7721

7906

8091

8275

8460

8645

49

8830

9015
1

9200

2

9385
3

9570
4

9754
5

9939
6

0124

7

0309

8

0494
9

D

9 187

N.

]

p.

N. 23500 L. 371

OF NUMBERS.

33

N.

2350

3710679

51

2526

52

4373

53

6219

54

8065

55

9909

56

3721753

1

57

58
59

0863
2711
4558
6104
8249

o094
1937
35961 3780
5438 5622

7279

2360 9120
6113730960
2799
4637
6475

8311
3740147
1983
3817
5651

7483
9316
3751147
2977
4807

6636
8464
3760292
2119
3944

5770
7594
9418
3771240
3063

4884
6704
8524
3780343
2161

3979
5796
7612
9427
3791241

3055
4868
6680
8492
3800302

7464

9304
1144
2983
4821
6658

8495
0331
2166
4000
5834

7667
9499
1330
3160
4990

6819
8647
0475
2301
4127

5952
7776
9600
1423
3245

5060
6886
8706
0525
2343

4161
5977
7793
9608
1423

3237
5049
6862
6673
0484

1

104S
2896
4742
6588
8434

0278
2122
3964
5806
7648

3

1233
3080
4927
6773
8618

5462
2306
4149
5991
7832

9488 9672
1328 1512

3167
5005

3350
5189

6842! 7026

8679 8862
0515 0698

2350
4184

2533
4367

6017 6201

7850 8033
9682.9865
1513,1696
3343; 3526
5173 5356

7002
8830
0657
2484
4310

6135
7959
9782
1605
3427

5248
7068

8888
0707
2525

4342
6159
7975
9790
1604

3418
5231
7043
8854
0665

7185
9013
0840
2666
4492

6317
9141
9965
1787
3609

5430
7250
9070
0889
2707

4524
6341
8156
9971
1786

3599
5412
7224
9035
0846

3

1418
3265
5112
6957

8802

0647
2490
4333
6175
8016

9S56
1696
3534
5372
7210

9046
0882
2716
4551
6384

8216
0046
1879
3709
5539

7367
9195
1023
2849
4675

6499
8323
0147
1969
3791

5612
7432
9252
1071
2889

4706
6522
8338
0153
1967

3780
5593
7405
9216
1027.

O

()

1603
3450
5296
7142
89S7

(1831
2674
4517
6359

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1879
3718
5556
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9230
1065
2900
4734
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8400
5231
2062
3892
5722

7550
9378
1205
3032

4857

6682
8506
0329
2152
3973

5794
7614
9434
1252
3070

4887
6704
8519
0334
2148

3962
5774
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9397
1208

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1787
3635
5481
7327
9171

1015
2859
4701
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8384

0224!
2063
3902
5740!
7577:

9413'
1249
3083
4917
67 50;

8583
5414
2245
4075
5905'

1972
3819
5666
7511
9356

1200
3043
4885
6727
8568

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u)GAinT»MS N. 29000 h. 462

N.

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1

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D ! p.- i

N. 39500 L. 469 of numbers. 45

N. 1

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3

4

5

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7

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94 2518

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N.I

1

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LOGARITHMS N. 30000 L. 477 )

N.

1

2

3

4

5

6

7

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Pro.

3000

1771213

1357

1502

1647

1792

1936

20S1

2226

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01

2660

2805

2949

3094

3239

3383

3528

3673

3818

3962

145

02

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4252

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4541

4686

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5119

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9271

9415

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1000

1144

1288

14

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1577

1721

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2873

3017

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29

2993

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3279

3423

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4140

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5000

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5286

5429

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6

2571
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2856
9

J

X

N. 30500 L. 484

OF NUMBERS.

N.

3050
51
52
53
54

55
56
57

58
59

3060
61
62
63
64

65
66
67
68
69

3070
71
72
73
74

75
76

I 77
78
79

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81

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88
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91
92
93
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8633

4860052

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4305
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7138
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9969

4871384
2798
4212
5626
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51

63

4881276

2686

4097

5507
6917
8326
9735
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2552
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5366
6773
8179

9585
4900990
2395
3799
5203

95; 6607
96 8010
971 9412
98 4910814
99 1 2216

N. I

1

3141
4564
5988
7410
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1676
3096
4517
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8775
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1612
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6272 6414
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1960 2102
3381 3523
480114943
6221 6363

7640 7782
9059 9201
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1895; 2037
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4730 4872
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6699

6841

7979

8121

8264

9401

9543

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0823

0965

1107

2244

2386

2528

3665

3807

3949

5085

5227

5369

6505

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6788

7924

8066

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2321

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6430

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2091

2232

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3505

3647

3788

4919

5060

5202

6332

6473

6615

7745

7886

8027

9157

9299

9440

0569

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2122

2263

3392

3533

3674

4802

4943

5084

6212

6353

6494

7622

7763

7904

9031

9172

9313

0440

5580

0721

1848

1989

2129

3256

3396

3537

4663

4804

4944

6070

6210

6351

7476

7617

7757

8882

9023

9163

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0428

0569

1693

1833

1973

3097

3238

3378

4501

4642

4782

5905

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6186

7308

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1249
2670
4091
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8350
9768
1186
2604
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5438
6855
8270
9686
1101

2515
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5343
6756
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9581
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3815
5225

6635
8045
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0862
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3678
5085
6492
7898
9304

0709
2114
3518
4922
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7729
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0534
1935
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4280
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79

3769*3884

3999

4114

4229

4343

4458

4573

4688

4803

3780

4918 5033 5148

5263

5378

5492

5607

5722

5837

5952

81

6067,' 6182 6296

6411

6526

6641

6756

6871

6986

7100

82

7215,7330

7445

7560

7675

7789

7904

8019

8134

8249

83

8363! 8478

8593

8708

8823

8937

9052

9167

9282

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84

9511

9626

9741

9856

9970

0085

0200

0315

0429

0544

85

5780659 0774

0888

1003

1118

1233

1347

1462

1577

1691

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86

1806 1921

2036

2150

2265

2380

2494

2609

2724

2838

87

2953 3068

3182

3297

3412

3526

3641

3756

3870

3985

88

4100 4214

43-29

4444

4558

4673

4788

4902

5017

5131

89

5246 5361

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5475

5590

5705

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5934

6048

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6392 6507

6621

6736

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7538 7652

7767

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8111

8225

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8683 8798

8912

9027

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115

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9828 9943

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95

2118 2232 2347

2461

2576

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3262 3376 3491

3605

3720

3834

3948

4063

4177

4292

5, 68

97

4406 4520

4635

4749

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104

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1 1

2

8

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62

LOGARITHMS

N. 38000 L. 579

N.

3800
01
02
03
04

05
06
07
08
09

3810
11
12
13
14

15
16
17
18
19

3820
21
22
23
24

25
26
27
28
29

3830
31
32
33
34

35
36
37

5797836
8979

5800121
1263
2405

3547

4688
5829
6969
8110

9250
5810389
1529
2668
3807

4945
6084
7222
8359
9497

5820634
1770
2907

1

7950
9093
0235
1377
2519

3661
4802
5943
7083
8224

9364
0503
1643
2782
3921

5059
6197
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9610

8065
9207
0350
1492
2633

3775
4916
6057
7197
8338

9478
0617
1757
28^6
4035

5173
6311
7449

8587
9724

0747 0861

1884 1998
3020 3134
4043' 4157| 4270
5179: 5292. 5406

6314 6428 6541

7450

8585

9719

5830854

1988
3122
4255

5388
6521

7563 7677
8698 8812
9833 9946

0967

2101
3235

1081

2215
3348

4368' 4482
5501 '5615
6634 6748

7654 7767

87S6 8899

991 8' 0031'

38 5841050' 1163i

39

3840
41
42
43
44

45
46
47
48
49

2181 2294 I

3312 3425
4443 4556
5574 5687
6704' 6817
7834: 7947

8963 9076

5850093 0206

1222 1335

2351
3479

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2463
3592

1

7880
9012
0144
1276
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3538
4669
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0319
1448
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9321
0464
1606
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9436
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3889 4003
5030 5144

6171
7312
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9592
0731
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0975
2111
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4384
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6655
7790
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3124
4262 :

5401 !
6539

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9951 ;
1089:

22251
3361 '
4497
5633

6769
7904
9039
6173
1307

2328; 2441
3462 3575
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5728 5841
6861 6974

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1389
2520

3652

4782
5913
7043
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8107
9239
0371
1502
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6026
7156
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9302 9415
0432 0544

5

1561
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1673
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6

3

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1834
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4117
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5515
6653
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1202
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2555
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8220
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5

8522
9664
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5937
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114

Pro.

115

13
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58

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98

104

113

114

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1

2
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N. 38500 L. 585 of numbers. 63

N.

3850

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3

4
5058

5
5171

6

5284

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5622

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2157

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75

2717

2829

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3053

3165

3277

3389

3502

3614

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112

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5518

5630

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5966

78

6078

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79

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7981 8093

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3880

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8877

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9101

9213

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81

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9772 9884 |

9996

0108

0220

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82

5890555

0667

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1003

1115

1227

1338

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83

1674

1786

1898

2009

2121

2233

2345

2457

2569

2680

84

2792

2904

3016

3128

3239

3351

3463

3575

3687

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1951

2063

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2509

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2732

112

93

2844

2956

3067

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3290

3402

3513

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3736

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4-294

4406

4517

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4740

4852

4963

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96

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6301

6412

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6970

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7304

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4

0089
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6

0812

7

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0535
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D

9 101

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Pis.

64

LOGAUITHMS

N. 3yi)0{) L. 591

1

3900
01
0?
03
04

05
06
07

oe<

09

3910
11
12
13
14

15
16
17
18
19

3920
21
22
23
24

25
26
27

28
29

3930
31
3?
33
34

35
36
37
39
39

3940
41
42
43
44

45
46
47

48
49

N.

•

5910646
1760
2873
3986

5098

1

0757
1871
2984
4097
5209

6210 6322

7322

8434

9546

5920657

1768

2S7H
39S8
5098
6208

7318
8427
9536
5930644
1753

2861
3968
5076
6183
7290

8397
9503
5940609
1715
2820

3926
5030
6135
7239
8344

9447
5950551
1654
2757
3860

4962
6064
7166
826.M
9369

5960470
1571
2671
3771
4871

7434
8545
9657
0768

1879
2989
4099
5209
6319

7429
8538
9647
0755
1863

2971
4079
5187
6294
7401

8507
9614
0720
1825
2931

4036
5141
6246
7350
8454

9558
0661
1764
2867
3970

5072
6175
7276

8378
9479

0580
1681
2781
3881
4981

1

2 3

0869' 0980
1982 2098
3095 3207
4208 4319
5321 5432

6433 6544
7545! 7656
8656| 8768
9768,9879
0879 0990

1990 2101
3100 3211
4210,4321
5320, 5431
6430 6541

7540 7650
8649,8760
9757,9868
0866; 0977
1974 2065

3082

4190;

5297

6404

7511

8618
9724'
0830 j
1936
3041

4147
5251
6356
7460
8564

9668
0772
1975
2978
4080

5183
6285
7387
8488
9589

0690
1791
2891
3991
5091

3193
4301
5406
6515
7622

8729
9835
0941
2046
3152

4257
5362
6466
7571
8675

9778
0882
1985
3088
4191

5293
6395
7497
8598
9699

0800
1901
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4101
5201

1091
2205
3318
4431
5543

6655
7767
8879
9990
1101

2212
3322
4433
5542
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7761
8870
9979
1088
2196

3304
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55rl9
6626
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8839
9945
1051
2157
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4368
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6577
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8785

9889
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2095
3198
4301

5403
6505
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3111
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4479
5583
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7792
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9999
1103
2206
3308
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5513
6615
7717
8818
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1020
2121
3221
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5

1203,1314
2316,2427
3429 3540
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9006 9116

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1213
2316
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1131
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N. 39500 L. 596 of numbers.

65

N-

1
6081

2

6191

3

6301

4
6411

5

6521

6

6631

7

6741

8

6850

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6060

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^ 1465

1575

1684

1794

1904

2014

2124

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5416

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59

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5965

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LOGARITHMS

N. 40000 L. 002

4000
01
02
03
04

05
06
07
08
09

4010
11
12
13
14

15
16
17

18
19

4020
21
22
23
24

25
26
27

28
29

4030
31
32
33
34

35
36
37
38
39

4040
41
42
43
44

45
46

47
48
49

N.

1
0708

2

0817

6020600

1686

1794

1903

2771

2879

2988

3856

3964

4073

4941

5049

5158

6025

6134

6242

7109

7218

7826

8193

8302

8410

9277

9385

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6030361

0469

0577

1444

1552

1660

2527

2635

2743

3609

3717

3826

4692

4800

4908

5774

5882

5990

6855

6964

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1396

2261

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3341

3449

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45-29

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5500

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5716

6580

6688

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7659

7767

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8738

8846

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9816

9924

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6050895

1002

1110

1973

2080

2188

3050

3158

3266

4128

4236

4343

5205

5313

5421

6282

6390

6498

7359

7467

7574

8435

8543

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9619

9727

6060587

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0803

1663

1771

1878

2739

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2954

3814

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4029

4889

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5103

5963

6071

6178

7037

7145

7252

8111

8219

8326

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9293

9400

6070259

0366

0473

1332

1439

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2405

2512

2620

3478

3585

1

3692
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0926
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3096
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6351
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9602
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1769
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3665
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5824
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7983
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3374
4451
5528
6605
7682

8758
9834
0910
1986
3061

4136
5211
6285
7360
8434

9507
0581
1654
2727
3800

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1034
2120
3205
4290
5375

6459
7543
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1877
2960
4042
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7288
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7240

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81

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LOGARITHMS N. 41000 L. 612

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0972

1078

1183

1288

1393

1498

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1708

1813

1918

2024

2129

2234

2339

2444

2549

33

2654

2759

2864

2969

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3179

3284

3390

3495

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34

3705

3810

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4020

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4230

4335

4440

4545

4650

35

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4860

4965

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5280

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5490

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105

36

5805 5910

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6120

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6750

37

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7065

7170

7275

7380

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7800

38

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8010

8115

8220

8325

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8744

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4140

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0213

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0423

0528

0633

0738

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0947

41

1052

1157

1262

1367

1472

1577

1682

1786

1891

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42

2101

2206

2311

2415

2520

2625

2730

2835,2940

3045

105

43

3149

3254

3359

3464

3569

3673

3778

3883,3988

4093

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4197

4302

4407

4512

4617

4721

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5664

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5979 6083

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6607

6712

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7026 7131

7236

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7759

7864

7969

8073 8178

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48

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8597

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9539

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9958
5

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D

9

95

N.

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Pi*.

N. 41500 L. 618 OF NUMBERS. 09

4150

1
0586

2

0690

3

0795

4

0900

5
1004

6

1109

7

1213

8

1318

9

1423

D

Pro.

6180481

51

1527

1632

1737

1841

1946

2050

2155

2260

2364

2469

104

52

2573

2678

2783

2887

2992

3096

3201

3306

3410

3515

1

10

53

3619

3724

3828

3933

4038

4142

4247

4351

4456

4560

2
3
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21
31
42

54

4665

4769

4874

4979

5083

5188

5292

5397

5501

5606

55

5710

5815

5919

6024

6128

6233

6337

6442

6546

6651

6

52

56

6755

6860

6964

7069

7173

7278

7382

7487

7591

7696

6

7
8

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73

57

7800

7905

8009

8114

8218

8323

8427

8531

8636

8740

58

8845

8949

9054

9158

9263

9367

9471

9576

9680
0725

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59

9889

9994

5098

0202

0307

0411

0516

0620

0829

4160

6190933

1038

1142

1246

1351

1455

1560

1664

1768

1873

61

1977

2082

2186

2290

2395

2499

2603

2708

2812

2916

62

3021

3125

3229

3334

3438

3542

3647

3751

3855

3960

63

4064

4168

4273

4377

4481

4586

4690

4794

4899

5003

64

5107

5212

5316

5420

5524

5629

5733

5837

5942

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6150

6254

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6463

6567

6671

6776

6880

6984

7088

66

7193

7297

7401

7505

7610

7714

7818

7922

8027

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67

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8860

8964

9069

9173

68

9277

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9485

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9902

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0111

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69

6200319

0423

0527

0631

0736

0840

0944

1048

1152

1256

4170

1361

1465

1569

1673

1777

1881

1985

2090

2194

2298

71

2402

2506

2610

2714

2818

2922

3027

3131

3235

3339

72

3443

3547

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5837

5941

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6149

6253

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75

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76

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7813

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0828

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4180

1763

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2075

2178

2282

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2490

2594

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81

2802

2906

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3113

3217

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82

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4463

4567

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3177

3280

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4213

4316

4420

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4627

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103

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5559

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5870

5974

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D

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70

LOGAKITHHS

N. 42000 L. 623

N.

1

2596

4200

6232493

01

3527

3630

02

4560

4664

03

5594

5697

04

6627

6730

05

7660

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06

8693

8796

07

9725

9828

08

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09

1789

1892

4210

2821

2924

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3852

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12

4884

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13

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6945

7048

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16

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17

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0139

18

1066

1169

19

2095

2198

4220

3125

3227

21

4154

4256

22

5182

5285

23

6211

6314

24

7239

7342

25

8267

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26

9295

9398

27

6260322

0425

28

1350

1453

29

2377

2480

4230

3404

3506

31

4430

4533

32

5457

5559

33

6483

6585

34

7509

7611

35

8534

8637

36

9560

9662

37

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38

1610

1712

39

2634

2737

4240

3659

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41

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42

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43

6730

6833

44

7754

7856

45

8777

8879

46

9800

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47

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48

1845

1947

49

2867

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2970

1

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2700
3734
4767
5801
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7867
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8027
4059
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6121
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8182
9212
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1272
2301

3330
4359

5388
6416
7445

8473
9500
0528
1555
2582

3609
4636
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6688
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5911
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5004
1027
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8837
4871
5904
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1067
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3130
4162
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3337
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62
72
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61
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71
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N. 42500 L. 628 of numbers. 71

N.

4250

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3991 4094

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4196

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5320

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3076

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5319

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63

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7561

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1226

1328

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1532

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1837

1939

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68

2244

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3058

3160

69

3262

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5499

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72

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1900

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6091

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6901

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1755

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LOGAKITHMS

"n".

13000 L. 63a

N.

4300

1
4786

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4887

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5089

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6334685

01

5694

5795

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6098

6199

6300

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101

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6704

6805

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7310

7411

7512

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N. 43500 L. 638

OF NUMBERS.

73

N

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6384893

51

5891

52

6889

53

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54

8884

55

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56

6390879

57

1876

58

2872

59

8869

4360

4865

61

5861

62

6857

63

7852

64

8847

65

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66

6400837

67

1832

68

2826

69

3820

4370

4814

71

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72

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73

7795

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75

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76

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78

2758

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3749

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82

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87

1676

88

2666

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3656

4390

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91

5634

92

6623

93

7612

94

8601

95

9589

96

6430577

97

1565

98

2552

99

3540

N.

1

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5991
6989
7986
8984

9981
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1975
2972
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4965
5960
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1931
2926
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74

LOGARITHMS N. 44000 L. 643

N.

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2
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4

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5

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5218

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1726

1825

1923

2022

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08

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2613

2711

2810

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27

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1193

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28

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9

N.

Pu.

N. 44500 L. 648

OF NUMBERS.

75

N.

1
3698

4450

6483600

51

4576

4674

52

5552

5649

53

6527

6624

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0816

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3265

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6269

6365

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8109

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8302

8980

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9948

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0141

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1012

1109

1206

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2076

2173

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3817

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4784

4881

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4478

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6332

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2180 2277

3154*3251

4128 4225

5101

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6074 6172

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0937 1034

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2881

2978

3852 8950

4824 4921

5795 5892

6766 6863

7736 7833

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16171 1714

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2586 2683

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3556 3653

4525 4622

5494 5591

6462 6559

7431

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8399 8496

9367 9464

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2270

2367

3237

3334

4204

4301

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5268

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7104

7200

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8166

9036

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0967

1063

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2029

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9

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Pro.

97

10
19
29
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49
68
68
78
87

96

1
2
3
4
5
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7
8
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19
29
38
48
68
67
77

Pu.

76

LOGARITHMS

N. 45000 L. 653

N.I

1

4500,6532125 2222
Oil 3090 3187

02 4055 4151

03 5019 5116

04

05
06
07
08
09

4510
11
12
13
14

15
16
17
18
19

4520
21
22
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24

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25

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27

28

29

5984

6948
7912
8876
9839
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1765
2728
3691
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6578
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7635
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2318
3283
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7141
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6770
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6060 6156
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8932 9028

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N. 45500 L. 658

OF NUMBERS.

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N. 46b00 U 662

N.

4600
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02
03
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05
06
07
08
09

14610
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I 12
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14

15
16
17
18
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4620
21
22
23
24

25
26
27
28
29

4630
31
32
33
34

35
36
37

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4640
41
42
43
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45
46
47
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1
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1717

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2658

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N.

46500 L. 667 of numbers. 79

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N. 47500 L. 676 of numbers. bl

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2269

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1189

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2189

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2461 2552

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2086

2176

2267

2358

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2448

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2811

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2992

3083

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2672
3556
4440

5324
6207
7090
7974

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9739
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5032
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6795
7676

8557
9438
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1199
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2960
3839
4719
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9994
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1751
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3507
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5412
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9828
0710
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5120
6002
6883
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2167

3048
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9203
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0960

1839
2717
3595

2227
3113
3999

4885
5770

6656
7541
8426
9311
0196

1080
1965
2849
3733
4617

5500
6384
7267
8150
9033

9916
0798
1681
2563
3445

4327
5209
6090
6971
7853

8733
9614
0495
1375
2256

3136
4015
4895
5775
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7533

8412
9291

0170
1048

1926

2805

3682

4172 4560

5262. 5351 »! 5138

1

3

2315
3201
4087
4973
5859

6744
7630
8515
9399
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1169
2053
2937
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5589
6472
7355

8238
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1769
2651
3533

4415
5297
6178
7059
7941

8822
9702
0583
1463
2344

3224

4103
4983
5863
6742

7621
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1136

2014
2892
3770
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G

2404
3290
4176
5062
5947

2493
3379
4265
5150
6036

6833 6921

771817807
8603J 8692
9468 9576
0373' 0461

I257I 1346
2I41|2230
3026 3114
3910 3998
4793 4882

5677
6560
7444
8327 :
9210

5765
6649
7532
8415
9298

0092 0181
0975 1063
1857, 1945
2739 2828
3521 3710

4503
5385
6266
7148
8029

8910
9790
0671
1551
2432

3312
4191
5071
5951
6830

4591
5473
6354
7236
8117

8998
9878
0759
1639
2520

3400
4279
5159
6039
6918

7709' 7797
858S 8676

9467
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9555
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12241 1312

4

2102 2190
2980' 3068
3858 3946

4736
5613

4824
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6

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2581
3467
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5239
6124

7010
7895
8780
9665
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1434
2318
3202
4086
4970

5854
6737
7620
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0269
1151
2034
2916
3798

4680
5561
6443
7324

8205

9086
9967
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1727
2608

3488
4367
5247
6126
7006

7885
8764
9643
0521
1399

2278
3156
4034
4911
5789

N. 49000 L. 090

2670
3556
4442
5327
6213

7098
7984
8869
9753
0638

1522
2407
3291
4175
5058

5942
6925
7709
8592
9474

0357
1240
2122
3004
3986

4769
5649
6531
7412
8293

9174
0055
0935
1815
2696

3576
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5385
6214
7094

7973

8852
9730
0609
1497

2366
3244
4121
4999

5877

"8~

9

2759
3644
4530
5416
6302

7187
8072
8957
9842
0726

1611
2495
3379
4263
5147

6030
6914
7797
8690
9563

0445
1328
2210
3092
3974

4956
5737
6619
7500

9381

9262
0143
1023
1903
2794

3664
4543
5423
6302
7192

9061
9940
9919
0697
1575

2458
3331
4209
5097
5964

9

D

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89
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3: ?7

4 36

5 46

6 53
7! 62

8, 71

9 80

I I

D

9

PU.

N. 41)500 L. 694

OF NUMBERS.

85

N.

4950
51
52
53
54

55
56
57

58
59

4960
61
62
63
64

65
66
67
68
69

4970
71
72
73
74

75
76
77

78
79

1980
81
82
83

84

I

85
86

87

88

6946052
6929
7806
8683
9560

6950437
1313
2189
3065
3941

4817
5692
6568
7443

8318

9193
6960067
0942
1816
2690

3564
4438
5311
6185
7058

7931
8804
9676
6970549
1421

2293
3165
4037
4909
5780

6652
7523
8394
9264

89. 6980135

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9l{

92

93'

94 1

95

96!
97
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99

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1876
2746
3616
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5355
6224
7093
7963

8831

1

6140
7017
7894
8771
9648

0524
1401
2277
3153
4029

4904
5780
6655
7530

8405

9280
0155
1029
1903
2777

3651
4525
5399
6272
7145

8018
8891
976-4
0636
1508

2381
3253
4124
4996
5867

6739
7610
8481
9352
0222

10Q2
1963
2833
3703
4572

5442
6311
7180
8049
8918

I

2

6227
7105
7982
8859
9735

0612
1488
2364
3240
4116

4992
5867
6743
7618
8493

9367
0242
1116
1991
2865

3739
4612
5486
6359
7232

8105
8978
9851
0723
1596

2468
3340
4212
5083
5955

6826
7697
8568
9439
0309

1180
2050
2920
3790
4659

5529
6398
7267
8136
9005

S

6315
7192
8069
8946
9823

0700
1576
2452
3328
4204

5079
5955
6830
7705

8580

9455
0330
1204
Ii078
2952

3826
4700
5573
6447
7320

8193
9066
9938
0811
1683

2555
3427
4299
5170
6042

6913
7784
8655
9526
0396

1267
2137

3007
3877
4746

5616
6485
7354
8223
9092

3

4

6403

6491

7280

7368

8157

8245

9034

9122

9911

9998

0787

0875

1663

1751

2540

2627

3416

3503

4291

4379

5167

5255

6042

6130

6918

7005

7793

7880

8668

8755

9542

9630

0417

0504

1291

1379

2166

2253

3040

3127

3913

4001

4787

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5661

5748

6534

6621

7407

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8280

8367

9153

9240

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D113

0898

0985

1770

1857

2642

2729

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3601

4386

4473

5257

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6129

6216

7000

7087

7871

7958

8742

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9613

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0483

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1354

1441

2224

2311

3094

3181

3964

4051

4833

4920

5703

5790

6572

6659

744:1

7528

8310

8397

9179

9266

4

5

6

7

6578
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9209
5086

0962
1839
2715
3591
4467

5342
6217
7093
7968

8843

9717
0592
1466
2340
3214

4088
4962
5835
6709

7582

8455
9327
0200
1072
1945

2817
3689
4560
5432
6303

7174
8045
8916
9787
0657

1528
2398
3268

4138
5007

5877
6746
7615
8484
9358

6

6666
7543
8420
9297
6174

1050
1926
2802
3678
4554

5430
6305
7180
8055
8930

9805
0679
1554
2428
3302

4176
5049
5923
6796
7669

8542
9415
5287
1160
2032

2904
3776
4647
5519
6390

7261
8132
9003
9874
0744

1615
2485
3355
4224
5094

5964
6833
7702
8571
9439

8

6754
7631
8508
9385
5261

1138
2014
2890
3766
4642

5517
6393
7268
8143
9018

9892
0767
1641
2515
3389

4263
5137
6010
6883
7756

8629
9502
5374
1247
2119

2991
3863
4735
5606
6477

7349
8220
9090
9961
0881

1702
2572
3442
4311
5181

6050
6920
7789
8658
9526

9

6842
7719
8596
9472
5349

1225
2102
2978
3854
4729

5605
6480
7355
8230
9105

9980
0854
1728
2603
3477

4350
5224
6097
6970

7844

8716
9589
5462
1334
2206

3078
3950
4822
5693
6565

7436

8307
9177
5048
0918

1789
2659
3529
4398
526S

6137
7007
7876
8744
9613

9

D

88

87

D

Pro.

87

1

9

2

17

3

26

4

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5

41

6

52

7

61

8

70

9

78

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26
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lis.

I&6

LOGARITHMS N. 50000 L. 698

N.

5000

1

6989700 9787

2

9874

3

4
0047

5
6134

6
5221

7

5308

8

5395

9

5482

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1

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9961

01

6990569 0655

0742

0829

0916

1003

1090

1176

1263

1850

87

02

1487

1524

1611

1697

1784

1871

1958

2045

2181

2218

1

9

03

2305

2392

2479

2565

2652

2789

2826

2918

2999

3086

87

2
S

4

17

26
35

04

8173

8260

8847

3483

3520

8607

8694

3780

8867

8954

05

4041

4128

4214

4301

4388

4475

4561

4648

4785

4822

5

mm

44

06

490S 4995

5082

5169

5255

5342

5429

5516

5602

5689

6

7
8

62

07

5776 5868

5949

6086

6128

6210

6296

6383

6470

6556

70

08

6643 6780

6817

6908

6990

7077

7168

725(1

7337

7424

9

78

09

7510 7597

7684

7770

7857

7944

8081

8117

8204

8291

1

5010

8877

8464

8551

8687

8724

8811

8897

8984

9071

9157

11

9244

9881

9417

9504

9591

9677

9764

9851

9937

5024

12

7000111

0197

0284

0871

0457

0544

0680

0717

0804

0890

13

0977

1064

1150

1287

1824

1410

1497

1588

1670

1757

14

1843

1930

2017

2108

2190

2276

2863

2450

2536

2628

15

2709

2796

2883

2969

3056

8142

3229

8816

8402

8489

16

3575. 3662

3748

3835

8922

4008

4095

4181

4268

4854

17

4441

4528

4614

4701

4787

4874

4960

5047

5188

5220

18

5307

5393

5480

5566

5653

5739

5826

5912

5999

6085

19

6172

6258

6345

6482

6518

6605

6691

6778

6864

6951

5020

7037

7124

7210

7297

7388

7470

7556

7643

7729

7816

21

7902

7989

8075

8162

8248

8335

8421

8508

8594

8681

22

8767

8854

8940

9027

9113

9199

9286

9872

9459

9545

23

1 9632,9718

9805

9891

9978

0064

5151

5287

0823

5410

24

7010496 0583

0669

0756

0842

0929

1015

1101

1188

1274

25

1361

1447

1584

1620

1706

1793

1879

1966

2052

2188

26

2225 2311

2898

2484

2570

2657

2748

2880

2916

8002

27

3089 3175

3262

3348

3484

3521

3607

3694

3780

3866

28

3953 4039

4125

4212

4298

4385

4471

4557

4644

4730

29

4816 4903

4989

5075

5162

5248

5334

5421

5507

5594

5030

5680 5766

5853

5939

6025

6112

6198

6284

6371

6457

31

6543 6629

6716

6802

6888

6975

7061

7147

7234

7320

32

7406

7493

7579

7665

7752

7838

7924

8010

8097

8183

33

8269 8356

8442

8528

8614

8701

8787

8873

8960

9046

34

9132 9218

9305

9391

9477

9563

9650

9736

9822

9908

35

9995

0081

5167

5254

0340

0426

0512

0598

5685

5771

36

7020857

0943

1030

1116

1202

1288

1375

1461

1547

1683

I

37

1720

1806

1892

1978

2064

2151

2237

2323

2409

2495

\

38

2582 2668

2754

2840

2926

3013

3099

3185

3271

8357

L

39

3444 3530

3616

3702

3788

3874

8961

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5040

4305 4392

4478

4564

4650

4736

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4909

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5081

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41

5167: 5253

5339

5425

5512

5598

5684

5770

5856

5942

§

42

6028 6115

6201

6287

6373

6459

6545

6631

6717

6804

86 1

43

6890 6976

7062

7148

7234

7320

7406

7492

7579

7665

1 »

44

7751

7837

7923

8000

8095

8181

8267

8853

8440

8526

S 17

3 «el

45

8612 869S

8784

8870

8956

9042

9128

9214

9300

9886

4

34

46

9472

9559

9645

9731

9817

9903

9989

5075

5161

5247

ft

43

47

7030333

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0505

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0763

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1021

1107

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7

s

ft8
fID

48

1193

1279

1366

1452

1538

1624

1710

1796

1882

1968

09

49

N.

2054

2140

1

2226
2

2312
3

2398
4

2484
5

2570
6

2656

7

2742

8

2828
9

86

9

77

1

Pit.

N. 50o00 L. 703

OF NUMBERS.

87

N.

5050

7032914

51

3774

52

4633

53

5493

54

6352

55

7212

56

8071

57

8930

58

9788

59

7040647

5060

1505

61

2363

62

3221

63

4079

64

4937

65

5794

66

6652

67

7509

68

8366

69

92-23

5070

7050080

71

0936

72

1792

73

2649

74

8505

75

4360

76

5216

77

6072

78

6927

79

7782

5080

8637

81

9492

82

7060847

83

1201

84

2055

85

2910

86

3764

87

4617

88

5471

89

6325

5090

7178

91

8031

92

8884

93

9737

94

7070589

95

1442

96

2294

97

3146

98

3998

I 99

4850

N.

I

3000
3860
4719
5579
6438

7298
8157
9015
9874
0733

1591
2449
3307
4165
5023

5880
6738
7595
8452
9309

0165
1022
1878
2734
3590

4446
5302
6157
7012
7868

8728
9577
0482
1287
2141

2995
8849
4703
5556
6410

7263
8116
8969
9822
0675

1527
2379
3232

4083
4935

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2

3086
3946
4805
5665
6524

7383
8242
9101
9960

0818

1677
2535
3393
4251
5108

5966
6823
7680
8537
9394

0251
1107
1964
2820
3676

4532
5387
6243
7098
7953

8808
9663
0518
1372
2226

3080
3934
4788
5642
6495

7348
8202
9055
9907
0760

1612
2465
3317
4169
5020

3172
4032
4891
5751
6610

7469
8328
9187
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1763
2621
3479
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6052
6909
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0337
1193
2049
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4617
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7184
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9748
0603
1457
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3166
4020
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5727
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7434
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1698
2550
3402
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4

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6

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3258

3344

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0132

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1076

1162

1248

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1934

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2106

2707

2792

2878

2964

3565

3650

3736

8822

4422

4508

4594

4680

5280

5366

5452

5587

6137

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6309

6395

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7080

7166

7252

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7938

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8109

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8795

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9737

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8457

8543

8628

9225

9310

9396

9481

0078

5163

0248

0384

0930

1016

1101

1186

1783

1868

1953

2089

2635

2720

2805

2891

3487

3572

8658

3743

4339

4424

4509

4595

5191

5276

5361

5446

4

1

5

6

7

8

3602
4461
5321
6181
7040

7899
8758
9617
0475
1834

2192
8050
3908
4765
5623

6480
7888
8195
9052
9908

0765
1621
2477
3833
4189

5045
5901
6756
7611
8466

9321
0176
1080
1885
2739

3593
4447
5300
6154
7007

7860
8713

9

3688
4547
5407
6266
7126

7985
8844
9702
0561
1419

2278
8186
3993
4851
5709

6566
7428
8280
9137
9994

0850
1707
2563
3419
4275

5181
5986
6841
7697
8552

9406
0261
1116
1970
2824

8678
4532
5386
6239

7092

7946
8799

D

Pro.

86

9566 9651
5419 0504

1271

2124
2976
3828
4680
5531

8

1357

2209
3061
3913
4765
5617

9

I
2
3
4

6
G

7
8
9

2G
34
43
5%
60
69
77

85
1 9

86

D

2
3
4
6
6

7

8
9

17
26
34
43
51
60
68
77

Pis.

88

LOGARITHMS N. 51000 L. 70?]

~n7

1

2

y

4

5

01 7

8

9

D

^

5100

7075702

57S7

5872

5957

6042

6128

6213 6298

6383

6468

01

0553

6638

6724

6809

6894

6979

7064 7149

7234

7319

66

02

7405

7490

7575

7660

7745

7830

7915 8000

8085

8171

03

8256

8341

8426

8511

H596

86S1

8766 8851

8936

9022

s 17

04

9107

919^

9277

9362

9447

9532

9617 9702

9787

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05

9957

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6298

0383

0468 6553

6638

0723

i a

06

7080S08

0893

0978

1063

1148

1233

1319 1403

1488

1574

e a

07

16^9

1744

1829

1914

1999

2094

■2169 2254

2339

2424

J CO

OS

2509

2594

26791 2764

2849

2934

3019 3104

3189

3274

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09

3359

3444

3529 3614

3699

37S4

3869 3954

4039

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fii

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5110

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4634

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5059

5144

5229 5314

5399

5484

5569 5654

5739

5B23

12

5908

5993

6078 6163

624S

6333

6419 6503

6588

6673

13

6758

6843

6928! 7013

7098

7183

7268 7352

7437

7522

14

7807

7692

7777.7862

7947

8032

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8287

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15

8456

8541

8626 8711

8796

8881

8966 9051

9136

9220

16

9305

9390

9475 9560

9645

9730

9915 9900

9984

6069

17

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0239

0324 0409

0494

0579

0663' 0748

0833

0918

1

18

1003

1088

1173 1257

1342

1427

1512 1597

1682

1766

19

1851

1936

2021 2106

2191

2275

2360 2445

2530

2615

5120

2700

2784

2869' 2954

3039

3124

3209' 3293

3378

3463

21

3548

3633

3717 3S02

3887

3972

4057 4141

4226

4311

22

4396

4481

4565 4650

4735

4820

4904 4989

5074

5159

23

5244

5328

5413 5498

55SS

5667

5752 5837

5922

6006

24

6091

6176

6261 6345

6430

6515

6600 6684

6769

6854

25

6939

7023

7108 7193

7278

7362

7447 7532

7617

7701

26

7786

7871

7955 8040

8125

8210

8294 8379

8464

9548

27

8633

8718

9S03 8887

S972

9057,9141'9226

9311

9395

29

9490

9565

9650 9734

9819

9904

9988 6073

6158

6242

29

7100327

0412

0496 0581

0666

0750

0935 0920

1004

1089

5130

1174

1258

1343' 1428

1512

1597

1682|]766

1851

1936

2020

2105

2189,2274

2359

2443

2529; 2613

2697

2782

32

2866

2951

3036,3120

3205

3290

3374 3459

3543

3628

33

3713

3797

3882

3966

4051

4136

4220,4305

4389

4474

34

4559

4643

4728

4312

4897

4982

5066 5151

5235

5320

35

5404

5489

5574

5655

5743

5927

5912: 5996

6081

6160

36

6250

6335

6419

6504

658S

6673

6757

6842

6927

7011

37

7096

7180

7265

7349

7434

7518

7603

7687

7772

7856

3S

7941

8026

8110

8195

8279

8364

8448

8533

8617

8702

39

8786

9S71

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9040

9124

9209

9293

9376

9462

9547

5140

9631

9716

9800 9885

9969

0054

6138

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7110476

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0645 0729

0814

0898

0983

1067

1152

1236

42

1321

1405

1490

1574

1659

1743

1827

1912

1996

2081

8b

43

216J

2250

2334

2419

2503

2587

2672

2756

2841

2925

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44

3010

3094

3178

3263

3347

3432

3516

3601

3685

3769

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45

3B54

393S

4023

4107

4191

4276

4360

4445

4529

4613

4 M

46

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4S67

4951

5035

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5204

5289

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47

554-2

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5795

5879

5964

6048

6132

6217

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48

6385

6470

6554

6638

6723

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6892

6976

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7145

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7398

7482

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7735

7819

7904

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1

2

;j

4

N. 51500 L. 711

OF NUMBERS.

89

I 1

7118072
8915
9759

7120601
1444

2287
3129
3971
4813
5655

6497
7339
8180
9021
9862

7130703
1544
2385
3225
4065

4905
5745
6585
7425
8264

9104
9943
7140782
1620
2459

3298
4136
4974
5812
6650

7488
8325
9162
7150000
0837

1674
S510
3347
4183
5019

5856
6691
7527
8363
9198

N.i

8157
9000
9843
0686
1528

2371
3213
4056
4898
5739

6581
7423

8264
9105
9946

0787
1628
2469
3309
4149

4989
58-29
6669
7509

8348

9187
5027
0866
1704
2543

3381

4220
5058
5896
6734

7571
8409
9246
0083
0920

1757
2594
3430
4267
5103

5939
6775
7611
8446
9282

1

8241
9084
9927
0770
1613

2455
3298

4140
4982
5824

6665
7507
8348
9189
0031

0871
1712
2553
3393
4233

8325
9168
0011
0854
1697

2539
3382
4224
5066
5908

6750
7591
8432
9274
0115

0956
1796
2637
3477
4317

5073} 5157
591315997

6753
7593
8432

9271
0110
0949
1788
2627

3465
4304
5142

5980
6817

7655
8493
9330
0167
1004

1841
2678
3514
4350
5187

6023
6859
7694
8530
9365

2

6837
7677
S516

9355
0194
JL033
4872
2711

3549

4387
^226
6063
6901

7739
8576
9414
0251
1088

1925
2761
3598
4434
5270

6106
6942
7778
8613
9449

"3"

8410
9253
0096
0939
1781

2624
3466
4308
5150
5992

6834
7675
8517
9358
0199

1040
1880
2721
3561
4401

5241
60S1
6921
7761
8600

9439
0278
1117
1956
2795

3633
4471
5309
6147
6985

7823
8660
9497
0335
1171

2008
2845
3681
4518
5354

6190
7026
7861
8697
9532

18494
9337
0180
1023
1865

2708
3550
4392
5234
6076

6918
7759
8601
9442
0283

1124
1964
2805
3645
4485

5325
6165
7005

7845
8684

9523
0362
1201
2040

2878

3717
4555
5393
6231
7069

7906
8744
9581
0418
1255

2092
2929
3765
4601
5438

6273
7109
7945
8780
9616

6

8578
9421
0264
1107
1950

2792
3634
4477
5319
6160

7002
7843
8685
9526
0367

1208
2048
2889
3729
4569

5409
6249
7089
7928

8768

9607
0446
1285
2124
2962

3801
4639
5477
6315
7153

7990
8828
9665
0502
1339

2176
3012
3849
4685
5521

6357
7193
8029
8864
9699

6

8663
9506
0349
1191
2034

2876
3719
4561
5403
6245

7086
7928
8769
9610
0451

1292
2132
2973
3813
4653

5493
6333

7173
8012

8852

9691
0530
1369
2208
3046

3884
4723
5561
6399
7236

8074
8911
9749
0586
1423

2259
3096
3932
4769
5605

6441
7276
8112
8948
9783

8 I 9

I

8747
9590
0433
1276
2118

2961
3803
4645
5487
6329

7170
8012
8853
9694
0535

1376
2217
3057
3897
4737

5577
6417
7257
8096
8936

9775
0614
1453
2-291
3130

3968
4806
5645
6482
7320

8158
8995
9832
0669
1506

2343
3180
4016
4852

5688

6524
7360
8196
9031
9866

8

8831
9674
0517
1360
2202

3045
3887
4729
5571
6413

7254
8096
8937
9778
0619

1460
2301
3141
3981
4821

5661
6501
7341

8180
9020

9859
0698
1537
2375
3214

4052
4890
5728
6566
7404

8241
9079
9916
0753
1590

2427
3263
4100
4936
5772

6608
7444
8279
9115
9950

9

D

84

Pro.

84

1

8

2

17

3

25

4

34

5

42

6

50

7

59

8

67

d

76

D

63

8
17

25
33
42
50
58
VS
75

Pi*.

90

LOGAIllTHMS

N. 52000 L. 716

5200
01
02
03
04

05
06
07
08
09

5210
11
12
13
14

15
16
17
18
19

5220
21
22
23
24

25
26
27

28
29

5230
31
32
33
34

35
36
37
38
39

5240
41
42
43
44

45
46

47

48
49

N.

7160033
0869
1703
2538
3373

4207
5042
5876
6710
7544

8877
9211
7170044
0877
1710

2543
3876

4208
5041
5873

6705
7537
8369
9200
7180QS2

0863
1694
2525
3356
4186

5017
5847
6677
7507
8337

9167

9996

7190826

1655

2484

3313
4142
4970
5799
6627

7455
8283
9111
9938
7200766

1

0117
0952
1787
2622
3456

4291
5125
5959
6798
7627

8461
9294
0127
0961
1794

2626
8459
4292
5124
5956

6788
7620
8452
9283
0115

0946
1777
2608
^439
4269

5100
5930
6760
7590
8420

9250
0079
0909
1738
2567

3396

4224
5053
5881
6710

7538
8366
9193
5021
0848

3

0200,
1036,
1870
2705'
3540

4374

5208
6043
6877
7710

0284
1119
1954
2789
3623

4458
5292
6126
6960
7794

8544' 8627

1

9377
0211
1044
1877

2710
3542
4375
5207
6089

6871
7703
8535
9367
0198

9461
0294
1127
1960

2793
3626
4458
5*290
6123

6955
7786
8618
9450
0281

1029 1112
1860 1943
2691 1 2774
3522 3605
4353 4436

5188 5266
6013 6096
6843 6926
7673 7756
8508 8586

9416
5245
1075
1904
2733

3562
4390
5219
6047
6875

7621 7703
8448,8531
9276 9359
5104' 5187

9338
5162
0992
1821
2650

3479'
4307
5136
5964
6792

0931
"2~

1014

"8"

0367
1203
2037

2872
3707

4541
5375
6209
7043

7877

8711
9544
0377
1210
2043

2876
8709
4541
5374
6206

7038
7870
8701
9533
0364

1195
2026
2857
3688
4519

5349
6179
7009
7839
8669

9499
5328
1157
1987
2816

3644
4473
5302
6130
6958

7786
8614
9442
5269
1097

0451
1286
2121
2956
3790

4625
5459
6293
7127
7960

8794
9627
0461
1294
2127

2959
3792
4625
5457
6289

7121
7953

8784
9616
0447

1279
2110
2940
8771
4602

5432
6262
7092
7922
8752

9582
5411
1240
2069
2898

3727
4556
5384
6218
7041

7869
8697
9524
5352
1179

0535
1370
2204
3039
8874

4708
5542
6376
7210
8044

8877
9711
0544
1377
2210

8043
8875
4708
5540
6372

7204
8036

8868
9699
0580

1362
2193
8023
3854

4685

5515
6345
7175
8005
8885

9665
5494
1323
2152
2981

3810
4639
5467
6296
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7952
8780
9607
5435
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6

0618
1453
2288
8128
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4791
5626
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8961
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0627
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4791
5623
6455

7287
8119
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9782
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1445
2276
3107
3937
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5598
6428
7258
8088
8918

9748
5577
1406
2285
3064

3893
4722
5550
6378
7207

8034
8862
9690
5518
1345

9

0702
1587
2871
8206
4040

4875
5709
6548
7877
8211

9044
9877
0711
1544
2377

8209
4042
4874
5707
6589

7371
8202
9034
9865
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1528
2859
8190
4020
4851

5681
6511
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8171
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0785
1620
2455
3289
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4958
5792
6626
7460
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9961
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1627
2460

8298
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4958
5790
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7454

8286
9117
9949
0780

1611
2442
8278
4103
4934

576A
6594
7424
8254
9084

9830 9913
5660 5743

1489
2818
3147

3976
4804
5688
6461
7289

8117
8945
9773
5600
1428

8

1572
2401
8280

4059
4887
5716
6544
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8200
9028
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9

D

Piro.

84
8

17
SS
34
42
50
59
(57

9| 76

88

D

88
1
2
3

4
5
6

7

8

»i7

N. 52500 L. 720

OF NUMBERS.

91

iN.

1 1 2

3

^ 1

5 |_6^
2007, 2089

2172,2255

9
2337

D

Pro.

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7201593

1676 1758

1841

19-24

51

2420

2503 2586

2668

2751

2834 2916

2999 3082

8164

82

52

3247

3330 3413

3495

3578

3661|3T43

3826 3909

3991

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53

4074

4157 4239

4322

4405

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4653 4736

4818

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5314 5397

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5562

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55

5727

5810 5892

5975

6058

6140 6223

6306

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56

6554

6636 6719

6801

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57

7380

7462 7545

7628

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7793:7875

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159X1 1874| 1756 L83S

1921

2004; 2086

2169

2251

63

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2416 2499 25811-2664

2746

2829 2911

2994

3076

64

3159

3241 3324' 3406' 3489

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5468

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5716 5798' 5881 5963

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6540 6623 6705 6787

6870

6952

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7282

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7777

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2052

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4204

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6
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8027

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3119

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73

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2651

2781

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74

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3127

8207

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1766

1845

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2083

2162

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2479

86

2558

2637

2716

2796

2875

2954

3033

3112

3191

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3666

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2837

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LOGARITHMS N. 55000 L. 740

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1
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3785

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LOGARITHMS N. 50000 L. 748

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7 fji

99

3531

3606

3681

3756

.1831

3906

3980

4055

4131

4205

T)

;i li';

I'l..

In.

~r

^5~

~T

4

102

LOGARITHMS N. 58000 L. 7

63

N.

5800

1
4355

2

4430

3

4505

4

4579

5

4654

6
4729

7

4804

8

4879

9

4954

D

1

Pro.

7634280

01

5029

5104

5178

5253

5328

5403

5478

5553

5628

5702

75

02

5777

5852

5927

6002

6077

6151

6226

6301

6376

6451

1

8

03

6526

6601

6675

6750

6825

6900

6975

7050

7124

7199

2

15

04

04

7274

7349

7424

7499

7573

7648

7723

7798

7873

7947

75

4

23
30

05

8022

8097

8172

8247

8321

8396

8471

8546

8621

8696

5

38

06

8770

8845

8920

8995

9070

9144

9219

9294

9369

9443

6

7
8

45
53
80

07

9518

9593

9668

9743

9817

9892

9967

5042

5117

5191

08

7640266

0341

0416

0490

0565

0640

0715

0789

0864

0939

9

68

09

1014

1089

1163

1238

1313

1388

1462

1537

1612

1687

5810

1761

1836

1911

1986

2000

2135

2210

2285

2S59

2434

11

2509

2583

2658

2733

2808

2882

2957

3032

3107

3181

12

3256

3331

3406

3480

3555

3630

8704

3779

3854

39-29

13

4003

4078

4153

4227

4302

4377

4451

4526

4601

4676

14

4750

4825

4900

4974

5049

5124

5198

5273

5348

5423

i

15

5497

5572

5647

5721

5796

5871

5945

6020

6095

6169

1

16

6244

6319

6393

6468

6543

6617 6692

6767

6841

6916

17

6991

7065

7140

7215

7289

7364

7439

7513

7588

7663

18

7737

7812

7886

7961

8036

8110

8185

8260

8334

8409

' 19

8484

8558

8633

8707

8782

8857

8931

9006

9081

9155

5820

9230

9304

9379

9454

9528

9603 9678

9752

9827

9901

21

9976

0051

5125

0200

5274

0349 0424

5498

5573

5647

22

7650722

0797

0871

0946

1020

1095 1170

1244

1319

1393

23

1468

1542

1617

1692

1766

1841

1915

1990

2065

2139

24

2214

2288

2363

2437

2512

2586 2661

2736

2810

2885

1

25

2959

3034

3108

3183

3258

3332 3407

3481

3556

3630

1

26

3705

3779

3854

3928

4003

4078:4152

4227

4301

4376

27

4450

4525

4599

4674

4748

4823

4897

4972

5046

5121

28

5195

5270

5344 5419

5493

5568 5643

5717

5792

5866

29

5941

6015

6090 6164

6239

6313 6388

6462

6537

6611

5830

6686

6760

6835

6909

698;1

705S 7132

7207

7281

7356

31

7430 7505

7 579:7654

7728

7803 7877

7952

8026

8101

32

8175 8250

8324' 6399

8473

8547

8622

8696

8771

8845

33

8920 8994 19069

9143

92*18

9292

9366

9441

9515

9590

34

9664

9739

9S13

9888

9962

5030

5111

5185

0260

5334

35

7660409

0483

0557

0632

0706

0781

0855

0930

1004

1078

36

1153

1227

1302 1376

1450

1525

1599

1674

1748

1823

37

1897

1971

2046 2120

2195

2269

2343

2418

2492

2567

38

2641

2715

2790 2864

2938

3013

3087

3162

3236

3310

39

3385

3459

3534

3608

3682

3757

3831

3905

3980

4054

5840

4-128

4203

4277

4352

4426

4500

4575

4649

4723

4798

41

4872

4946

5021

5095

5169

5244

5318

5393

5467

5541

42

5616

5690

5764

5839

5913

5987

6062

6136

6210

6285

74

43

6359

6433

6508

6582

6656

6730

6805

6879

6953

7028

1' 7

44

7102

7176

7251

7325

7399

7474

7548

7622

7697

7771

2: 15

45

7845

7919

7994

8068

8142

8217

8291

8365

8440

8514

74

3

4

4CZ

30

46

8588

8662

8737

8811

8885

8960

9034

9108

9182

9257

5

37

47

9331

9405

9479

9554

9628

9702

9777

9851

9925

9999

6

7

8

44

48

7670074

0148

0222

0296

0371

0445

0519

0593

0668

0742

52
50

49

N.

0816

0890
1

0965
2

1039
3

1113
4

1187
5

1262
6

1336

7

1410

8

1484

9

Id

9

67

I

Is.

N. 58500 L. 767

OF NUMBERS.

5850
51
52
53
54

55
56
57

58
59

5860
61
62
63
64

65
66
67
68
69

5870
71
72
73
74

75
76
77

78
79

5880
81
82
83
84

85
86
87
88
89

5S90
91
92
93
94

95
96
97
98

i 99

7671559
2301
3043
3785
4527

5269
6011
6752
7494
8235

8976
9717
7680458
1199
1940

2680
3421
4161
4901
5641

6381
7121
7860
8600
9339

1

1633
2375
3117
3859
4601

5343
6085
6826
7568
8309

9050
9791
0532
1273
2014

2754
3495
4235
4975
5715

6455
7195
7934
8674
9413

7690079 0153

0818
1557
2296
3035

3773
4512
5250
5988
6727

7465
8203
8940
9678
7700416

1153
1890
2627
3364
4101

4838
5575
6311
704S
7784

0892
1631
2370
3108

3847
4586
5324
6062
6800

7538
8276
9014
9752
0489

1227
1964
2701
3438
4175

4912
5648
6385
7121

7858

2

1707
2449
3192
3934
4676

5417
6159
6901
7642
8383

9124
9865
0606
1347

208S

2828
3569
4309
5049
5789

6529
7269
8008
8748
9487

0227
0966
1705
2444
3182

3921
4659
5398
6136
6874

7612
8350
9088
9826
0563

1300
2038
2775
3512
4249

4985
5722
6459
7195
7931

3

I

1781
2524
3266

4008
4750

5492
6233
6975
7716

8457

9198
9940
0680
1421
2162

2902
3643
4383
5123
5863

6603
7343
8082

8822
9561

0300
1040
1779
2517
3256

3995
4733
5472
6210
6948

7686
8424
9162
9899
0637

1374
2111
2849
3585
4322

5059
5796
6532
7269
8005

O

1856
2598
3340

4082
4824

5566
6307
7049
7790
8531

9273
0014
0754
1495
2236

2976
3717
4457
5197
5937

6677
7417
8156
8896
9635

0374
1114
1852
2591
3330

4069
4807
5546
6284
7022

7760
8498
9235
9973
0711

1448
2185
2922
3659
4396

5133
5869
6606
7342

8078

5

6

3 4

1930
2672
3414
4156

4898

5640
6381
7123
7864
8606

9347
(1088
0829
1569
2310

3050
3791
4531
5271
6011

6751
7491
8230
8970
9709

0448
1187
1926
2665
3404

4143
4881
5619
6358
7096

7834
8571
9309
5047
0784

1522
2259
2996
3733
4470

5206
5943
6679
7416
8152

2004
2746
3488
4230
497'2

5714
6456
7197
7938
8680

9421
0162
0903
1643
2384

3124
3865
4605
5345
6085

6825
7565
8304
9044
9783

0522
1261
2000
2739

3478

4216
4955
5693
6431
7169

7907
8645
9383
6121

0858

1595
2333
3070
3807
4543

5280
6017
6753
7489
8226

2078
2821
3563
4305
5046

5788
6530
7271
8013

8754

9495
0236
0977
1717
2458

3198
3939
4679
5419
6150

6899
7639
8378
9118
9857

0596
1335
2074
2813
3552

4290
5029
5767
6505
7243

7981
8719
9457
5194

8

2153
2895
3637
4379
5121

5862
6604
7345
8087

8828

9569
5310
1051
1791
2532

3273
4013
4753
5493
6233

6973
7713
8452
9192
9931

0670
1409
2148
2887
3626

4364
5103
5841
6579
7317

8055
8793
9530
5268

D

0932 1005

O

6

1669
2406
3143
3880
4617

5354
6090
6827
7563
8299

1743
2480
3217
3954
4691

5427
6164
6900
7637
8373

7 8

2227
2969
3711
4453
5195

5937
6678
7420
8161
8902

9643
5384
1125
1866
2606

3347

4087
4827
5567
6307

7047
7787
8526
9265
5005

0744
1483
2222
2961
3699

4438
5176
5915
6653
7391

8129
8867
9604
5342
1079

1817
2554
3291
4028
4764

5501
6238
6974
7710

8447

9

74

1031

Pro.
74

7

15
22

37
44
62
8 59
67

1
2
3
4
5
6

78

1
2
3
4
5
6

7

8

D

7

15
22
20

37
44
54
58
06

Pm.

104

LOGARITHMS N. 5<I0(X) L. 770 1

N.

1

■2

3

4

5 1 6

7

h

•J

D

Pn

5900

77085-211

8594

8667

8741

8815

8886

8962

9035

9109

9183

01

9256

9330

9403

9477

9551

9624

9698

9771

9845

9918

74

02

9992

0066

0139

0213

0266

0360

6434

0507

0581

()654

h 7

03

77107-28

0801

0875

0949

1022

1096

1169

1243

1316

1390

P

04

1463

1537

1611

1684

1758

1831

1905

1978

2052

2125

05

2199

2273

2346

2420

2493

3567' 2640

2714

2797

2861

2 2

06

2934

3008

3081

3155

3229

3302' 3376

3449

3523

3596

it-

07

3670

3743

3817

3890

3964

403714111

4164

4258

4331

k^%

OS

4405

4478

4552

4625

4699

477214846

4919

4993

5066

:\ 67

09

5140

5213

5287

5360

5434

5507 55S1

5654

5728

5801

5910

5875

5948

6022

6095

6169

6242,6316

6389

6463

6536

11

6610

6683

6757

6830

6903

6977 7050

7124

7197

7271

12

7344

7416

7491

7565

7638

77I2I77S5

7858

7932

8005

13

H079

8152

8226

8299

8373

844618519

85H3

8666

S740

14

8S13

B8S7

8960 9034

9107

9180 9254

9327

9401

9474

15

9347

9621

9694 9768

9841

9915

9988

O061

0135

0208

Iti

7720282

0355

0426; 0502

0575

0649

0722

0795

0S69

0942

17

1016

1089

1162

1236

1309

1383

1456

1529

1603

1676

is

1750

1823

1896

1970

2043

2117

2190

2263

2337

2410

19

24H3

■2557

2630

2704

2777

2850

2924

2997

3070

3144

i92l)

3217

3290

3364

3437

3510

3584

3657

3;3I

3804

3S77

21

3951

4024

4097i4l71

4244

4317

43}))

4464

4537

4611

22

46S4

4757

4831 4904

4977

5051

5124

5197

5271

5344

i3

5417

5491

55641 5637

5711

5784

5857

5931

6004

6077

24

6150

6224

6297,6370

6444

6517

6590

6664

6737

6810

25

6KS4

6957

7030 7103

7177

7250

7323

7397

7470

7543

26

7616

7690

77637836

7910

7983

8056

8129

8203

8276

■21

8349

8423

S496

S569

8642

8716

8789

S862

8935

9009

2S

90&2

9155

9228

9302

9373

9448

9521

9595

9668

9741

29

9815

9988

9961

6034

0107

0181

0254

0327

0400

5474

b930

773(ra47

0620

0693

0767

0840

0913

0996

1060

1133

1206

3!

1279

1352

1426

1499

1572

1645

1719

1792

1805

1938

32

2011

2085

2159

2231

2304

2377

2451

2524

2597

2670

33

2743

2S17

2890

2963

3036

3109

3183

3256

3329

3402

34

3475

3549

3622

3695

3768

3841

3915

3988

4061

4134

35

4207

4280

4354

4427

4500

4573

4646

4719

4793

4S66

36

4939

5012

5085

5158

5232

5305

5378

5451

5524

5597

3T

5670

5744

5S17

5890

5963

6036

6109

6183

H256

6329

38

6402

6475

6548

6621

6694

6768

6841

6914

6987

7060

39

7133

7206

7280

7353

7426

7499

7572

7645

7718

7791

5940

7864

7938

8011

8084

8157

h230

^303

8376

5449

8522

41

S596

8669

8742

8815

88^8

8961

9034

9107

9180

9253

4:;

9326

9400

9473

9546

9619

9692

9765

9838

9911

9984

73

43

7740057

0130

020310277

0350

0423

0496

0569

0642

0715

1 7

44

0786

0S61

09*1 1007

1080

1153

1226

1299

1372

1446

3 lo

45

1519

1592

1665 1738

1811

1884

1957

2030

2103

2176

4 3U

4e

2249

2322

2395 2461-

2541

2614

2687

2760

2833

2906

6 37

47

2979

3052

3125 3l9f

3271

3345

3418

3491

3564

3637

n u

7 41

R M

4S

3710

3783

3856 3929

4002

4075

4148

4221

4294

4367

49

4440

45! :j

45861 465!'

473?

4^05

4S78

4951

50->4

5097

N.

1

^" 1 ^ ;i"

J_

•J

"(T

.L.

^

i)

T)

It.. 1

N.

59500 L. 774

OF NUMBERS.

105

N.

1

2

5316

3
5389

4

5462

5
5535

6
5608

7

5681

8

5754

9

5827

D

73

Pro.

5950

7745170

, 5243

51

5900 5972

6045

6118

6191

6264

6337

6410

6483

6556

73

52

6629' 6702

6775

6848

6921

6994

7067

7140

7213

7286

I

7

53

7359,7432

7505

7578

7651

7724

7797

7869

7942

8015

2

a

4

15
22
29

54

608S 8161

8234

8307

8380

8453

8526

8599

8672

8745

55

8818 8891

8964

9036

9109

9182

9255

9328

9401

9474

6

37

56

9547 9620

9693

9766

9839

9911

9984

0057

0130

0203

6

7
8

44

51
58

57

7750276 0349

0422

0495 0568

0641

0713

0786

0859

0932

58

1005' 1078

1151

1224

1297

1369

1442

1515

1588

1661

9

66

59

1734 1807

1880

1952

2025

2098

2171

2244

2317

2390

5960

2463' 2535

2608

2681

2754

2827

2900

2973

3046

3118

61

3191 3264

3337

3410 3483

3555

3628

3701

3774

3847

62

3920 3993

4065

4138 4211

4264

4357

4430

4502

4575

63

4648 4721

4794

4867 j 4939

5012

5085

5158

5231

5304

64

5376 5449

5522

5595 5668

5740

5813

5886

5959

6032

65

6104' 6177

6250

6323; 6396

6469

6541

6614

6687

6760

66

6832 6905

6978

70511 7124

7196

7269

7342

7415

7488

67

7560 7633

7706

7779 7851

7924

7997

8070

8143

8215

68

8288 8361

6434

8506 8579

8652

8725

8798

8870

8943

69

9016 9089

9161

9234 9307

9380

9452

9525

9598

9671

5970

9743 9816

9889

9962 0034

0107

0180

0253

0325

0398

71

7760471 0543

0616

0689! 0762

0834

0907

0980

1053

1125

72

1198 J 271

1343

1416 1489

1562

1634

1707

1780

1852

73

1925 1998

2071

2143 2216

2289

2361

2434

2507

2579

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7636

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7765

7830

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7960

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19
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8154

8219

8284

8349

8414

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8544

8608

8673

8738

5

32

97

8803

8868

8933

8998

9062

9127

9192

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120

LOGARITHMS N. 670 L.

836

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3

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5 6

1072,1137

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1202

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1267

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1331

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Pm.

8260748

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01

1396

1461

1526

1591

1655

1720, 1785

1850

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2044

2109 2174

2289

2303

2368, 2433

2498 2563

2627

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2692

2757 2822

2887

2951

3016,3081

3146

3210

3275

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13

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3405 3470

3534

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3664 3729

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4117

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6190

6254 6319

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6772

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6902 6966

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7549.7614

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7937

8002

8067

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8196 8261

8325

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12

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8584

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8843 8908

8972

9037

9102

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9361

9425

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0784 0848

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1042

16

1107

1172

1236

1301

1366

1430 1495

1560

1624

1689

17

1753

1818

1883

1947

2012

2077,2141

2206

2271

2335

64

18

2400

2465

2529

2594

2659

2723 2788

2852

2917

2982

19

3046

3111

3176

3240

3305

3370| 3434

3499

3563

3628

6720

3693

3757

3822

3887

3951

4016 4080

4145

4210

4274

21

4339

4404

4468

4533

4597

4662 1 4727

4791

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4920

22

4985

5050

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5179

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5308 5373

5437

5502

5567

23

5631

5696

5760

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5954 6019

6083

6148

6212

24

6277

6342

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25

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7310

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7439

7504

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7569

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8021

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27

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28

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9183 9247

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9376

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29

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9828.9893

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6730

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0473, 0538

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31

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0860

0925

0989

1054

1119

1183

1248

1312

1377

32

1441

1506

1570

1635

1699

1764

1828

1893

1957

2022

33

2086

2151

2215

2280

2344

2409 2473

2538

2602

2667

34

2731

2796

2860

2925

2989

3054 3118

3183

3247

3312

35

3376

3440

3505

3569

3634

3698

3763

3827

3892

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4214

4279

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4472

4537

4601

37

4665

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4923

4988 5052

5117

5181

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5310 5375

5439

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5568

5632 5697

5761

5826

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6083

6148

6212

6277 6341

6406

6470

6535

6740

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6663

6728

6792

6857

6921 6986

7050

7114

7179

41

7243 7308

7372

7437

7501

7565

7630

7694

7759

7823

42

7887 7952

8016

8081

8145

8210

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8725

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8854

8918

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1107

1171

1236

1300

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1429| 1493

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1622

1686

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2201

2266

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1

N. 675 L. 829 of numbers.

121

N.

6750

1
3102

2

3166

3

3231

4

3295

5
3359

6

3424

7

3488

8 9

3552 3617

D

Pro.

8293038

51

3681

3745

3810

3874

3938

4003

4067

4131

4196 4260

64

52

4324

4389

4453

4517

4582

4646

4710

4775

4839 4903

1

53

4967

5032

5096

5160

5225

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5418

5482 5546

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3

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54

5611

5675

5739

5803

5868

5932

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6061

6125 6189

55

6254

6318

6382

6446

6511

6575

6639

6704

6768 6832

5

32

56

6896

6961

7025

7089

7154

7218

7282

7346

7411 7475

7

8

38

57

7539

7603

7668

7732

7796

7861

7925

7989

8053 8118

51

58

8182

8246

8310

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8567

8632

8696 8760

V

58

59

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8889

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9017

9081

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9210

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6760

9467

9531

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9660

9724

9788

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9917

9981 0045

61

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0366

0431

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0623 0687

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1009

1073

1137

1201

1265 1330

63

1394

1458

1522

1587

1651

1715

1779

1843

1908 1972

64

2036

2100

2164

2229

2293

2357

2421

2485

2550 2614

65

2678

2742

2806

2871

2935

2999

3063

3127

3192 3256

66

3320

3384

3448

3512

3577

3641

3705

3769

3833 3898

67

3962

4026

4090

4154

4218

4283

4347

4411

4475 4539

68

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4732

4796

4860

4924

4988

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5117 5181

69

5245

5309 5373

5438

5502

5566

5630

5694

5758 5823

6770

5887

5951

6015

6079

6143

6207

6272

6336

6400 6464

71

6528

6592

6656

6721

6785

6849

6913

6977

7041 7105

72

7169

7234

7298

7362

7426

7490

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7618

7683 7747

73

7811

7875

7939

8003

8067

8131

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8260

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8837

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75

9093

9157

9221

9285

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9413

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9542

9606 9670

76

9734

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9862

9926

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0054

0119

0183

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78

1016

1080

1144

1208

1272

1336

1400

1464

1528 1592

79

1656

1720

1784

1849

1913

1977

2041

2105

2169 2233

6780

2297

2361

2425

2489

2553

2617

2681

2745

2809 2873

81

2937

3001

3066

3130

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3258

3322

3386

3450 3514

82

3578

3642

3706

3770

3834

3898

3962

4026

4090 4154

83

4218

4282

4346

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4538

4602

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4730 4794

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4922

4986

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5371 5435

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5499

5563

5627

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5819

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6011 6075

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6651 1 6715

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6778

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7034

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7162

7226

7290,7354

88

7418

7482

7546

7610

7674

7738

7802

7866

7930' 7994

89

8058

8122

8186

8250

8314

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8442

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8570 8634

6790

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8762

8826

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9018

9081

9145

9209 9273

91

9337

9401

9465

9529

9593

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92

9977

0041

5105

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0424

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94

1255

1319

1383

1447

1511

1575

1639

1703

1767

1831

2
3
4

13
19
25

95

1895

1959

2022

2086

2150

2214

2278

2342

2406

2470

96

2534

2598

2662

2725

2789

2853

2917

2981

3045

3109

5

32

97

3173

3237

3300

3364

3428

3492

3556

3620

3684

3748

6

7

8

38
44
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98

3812

3875

3939

4003

4067

4131

4195

4259

4323

4387

99

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4450

4514
1

4578

2

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4

4770

5

4834

6

4898

7

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122

LOGARITHMS

N. 680 L. 832

N.

6800
01
02
03
04

05

06
07
08

8325089
5728
6366
7005
7643

8281

8919

9558

8330195

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6810

1471

11

?109

12

2746

13

3384

14

4021

15

4659

16

5296

17

5933

18

6570

19

7207

6820

7844

21

8480

22

9117

23

9754

24

8340390

25

1027

26

1663

27

2299

28

2935

29

3571

6830

4207

31

4843

32

5479

33

6114

34

6750

35

7385

36

8021

37

8656

38

9291

39

9926

6840

8350561

41

1196

42

1831

43

2465

44

3100

45

3735

46

4369

47

5003

48

5638

49

6272

N.

1

5153
5792
6430
7069
7707

8345

8983
9621
0259
0897

1535
2173
2810
3448
4085

4722
5360
5997
6634
7271

7907
8544
9181
9817
0454

1090
1726
2363
2999
3635

4271
4906
5542
6178
6813

7449
8084
8719
9354
9990

0625
1259
1894
2529
3163

3798
4432
5067
5701
6335

1

5217
5855
6494
7132
7771

8409
9047
9685
0323
0961

1599
2236
2874
3511
4149

4786
5423
6060
6697
7334

7971
8608
9244
9881
0517

1154
1790
2426
3062
3698

4334
4970
5606
6241
6877

7512
8148
8783
9418
0053

0688
1323
1958
2592
3227

3861
4496
5130
5764
6398

5281
5919
6558
7196
7835

8473
9111
9749
0387
1025

1662
2300
2938
3575
4212

4850
5487
6124
6761
7398

8035
8672
9308
9945
0581

1217
1854
2490
3126
3762

4398
5034
5669
6305
6940

7576
8211
8846
9481
0117

0751
1386
2021
2656
3290

3925
4559
5194
5828
6462

5345
5983
6622
7260
7898

8537
9175
9813
0451
1088

1726
2364
3001
3639
4276

4913
5551
6188
6825
7462

8098
8735
9372
0008
0645

1281
1917
2553
3190
3826

4461
5097
5733
6368
7004

7639

8275
8910
9545
0180

0815
1450
2085
2719
3354

3988
4623
5257
5891
6525

5

5408
6047
6686
7324
7962

8600
9238
9877
0514
1152

1790
2428
3065
3703
4340

4977
5614
6251
6888
7525

8162
8799
9435
O072
0708

1345
1981
2617
3253
3889

4525
5161
5796
6432
7067

7703
8338
8973
9609
0244

0878
1513
2148
2783
3417

4052
4686
5320
5955
6589

5

6

5472
6111
6749

7388
8026

8664
9302
9940
0578
1216

1854
2491
3129
3766
4404

5041
5678
6315
6952
7569

8226
8862
9499
6136
0772

1408
2045
2681
3317
3953

4589
5224
5860;
6496
7131

7766
8402
9037
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0307

0942
1577
2212
2846
3481

4115
4750
5384
6018
6652

6

5536
6175
6813
7452
8090

8728
9366
6004
0642
1280

1918
2555
3193
3830
4467

5105
5742
6379
7016
7653

8289
8926
9563
6199
0836

1472
2108
2744
3380
4016

4652
5288
5924
6559
7195

7830
8465
9100
9736
6371

1005
1640
2275
2910
3544

4179
4813
5447
6081
6716

8

5600
6239
6877
7515
8154

8792
9430
6068
0706
1344

1981
2619
3256
3894
4531

5168
5806
6443
7080
7716

8353

8990
9626
6263
0899

1536
2172

2808
3444
4080

4716
5351
5987
6623
7258

7893
8529
9164
9799
6434

1069
1704
2338
2973
3608

4242
4876
5511
6145
6779

9

5664
6302
6941
7579
8217

8856
9494
6132
0770
1407

2045
2683
3320
3958
4595

5232
5869
6506
7143

7780

8417
9053
9690
6327
0963

1599
2235

2872
3508
4143

4779
5415
6051
6686
7322

7957
8592
9227
9863
6498

1132
1767
2402
3037
3671

4306
4940
5574
6208
6842

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D

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64

11 6
2' 13

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D

N.

685 L. 835 of numbers.

123

N.

6850

1

6969

2

7033

3 1 4

7096,7159

5
7228

6
7286

7

7349

8

7413

9

7476

D

Pro.

8356906

51

7540

7603

7666

7730

7793

7857

7920

7983

8047

8110

63

52

8174

8237

8300

8364

8427

8490

8554

8617

8681

8744

1 G

53

8807

8871

8934

8997

9061

9124

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9251

9314

9378

2 13

54

9441

9504

9568

9631

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9821

9885

9948

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8 60<,

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56

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0771

0835

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0961

1025

1088

1151

1215

1278

57

1341

1405

1468

1531

1595

1658

1721

1785

1848

1911

58

1975

2038

2101

2165

2228

2291

2355

2418

2481

2545

59

2608

2671

2735

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2861

2925

2988

3051

3115

3178

6860

3241

3304

3368

3431

3494

3558

3621

3684

3748

3811

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3874

3937

4001

4064

4127

4191

4254

4317

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4507

4570

4634

4097

4760

4824,

4887

4950

5013

5077

63

5140

5208

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5330

5393

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5520

5583

5646

5709

64

5773

5836

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5963

6026

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6152

6216

6279

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65

6405

6469

6532

6595

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6722

6785

6848

6911

6975

66

7038

7101

7164

7228

7291

7354

7417

7481

7544

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67

7670

7734

7797

7860

7923

7987

8050

8113

8176

8240

68

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8866

8429

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8556

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69

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1843

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2032

74

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OF NUMBERS.

125

N.

1

2

9973

3

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6950

8419b48

9911

51

8420473 0535

0598

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52

1098

1160

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3596

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4969

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5468

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6716

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62

7340

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7964

8026

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64

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67

8430458

0520

0583

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63

1081

1144

1206

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2328

2390

2452

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71

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3013

3075

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73

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8450360

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2

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0098
0723
1348
1972
2597

3221
3845
4470
5094
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6342
6966
7590
8213

8837

9461
0084
0707
1331
1954

2577
3200
3823
4446
5069

5691
6314
6936

6

0160
0785
1410
20351
2659

3284
3908
4532
5156
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6404
7028
7652
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9523
6146
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1393
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2639
3262

3885
4508
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6376
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1975
2597
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5082
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6325
6946
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8188
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9429
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8803
9425
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1913
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3156
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2702
3325
3948
4570
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5816
6138
7061
7683
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8928
9550
0172
0794
1415

2037
2659
3280

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0910 0973
1535 1597
2160' 2222
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126

LOGARITHMS

N. 7(K)L.bl6

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01
02
03
04

05
06
07
08
09

7010
11
12
13
14

15
16
17
18
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7020
21
22
23
24

25
26
27
28
29

7030
31
32
33
34

35
36
37
38
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7040
41
42
43
44

45
46
47
48
49

N.

8450980
1601
2221
2841
3461

4081
4701
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5941
6561

7180
7800
8419
9038
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8460277
0896
1515
2134
2752

3371
3990
4608
5227
5845

6463
7081
7700
8318
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8470171
0789
1406
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2641
3258
3876
4493
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5727
6343
6960
7577
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9426
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1275

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1042
1663
2283
2903
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4143
4763
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9720

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1577
2196
2814

3433

4052
4670
5289
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6525
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7761
8379
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0850
1468
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2703
3320
3937
4554
5171

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7022
7639
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9488
0104
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1104
1725
2345
2965
3585

4205
4825
5445
6065
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7304
7924
8548
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1639
2257
2876

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4113
4732
5350
5969

6587
7205
7823
8441
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0912
1530
2147

2764
3382
3999
4616
5233

5850
6467
7084
7700
8317

8933
9550

0166
0782
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3

4

5

1167

1229

1291

1787

1849

1911

2407

2469

2531

3027

3089

3151

3647

3709

3771

4267

4329

4391

4887

4949

5011

5507

5569

5631

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7428

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1143

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2938

3000

3062

3557

3619

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4175

4237

4299

4794

4856

4917

5412

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5536

6031

6092

6154

6649

6711

6772

7267

7329

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7947

8009

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9244

9739

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1036

1097

1591

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2209

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7145

7207

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7762

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9118

9611

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9735

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0905

0967

1460
3

1522
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1583

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1353
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2593
3213
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5073
5693
6313
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7552
8171
8791
9410
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1267
1886
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4979
5598
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1159
1777
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3629
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2035
2655
3275
3895

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1948
2567
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1477
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2717
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5817
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8915
9584
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1391
2010
2629
3247

3866
4485
5103
5721
6340

6958
7576

8194
8812
9430

5047
0665
1283
1900
2518

3135
3752
4369
4986
5603

6220
6837
7454
8070
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9303
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0536
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2159
2779
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1458
2072
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3928
4546
5165
5783
6401

7020
7638
8256
8874
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5109
0727
1344
1962
2579

3197
3814
4431
5048
5665

6282
6899
7515
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8748

9365
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8573325

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06

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07

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7786
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8991

9594
5196
0798
1400
2002

2604
3206

3808
4409
50U

5613
6214
6815
7417
8018

8619
9220
9821
0422
1023

1623
2224

2824
3425

4029

4625
5226
5826

7566
8165
8765
9365
9964 1

0564'
1163
1762
2362
2961

3

7626
8225

8825
9425
5024

0624
1223
1822
2422
3021

5

6

7

3627

3687

3747

4230

4290

4350

4833

4893

4953

5436

5496

5556

6038

6099

6159

6641

6701

6762

7244

7304

7364

7847

7907

7967

8449

8509

8570

9051

9112

9172

9654

9714

9774

5256

5316

5377

0858

0918

0979

1460

1521

1581

2062

2123

2183

2664

2724

2785

3266

8326

3387

3868

3928

3988

4470

4530

4590

5071

5131

5192

5673

5733

5793

6274

6334

6394

6876

6936

6996

7477

7537

7597

8078

8138

8198

8679

8739

8799

9280

9340

9400

9881

9941

5001

0482

0542

0602

1083

1143

1203

1683

1743

1803

2284

2344

2404

2884

2944

3005

3485

3545

3605

4085

4145

4205

4685

4746

4806

5286

5346

5406

5886

5946

6006

6486

6546

6606

7086

7146

7206

7686

7746

7806

8285

8345

8405

8885

8945

9005

9485

9545

9605

5084

5144

5204

0684

0744

0803

1283

1343

1403

1882

1942

2002

2481

2541

2601

3081

3140

3200

5

6

7

8 9

380713868
4411 4471
5014,5074
5616 5677
6219 6280

6822 6882
7425 7485
8027! 8088
8630 8690
9232 9292

9835
5437
1039
1641
2243

2845
3447

4048
4650
5252

5853
6455
7056
7657

8258

8859
9460
0061
0662
1263

1863
2464
3065
3665
4265

4866
5466
6066
6666
7266

7866
8465
9065
9665
5264

0663
1463
2062
2661
3260

8

9895
5497
1099
1701
2303

2905
3507
4109
4710
5312

5913
6515
7116
7717
8318

8919
9520
5121
0722
1323

1924
2524
3125
3725
4325

4926
5526
6126
6726
7326

7925
8525
9125
9724
5324

0923
1523
2122
2721
3320

D

60

D

Pro.

60

6
12
18
24
90
36
42
48
9| 54

59

6
12
18
24
SO
35
41
47

a

PU.

1

2
3

4
5
6

7
8
9

N.

72oL. 860 OF NUMBEKS. 131 1

N.

1

•2

3

4

5

(i

7

b

9

D

Pm.

7350

8603380

3440

3500

3560

3620

3M0

3739

3799

3859

3919

51

3979

4039

4099

4159

4219

4279

4338

4398

4458

4518

60

b2

4578

4638

4698

4756

4817

4877

4937

4997

5057

5117

I G

53

5177

5237

5297

5356

5416

5476

5536

5596

5656

5716

3 IS

54

5776

5835

5895

5955

6015

6075

6135

6195

6254

6314

4 'M

56

6374

6434

6494

6554

6614

6673

6733

6793

6853

6913

a 311

56

6973

7033

7099

7152

7212

7272

7332

7393

7452

75H

It 3ii

57

7571

7631

7691

7751

7811

7870

7930

7990

8050

8110

58

B170

8229

8289

8349

8409

8469

8529

8589

8648

870S

r, _,,j

59

S768| 8828

8888

8947

9007

9067

9127

9187

9247

9306

—

7860

9366 9426

9486

9546

9605

9665

9725

9785

9845

9905

61

9964 6024

6084

(>144'0204

0263

5323

0383

0443

0503

62

8610562 0622

0682

0742! 0802

0861

0921

0981

1041

llOI

63

1160 1220

1280

1340 1400

1459

1519

1579

1639

1699

64

1758 ISIS

1878

193S: 1997

2057

2117

2177

2237

2296

65

2356 2416

2476

2536 2595

2655

2715

2775

2834

2894

■ 66

2954 3014

3073

313313193

3253

3313

3372

3432

3492

67

3552 3611

367 i

3731! 3791

3850

3910

3970

4030

4089

6S

4149 4209

4269

432^' 4388

4448

4508

4567

4627

4687

4747, 4806

4866

4926 4986

5045

5105

5165

5225

5284

7270

5344: 5404

5464

5523! 5583

5643

5703

5762

5622

5882

71

594116001

6061

6I21I6I8O

6240

6300

6360

6419

6479

72

6539, 6598

6658

6718i6778

6837

6897

6957

7016

7076

73

7136 7196

7255

7315.7375

7434

7494

7554

7614

7673

74

773S 7793

7852

7912

7972

8.031

8091

8151

6211

8270

75

833o' 8390

8449

8509

8569

S62B

8668

8748

8608

6867

76

8927

S967

9046

9106

9166

9225

9285

9345

9404

9464

77

9524

9583

9643

9703

9762

9822

9862

9941

0001

0061

78

8620131

0180

0240

0300

0359

0419

0479

0538

0596

0658

79

0717

0777

0837

0896

0956

1016

1075

1135

1194

1254

7880

1314

1373

1433

1493

1552

1612

1672

1731

1791

1851

81

1910

1970

2030

2089

2149

2209

226S

2328

2387

2447

82

2507

2566

2626

2686

2745

2805

2865

2924

2984

3043

83

31U3

3163

3222

3282

3342

3401

3461

3520

3580

3640

84

3699

3759

3819

3878

3938

3997

4057

4117

4176

4236

85

4296

4355

4415

4474

4534

4594

4653

471S

4772

4632

86

4892

4951

5011

5070

5130

5190

5249

5309

5368

5428

87

5488

5547

5607

5666

5726

5786

5845

5905

5964

6024

88

6084

6143

6203

6262

6322

6382

6441

6501

6560

6620

89

6680

6739

6799

685S

6918

6977

7037

7097

7156

7216

5*90

7275

7335

7394

7454

7514

7573

7633

7692

775a

7811

91

7871

7931

7990

8050

8109

6169

8228

6286

8347

6407

92

8467

8526

8586

8645

3705

8764

8824

S883

6943

9003

59

93

9062

9122

9181

9241

9300

9360

9419

9479

9539

9598

1

94

9658

9717

9777

9836

9S96

9955

0015

0074

0134

0193

2 12

3 18

4 M

5b

8630253

0312

0372

0432

0491

0551

0610

0670

0729

0789

96

0848

0908

0967

1027

1086

1146

1205

1265

1324

1384

S 30
e 36

97

1443

1503

1562

1622

[0S2

1741

1801

I960

1920

1979

9S

2039

209&

215b

2217

2277

2336

2396

2455

2515

2574

8 47

\~^

2634

2693

2753

2812

2872

2931
5

2991
6

3050

7

3110

8

3169
9

"D

9 63
Pli.

In.

U ( I

~V

3

4

132

LOGARITHMS N. 730 L. 863

N.

7300

1

2
3348

3

3407

4

3467

5

3526

6

7

3645

8

3705

9

D

Pro.

8633229

3288

3586

3764

01

3823

3883

3942

4002

4061

4121

4180

4240

4299

4359

60

02

4418

4478

4537

4597

4656

4716

4775

4835

4694

4954

1 6

03

5013

5072

5132

5191

5251

5310

5370

5429

5489

5548

2 12

4t 1

04

5608

5667

5727

5766

5845

5905

5964

6024

6083

6143

3 18

4 24

05

6202

6262

6321

6381

6440

6499

6559

6618

6678

6737

5 30

06

6797

6856

6916

6975

7034

7094

7153

7213

7272

7332

6 36

7 42

8 48

07

7391

7451

7510

7569

7629

7668

7748

7807

7867

7926

OS

7985

8045

8104

8164

8223

8283

8342

8401

8461

8520

9 54

09

8580

8639

8698

8758

8817

8877

8936

8996

9055

9114

7310

9174

9233

9293

9352

9411

9471

9530

9590

9649

9708

11

9768

9827

9887

9946

0005

0065

0124

0184

0243

0302

12

8640362

0421

0481

0540

0599

0659

0718

0778

0837

0896

13

0956

1015

1075

1134

1193

1253

1312

1371

1431

1490

14

1550

1609

1668

1728

1787

1846

1906

1965

2025

2084

15

2143

2203

2262

2321

2381

2440

2500

2559

2618

2678

16

2737

2796

2856

2915

2974

3034

3093

3152

3212

3271

17

3331

3390

3449

8509

3568

3627

3687

3746

3805

3865

IS

3924

3983

4043

4102

4161

4221

4280

4339

4399

4458

19

4517

4577

4636

4695

4755

4814

4873

4933

4992

5051

7320

5111

5170

5229

5269

5348

5407

5467

5526

5585

5645

1

21

5704

5763

5823

5882

5941

6001

6060

6119

6179

6238

22

6297

6357

6416

6475

6534

6594

6653

6712

6772

6831

23

6890

6950

7009

7068

7128

7167

7246

7305

7365

7424

,

24

7483

7543

7602

7661

7721

7780

7839

7898

7958

8017

25

8076

8136

8195

8254

8313

8373

8432

8491

6551

8610

26

8669

8728

8788! 8847

8906

6966

9025

9084

9143

9203

1

27

9262

9321

9380 9440

9499

9556

9616

9677

9736

9795

28

9855

9914

9973

0032

0092

0151

0210

0269

0329

0388

29

8650447

0506

0566

0625

0684

0743

0803

0662

0921

0980

7330

1040

1099

1158

1217

1277

1336

1395

1454

1514

1573

31

1632

1691

1751

1810

1869

1928

1968

2047

2106

2165

32

2225

2264

2343 2402

2461

2521

2560

2639

2698

2758

\

33

2617

2876

2935*2995

3054

3113

3172

3231

3291

3350

\

34

3409

3468

3527

3587

3646

3705

3764

3824

3883

3942

\

35

4001

4060

4120

4179

4238

4297

4356

4416

4475

4534

}

36

4593

4652

4712

4771

4830

4889

4948

5008

5067

5126

37

5185

5244

5304

5363

5422

5481

5540

5600

5659

5718

38

5777

5836

5»95

5955

6014

6073

6132

6191

6251

6310

39

6369

6426

6487

6546

6606

6665

6724

6783

6842

6901

7340

6961

7020

7079

7136

7197

7256

7316

7375

7434

7493

41

7552

7611

7671

7730

7789

7848

7907

7966

8025

8065

42

8144

8203

8262

8321

6380

8440

6499

8558

8617

8676

59 ^

43

8735

8794

8854

8913

6972

9031

9090

9149

9208

9268

1 6 ^

44

9327

9386

9445

9504

9563

9622

9661

9741

9600

9859

2 12

3 18

4 24^ ^

45

9918

9977

0036

5095

0155

0214

0273

0332

0391

0450

46

8660509

0568

0627

0687

0746

0805

0664

0923

0962

1041

5 30^

47

1100

1160

1219

1278

1337

1396

1455

1514

1573

1632

48

1691

1751

1810

1869

1928

1987

2046

2105

2164

2223

7 41

8 4:;

9 &:i

Pte.

r

49

N.

2282

2342
1

240112460

2519

2578

5

2637
6

2696

7

2755
8

2814
9

D

(

1 2

3

4

N. 735 L. 866

OP NUMBERS.

133

N

7350
51
52
53
54

55
56
57

58
59

7360
61
62
63
64

6^
66
67
68
69

7370
71
72
73
74

75
76
77

78
79

7380
81
82
83
84

85
86
87
88
89

390
91
92
93
94

95
96
97
98
JI9

N.

8662873
3464
4055
4646
5236

5827
6417
7008
7598

8188

8778
9368
9958
8670548
1138

1728
2317
2907
3496
4086

4675
5264
5853
6442
7031

7620
8209
8798
9387
9975

8680564
1152
1740
2329
2917

3505
4093
4681
5269
5857

6444
7032
7620
8207
8794

9382
9969
8690556
1143
1730

1

2932
3523
4114
4705
5295

5886
6476
7067
7657
8247

8837
9427
5017
0607
1197

2992
3582
4173
4764
5354

5945
6535
7126
7716
8306

S896
9486
0076
0666
1256

1786 1845
2376, 2435
2966 3025
3555' 3614
4145' 4203

4734; 4793
5323 5382
5912 5971
6501 6560
7090 7149

7679 773S
8268 8327
8857 8916
9445 9504
6034 0093

0622 0681
1211 1270
1799 1858
238812446
2976 i 3035

3564: 3623
4152|4211
4740: 4799

5328
5915

6503
7091
7678
8266
8853

9441
6028
0615
1202
1789

"r

5386
5974

6562
7150
7737
8325
8912

9499
0086
0674
1261
1848

3

4

5

3051

3110

3169

3641

3701

3760

4232

4291

4350

4823

4882

4941

5413

5472

5532

6004

6063

6122

6594

6653

6712

7185

7244

7303

7775

7834

7893

8365

8424

8483

8955

9014

9073

9545

9604

9663

0135

6194

6253

0725

0784

0843

1315

1374

1433

1904

1963

2022

2494

2553

2612

3084

3142

3201

3673

3732

3791

4262

4321

4380

4852

4911

4970

5441

5500

5559

6030

6089

6148

6619

6678

6737

7208

7267

7326

7797

7856

7915

8386

8445

8503

8974

9033

9092

9563

9622

9681

6152

6211

6269

0740

0799

0858

1329

1387

1446

1917

1976

2035

2505

2564

2623

3093

3152

3211

3681

3740

3799

4269

4328

4387

4857

4916

4975

5445

5504

5563

6033

6092

6151

6621

6679

6738

7208

7267

7326

7796

7855

7913

8383

8442

8501

8971

9029

9088

9558

9617

9675

6145

6204

6263

0732

0791

0850

1319

1378

1437

1906

1965

2024

3

\

[ 5

6

3228
3819
4409
5000
5591

6181
6771
7362
7952
8542

9132
9722
6312
0902
1492

2081
2671
3260
3850
4439

5028
5618
6207
6796
7385

7974
8562
9151
9740
6328

0917

3287
3878
4468
5059
5650

6240
6830
7421
8011
8601

9191
9781
6371
0961
1551

2140
2730
3319
3909
4498

5087
5677
6266
6855
7444

8032
8621
9210
9799
6387

0976

1505' 1564

2093
2682
3270

3858
4446
5034
5622
6209

6797
7385
7972
8560
9147

9734
6321
0908
1495
2082

2152
2740
3329

3917
4505
5093
5680
6268

6856
7443
8031
8618
9206

9793

6380
0967
1554
2141

8

9

3346
3937
4528
5118
5709

6299
6889
7480
8070
8660

9250
9840
6430
1020
1610

2199
2789
3378
3968
4557

5146
5735
6325J 6383

3405
3996

4587
5177
576S

6358
6949
7539
8129
8719

9309
9899
6489
1079
1669

2258
2848
3437
4027
4616

5205
5794

6914
7502

8091
8680
9269
9857
6446

1034
1623
2211
2799
3387

3975
4563
5151
5739
6327

6915
7502
8090
8677
9264

9852
6439
1026
1613
2200

6972
7561

8150
8739
9328
9916
6505

1093
1682
2270
2858
3446

4034
4622
5210
5798
6386

6973
7561
8148
8736
9323

9910
6497
1085
1672
2259

"9"

ID

59

Pro.

59

6
12
18
24
30
35
41

47
63

D

5'

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2! 12

3
4
5
6

7

8

9

17
23
21>
35
41
4G
52 ;

PtH. !

r

134

LOGARITHMS N. 740 L. 869

7400

1 1 2 3

2376 2435 2493

4
2552

5

2611

6

2669

7

2728

8

2787

9

2845

D

Pro.

1

8692317

01

2904

2963 3021 3080

3139

3197

3256

3315

3373

3432

59

02

3491

3549 3608 3667

3725

3784

3843

S901

8960

4019

03

4077

4136 4195 4253

4312

4371

4429

4488

4547

4605

m

2

1 *'

12

04

4664

4723 4781

4840

4899

4957

5016

5075

5133

5192

»

18

Ail

05

5251

5309 5368

5427

5485

5544

5603

5661

5720

5778

4
5

24
,10

06

5637

5896 5954

6013

6072

6130

6189

6248

6306

6365

G

S5

07

6423

6482 6541

6599

6658

6717

6775

6834

6892

6951

7

41

08

7010

7068 7127

7186

7244

7303

7361

7420

7479

7537

8

47

09

7596

7655 7713

7772

7830

7889

7948

8006

8065

8123

9) 00

7410

8182

8241 8299

8358

8417

8475

8534

8592

8651

8710

11

8768

8827 8885 8944

9003

9061

9120

9178

9237

9296

12

9354

9413 9471

9530

9588

9647

9706

9764

9823

9881

13

9940

9999 0057

0116

0174

0233

0292

0350

0409

0467

14

8700526

0584 0643 0702

0760

0819

0877

0936

0994

1053

15

1112

1170 1229 1287

1346

1404

1463

1522

1580

1639

16

1697

1756 18141 1873

1931

1990

2049

2107

2166

2224

17

2283

2341 2400 2458

2517

2576 2634

2693

2751

2810

18

2868

2927 2985 3044

3102

3161 3220

3278

3337

3395

19

3454

3512 357 1| 3629

3688

3746

3805

3863

3922

3981

7420

4039

4098* 4156

4215

4273

4332

4390

4449

4507

4566

21

4624

4683 4741

4800

4858

4917

4975

5034

5092

5151

1

22

5210

5268 5327 5385

5444

5502

5561

5619

5678

5736

1

23

5795

5853 59121 5970

6029

6087

6146

6204

6263

6321

1
1

24

6380

6438 6497 6555

i

6614

6672

6731

6789

6848

6906

1

25

6965

7023 7082,7140

7199

7257

7316

7374

7432

7491

26

7549

7608 766617725

7783

7842

7900

7959

8017

8076

27

8134

8193 825118310

8368

8427

8485

8544

8602

8660

1

1

28

8719

8777; 8836: 8894

8953

9011

9070

9128

9187

9245

1

29

9304

9362; 9421

9479

9537

9596

9654

9713

9771

9830

7430

9888

9947' 5005

0063

0122

0180

0239

0297

0356

0414

1

31

8710473

0531 0589

0648

0706

0765

0823

0882

0940

0999

32

1057

1115

11174

1232

1291

134&

1408

1466

1524

1583

33

1641

1700! 1758

1817

1875

1933

1992

2050

2109

2167

34

2226

2284 2342

2401

2459

2518

2576

2634

2693

2751

35

2810

2868

2927 2985

3043

3102

3160

3219

3277

3335

36

3394

3452

3511 3569

3627

3686

3744

3803

3861

3919

37

3978

4036

4095

4153

4211

4270

4328

4387

4445

4503

3S|

4j62 4620

4679

4737

4795

4854

4912

4970

5029

5087

39 1

5146

5204

5262

5321

5379

5437

5496

5554

5613

5671

7440

5729

5768

5846

5904

5963

6021

6080

6138

6196

6255

41i

6313

6371

6430

6488

6546

6605

6663

6722

6780

6838

42]

6897

6955

7013

7072

7130

7188

7247

7305

7363

7422

58

43!

7480

7539

7597

7655

7714

7772

7830

7889

7947

8005

1 a

44

8064

8122

8U0

8239

8297

8355

8414

8472

6530

8589

2
3
4

12
17

45

8647

8705

8764

8822

8880

8939

8997

9055

9114

9172

2:«

46

9230

9289

9347

9405

9464

9522

9580

9639

9697

9755

6

2!l

47

9814

9872

9930

9988

0047

0105

0163

0222

0280

0338

6

7
8

3.%
41
4(i

48

8720397

0455

0513

0572

0630

0688

0747

0605

0863

0921

49

0980

1038

1096

1155

1213

1271

1330

13S8
7

1446

8

1 504

!l

52

1

^

D

1

FMs.

1 K. 745 L. 872

OF NUMBERS.

N.

7450
51
52
53
54

55
56
57

58
59

7460
61
62
63
64

65
66
67
68
69

7470
71
72
73

74

75
76

77
78
79

7480
81

82
83
84

85
86
87
88
89

7490
91
92*
93i
94

95
96
97
98

1
1621

2

1679

3

1738

4
1796

8721563

2146

2204

2262

2320

2379

2728

2787

2845

2903

2962

3311

3369

3428

3486

3544

3894

8952

4010

4069

4127

4476

4535

4593

4651

4709

5059

5117

5175

5234

5292

5641

5700

5758

5816

5874

6224

6282

6340

6398

6457

6806

6864

6923

6981

7039

7388

7446

7505

7563

7621

7970

8029

8087

8145

8203

8552

8611

8669

8727

8785

9134

9193

9251

9309

9867

9716

9774

9838

9891

9949

8730298

0356

0414

0473

0581

0880

0938

0996

1054

1113

1462

1520

1578

1636

1694

2043

2101

2159

2218

2276

2625

2683

2741

2799

2857

8206

3264

3322

8380

3489

8787

3845

3904

3962

4020

4369

4427

4485

4543

4601

4950

5008

5066

5124

5182

5531

5589

5647

5705

5763

6112

6170

6228

6286

6344

6693

6751

6809

6867

6925

7274

7332

7390

7448

7506

7855

7913

7971

8029

8087

8435

8493

8551

8610

8668

9016

9074

9132

9190

9248

9597

9655

9713

9771

9829

8740177

0235

0293

0351

0409

0757

0815

0874

0932

0990

1338

1396

1454

1512

1570

1918

1976

2034

2092

2150

2498

2556

2614

2672

2730

3078

3136

3194

3252

3310

3658

3716

3774

3832

8890

4238

4296

4354

4412

4470

4818

4876

4934

4992

5050

5398

5456

5514

5572

5630

5978

6036

6094

6152

6210

6557

6615

6673

6731

6789

7137

7195

7253

7311

7869

7716

7774

7832

7890

7948

8296

8354

8412

8470

8528

8875

8933

8991

9049

9107

9454

9512

9570

9628

9686

8750034

0091

0149

0207
3

0265
4

1 2

1854
2487
8020
8603
4185

4768
5850
5938
6515
7097

7679
8261
8848
9425
0007

0589
1171
1752
2334
2915

3497
4078
4659
5240
5821

6402
6983
7564
8145
8726

9306
9887
0467
1048
1628

2208

2788
^8
3948

4528

5108
5688
6268
6847
7427

8006
8585
9165
9744
0328

to

6

1912
2495
3078
8661
4243

4826
5408
5991
6573
7155

7789
8820
8902
9484
6065

0647
1229
1810
2892
2973

8555
4136
4717
5298

5880

6461
7041
7622
8208

8784

9364
9945
0525
1106
1686

2266
2846
3426
4006
4586

5166
5746
6325
6905
7485

8064
8648
9223
9802
0881

1971
2554
3186
8719
4302

4884
5467
6049
6631
7214

7796
8378
8960
9542
0124

0705
1287
1869
2450
3082

3613
4194
4775
5357
5938

6519
7100
7680
8261

8842

9422
5003
0588
1164
1744

2324
2904
3484
4064
4644

5224
5804
6888
6968
7543

8122
9701
9281
9860
0439

8

2029
2612
8195
8777
4860

4942
5525
6107
6690
7272

7854
8486
9018
9600
0182

0764
1345
1927
2508
8090

8671
4252
4884
5415
5996

6577
7158
7788
8819
8900

9480
0061
0641
1222
1802

2882
2962
8542
4122
4702

5282
5862
6441
7021
7600

8180
8759
9839
9918
0497

I 7 I 8

9^

2087
2670
3258
8886
4418

5001
5588
6166
6748
7880

7912
8494
9076
9658
0240

0822
1408
1985
2566
8148

8729
4811
4892
5478
6054

6635
7216
7797

8377
8958

9538
0119
0699
1280
1860

2440
3020
8600
4180
4760

5840
5920
6499
7079
7658

8238
8817
9396
9976
0555

D

135

Pro.

58

58

1
2
3
4
6
6

7

8
9

6
12

17
23
29
35
41
46
52

57

I
2
3
4

5
6

7
8

D

6
II

17
23
29
34
40
46
51

Pin.

136

) LOGARITHMS N. 750 L. 875

N.

7500

1
0671

2

0728

3

0786

4
0844

5
0902

6
0960

7

1018

8

1076

9

1134

D

Pro.

8750613

01

1192

1250

1307

1365

1423

1481

1539

1597

1655

1718

58

02

1771

1828

1886

1944

2002

2060

21liB

2176

2234

2292

1

03

2349

2407

2465

2523

2581

2639

2697

2755

2813

2870

2 12

04

2928

2986

3044

3102

3160

3218

3275

3333

3391

3449

•f

4

23

05

3507

3565

3623

3681

3738

3796

3854

3912

3970

4028

6

29

06

4086

4143

4201

4259

4317

4375

4433

4491

4548

4606

6

7

8

36

41

07

4664

4722

4780

4838

4896

4953

5011

5069

5127

5185

* 1
46

08

5243

5300

5358

5416

5474

5532

5590

5648

5705

5763

9

62

09

5821

5879

5937

5995

6052

6110

6168

6226

6284

6342

7510

6399

6457

6515

6573

6631

6689

6746

6804

6862

6920

11

6978

7035

7093

7151

7209

7267

7325

7382

7440

7498

12

7556

7614

7671

7729

7787

7845

7903

7960

8018

8076

13

8134

8192

6249

8307

8365

8423

8481

8539

8596

8654

14

8712

8770

8828

8885

8943

9001

9059

9116

9174

9232

15

9290

9348

9405

9463

9521

9579

9637

9694

9752

9810

16

9868

9925

9983

6041

0099

5157

0214

5272

5330

[5388

17

8760446

0503

0561

0619

0677

0734

0792

0850

0908

0965

18

1023

1081

1139

1197

1254

1312

1370

1428

1485

1543

19

1601 1659

1710

1774

1832

1890

1947

2005

2063

2121

7520

2178

2236

2294 2352

2409

2467

2525

2583

2640

2698

21

2756

2814

2871

2929

2987

3045

3102

3160

3218

3276

22

3333

3391

3449

3506

3564

3622

3680

3737

3795

3853

23

3911

3968

4026

4084

4142

4199

4257

4315

4372

4430

24

4488

4546

4603

4661

4719

4776

4834

4892

4950

5007

25

5065

5123

5180

5238

5296

5354

5411

5469

5527

5584

26

5642

5700

5758

5815

5873

5931

.5988

6046

6104

6161

27

6219

6277

6335

6392

6450

6508

6565

6623

6681

6738

28

6796

6854

6911

6969

7027

7085

7142

7200

7258

7315

29

7373

7431

7488

7546

7604

7661

7719

7777

7834

7892

7530

7950

8007

8065

8123

8180

8238

8296

8353

8411

8469

31

8526

8584

8642

8699

8757

8815

8872

8930

8988

9045

32

9103

9161

9218

9276

9334

9391

9449

9507

9564

9622

33

9680

9737

9795

9853

9910

9968

0026

5083

5141

5199

34

8770256

0314

0371

0429

0487

0544

0602

0660

0717

0775

35

0833

0890

0948

1005

1063

1121

1178

1236

1294

1351

36

1409

1467

1524

1582

1639
2216

1697

1755

1812

1870

1928

37

1985

2043

2100

2158

2273

2331

2388

2446

2504

38

2561

2619

2677

2734

2792

2849

2907

2965

3022

3080

39

3137

3195

3253

3310

3368

3425

3483

3541

3598

3656

7540

3713

37*1

3829

3886

3944

4001

4059

4117

4174

4232

41

4289

4347

4405

4462

4520

4577

4635

4693

4750

4808

42

4865

4923

4980

5038

5096

5153

5211

5268

5326

5384

57

43

5441

5499

5556

5614

5671

5729

5787

5844

5902

5959

1 6

44

6017

6074

6132

6189

6247

6305

6362

6420

6477

6535

2

11

• m

45

6592

6650

6708

6765

6823

6880

6938

6995

7053

7110

3

4

17
23

46

7168

7226

7283

7341

7398

7456

7513

7571

7628

7686

6

29

47

7743

7801

7859

7916

7974

8031

8089

8146

8204

8>61

6

am

34

48

8319

8376

8434

8492

8549

8607

8664

8722

8779

8837

7

40
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49

N.

8894

8952
1

9009
2

9067
3

9124
4

9182
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9239

9297

i

9354

8

9412

9

I)

o
9

51

1

H%.

N.

755 L. 877 of numbers. 137

N.

1
9527

2

9585

3

9642

4
9700

5
9757

&

7

9872

8

9930

9
9987

D

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7550

8779470

9815

51

8780045

0102

0160

0217

0275

0332

0390

0447

0505

0562

58

52

0620

0677

0735

0792

0850

0907

0965

1022

1080

1137

1

6

53

1195

1252

1310

1367

1425

1482

1540

1597

1655

1712

2

12

4 ^

54

1770

1827

1885

1942

2000

2057

2115

2172

2230

2287

3
4

17
23

55

2345

2402

2460 2517

2575

2632

2690

2747

2805

2862

6

29

56

2919

2977

3034; 3092

3149

3207

3264

3322

3379

3437

6

7

8

36

41
46

57

3494

355(2

3609 3667

3724

3782

3839

3896

3954

4011

58

4069

4126

4184

4241

4299

4356

4414

4471

4529

4586

9

62

59

4643

4701

4758 4816

4873

4931

4988

5046

5103

5161

7560

5218

5275

5333 5390

5448

5505

5563

5620

5678

5735

61

5792

5850

5907.5965

1

6022

6080

6137

6194

6252

6309

62

6367

6424

6482 6539

6596

6654

6711

6769

6826

6884

63

6941

6998

7056 7113

7171

7228

7286

7343

7400

7458

64

7515

7573

7630

7687

7745

7802

7860

7917

7975

8032

65

8089

8147

8204 8262

8319

8376

8434

8491

8549

8606

66

8663

8721

8778 8836

8893

8950

9008

9065

9123

9180

67

9237

9295

9352,9410 9467

9524

9582 9639

9696

9754

68

9811

9869

9926 9983 0041

0098

0156,0213

0270

0328

69

8790385

0442

0500 0557

0615

0672

0729

0787

0844

0901

7570

0959

1016

1074 1131

1188

1246

1303

1360

1418

1475

71

1532

1590

1647

1705

1762

1819

1877

1934

1991

2049

'

72

2106

2163

2221

2278

2335

2393, 2450

2508

2565

2622

73

2680

2737

2794

2852

2909

2966 3024

3081

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8426

8844

8897

K949

9368

9420

9473

|9891

9944

9996

0415

0467

0519

3

4

5

4855
5382
5908
6434
6960

7486
8012
8538
9064
9590

0116
0642
1167
1693
2218|

2744
3269;
3795
4320
4845|

5370
5895
6420
6945
7470|

7995
8520,
9044,
9569
0094

0618
1143
1667
2191
2715

3240
3764
4288
4812
5336

5860
6383
6907
7431
7954

8478
9002
9525
O048
0572

6

490S
5434
5961
6487
7013

7539
8065
8591
9117
9643

0169
0694
1220
1745
2271

2796
3322
3847
4372

4898

5423
5948
6473
6998
7523

8047
8572
9097
9621
0146

0671
1195
1719
2244
2768

3292
3816
4340
4864
5388

5912
6436
6960
7483
8007

8530
9054
9577
0101
0624

8

4961
54S7
6013
6539
7066

7592
8118
8644
9169
9695

0221
0747
1272
1798
2323

2849
3374
3900
4425
4950

5475
6000
6525
7050
7575

8100
8625
9149
9674
0198

0723
1247
1772
2296

2820

3344
3869
4393
4917
5441

5964
6488
7012
7536
8059

8583
9106
9630
0153
0676

8

9

5013
5540
6066
6592

7118

7644
8170
8696
9222

9748

0274
0799
1325
1851
2376

2901
3427
3952
4477
5003

5528
6053
6578
7103
7628

8152
8677
9202
9726
0251

0775
1300
1824
2348
2873

3397
3921
4445
4969
5493

6017
6541
7064
7588
8112

8635
9159
9682
0205
0729

9

D

151

Pro.

53

1
2
3
4
6
6

7
8

6
II
16
21

27
32

37
42

48

52

1 5

2 10

3 16
A 21

5 28

6 31

7 38

8 42
9 47

D I PI-. I

152

LOGARITHMS N. 830 L. 919

N.

8300

1
0833

2

0886

3

0938

4

0990

5

1043

6

1095

7

1147

8

1200

9

1252

D

Pro,

9190781

01

1304

1356

1409

1461

1513'

1566

1618

1670

1723

1775

53

02

1827

1880

1932

1984

2037

2089

2141

2193

2246

2298

1

5

03

2350

2403

2455

2507

2560

2612

2664

2717

2769

2821

2

11

1 4*

04

2873

2926

2978

3030

3083 '

i

3135

3187

3239

3*292 3344 1

3

4

16
21

05

3396

3449

3501

3553

3606

3658

3710

3762

3815

3867

5

27

06

3919

3972

4024

4076

4128;

4181

4233

4285

4338

4390

6

7
8

32

37
4i

07

4442

4494

4547

4599

4651 !

4703

4756

4808

4860

4913

08

4965

5017

5069

5122

51741

1

5226

5279

5331

5383

5435

^

48

09

5488

5540

5592

5644

56971

1

5749

5801

5853

5906

5958

8310

6010

6062

6115

6167

62191

6272

6324

6376

6428

6481

11

6533

6585

6637

6690

6742

6794

6846

6899

6951

7003

12

7055

7108

7160

7212

7264

7317

7369

7421

7473

7526

13

7578

7630

7682

7735

7787

7839

7891

7943

7996

8048

14

8100

8152

8205

8257

8309

8361

8414

8466

8518

8570

15

8623

8675

8727

8779

8831 !

8884

8936

8988

9040

9093

16

9145

9197

9249

9301

9354

9406

9458

9510

9563

9615

17

9667

9719

9771

9824

9876

9928

9980

0033

0085

5137

18

9200189

0241

0294

0346

0398

0450

0502

0555

0607

0659

19

0711

0763

0816

0868

0920

0972

1024

1077

1129

1181

8320

1233

1285

1338

1390

1442

1494

1546

1599

1651

1703

21

1755

1807

1860

1912 1964

2016

2068

2121

2173

2225

22

2277

2329

2381

2434 24S6

2538

2590

2642

2695

2747

23

2799

2851

2903

2955 3008'

3060

3112

3164

3216

3269

24

3321

3373 3425

3477

3529 ,

3582

3634

3686

3738

3790

25

3S42

3895 3947

3999

40511

4103

4155

4208

4260

4312

26

4364

4416

4468

4521

4573

4625

4677

4729

4781

4833

27

4886

4938

4990

5042 5094 j

5146

5199

5251

5303

5355

28

5407

5459 5511

1

5564 5616

5668

5720

5772

5824

5876

29

5929

5981 6033

6085' 6137

6189

6241

6294

6346

6398

8330

6450

6502 16554

6606 6659 j

6711

6763

6815

6867

6919

31

6971

7023; 7076

7128i7180

7232

7284 7336

7388

"t&io

7440

32

7493

7545' 7597

7649; 77011

7753

7805 7857

7962

33

8014

8066 8118

8170 8222'

8274

8327

8379

8431

8483

\

34

8535

8587 S639

8691 8743

8796

8848

8900

8952

9004

\

35

9056

9108 9160

9212 9264 19317

9369

9421

9473

9525

\

36

9577

9629 9681

9733 97851

9838

9890 9942

9994

0046

\

37

9210098

0150:0202

0254 0306 1

0358

0411

0463

0515

0567

38

0619

067 1 ! 0723

0775 0827

0879

0931

0983

1036

1088

39

1140

1192il244

1

1296 1348 i

1

1400

1452

1504

1556

1608

8340

1661

1713 1765

1817 1869;

1921

1973 2025

2077

2129

41

2181

2233 2285

2337 2389!

2442

2494,2546

2598

2650

42

2702

27541 2806

2858 2910

2962

3014 3066

3118

3170

52 i

43

3222

3274' 3327

3379,3431

3483

3535

3587

3639

3691

1

5|

44

3743

3795 3847

3899, 3951

4003

4055

4107

4159

4211

2
3

4

10
IG
21

45

4263

4315

4367

4420l 4472

4524

4576 4628

4680

4732

46

4784

4836

4888

4940; 4992

5044

5096 5148

5200

5252

6 26i

47

5304

5356

5408

5460

5512

5564

5616 5668

5720

5772

6

7
8

31

48

5824

5876

5928

5980

6032;

6085

6137, 6189

6241

6293

36
42

49

6345

6397
1

6449

2

6501 6553

6605
5

665716709

6761

8

6813

9

;d

9

47

3

4

6

7

^

Pt*.

N.

835 L. 921 OP NUMBERS.

153

N

8350

1

6917

2

6969

3

7021

4
7073

5 1 6

7

8

7281

9
7333

D

Pro.

9216865

7125 7177 7229

51

7385

7437

7489

7541

7593

7645

7697

17749

7801

7853

52

1 ^

52

7905

7957

8009

8061

8113

8165

8217 8269

8321

8373

53

8425

8477

8529

8581

8633

8685

8737 8789

8841

8893

52

1
2

10

54

8945

8997

^49

9101

9153

9205

9257 9309

9361

9413

3

16

55

9465

9517

9569

9620

9672

9724

9776 9828

9880

9932

4

21

56

9984

0036

5088

0140

5192

0244

5296 0348

5400

5452

«.w

Q 31

57

9220504

0556

0608

0660

0712

0764

0816 0868

0920

0972

1

7

36

58

1024

1076

1128

1180

1232

1283

1335 1387

1439

1491

8

42

59

1543

1595

1647

1699

1751

1803

1855 1907

1959

2011

9 47

8360

2063

2115

2167

2219

2271

2323

2374 2426

2478

2530

61

2582

2634

2686

2738

2790

2642

2894 2946

2998

3050

62

3102

3154

3206

3257

3309V3361

3413 3465

3517

3569

63

3621

3673

3725

3777

3829

3881

3933 3984

4036

4088

64

4140

4192

4244

4296

4348

4400

4452 4504

4556

4608

65

4659

4711

4763

4815

4867

4919

4971

5023

5075

5127

66

5179

5231

5282

5334

5386

5438

5490 5542

5594

5646

67

5698

5750

5801

5853

5905

5957

6009 6061

6113

6165

68

6217

6269

6321

6372

6424

6476

6528

6580

6632

6684

69

6736

6788

6839

6891

6943

6995

7047

7099

7151

7203

8370

7255

7306

7358

7410

7462

7514

7566

7618

7670

7722

71

7773

7825

7877

7929

7981

8033

8085

8137

8188

8240

72

8292

8344

8396

8448

8500

8552

8603

8655

8707

8759

73

8811

8863

8915

8967

9018

9070

9122

9174

9226

9278

74

9330

9381

9433

9485

9537

9589

9641

9693

9744

9796

75

9848

9900

9952

5004

0056

0107

5159

5211

5263

5315

76

9230367

0419

0470

0522

0574

0626

0678

0730

0781

0833

77

0885

0937

0989

1041

1093

1144

1196

1248

1300

1352

78

1404

1455

1507

1559

1611

1663

1715 1766

1818

1870

79

1922

1974

2026

2077

2129

2181

2233 2285

2337

2388

8380

2440

2492

2544

2596

2647

2699

2751

2803

2855

2907

81

2958

3010

3062

3114

3166

3217

3269

3321

9373

3425

82

3477

3528

3580

3632

3684

3736

3787

3839

3891

3943

83

3995

4046

4098

4150

4202

4254

4305 4357

4409

4461

84

4513

4564

4616

4668

4720

4772

4823

4875

4927

4979

S5

5031

5082

5134

5186

5238

5290

5341

5393

5445

5497

ee

5549

5600

5652

5704

5756

5808

5859

5911

5963

6015

S7

6066

6118

6170

6222

6274

6325

6377

6429

6481

6532

S8

6584

6636

6688

6740

6791

6843

6895

6947

6998

7050

%9

7102

7154

7205

7257

7309

7361

7413

7464

7516

7568

190

7620

7671

7723

7775

7827

7878

7930

7982

8034

8085

91

8137

8189

8241

8292

8344

8396

8448

8499

8551

8603

92

8655

8707

8758

8810

8862

8913

8965

9017

9069

9120

51

93

9172

9224

9276

9327

9379

9431

9483

9534

9586

963H

1

5

S>4

9690

9741

9793

9845

9897

9948

5000

5052

5104

5155

2
3
4

10
15
20

95

9240207

0259

0310

0362

0414

0466

0517

0569

0621

0673

96

0724

0776

0828

0879

0931

0983

1035

1086

1138

1190

5

20

97

1242

1293

1345

1397

1448

1500

1552

1604

1655

1707

G

7

8

.^1

30
41

\ 98
\ 99

1759

1810

1862

1914

1966

2017

2069

2121

2172

2224

2276

2328

2379

2431

2483

4

2534
5

2586

2638

2689

8

2741
9

[d

»

4(;

IN.

1

2

3

6

7

J

Pis.

154

LOGARITHMS N. 840 L. 924

N.

8400

1

2845

2

2896

3

2948

4

3000

5

3051

6

3103

7
3155'

8

.3206

9

3258

D

pitL

9242793

01

3310

3362

3413

3465

3517

3568

3620

3672

3723

3775

52

02

3827

3878

3930

3982

4034

4085

4137

4189

4240

4292

li i\

03

4344

4395

4447

4499

4550

4602

4654

4705

4757

4809

S* 10

3; 16
4i 21

04

4860

4912

4964

5015

5067

5119

5170

5222

5274

5326

05

5377

5429

5481

5532

5584

5636

5687

5739

5791

5842

b\ 26

06

5894

5946

5997

6049

6101

6152

6204

6255

6307

6359

51

31

7. »
8 a

07

6410

6462

6514

6565

6617

6669

6720

6772

6824

6875

08

6927

6979

7030

7082

7134

7185

7237

7289

7340

7392

9 47

09

7444

7495

7547

7598

7650

7702

7753

7805

7857

7908

8410

7960

8012

8063

8115

8167

8218

8270

8321

8373

8425

11

8476

8528

8580

8631

8683

8734

8786

8838

8889

8941

12

8993

9044

9096

9148

9199

9251

9302

9354

9406

9457

13

9509

9561

9612

9664

9715

9767

9819

9870

9922

9973

14

9250025

0077

0128

0180

0232

0283

0335

0386

0438

0490

1

15

0541

0593

0644

0696

0748

0799

0851

0902

0954

1006

16

1057

1109

1160

1212

1264

1315

1367

1418

1470

1522

17

1573

1625

1676

1728

1780

1831

1883

1934

1986

2038

18

2089

2141

2192

2244

2296

2347

2399

2450

2502

2554

1

19

2605

2657

2708

2760

2811

2863

2915

2966

3018

3069

f

8420

3121

3172

3224

3276

3327

3379

3430

3482

3534

3585

!

21

3637

3688

3740

3791

3843

3895

3946

3998

4049

4101

1
1

22

4152

4204

4256

4307

4359

4410

4462

4513

4565

4616

1

23

4668

4720

4771

4823

4874

4926

4977

5029

5080

5132

'

24

5184

5235

5287

5338

5390

5441

5493

5544

5596

5648

1

25

5699

5751

5802

5854

5905

5957

6008

6060

6111

6163

1
1

26

6215

6266

6318

6369

6421

6472

6524

6575

6627

6678

1

27

6730

6781

6833

6885

6936

6988

7039

7091

7142

7194

28

7245

7297

7346

7400

7451

7503

7554

7606

7657

7709

29

7761

7812

7864

7915

7967

8018

8070

8121

8173

8224

8430

8276

8327

8379

8430

8482

8533

8585

8636

8688

8739

31

8791

8842

8894

8945

8997

9048

9100

9151

9203

9254

32

9306

9357

9409

9460

9512

9563

9615

9667

9718

9770

1

33

9821

9873

9924

9975

CH)27

0078

0130

0181

0233

0284

1

1
1

34

9260336

0387

0439

0490

0542

0593

0645

0696

0748

0799

1

35

0851

0902

0954

1005

1057

1108

1160

1211

1263

1314

1

\

36

1366

1417

1469

1520

1572

1623

1675

1726

1778

1829

\

37

1880

1932

1983

2035

2086

2138

2189

2241

2292

2344

38

2395

2447

2498

2550

2601

2653

2704

2755

2807

2858

39

2910

2961

3013

3064

3116

3167

3219

3270

3322

3373

8440

3424

3476

3527

3579

3630

3682

3733

3785

3836

3888

41

3939

3990

4042

4093

4145

4196

4248

4299

4351

4402

42

4453

4505

4556

4608

4659

4711

4762

4814

4865

4916

1

51

43

4968

5019

5071

5122

5174

5225

5277

5328

5379

5431 !

1

44

5482

5534

5585

5637

5688

5739

5791

5842

5894

5945

4

I
I

45

5997

6048

6099

6151

6202

6254

6305

6357

6408

6459

46

6511

6562

6614

6665

6716

6768

6819

6871

6922

6974

5

2?

47

7025

7076

7128

7179

1231

7282

7333

7385

7436

7488

6

7

8

48

7539

7590

7642

7693

7745

7796

7847

7899

1

7950

8002

4

49

IN.

8053

8105
I

8156
1 --i

8207

8259

8310

8362
6

8413

7

8464

8

8516
9

D

9

k^

3

! 4

1

Pte^

N.S45L.926

OF NUMBERS.

155

N-

1
8618

2
8670

8450

9268567

51

9081

9132

9184

52

9595

9646

9698

53

9270109

0160

0211

54

0622

0674

0725

55

1136

1187

1239

56

1650

1701

1752

57

2163

2215

2266

58

2677

2728

2780

59

3190

3242

3293

8460

3704

3755

3806

61

4217

4268

4320

62

4730

4782

4833

63

5243

5295

5346

64

5757

5808

5859

65

6270

6321

6372

66

6783

6834

6885

67

7296

7347

7398

68

7808

7860

7911

69

8321

8373

8424

8470

8834

8885

8987

71

9347

9396

9449

72

9859

9911

9962

73

9280372

0423

0475

74

0885

0936

0987

75

1397

1448

1500

76

1909

1961

2012

77

2422

2473

2524

78

2934

2985

3037

79

3446

3498

3549

8480

3959

4010

4061

81

4471

4522

4573

1 82

4983

5034

5085

83

5495

5546

5597

84

6007

6058

6109

8^

6518

6570

6621

86

7030

7081

7133

87

7542

7593

7644

88

8054

8105

8156

89

8565

8616

8668

B490

9077

9128

9179

91

9588

9640

9691

92

9290100

0151

0202

93

0611

0662

0714

94

1123

1174

1225

95

1634

1685

1736

96

2145

2196

2247

97

2656

2707

2758

98

3167

3218

3269

^9

3678

3729
1

3780

2

N.

8721
9235
9749
0263

0777

1290
1804
2317
2831
3344

3858
4371
4884
5397
5910

6424
6937
7449
7962
8475

8988
9501
0013
0526
1038

1551
2063
2576
3088
3600

4112
4624
5136
5648
6160

6672

7184
7696
8207
8719

9230
9742
0253
0765
1276

1787
2298
2810
3321
3832

8773
9287
9800
0314
0828

1342
1855
2369

2882
3396

3909
4422
4935
5449
5962

6475
6988
7501
8014
8526

9039
9552
0065
0577
1090

1602
2114
2627
3189
8651

4163
4675
5187
5699
6211

6723
7235
7747

8258
8770

9282
9793
0304
0816
1327

1838
•2350
2861
3372
3883

8824
9338
9852
0366
0879

1393
1907
2420
2934
3447

3960
4474
4987
5500
6013

6

8875
9389
9903
0417
0931

1444
1958
2471
2985
3498

4012
4525
5038
5551
6064

I

6526 6577
7039 7090
7552 7603
8065 8116
8578; 8629

9090
9603
0116
0628
1141

1658
2166
2678
3190
3702

4215
4727
5239
6751
6263

6774
7286
7798
8310

8821

9333
9844
0356
0867
1378

1889
2401
2912
3423
3934

9142
9654
6167
0680
1192

1705
2217
2729
3241
3754

4266
4778
5290
5802
6314

6826
7337
7849
8361

8872

9384
9895
0407
0918
1429

1941
2452
2963
3474
3985

"6

8927
9441
9955
0468
0982

1496
2009
2523
3036
3550

4063
4576
5089
5603
6116

6629
7142
7655
8167
8680

9193
9706
0218
0731
1243

1756
2268
2780
3293
3805

4317
4829
5341
5853
6365

6877
7389

7900
8412
8923

9435
9946
0458
0969
1480

1992
2503
3014
3525
4036

7

8978
9492
0006
0520
1033

1547
2061
2574

3088
3601

4114
4628
5141
5654
6167

6680
7193
7706
8219
8732

9244
9757
0270
0782
1295

1807
2319
2832
3344
3856

4368
4880
5392
5904
6416

6928
7440
7951
8463
8975

9486
9998
0509
1020
1532

2043
2554
3065
3576
4087

8

__9

9030
9543
0057
0571
1085

1598
2112
2625
3139
3652

4166
4679
5192
5705
6218

6731
7244
7757
8270

8783

9296
9808
0321
0833
1346

1858
2371
2883
3395
3907

4419
4931
5443
5955
6467

6979
7491
8003
8514
9026

9537
0049
0560
1071
1583

2094
2605
3116
3627
4138

9

D

Pro.

52

1

2
3
4
5
6

7
8

9

5
10
16
21
26
31
36
42
47

51

1
2
3
4
6
6

m
i

8
9

D

5
10
15
20
26
31
36
41

i?
Pts.

156

LOGARITHMS N. 850 L. 929

N.

8500

1
4240

2

4291

3

4343

4

4394

5
4445

6
4496

7

4547

8

4598

9

4649

D

Pto.

9294189

01

4700

4751

4802

4853

4905

4956

5007

5058

5109

5160

52

02

5211

5262

5313

5364

5415

5466

5517

5569

5620

5671

I

5

1 A

03

5722

5773

5824

5875

5926

5977

6028

6079

6130

6181

.

2
3
4

10
IG
21

04

6233

6284

6335

6386

6437

6488

6539

6590

6641

6692

05

6743

6794

6845

6896

6947

6998

7050

7101

7152

7203

5 26

gt\ ml

06

7254

7305

7356

7407

7458

7509

7560

7611

7662

7713

7

8

36

07

7764

7815

7866

7917

7969

8020

8071

8122

8173

8224

42

08

8275

8326

8377

8428

8479

8530

8581

8632

8683

8734

9

47

09

8785

8836

8887

8938

8989

9040

9091

9142

9194

9245

8510

9296

9347

9398

9449

9500

9551

9602

9653

9704

9755

11

9806

9857

9908

9959

5010

0061

5112

5163

5214

5265

12

9300316

0367

0418

0469

0520

0571

0622

0673

0724

0775

13

0826

0877

0928

0979

1030

1081

1132

1183

1234

1285

14

1336

1387

1438

1489

1540

1591

1643

1694

1745

1796

i* V

15

1847

1898

1949

2000

2051

2102

2153

2204

2255

2306

51

16

2357

2408

2459

2510

2561

2612

2663

2713

2764

2815

17

2866

2917

2968

3019

3070

3121

3172

3223

3274

3325

18

3376

3427

3478

3529

3580

3631

3682

3733

3784

3835

19

3886

3937

3988

4039

4090

4141

4192

4243

4294

4345

8520

4396

4447

4498

4549

4600

4651

4702

4753

4804

4855

21

4906

4957

5008

5059

5110

5160

5211

5262

5313

5364

22

5415

5466

5517

5568

5619

5670

5721

5772

5823

5874

23

5925

5976

6027

6078

6129

6180

6231

6282

6333

6383

24

6434

6485

6536

6587

6638

6689

6740

6791

6842

6893

25

6944

6995

7046

7097

7148

7199

7250

7300

7351

7402

26

7453

7504

7555

7606

7657

7708

7759

7810

7861

7912

27

7963

8014

8064

8115

8166

8217

8268

8319

8370

8431

28

8472

8523

8574

8625

8676

8727

8777

8828

8879

8930

29

8981

9032

9083

9134

9185

9236

9287

9338

9388

9439

8530

9490

9541

9592

9643

9694

9745

9796

9847

9898

9949

31

9999

0050

6101

0152

0203

(1254

0305

5356

5407

5458

32

9310508

0559

0610

0661

0712

0763

0814

0865

0916

0967

33

1017

1068

1119

1170

1221

1272

1323

1374

1425

1475

34

1526

1577

1628

1679

1730

1781

1832

1883

1933

1984

1

35

2035

2086

2137

2188

2239

2290

2341

2391

2442

2493

I

36

2544

2595

2646

2697

2748

2798

2849

2900

2951

3002

\

37

3053

3104

3155

3205

3256

3307

3358

3409

3460

3511

\

38

3562

3612

3663

3714

3765

3816

3867

3918

3968

4019

1

39

4070

4121

4172

4223

4274

4324

4375

4426

4477

4528

8540

4579

4630

4680

4731

4782

4833

4884

4935

4986

5036

41

5087

5138

5189

5240

5291

5341

5392

5443

5494

5545

42

5596

5647

5697

5748

5799

5850

5901

5952

6002 6053

51

43

6104

6155

6206

6257

6307

6358

6409

6460

651 1; 6562

1

g^

44

6612

6663

6714

6765

6816

6867

6917

6968

7019' 7070

2
3

4

V0

45

7121

7171

7222

7273

7324

7375

7426

7476

752717578

46

7629

7680

7731

7781

7832

7883

7934

7985

8O35I 8066

5

2^

47

8137

8188

8239

8289

8340

8391

8442

8493

8544

8594

6

7
8

3E-

48

8645

8696

8747

8798

8848

8899

8950

9001

9052

9102

4W

49

N.

9153

9204

1

9255
2

9306
3

9356
4

9407

9458
()

9509

9560

9610

D

9

jl^

7

8

y

Pis.

j N. boo L. 931

OK NUMBEKS.

157 I

N.

1
9712

8550

9319661

51

9320169 0220

52

0677)0728

53

1185,1235

54

1692 1743

55

220012251

56

2708 2759

57

3215 3266

58

3723 3774

59

4230

4281

8560

4738 4788

61

5245 5296

62

5752 5803

63

6259 6310

64

6767 6817

1

65

727417324

66

778117831

67

8288 8338

68

8795 8845

69

930 1| 9352

8570

9808 9859

71

9330315, 0366

72

0822 0872

73

1328

1379

74

1835

1885

75

2341

2392

76

2848

2898

77

3354

3405

78

3860

3911

79

4367

4417

8580

4873

4923

81

5379

5430

82

5885

5936

83

6391

6442

84

6897

6948

85

7403

7454

86

7909

7959

87

8415

8465

88

8920

8971

89

9426

9477

S590

9932

9982

91

P340437

0488

92

0943

0993

93

1448

1499

94

1953

2004

95

2459

2509

96

2964

3015

97

3469

3520

98

3974

4025

99

4479

4530
1

N.

2

9763
0271
0778
1286
1794

2302
2809
3317
3824
4332

4839
5346
5854
6361
6868

7375

7882
8389
8696
9403

9910
0416
0923
1430
1936

2443
2949
3455
3962
4468

4974
5480
5986
6492
6998

7504
8010
8516
9021
9527

0033
0538
1044
1549
2055

2560
3065
3570
4075
4580

2

9814
0321
0829
1337
1&45

2352
2860
3368
3875
4382

4890
5397
5904
6412
6919

7426
7933
8440
8947
9453

9960
0467
0974
1480
1987

2493
3000
3506
4012
4519

5025
5531
6037
6543
7049

7555
8061
8566
9072
9578

0083
0589
1094
1600
2105

2610
3116
3621
4126
4631

3

4

5

6

9b64

9915

9966

0372

0423

0474

0880

0931

0982

1388

1439

14.S9

1696;

1946

1997

2403

2454

2505

2911

2962

3012

3418

3469

3520

3926

3977

4027

4433

4484

4535

4941

4991

5042

5448

5499

5549

5955

6006

6057

6462

6513

6564

6969

7020

7071

7476

7527

7578

7983

8034

8085

8490

8541

8592

8997

9048

9099

9504

9555

9606

0011

0062

0112

0518

0568

0619

1024

1075

1126

1531

1582

1632

2037

2088

2139

2544

2595

2645

3050

3101

3152

3557

3607

3656

4063

4114

4164

4569

4620

4670

5075

5126

5177

5581

5632

5683

6088

6138

6189

6594

6644

6695

7099

7150

7201

7605

7656

7707

8111

8162

8212

8617

8668

8718

9123

9173

9224

9628

9679

9729

0134

0184

0235

0639

0690

0740

1145

1195

1246

1650

1701

1751

2156

2200

2257

2661

2711

2762

3166

3217

3267

3671

3722

3772

4176

4227

4277

4682

4732

4783

4

5

6

8

0017
0525
1032
1540
2048

2555
3063
3571
4078
4585

5093
5600
6107
6614
7122

7629
8136
8643
9149
9656

0163
0670
1176
1683
2189

2696
3202
3709
4215
4721

5227
5733
6239
6745
7251

7757
8263
8769
9274
97S0

0286
0791
1296
1802| 1852
2307 2358

2812! 2863
3318| 3368
3823* 3873
4328| 4378
4833, 4884

0067
0575
1083
1591
2099

2606
3114
3621
4129
4636

5144
5651
6158
6665
7172

7679
8186
6693
9200
9707

0214
0720
1227
1733
2240

2746
3253
3759
4265
4772

5278
5784
6290
6796
7302

7808
6313
8819
9325
9831

0336
0842
1347

9

0118
0626
1134
1642
2149

2657
3165
3672
4160
4687

5194
5702
6209
6716
7223

7730
6237
6744
9251
9758

0264
0771
1276
1784
2291

2797
3303
3810
4316
4822

5328
5834
6341
6846
7352

7858
8364
8870
9375
9881

0387
0892
1398
1903
2408

2914
3419
3924
4429
4934

9

I)

Pro.

51

1

2
3
4

6
6

7
8

6
10
15
20
26
31
36
41
46

50

1
2
3
4
5
6

7
8

9

D

10
15
20
25
30
35
40
46

PU.

158

LOGARITHMS N. 860 Ll 934

N.

86U0

1
5035

2

5086

3

5136

4
5187

5
5237

6
5287

7

5338

8

5388

9

D

ft«.

9344985

5439

01

5489

5540

5590

5641

5691

5742

5792

5843

5893

5944

51

02

5994

6045

6095

6146

6196

6247

6297

6348

6398

6449

• 5

03

6499

6550

6600

6651

6701

6752

6802

6853

6903

6954

21 10
3 15

4| 20

04

7004

7054

7105

7155

7206

7256

7307

7357

7408

7458

05

7509

7559

7610

7660

7711

7761

7812

7862

7912

7963

5; 26

06

8013

8064

8114

8165

8215

8266

8316

8367

8417

8468

6: SI
7 ^

07

8518

8568

8619

8669

8720

8770

8821

8871

8922

8972

8

41

08

9023

9073

9123

9174

9224

9275

9325

9376

9426

9477

9

46

09

9527

9578

9628

9678

9729

9779

9830

9880

9931

9981

8610

9350032

0082

0132

0183

0233

0284

0334

0385

0435

0485

11

0536

0586

0637

0687

0738

0788

0838

0889

0939

0990

12

1040

1091

1141

1191

1242

1292

1343

1393

1444

1494

13

1544

1595

1645

1696

1746

1797

1847

1897

1948

1998

14

2049

2099

2150

2200

2250

2301

2^51
2855

2402

2452

2502

15

2553

2603

2654

2704

2754

2805

2906

2956

3006

16

3057

3107

3158

3208

325#

9309

3359

3410

3460

3511

17

3561

3611

3662

3712

3763

3813

3863

3914

3964

4015

18

4065

4115

4166

4216

4266

4317

4367

4418

4468

4518

19

4569

4619

4670

4720

4770

4821

4871

4922

4972

5022

8620

5073

5123

5173

5224

5274

5325

5375

5425

5476

5526

21

5576

5627

5677

6728

5778

5828

5879

5929

5979

6030

22

6080

6131

6181

6^3 1

6282

6332

6382

6433

6483

6533

23

6584

6634

6685

6735

6785

6836

6886

6936

6987

7037

24

7087

7138

7188

7239

7289

7339

7390

7440

7490

7541

25

7591

7641

7692

7742

7792

7843

7893

7943

7994

8044

26

8095

8145

8195

8246

8296

8346

8397

8447

849T

8548

27

8598

8648

8699

8749

8799

8850

8900

8950

9001

9051

28

9101

9152

9202

9252

9303

9353

9403

9454

9504

9554

f

29

9605

9655

9705

9756

9806

9856

9907

9957

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0058

8630

9360108

0158

0209

0259

0309

0360

0410

0460

0511

0561

31

0611

0661

0712

0762

0812

0863

0913

0963

1014

1064

32

1114

1165

1215

1265

1316

1366

1416

1466

1517 1567 1

33

1617

1668

1718

1768

1819

1869

1919

1970

2020

2070

34

2120

2171

2221

2271

2322

2372

2422

2473

2523

2573

35

2623

2674

2724

2774

2825

2875

2925

2975

3026

3076

1

36

3126

3177

3227

3277

3327

3378

3428

3478

3529

3579

\

37

3629

3679

3730

3780

3«30

3881

3931

3981

4031

4082

\

38

4132

4182

4233

4283

4333

4383

4434

4484

4534

4584

\

39

4635

4685

4735

4786

4836

4886

4936

4987

5037

5087

\

8640

5137

5188

5238

5288

5338

5389

5439

5489

5540

5590

\

41

5640

5690

5741

5791

5841

5891

5942

5992

6042

6092

42

6143

6193

6243

6293

6344

6394

6444

6494

6545

6595

50

43

6645

6695

6746

6796

6846

6896

6947

6997

7047

7097

I

^

44

7148

7198

7248

7298

7349

7399

7449

7499

7550

7600

2
3

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45

7650

7700

7750

7801

7851

7901

7951

8002

8052

8102

4

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46

8152

8203

8253

8303

8353

8403

8454

8504

8554

8604

6

30^

35^

4^

47

8655

8705

8755

8805

8855

8906

8956

9006

9056

9107

6

48

9157

9207

9257

9307

9358

9408

9458

9508

9559

9609

7
a

49

N.

9659

9709

9759

2.

9810
3

9860
4

9910
5

9960
6

0010

7

0061

dill

9

D

9

4ft--

_1_

8

1

Pls.

N.

865 L. 9.S7 OF NUMBERS. 159

N.

8650

I
0211

2

0261

3

0312

4

0362

5
0412

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0462

1

0513

8
0563

9

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9370161

51

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0713

0764

0814

0864

0914

0964

1015

1065

1115

50 i

52

1165

1215

1265

1316

1366

1416

1466

1516

1567

1617

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53

1667

1717

1767

1818

1868

1918

1968

2018

2069

2119

2 10

o ■ ■

54

2169

2219

2269

2319

2370

2420

2470

2520

2570

2621

3 15

4 20

55

2671

2721

2771

2821

2871

2922

2972

3022

3072

3122

5! 25

56

3172

3223

3273

3323

3373

3423 3474

3524

3574

3624

n\ 30

71 35
8 40

57

3674

3724

3775

3825

3875

3925 3975

4025

4075

4126

58

4176

4226

4276

4326

4376

442714477

4527

4577

4627

i) 45

59

4677

4728

4778

4828

4878

4928 4978

1

5028

5079

5129

8660

5179

5229

5279

5329

5380

5430

5480

5530

5580

5630

61

5680

5731

5781

5831

5881

5931

5981

6031

6082

6132

62

6182

6232

6282

6332

6382

6432

6483

6533

6583

6633

63

6683

6733

6783

6834

6884

6934

6984

7034

7084

7134

64

7184

7235

7285

7335

7385

7435

7485

7535

7585

7636

65

7686

7736

7786; 7836

7886

7936

7986

8037

8087

8137

66

8187

8237

82871 8337 i 8387

8437

8488

8538

8588

8638

67

8688

8738

87881 8838' 8888

8939 8989

9039

9089

9139

68

9189

9239

9289 9339:9389

94401 9490

9540

9590

9640

69

9690

9740

9790

9840 9890

1

9941

9991

5041

0091

0141

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1

8670

9380191

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0492

0542

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71

0692

0742

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084210892

0942

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1042

1093

1143

72

1193

1243

1293

1343; 1393

1443

1493

1543

1593

1643

73

1693

1744

1794

1844; 1894

1944

1994

2044

2094

2144

74

2194

2244

2294

2344! 2394

2445

2495

2545

2595

2645

75

2695

2745

2795

2845 2895

2945

2995

3045

3095

3145

76

3195

3245

3296

3346 3396

3446

3496

3546

3596

3646

77

3696

3746

3796

3846 3896

3946

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4046

4096

4146

78

4196 4247

4297

4347 4397

4447

4497

4547

4597

4647

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4797

484714897

i

4947

4997

5047

5097

5147

8680

5197 5247

5297

5347! 5397

5447

5497

5547

5598

5648

81

5698 5748

5798

5848 5898

5948

5998

6048

6098

6148

82

6198J6248

6298

6348 6398

6448

6498

6548

6598

6648

83

6698; 6748

6798

6848 6898

6948

6998

7048

7098

7148

84

719817248

7298

7348| 7398

7448

7498

7548

7598

7648

50

85

7698 7748

7798

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7948

7998

8048

8098

8148

86

8198 8248

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87

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8798

8848! 8898

8948

8998

9048

9098

9148

88

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9298

9348; 9398

9448

9498; 9548

9598

9648

89

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0098

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1097

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1197 1247

1297

1347

1397

1447

149711547

1597

1647

49

93

1697 j 1747

1797

1847

1897

1947

1997] 2046

2096

2146

1

5

94

2196 2246

2296

2346

2396

2446

2496

2546

2596

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95

2696 2746

2796

2846

2896

2946

2996

3045

3095

3145

3 lu

4 20

96

3195 3245

3295

3345

3395

3445

3495

35451 3595

3645

5 25

97

3695! 3745

3795

3845

3894

3944

3994

4044

4094

4144

6 29
71 34

8: so

98

4194*4244

4294

4344

4394

4444

4494

4544

4593

4643

99

4693

4743
1

4793

2

4843
3

4898
4

4943

5

4993
6

5043
7

5093

8

5143
9

D"

0' 44

N.

Pll.

160

LOGARITHMS N. 870 L. 9

39

N.

8700

1
5242

2

3

5342

4
5392

5

6
5492

7

5542

8

5592

9
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D

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5742

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5941

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6041

6091

6141

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6191

6241

6291

6341

6390

6440

6490

6540

6590

6640

50

03

6690

6740

6790 6840

6889

6939

6989

7039

7069

7139

1
2
3

10
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04

7189

7239

7289

7339

7388

7438

7488

7538

7588

7638

05

7688

7738

7788

7837

7887

7937

7987

8037

8087

8137

4

5
6

20

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06

8187

8237

8286

8336

8386

8436

8486

8536

8586

8636

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SO

07

8685

8735

8785

8835

8885

8935

8985

9035

9084

9134

7

SA

08

9184

9234

9284 9334

9384

9434

9483

9533

9583

9633

8

40

09

9683

9733

9783

9833

9882

9932

9982

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5082

0132

9 4i

8710

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0331

0381

0431

0481

0531

0580

0630

1

11

0680

0730

0780

0830

0880

0929

0979

1029

1079

1129

12

1179

1229

1278 1328

1378

1428

1478

1528

1577

1627

13

1677

1727

1777

1827

1877

1926

1976

2026

2076

2126

14

2176

2225

2275 2325

2375

2425

2475

2524

2574 2624

15

2674

2724

2774 2823

2873

2923

2973

3023

3073 3122

16

3172

3222

3272

3322

3372

3421

3471

3521

3571

3621

17

3670

3720

3770

3820

3870

3920

3969

4019

4069

4119

18

4169

4218

4268

4318

4368

4418

4468

4517

4567

4617

19

4667

4717

4766

4816

4866

4916

4966

5015

5065

5115

8720

5165

5215

5264

5314

5364

5414

5464

5513

5563

5613

1

21

5663

5713

5762

5812

5862

5912

5962

6011

6061

6111

22

6161

6211

6260

6310

6360

6410

6460

6509

6559

6609

23

6659

6709

6758

6808

6858

6908

6957

7007

7057

7107

24

7157

7206

7256

7306

7356

7405

7455

7505

7555

7605

25

7654

7704

7754

7804

7853

7903

7953

8003

8053

8103

26

8152

8202

8252

8301

8351

8401

8451

8500

8550

8600

1

27

8650

8700

8749

8799

8849

8899

8948

8998

9048

9098

1

28

9147

9197

9247

9297

9346

9396

9446

9496

9545

9595

29

9645

9695

9744

9794

9844

9894

9943

9993

0043

0093

1

8730

9410142

0192

0242

0292

0341

0391

0441

0491

0540

0590

31

0640

0690

0739

0789

0839

0889

0938

0988

1038

1088

32

1137

1187

1237

1286

1336

1386

1436

1485

1535

1585

33

1635

1684

1734

1784

1834

1883

1933

1983

2032

2082

34

2132

2182

2231

2281

2331

2380

2430

2480

2530

2579

35

2629

2679

2729

2778

2828

2878

2927

2977

3027

3077

1

36

3126

3176

3226

3275

3325

3375

3425

3474

3524

3574

\

37

3623

3673

3723

3772

3822

3872

3922

3971

4021

4071

\

38

4120

4170

4220

4270

4319

4369

4419

4468

4518

4568

\

39

4617

4667

4717

47,66

4816

4866

4916

4965

5015

5065

\

8740

5114

5164

5214

5263

5313

5363

5412

5462

5512

5562

\
\

41

5611

5661

5711

5760

5810

5860

5909

5959

6009

6058

y

42

6108

6158

6207

6257

6307

6356

6406

6456

6505

6555

49

43

6605

6654

6704

6754

6803

6853

6903

6952

7002

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44

7101

7151

7201

7250

7300

7350

7399

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7499

7548

S 1^

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45

7598

7648

7697

7747

7797

7846

7896

7946

7995

8045

46

8095

8144

8194

8244

8293

8343

8393

8442

8492

8542

5

^^'^^^

47

8591

8641

8691

8740

8790

884G

8889

8939

8988

9038

6

2^
3^

48

9088

9137

9187

9237

9286

9336

9386

9435

9485

9535

7

49

9584

9634

I

9683
2

9733
3

9783
4

9832
5

9882

6

9932

7

9981
8

0031
9

D

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N.

Pit.

-

In. 87o L. i) 12

OF NUMDEUS.

161

N.

8750

1

013U

2

0180

0229

4

9420U81

0279

51

0577

0626

0676

0726

0775

52

1073

1123

1172

1222

1272

53

1569

1619

1669

171b

1768

54

2065

2115

2165

2214|2264

55

2562

2611

2661

2710

2760

56

3058

3107

3157

3206

3256

57

3553

3603

3653

3702

3752

58

4049

4099

4149

4198

4248

59

4545

4595

4644

4694

4744

8760

5041

5091

5140

5190

5239

61

5537

5586

5636

5686

5735

62

6032

6082

6132

6181

6231

63

6528

6578

6627

6677

6726

64

7024

7073

7123

7172

7222

65

7519

7569

7618

7668

7717

66

8015

8064

8114

8163 8213

67

8510

8560

8609

8659

8708

6S

9005

9055

9104

9154

9204

69

9501

9550

9600 9649

9699

8770

9996

0045

6095 0144

0194

71

9430491

0541

0590

0640

0689

72

0986

1036

1085

1135

1184

73

1481

1531

1580

1630

1679

74

1976

2026

2075

2125

2174

75

2471

2521

2570

2620

2669

76

2966

3016

3065

3115

3164

77

3461

3510

3560

3609

3659

78

3956

4005

4055

4104

4154

79

4450

4500

4549

4599

4648

16780

4945

4995

5044

5094

5143

81

5440

5489

5539

5588

5638

82

5934

5984

6033

6083

6132

83

6429

6478

6528

6577

6627

84

6923

6973

7022

7072

7121

85

7418

7467

7517

7566

7615

' 86

7912

7961

8011

8060

8110

87

8406

8456

8505

8555

8604

88

8900

8950

8999

9049

9098

' 1 89

9395

9444

9493

9543

9592

/«790

9889

9938

9988

5037

5086

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94403153

0432

0482

0531

0580

/ 92

0877

0926

0976

1025

1074

/ »3

1371

1420

1470

1519

1568

/ 94

1865

1914

1963

2013

2062

Q5

2358

2408

2457

2507

2556

96

2852

2902

2951

3000

30^0

97

3346

3395

3445

3494

3543

9S

3840

3889

3938

3988

4037

99

4333

43S3

1

4432

2

4481

3

4531

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4

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0825
1321
1817
2313

2810
3306
3801
4297
4793

5289
5785
6280
6776
7271

7767
8262

8758
9253
9748

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0739
1234
1729
2224

2719
3214
3708
4203
4698

5192

5687

6182i

6676

7170

7665
8159
8653
9148
9642

0136
0630
1124
1618
2112

2605
3099

3593

4086
4580

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7

0378
0875
1371
1867
2363

2859
3355
3851
4347
4843

5339
5834
6330
6825
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7816
83121
88071
93031
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8

0428
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1420
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3405

3901

4397

4892

5388
5884
6379;
6875
7371

7866
8361
8857
9352
9847

5343

0838
1333
1828
2323

2768 2818;
3263 3313;
3758 3807
4253' 4302
4747 4797

5242
5737
6231

5291
5786
6280

0478
0974
1470
1966
2462

2958
3454
3950
4446
4942

5438
5933
6429
6925
7420

7916
8411
8906
9402
9897

5392
0887
1382
1877
2372

2867
3362
3857
4352
4846

5341

9

0527
1023
1520
2016
2512

3008
3504
4000
4496
4991

5487
5983
6479
6974
7470

7965
8461
8956
9451
9946

5442
0937
1432
1927
2422

2917
3412
3906
4401
4896

5390

672616775
7220 7269

7714
8209
8703
9197
9691

5185
0679
1173
1667
2161

2655
3148
3642
4136
4629

7764
8258
8752
9246
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5235
0729
1223
1716
2210

2704
3198
3691
4185
4679

5835 5885
6330^6379
6824 6874
7319:7368

7813; 7863
8307' 8357
8802,8851
9296 1 9345
9790 9839

D

Pro.

5284
0778
1272
1766
2260

2753
3247
3741
4234
4728

5333
0827
1321
1815
2309

2803
3297
3790
4284
4777

9

50

1

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4

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7
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6
10
15
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35
40
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49

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2
3
4
5
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7

8
9

D

5
10

15
20
25
29
34
3.9
44

l&^

LOGAKITHMS N. 8S0 L. 944

bhUO

1

4876

2

4925

3

4975

4

5024

5
5073

6

7

8

9

5271

D

Pro.

9444827

5123

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OF NUMBERS.

167

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6582

3

6630

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6726

6
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8

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1042

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1138

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1282

1330

1378

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61

1761

1809

1857

1905

1953

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2049

2097

2145

2198

62

2241

2289

2336

2384

2432

2480

2528

2576

2624

2672

63

2720

2768

2816

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3007

3055

3103

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64

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3247

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65

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5067

68

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5163

5211

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69

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77

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1145

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81

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1432

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1576

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82

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2437

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3058

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92

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6738

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6929

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93

7072

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168

LOOAKITHHS

N.

9100

9590414

01

0891

02

1368

03

1845

04

2322

05

2S00

06

3276

07

3753

08

4230

09

4707

9110

5184

11

5660

12

6137

13

6614

14

7090

15

7567

16

8043

17

8520

18

8996

19

9472

9120

9948

21

9600425

22

0901

23

1377

24

1853

25

2329

26

2805

27

3281

28

3756

29

4232

0130

4708

31

5183

32

5659

33

6135

34

6610

35

7086

36

7561

37

8036

38

8512

39

8987

9140

9462

41

9937

42

9610412

43

0887

44

1362

45

1837

46

2312

47

2787

48

3262

49

3736

1

N.

0462
0939
1416
1893
2370

2847
3324
3801
4278
4755

5231
5708
6185
6661
7138

7614
8091
8567
9044
9520

9996
0472
0948
1424
1900

2376
2852
3328

3804

4280

4755
5231
5707
6182
6658

7133
7008
8084
8559
9034

9509
9985
0460
0935
1410

1885
2359
2834
3309

3784

I

0509
0987
1464
1941
2418

2895
3372
3849
4326

4802

5279
5756
6232
6709
7186

7662

8138
8615
9091
9567

0044
0520
0996
1472
1948

2424
2900
3376
3851
4327

4803
5279
5754
6230
6705

7181
7656
8131
8607
9082

9557
5032
0507
0982
1457

1932
2407
2882
3357
3831

0557
1034
1511
1989
2466

2943
3420
3b96
4373

4850

5327
5803
6280
6757
7238

7710
8186
8662
9139
9615

0091
0567
1044
1520
1996

2472
2947
3423
3899
4375

4850
5326
5802
6277
6753

7226
7704
8179
8654
9129

9605
5080
0555
1030
1505

1980
2454
2929
3404
3H79

"1~

0605
1082
1559
2036
2513

2990
3467
3944
4421

4898

5374
5851
6328
6804
7281

7757
8234
8710
9186
9663

5139
0615
1091
1567
2043

2519
2995
3471
3947
4422

4898
5374
5849
6325
6800

7276
7751
8226
8702
9177

9652
5127
06«>2
1077
1552

2027
2502
2977
3451
3926

0653

1130i

1607

2084

2561

3038
3515
3992
4469
4945

5422
5899
6375
6852
7328

7805
8281
8758
9234
9710

r*186
0663
1139
1615
2091

2567
3043

0700
1177
1655
2132
2609

3086
3563
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4516
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5470
5946
6423
6900
7376

7853
8329
8805
9282
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5234
0710
1186
1662
2138

2614
3090

3518 3566

4

3994
4470

4946
5421
5897
6372

6848

7323
7799
8274
8749
9224

9700
5175
0650
1125
1600

2075
2549
3024
3499
3974

5

4042
4517

4993
5469
5044
6420
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7371
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8797
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3133
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4087
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1710
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1273
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5564
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7466
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8416
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2692
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8

9

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1321
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3706
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7043
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7513
7989
8464
8939
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9890
5365
0840
1315
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2264
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9

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5
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34
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Pi

I
IJ

N. 915 L. 961

OF NUMUERS

169

N.

9150

9614211

51

4686

52

5160

53

5635

54

6109

55

6583

56

7058

57

7532

58

8006

59

8481

9160

8955

61

9429

62

9903

63

9620377

64

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65

1325

66

1799

67

2272

68

2746

69

3220

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3S
39

* 9540
41
42
43
44

43
46
47

48

-1?

NT

3

9777236
7693
8150
8607
9064

9521
9978
9780435
0892
1348

1805
2262
2718
3175
3631

4088
4544
5001
5457
5913

6369
6826
7282
7738
8194

8650
9106
9562
9790017
0473

0929
1385
1840
2296
2751

3207
3662
4118
4573

5028

5484
5939
6394
6849
7304

7759
8214
8669
9124
9579

1

7282
7739
8196
8653
9110

9567
(1024
0481
0937
1394

1851
2307
2764
3221
3677

4134
4590
5046
5503
5959

6415
6871
7327
7783
8239

8695
9151
9607
0063
0519

0975
1430
1886
2341
2797

3253
3708
4163
4619
5074

5529
5984
6440
6895
7350

7805
8260
8715
9170
9624

I

732^
7785
8242
8699
9156

9613
d069
0526
0983
1440

1897
2353
2810
3266
3723

4179
4636
5092
5548
6005

6461
6917
7373
7829
8285

8741
9197
9653
0109
0564

1020
1476
1931
2387

2843

3298
3754
4209
4664
5120

5575
6030
6485
6940
7395

7850
8305
8760
9215
9670

2

7373
7830

8267
8744
9201

9658
5115
0572
1029
1485

1942
2399
2855
3312
3768

4225
4681
5138
5594
6050

6506
6962
7419

7875
8331

878T
9243
9698
0154
0610

1066
1521
1977
2433

2888

3344
3799
4254
4710
5165

5620
6076
6531
6986
7441

7896
8351

sme

9261
9715

3

7419
7876
8333
8790
9247

9704
0161
0618
1074
1531

1988
2444
2901
3358
3814

4270
4727
5183
5640
6096

6552
7008
7464
7920
8376

8832
9283
9744
0200
0656

nil

1567
2023
2478
2934

3389
3845
4300
4755
5211

5666
6121
6576
7031
7486

7941
8396
8851
9306
9761

7465
7922
8379
8836
9293

9750
0207
0663
1120
1577

2033
2490
2947
3403
3860

4316
4773
5229
5685
6\A]

6598
7054
7510
7966
8422

8878
9334
9790
0245
0701

1157
1613
2068
2524
2979

3435
3890
4346
4801
5256

5711
6167
0622
7077
7532

7987
8442
8897
9352
9806

6

7510
7967
8424
8881
9338

9795
0252
0709
1166
1622

2079
2536
2992
3449
3905

4362

4818
5274
5731
6187

6643
7099
7555
8011
8467

8923
9379

7

7556
8013
8470
8927
9384

9841
0296
0755
1211
1668

2125
2581
3038
3495
3951

4407
4864
5320
5776
6233

6689
7145
7601

6057
8513

8969
9425

9835-9881

0291
0747

1202
1658
2114
2569
3025

3480
3936
4391
4846
5302

5757
6212
6667
7122
7577

8032
8487
8942
9397
9852

6

0337
0792

1248
1704
2159
2615
3070

3526
3981
4437
4892
5347

5802
6258
6713
7168
7623

8078
8533
8988
9442
9897

8

7602
8059
8516
8973
9430

9887
0344
0800
1257
1714

2170
2627
3084
3540
3997

4453
4909
5366
5822
6278

6734
7191
7647
8103
8559

9015
9470
9926
0382
0838

1294
1749
2205
2660
3116

3571
4027
4482
4937
5393

5848
6303
6758
7213
7668

8123
8578
9033

9

9486 9533

9943
8

7647
8105
8562
9019
9476

9932
0389
0846
1303
1760

2216
2673
3129
3586
4042

4499
4955
5411
5868
6324

6780
7236
7692

8148
8604

9060
9516
9972

0428
0883

1339
1795
2250
2706
3161

8617
4072
4528
4983
5438

5893
6349
6804
7259
7714

8169
8624
9079

9988

D Pro.

46

5
9
14
18
23
28
32
37
41

N. 955 L. 980

OF NUMBERS.

N.

9550
51
52
53
54

55
5G
57

58
59

9560
61
62
63
64

65
66!
671
68'
69.

95T0

7ll
72
73

74

I

7:>

76
■ 77

78'

79

I

9580
81
82
83
84

81J

87
88
89

9590
91
92
93
94

95
96
97
9ft
99

N.

1

0079

2

0125

9800034

0488 1 0534

0579

0943 0989

1034

1398! 1443

1489

1852 1898

1943

2307 2352

2398

2761 2807

2852

3216 3261

3307

3670 3716

3761

4125 4170

4215

4579' 4624

4670

5033 5079

5124

5487 5533

5578

5942 5987

6032

6396 6441

6486

6850 6895

6941

7304 7349

7395

7758 7803

7849

8212 8257

8302

8666 8711

8756

9119 9165

9210

9573 9619

9664

9810027 0072

0118

0481' 0526

0571

0934 0980

1025

1388' 1433

1479

1841 1887

1932

2295 2340

2386

2748 2794

2839

3202 3247

3292

3655

8700

3746

4108

4154

4199

4562

4607.

i652

5015

5060

5106

5468

5513

5559

5921

5966

6012

6374

6420

6465

6827

6873

6918

72180

7326

7371

7733

7778

7824

8186

8231

8277

8639

8684

8729

9092

9137

9182

9544

9590

9635

9997

0042

0088

9820450

0495

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0902

0948

0993

1355

1400

1445

1807

1853

1898

2260

2305
I

2350
2

0170
0625
1080
1534
1989

2443
2898
3352
3807
4261

4715
5169
5624
6078
6532

0216
0670
1125
1580
2034

2489
2943
3398
3852
4306

4761
5215
5669
6123
6577

6986 7031
7440j 7485
7894, 7939
8348 8393
8802 8847

9256
9709
0163
0617
1070

1524
1977
2431
2884
3338

3791
4244
4698
5151
5604

6057
6510
6963
7416
7869

8322

8775
9228
9680
0133

0586
1038
1491
1943
2396

2 \^

9301
9755
0208
0662
1116

1569
2023
2476
2930
3383

3836
4290
4743
5196
5649

6102
6555
7008
7461
7914

8367
8820
9273
9726
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0631
1083
1536
1988
2441

5

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0716
1170
1625
2080

2534
2989
3443
3897
4352

4806
5260
5714
6169
6623

7077
7531
7985
8439

8892

9346
9800
0254
0707
1161

1615
2068
2522
2975
3428

3882
4335
4788
5241
5695

6148
6601
7054
7507
7960

8412
8865
9318
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0676

6

0307
0761
1216
1671
2125

2580
3034
3489
3943
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4851
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5760
6214
6668

7122
7576
8030
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8938

9392
9845
0299
0753
120^

1660
2113
2567
3020
3474

3927
4380
4834
5287
5740

6193
6646
7099
7552
8005

8458
8911
9363
9816
0269

0721

I129fll74

1581
2034
2486

1626
2079
2531

0352
0807
1261
1716
2171

2625
3080
3534
3988
4443

4897
5351
5805
6259
6714

7168
7622
8075
8529
8983

9437
9891
0344
0798
1252

1705
2159
2612
3066
3519

3972
4426
4879
5332

5785

6238
6691
7144
7597
8050

8503
8956
9409
9861
0314

0767
1219
1672
2124
2577

8

0398
0852
1307
1761
2216

2671
3125
3579
4034

4488

4942
5397
5851
6305
6759

7213
7667
8121
8575
9029

9482
9936
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1751
2204
2658
3111
3564

4018
4471
4924
5377
5831

6284
6737
7190
7643
8095

8548
9001
9454
9907
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1264
1717
2169
2622

9

0443
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1352
1807
2261

2716
3170
3625
4079
4533

4988
5442
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6350
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7258
7712
8166
8620
90744

9528
9982
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1342

1796
2250
2703
3156
3610

4063
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7688
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LOGARITHMS N. 960 L. 9S^ j

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1

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5064

5109

5155

5200

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5 S3

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5426

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5516

5561

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6104

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6420

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6556

6601

6646

6692

6737

9 41

09

6782

6827

6872

6918

6963

700S

7053

7098

7143

7189

9610

7234

7279

7324

7369

7415

7460

7505

7550

7595

7641

11

7686

7731

7776

7821

7867

7912

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8047

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12

8138

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1028

1073

1119

1164

1209

1254

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1299

1344

1390

1435

1480

1525

1570

1615

1660

1706

9620

1751

1796

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1886

1931

1976

2022

2067

2112

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2202

2247

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2428

2473

2518

2563

2608

2,1

2654

2699

2744

2789

2834

2979

2924

2969

3015

3060

23

3105

3150

3195

3210

3285

3331

3376

3421

3466

3511

24

3556

3601

3646

3692

3737

3782

3827

3872

3917

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4007

4053

4098

4143

4188

4233

427S

4323

4368

4413

26

4459

4504

4549

4594

4639

4684

4729

4774

4819

4865

27

4910

4955

5000

5045

5090

5135

5180

5225

5271

5316

28

5361

5406

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5496

5541

5586

5631

5677

5722

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29

581^

5857

5902

5947

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6037

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6128

6173

6218

9630

6263

6308

6353

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6443

6488

6533

6579

6624

6669

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6714

6759

6804

6849

6894

6939

6984

7029

7'075

7120

32

7165

7210

7255

7300

7345

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7435

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7G16

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7751

7796

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7886

7931

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8157

8202

8247

8292

8335

8362

8427

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8562

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39

9840320

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0455

0500

0545

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0635

0680

0725

9640

0770

0815

0860

0905

0951

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1041

1086

1131

1176

41

1221

1266

1311

1356

1401

1446

1491

1536

1581

1626

42

1671

1716

1761

1806

1851

1896

1942

1987

2032

2077

45

43

2122

2167

2212

2457

2302

2347

2392

2437

2482

2527

44

2572

2617

2662

2707

2752

2797

2842

2887

2932

2977

3 tl

3 14

4 IH

45

3022

3067

3112

3157

3202

3247

3292

3338

3383

3428

46

3473

3518

3563

3608

3653

3698

3743

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3833

3879

5 !.l

47

3923

3968

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4058

4103

4148

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49

4373

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4463

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N. 965 L. 984 of nu?ibers.

f

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N.

9650

1
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5363

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9845273

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6263

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6443

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59

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63

1120

1165

1210

1255

1300

1345

1389

1434

1479

1524

64

1569

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65

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2243

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3007

3052

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5432

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5522

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5612

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82

9651

9696

9740

9785

9830

9875

9920

9965

5010

0054

83

9860099

0144

0189

0234

0279

0324

0368

0413

0458

0503

84

0548

0593

0637

0682

0727

0772

0817

0862

0907

0951

85

0996

1041

1086

1131

1176

1220

1265

1310

1355

1400

/ 86

1445

1489

1534

1579

1624

1669

1714

1758

1803

1848

/ 87

1893

1938

1983

2027

2072

2117

2162

2207

2252

2296

' 88

2341

2386

2431

2476

2521

2565

2P10

2655

2700

2745

89

2790

2834

2879

2924

2969

3014

3058

3103

3148

3193

«

^mo

3238

3283

3327

3372

3417

3462

3507

3551

3596

3641

91

3686

3731

3776

3820

3865

3910

3955

4000

4044

4089

92

4134

4179

4224

4268

4313

4358

4403

4448

4493

4537

44

93

4582

4627

4672

4717

4761

4806

4851

4896

4941

4985

1

4

94

5030

5075

5120

5165

5209

5254

5299

5344

5389

5433

2
3
4

9
13
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95

5478

5523

5568

5613

5657

5702

5747

5792

5836

5881

96

5926

5971

6016

6060

6105

6150

6195

6240

6284

6329

6

22

97

6374

6419

6464

6508

6553

6598

6643

6687

6732

6777

7 31

98

6822

6867

6911

6956

7001

7046

7090

7135

7180

7225

99

7270

7314
1

7359

7404

3

7449
4

7493
5

7538

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7583

7

7628
8

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In:

2

eis.

n2

180

N.

^

LOGARITHMS

N. 970 L. 986

9700
01
02
03
04

05
06
07
OS
09

9710
11
12
13
14

15
16
17
18
19

9720
21
22
23
24

25
26
27
28
29

9730
31
32
33
34

35
36
37

38
39

9740
41
42
43
44

45
46
• 47
48
49

N.

9S67717
8165
8613
9060
9508

9955
9870403
0850
1298
1745

2192
2640
3087
3534
3981

4428
4875
5322
5769
6216

6663
7109
7556
, 8003
8450

8896
9343
9789
9880236
0682

1128
1575
2021
2467
2913

3360
3806
4252
4698
5144

5590
6035
6481
6927
7373

7818
8264
8710
9155
9601

I

7762
8210
8657
9105
9553

0000
0448
0895
1342
1790

2237
2684
3131
3579
4026

4473
4920
5367
5814
6261

6707
7154
7601
8048
8494

8941
9387
9834
0280
0727

1173
1619
2066
2512
2958

3404
3850
4296
4742

5188

5634

6080
6526
6972
7417

7863

8309
87 54
9200
9645

3

7807
8255
8702
9150
9597

0045
0492
0940
1387
1834

2282
2729
3176
3623
4070

4517
4964
5411

5858
6305

6752
7199
7646
8092
8539

8985
9432
9878
0325
0771

1218
1664

7852
8299
8747
9195
9642

O090
0537
0985
1432
1879

2326
2774
3221
3668
4115

4562
5009
5456
5903
6350

6797
7243
7690
8137

8583

9030
9477
99:i3
0370
0816

1262
1709

2110 2155
2556' 2601
3003. 3047

3449: 3493
3895' 3939

1

4341

4787
5233

5679
6125
6570
7016
7462

7908
8353
8799
9244
9690

4386
4831
5277

5723
6169
0615
7061
7506

7952
8398
8843
9289
9734

7896
8344
8792
9239
9687

5134
0582
1029
1477
1924

2371
2818
3266
3713
4160

4607
5054
5501
5948
6395

6841

7288
7735
8182
8628

9075
9521
9968
0414
0861

1307
1753
2200
2646
3092

3538
3984
4430
4S76
5322

5768
6214
6660
7105
7551

7997
8442
8688
9333
9779

7941
8389
8837
9284
9732

0179
0627
1074
1521
1969

2416
2863
3310
3757
4205

4652
5099
5545
5992
64.S9

68ft6
7333
7780
8226
8673

9119
9566
0012
0459
0905

1352
1798
2244
2690
3136

3583
4029
4475
4921
5367

5813
6258
6704
7150
7596

8041
8487
8932
9378
9823

6

7

7986
8434
8881
9329
9776

0224
0671
1119
1566
2013

2461
2908
3355
3802
4249

4696
5143
5590
6037
6484

6931
7377
7824
8271
8717

9164
9611
0057
0503
0950

8031
8478
8926
9374
9821

0269
0716
1163
1611
2058

2505
2953
3400

3847
4294

4741
5188
5635
6082
6529

6975
7422
7869
8316
8762

9209
9655
0IO2
0548
0994

1396 1441
1842 1887

2289
2735
3181

3627
4073
4519
4965
5411

5857
6303
6749
7194
7640

8086
8531
8977
9423
9868

2333
2780
3226

3672
4118

8

8076
8523
8971
9418
9866

5313
0761
1208
1656
2103

2550
2997
3444
3892
4339

4786
5233
5680
6126
6573

7020
7467
7914
8360
8807

9253
9700
5146
0593
1039

1485
1932
2378
2824
3270

3716
4162

4564 4 60Q
5010 5054

9

5456

5902
6348
6793
7239
7-685

8130
8576
9022
9467
9913

5500

5946
6392

6838
7284
7729

8175
8621
9066
9512
9957

7 . 8

8120
8568
9016
9463
9911

0358
0806
1253
1700
2148

2595
3042
3489
3936
4383

4830
5277
5724
6171
6618

7065
7511
7958
8405
8851

9298
9745
5191
0637
1084

1530
1976
2423
2869
3315

3761
4207
4653
5099
5545

5991
6437
6882
7328
7774

8220
8665 !
9111
9556
5002

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Pro.

45

2I 9

3! 14
4

O

6

7
8
9

18
23

27
32

36
41

1
2
3

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6'

7.
8

9

P»=-*^

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1)75 L. 989 OF NUMBERS. 181

N.

I

a i 3

4

5

6

7

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9

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975

989UU4

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0224

0269

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0536

0581;()025

0670

0714

07 53

0803

084 k

0892

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5

093

098

1026 107

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1160

1204

1249

1293

1339

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5.

138

1427

1471' 151G

1560

1605

1649

1694

1738

1783

2 3

3-1

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1872

1917 1961

2006

205U

2095

2139

2184

2228

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b

237.

2317

2303 2406

2451

2495

2540

2594

2629

2673

5 aa

M

271S

2762

2807 2951

2896

2940

2985

3030

3074

3119

ol 27

7l 32
111 3(i

57

316S

3208

3252 3297

3341

3366

3430

3475

3519

3564

58

S60t

3653

3697 3742

3786

3831

3875

3920

3^64

4009

al A\

59

4053

4098

4142 4187

4231

4276

4330

4305

4409

4454

0760

4498

4543

4587 4632

4676

4721

4765

4810

4854

4899

61

4943

4988

5032 5U77

5121

5166

5210

5255

5299

5344

m

5389

5433

5477 5521

5566

5610

5655

5699

5744

5788

sa

5833

5877

5922 5966

6011

6055

6100

6144

6199

6233

64

6278

6322

6367 6411

6456

6500

6545

6589

6634

6679

65

6722

6767

6811 '6856' 6900

6945

6999

7034

7079

7123

66

7167

7212

7256 7301I7345

7390

7434

7478

7523

7567

67

761217656

7701 7745*7790

7834

7879

7923

7968

8012

6S

S057 8101

8145 81908334

8279' 8323

8368

9412

8457

69

8501 8546

8590 8634 '8679

8723

8769

8812

8957

8901

g770

8946 8990

9035'9079:9123

9168

9212

9257

9301

9346

71

9390,9435

9479 952319568

9612

9657

9701

9746

9790

72

9835,9879

9923 9968 6012

0057

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0146

0190

0235

73

99002T9 03^3

0369 0412' 0457

0501

0546

0590

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74

0723, 0769

0812 0857 0901

0946

0990

1034

1079

1123

75

1168|l.212

I257I 1301! 1345

1390

1434

1479

1523

1566

1

76

1612! 1656

1701 1745 1790

1834

1878

1923

1967

2012

77

2056 3101

2145 2189 2234

2278

2323

2367

2411

2456

78

2500; 2545

2589 2634 2078

2722

2767

2811

2856

2900

79

294412989

3033 3078 3122

3167

3211

3255

3300

3344

97S0

3389' 3433

3477 3522' 3566

3611

3655

3699 3744

3788

SI

3833: 3877

3921 3966 4010

4055

4099

4143 4189

4232

82

4277 4321

4365 4410 4454

4499

4543

4597 4632

4676

S3

4721

4765

490914854 489S

4943

4987

5031 5076

5120

S4

5164

5209

5253

5298 5342

5386

5431

5475 5520

5564

85

5608

5653

5697

574115786

5830

5875

5919 5963

6008

86

6052

6096

6141

6185^6230

6274

6319

63631 6407

6452

87

6496 6540

6585

6629^^673

6718

6762

6806

6951

6895

1

88

6940 69841

7028

7073:7117

7161

7306

7250

7295

7339

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7383!7428|

7472

7516 7561

7605

7549

7694

T738

7793

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7827

7S71

7916

796ol 6004

8049

8093

9137

8192

9226

91

8271

83151

8359

840418448

8492

8537

8581

8025

8670

U

8714

8758

8803

8847 8891

9936

8980

9025

9069

9U3

44

n

91 5S

9302] 9246

9291 9335

9379

9424

9468

9512

9557

94

9601

9645 9690

9734

9778

9823

9S67

9911

9956

0000

u

95

9910044

0089 0133

0177

03:?2

0266

0310

0355

0399

0443

96

0488

0532 0576

0621

0665

070S

0754

0798

0842

0887

i^

97

0931

0975 1020

1064

1108

1153

1197

1241

1286

1330

(i 9tl

7 m

a 3r>

9S

1374

14 lu 1463

1507

1552

1596

1640

1685

1729

1773

99

I81S

I8r,j|l906

1951

1995

3039
5

2083
6

212s

2172

"8"

3216

',1

u"

9 40
I'l..

N.

I rj_

;i

IT

182

LOGAKITUMS

N. 980 L. 991

N.

1
2305

2

2349

9800

9912261

01

2704

2748

2793

02

3147

3191

3236

03

3590

3634

3679

04

4033

4077

4122

05

4476

4520

4565

06

4919

4963

5007

07

5362

5406

5450

08

5805

5849

5893

09

6247

6292

6336

9810

6690

6734

6779

11

7133

7177

7221

12

7575

7620

7664

13

8018

8062

8107

14

8461

8505

8549

15

8903

8947

8992

16

9345

9390

9434

17

9788

9832

9876

la

9920230

0275

0319

19

0673

0717

0761

9820

1115

1159

1203

21

1557

1601

1646

22

1999

2044

2088

23

244]

2486

2530

24

2884 2928

2972

25

3326

3370

3414

26

3768

3812

3856

27

4210

4254

4298

28

4651

4696

4740

29

5093

5138

5182

9880

5535

5579

5624

31

5977

6021

6065

82

6419

6463

6507

33

6860

6905

6949

34

7302

7346

7390

85

7744

7788

7832

36

8185

8229

8274

87

8627

8671

8715

38

9068

9112

9156

39

9510

9554

9598

9840

9951

9995

0039

41

9930392

0436

0481

42

0834

0878

0922

43

1275

1319

1363

44

171*6

1760

1804

45

2157

2201

2245

46

2598

2642

2687

47

3039

3083

3128

48

8480

3524

3569

49

8921

3965

1

4010
2

N.

3

2394
2837
3280
3723
4166

4609
5052
5495
5937
6380

2438
2881
3324
3767
4210

4653
5096
5539
5982
6424

6823 6867
7266 7310

7708
8151

7752
8195

8593 8638

9036
9478
9921
0363
0805

1248
1G90
2132
2574
30iaj

3458
3900
4342

4784
5226

5668
6109
6551
6993
7435

7876
8318
8759
9201
9642

5083
0525
0966
1407
1848

2290
2731
3172
3613
4054

9080
9522
9965
0407
0850

1292
1734
2176
2618
3060

3502
3944
4386

4828
5270

5712
6154
6595
7037
7479

7920
8362
8803
9245
9686

0128
0569
1010
1451
1893

2334
2775
3216
3657
4098

2482
2925
3369
3812
4255

4697
5140
5583
6026
6469

6911
7354

2527
2970
3413
38^6
4299

4742
5185
6627
6070
6513

6956
7398

77^7' 7841
8239J 8284
8662 8726

9124
9567
r)009
0451
0894

1336
1778
2220
2662
3105

3547
3989
4431

4872
5314

5756
6198
6640
7081
7523

7964
8406
8847
92S9
9730

0172
0613
1054
1495
1937

2378
2819
3260
3701
4142

9169
9611
0053
0496
0938

1380
1822
2265
2707
3149

3591
4033
4475
4917
5358

5800
6242
6684
7125
7567

8009
8450
8892
9333
9774

0216
0657
1098
1540
1981

2422
2863
3304
3745
4186

"6

2571
3014
3457
3900
4343

4786
52-29
5672
6115
6557

7000
7443

7885
8328
8770

9213
9655
0098
0540
0982

1424
1867
2309
2751
3193

3635
4077
4519
4961
5403

5844
6286
6728
7170
7611

8053
8494
8936
9377
9819

0260
0701
1142
1584
2025

2466
2907
3348
3789
4230

26lt>
3058

9

2660
6103

3501 3546
3944* 3989
43871 4432

4830 4875
5273 5317
5716^5760
6159 6203
6602! 6646

7044; 7088
7487' 7531
7929 7974

8372
8815

9257
9699
0142
0584
1026

1469
1911
2353
2795
3237

3679
4121
4563
5005
5447

5889
6330
6772
7214
7655

8097
8538
8980
9421
9863

0304
0745
1187
1628
2069

2510
2951
3392
3833
4274

8416
8859

9301
9744
0186
0628
1071

1513
1955
2397
2839
3281

3723
4165
4607
5049
5491

5933
6375
6816
7258
7699

8141
8583
9024
9465
9907

0348
0789
1231
1672
2113

2554
2995
3436
3877
4318

9

D

Pro.

45

6

9

14

18

23

27
32
3(i
41

44

D

4

9

13

181

«w

26
31
35
40

Pis.

• I

N. 985 L. 993 of numbers. 183

N.

9850

1
4406

2

4450

3

4495

4

4539

5

4583

6

4627

7

4671

8

4715

9

4759

D

Pro.

9934362

51

4803

4847

4891

4935

4980

5024

5068

5112

5156

5200

44

52

5244

5288

5332

5376

5420

5464

5509

5553

5597

5641

1

4

53

5685

5729

5773

5817

5861

5905

5949

5993

6037

6082

2
3
4

9
13
18

54

6126

6170

6214

6258

6302

6346

6390

6434

6478

6522

55

6566

6610

6654

6698

6743

6787

6831

6875 6919
7315 7859
7756 7800

6963

6

22

A0

; j>fi

7007

7051

7095

7139

7183

7227

7271

7404

6

7
8

26
31

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7448

7492

7536

7580

7624

7668

7712

7844

35

58

7888

7932

7976

8020

8064

8108

8152

8197

8241

8285'

9

40

59

8329

8373

8417

8461

8505

8549

8593

8637

8681

8725

1

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194

LOGARITHMS

N. 1040 L. O170

N.

1
3752

2

4169

10400

01703334

01

7510

7927

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02

01711685

2102

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5107

5524

5940

23

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01803440

3857

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8023

8440

26

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2189

2605

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5937

6354

6770

28

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4267

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10430

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3011

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9680
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3775
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2092
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4

5

6

7

8

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6257

6675

9180

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8865

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2607

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5

6

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1267
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9617
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292
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Pu

N. 1045 L. 0191

OF NUMBEKS.

19o

N.

10450

01911629

51

5785

52

9940

53

01924095

54

8250

55

01932404

56

6557

57

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58

4864

59

9016

10460

01958168

61

7320

62

01961472

63

5623

64

9778

65

01978923

66

8078

67

01982222

68

6871

69

01990520

10470

4668

71

8816

72

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78

7110

74

02011257

75

5408

76

9549

77

02028694

78

7839

79

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10480

6128

81

02040272

82

4416

88

8559

84

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85

6848

86

02060965

87

5127

88

9268

89

02073409

10490

7549

91

02081689

92

5828

98

9967

94

02094106

95

8244

96

02102882

97

6520

9B

02110657

99

4794

N.

1

2045
6200
0856
4510
8665

2819

6978

11261

5279

9482

8584
7785
1887
6088
5188

4888

8488
2687
6786
0935

5083
9231
8378
7525
1672

5818
9964
4109
8254
2399

6548
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4830
8978
8116

7258
1400
5541
9682
8828

7963
2108
6242
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4520

8658
2796
6934
1071
5207

1

2460
6616
5771
4926
9080

8285

7388
1541
5694
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8999
8150
2802
6458
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4758
8908
8052
7201
1850

5498
9645
8793
7940

2086

6282
5878
4528
8668
2818

6957
1101
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7672
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8877
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6656
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9072
8210
7847
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2876
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8650
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1957
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4414
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2717
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5918
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6647
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8086
2228
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8791
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1209
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7761
1898
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3

3291
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4065
8219
2872
6525
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4829
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5588
9788
8882
8081
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6827
5475
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7062
1207
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1092

5244
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4297
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6742
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7476
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5767
9912
4056

8200
2844
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5680
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8915
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5813
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2725
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5659
9811
8962
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7157
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7891
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6181
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8615
2758
6901
1044
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8470
7612
1752
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5038
4178
8812
2451
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5727
4865
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4538
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1141
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9416
8558
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CI 2

4954
9109
3264
7419
1573

5727
9880
4088
8186
2838

6490
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4792
8948
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7248
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1155
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9444
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5157
4299
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5861
5000
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3278
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1555
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5869
9525

S680
7834
1988

6142
5296
4449
8601
2758

6905
1056
5208
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7658
1807
5957
5105
4253

8401
2549
6696
5842
4989

9185
5280
7425
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5714

9858
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5571
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2995
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5414
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1969
6106
5248
4880
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9

415

415

1
2
3
4
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7
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42
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LOGARITHMS

N. 1050 L. 0211

N.

10500
01
02
03
04

05
06
07

08
09

10510
11
12
13
14

15
16
17
18
19

10520
21
22
23
24

25
26
27

28
29

10530
31
32
33
34

35

36
37
38
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10540
41
42
43
44

45
46
47

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1
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02118930

02123066

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3080

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4370

6084

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5000

8713

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3250

6961

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1497

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8028

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5664

6071

6477

6884

7290

7697

8103

8510

8916

83

9323

9729

0136

5542

5949

1355

1762

2168

2575

2981

. 84

02873388

3794

4201

4607

5014

5420

5827

6233

6640

7046

85

7453

7859

8265

8672

9078

9485

9891

5298

5704

1111

86

02881517

19-23

2330

2736

3143

3549

3955

4362

4768

5175

87

5581

5987

6394

6800

7206

7613

8019

8425

8832

9238

88

9645

(K)51

5457

5864

1270

1676

g083

2489

2995

3301

89

02893708

4114

4520

4927

5333

5739

6146

6552

6958

7364

10690

7771

8177

8583

8989

9395

9802

5208

5614

1020

1427

91

02901833

2239

2645

3052

3458

3864

4270

4676

5083

5489

92

5895

6301

6707

7114

7520

7926

8332

8738

9144

9550

405

405

93

9957

0363

5769

1175

1581

1987

S394

2800

3206

3612

^^\^ %^

]i 41

94

02914018

4424

4830

5236

5642

6049

6455

6861

7267

7673

2

81

1 C%£\

95

8079

8485

8891

9297

9703

5109

5515

5921

1327

T733

3
4

122
162

96

02922139

2546

2952

3358

3764

4170

4576

4982

5388

5794

5

203

97

6200

6606

7012

7418

7824

8230

8635

9041

9447

9853

6

243

98

02930259

0665

1071

1477

1883

2289

2695

3101

3507

3913

7'2H4

8' 324
U36»

Pis.

1

99

N.
1

4319

4725
1

5131
2

5536
3

5942
4

6348

5

6754
6

7160

7

7566
8

7972
9

u

20() LOGARITHMS N. 1070 L. 0293

N.

1

8784

2
9190

3

9595

4

0001

5
0407

6

0818

7

iai9

8

1625

9

D

Pto.

107U0

02938878

2081

01

02942436

2842

3248

3654

4060

4465

4871

5277

5688

6089

406

406

02

6495

6901

7807

7712

8118

8524

8980

9385

9741

0147

1 41

03

02950553

0958

1864

1770

2176

2581

2987

8893

8799

4205

2 81
S1S2
4163

04

4610

5016

5422

5827

6288

6689

7044

7450

7856

8261

05

8667

9078

9479

9884

0290

0696

1101

1507

1918

2318

620

06

02962724

8180

8585

3941

4347

4752

5158

5568

5969

6875

6244

7284

07

6780

7186

7592

7997

8408

8808

9214

9620

0025

0431

8325

08

02970836

1242

1647

2053

2458

2864

8270

8675

4081

4486

9|363

09

4892

5298

5708

6109

6514

6920

7825

7781

8186

8542

10710

8947

9858

9758

0164

0569

0975

1880

1786

2191

2597

11

02983002

3407

3813

4218

4624

5029

5485

5840

6246

6651

12

7056

7462

7867

8278

8678

9084

9489

9894

0800

0705

13

02991111

1516

1921

2327

2782

8187

8548

8948

4854

4759

14

5164

5569

5975

6880

6786

7191

7596

8002

8407

8812

15

9218

9628

0028

0433

0889

1244

1649

2055

2460

2865

16

03003271

8676

4081

4486

4892

5297

5702

6107

6518

6918

17

7323

7728

8134

8539

8944

9849

9755

0160

0565

0970

18

03011375

1781

2186 2591

2996

8401

3807

4212

4617

5022

19

5427

5882

6238

6648

7048

7458

7858

8268

8668

9073

10720

9479

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0289

0694

1099

1504

1909

2814

2719

3124

21

03023529

3935

4340

J745

5150

5555

5960

6365

6770

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22

7580

7985

8391

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9201

9606

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0416

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405

405

23

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2036

2441

2846

3251

3656

4061

4466

4871

5276

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24

5681

6086

6491

6896

7301

7706

8111

8515

8920

9325

2 81

3 122!

25

9730

0135

5540

0945

1350

1755

2160

2565

2970

8874

4|16S

26

03043779

4184

4589

4994

5399

5804

6209

6614

7019

7428

5203
6243

7 aw

8324

27

7828

8233

8638

9043

9448

9858

0257

0662

1067

1472

28

03051877

2281

2686

3091

3496

3901

4305

4710

5115

5520

29

5925

6329

6734

7139

7544

7949

8358

8758

9163

9568

9 36A

10730

9972

6377

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2401

2805

3210

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31

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4424

4829

5234

5638

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6448

6852

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32

8066

8471

8876 9281

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0495

0899

1304

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33

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2518

2922

Bd21

3732

4136

4541

4945

5350

5755

34

6159

6564

6968

7373

7777

8182

8587

8991

9896

9800

35

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0610

1014

1419

1823

2228

2682

8037

3441

8846

36

4250

4655

5059

5464

5868

6273

6677

7082

7486

7891

37

8295

8700

9104 9509

9913

0318

0722

1127

1531

1986

38

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2745

3149| 3553

3958

4362

4767

5171

5575

5980

39

6384

6789

7193

7597

8002

8406

8811

9215

9619

0024

10740

03100428

0833

1237

1641

2046

2450

2854

3259

3663

4067

41

4472

4876

5280

5685

6069

6493

6898

7302

7706

8111

42

8515

8919

9328 9728

0132

0536

0941

1345

1749

2153

404

404

43

03112558

2962

3366

3771

4175

4579

4983

5387

5792

6196

1 40 j

44

6600

7004

7408

7813

8217

8621

9025

9429

9834

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2 81 !

3 121

4 162

45

03120642

1046

1450

1855

2259

2663

3067

3471

8875

4280

46

4684

5088

5492

5896

6300

6704

7109

7513

7917

8821

5 202

47

8725

9129

9533

9937

0341

0745

1150

1554

1958

2362

6 242

7 283

8 323

48

03132766

3170

3574

3978

4382

4786

5190

5594

5998

6402

49

6806

7210

7614

8018

8422

8826

9230

9634

0038

0442

!I364

N.

I

2

3

4

5

()

7

8

9

P.

Ptj^

N. 1075 L. 0314

OF NUMBERS

)•

201

N.

1
1250

2

1654

3

2058

4
2462

5

2866

6

3270

7

8

9

4482

D

Pro.

,10750

03140846

3674

4078

51

4886

5290

5694

6098

6502

6906

7310

7714

8118

8522

404

404

52

8926

9330

9733

0137

0541

0945

1349

1753

2157

2561

1

2

40

81

121

53

03152965

3369

3772

4176

4580

4984

5388

5792

6196

6599

54

7003

7407

7811

8215

8619

9023

9426

9830

0234

0638

4

\G2

55

03161042

1445

1849

2253

2657

3061

8464

3868

4272

4676

5

7

202
242
283

56

5080

5483

5887

6291

6695

7098

7502

7906

8310

8713

57

9117

9521

9924

0328

r>732

1136

1539

1943

2347

2750

f

8

323

58

03173154

3558

3961

4365

4769

5173

5576

5980

6384

6787

9

304

59

7191

7594

7998

8402

8806

9209

9613

0016

0420

0824

10760

03181227

1631

2034

2438

2842

3245

3649

4052

4456

4860

«

61

5263

5667

6070

6474

6878

7281

7685

8088

8492

8895

62

9299

9702

0106

0510

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i317

1720

2124

2527

2931

63

03193334

3738

4141

4545

4948

6352

5755

6159

6562

6966

64

7369

7772

8176

8579

8983

9386 9790

0193

0597

1000

65

03201403

1807

2210

2614

3017

342113824

4227

4631

5034

66

5438

5841

6244

6648

7051

7455

7858

8261

8665

9068

67

9471

9875

0278

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1085

1488

1892

2295

2698

3101

68

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5118

c5521

5925

6328

6731

7134

69

7538

7941

8344

8748

9151

9554

9958

0361

5764

1167

10770

03221570

1974

2377

2780

3183

3587

3990

4393

4796

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71

5603

6006

6409

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7215

7619

8022

8425

8828

9231

72

9635

0038

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0844

1247

1651

2054

5457

2860

3263

403

403

73

03233666

4069

4472

4875

5279

5682 6085

6488

6891

7294

1

40

74

7697

8100

8503

8906

9310

9713 0116

0519

0922

1325

%

2
3

81
121

75

03241728

2131

2534

2937

3340

3743

4146

4549

4952

5355

4

101

76

5758

6161

6564

6967

7370

7773 81761

8579

8982

9385

6
7

202
242
282

77

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1400

1803

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f

3-22

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7847

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9

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10780

03261876

2279

2682

8085

3488

3891

4293

4696

5099

5502

81

5905

6308

6710

7113

7516

7919

8322

8724

9127

9530

82

9933

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0738

1141

1544

1947

2350

2752

3155

3558

83

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4363

4766

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5572

5974

6377

6780

7183

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84

7988

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8793

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1210

1612

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2418

2820

3223

3626

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1 ^'^

6042

6444

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2081

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2886

3289

3691

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4094

4496

4899

5302

5704

6107

6509

6912

7314

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1 89

8119

8522

8925

9327

9730

0132

0535

0987

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03302145

2547

2950

3352

3755

4157

4560

4962

5365

5767

I 91

6169

6572

6974

7377

7779

8182

8584

8987 9389

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1 92

03310194

0596

0999

1401

1803

2206

2608

3011

3413

3815

402

4 OS

1 93

4218

4620

5023

5425

5827

6230

6632

7035

7437

7839

1

40

94

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8644

9046

9449

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0253

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1058

1460

1862

2
3

m

121

95

03322265

2667

3069

3472

3874

4276

4679

5081

5483

5885

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4

161

96

6288

6690

7092

7495

7697

8299

8701

9104

9506

9908

51201
6 241
7l2fil

97

03330310

0712

1115

1517

1919

2321

2724

3126

3528

3930

98

4332

4735

5137

5539

5941

6343

6746

7148

7550

7952

8

322

99

8354

8756

1

9159
2

9561
3

9963
4

0365
5

0767

1169

1571

1973

D

9

362

Vn.

6

7

8

9

Pis.

202 TABLE II.

For finding Loganthms and Numberx tn 20 Places of Fufu)

N.

Logarithms.

N.

"si

Logarithms.

00000 OOOOU 00000 00000

70757

01760 97936 36584

2

30102 99956 63981 19521

52

71600

33436 34799 15963

3

47712 12547 19662 43730

53

72427

58696 007S9 04563

4

60205 99913 27962 39043

54

73239

37598 22968 50710

5

69897 00043 36018 80479

55

74036

26894 94243 84554

6

77315 12503 83643 63251

56

74818

80270 06200 41635

7

84509 80400 14256 63071

57

75587

48556 72491 39SS3

8

90308 99869 91943 58564

58

76342

79935 62937 28255

9

95424 25094 39324 87459

59

77685 20116 42144 19026 1

10

OOOOU 00000 00000 00000

60

77815

12503 63643 63251

U

04139 26851 58225 04075

61

78532 98350 10767 03389 |

12

07918 12460 47624 82772

62

79239

16894 98253 87488

13

11394 33523 06836 76921

63

79934

05494 53581 70530

14

14612 80356 78238 02593

64

80617

99739 83887 17128

15

17609 12590 55681 2420S

65

81291

33566 42855 57399

16

20411 99826 55924 78085

66

81954

39355 41868 67326

17

23044 89213 7B273 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

32221 92947 33919 26801

71

85125

83487 19075 28609

22

34242 26808 22206 23596

72

85733

24964 31268 46023

2.1

36172 78360 17592 87887

73

86332

26601 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

88081

35922 80791 35196

27

43136 37641 58987 31189

77

88649

07251 72481 87146

28

44715 80313 42219 22114

78

89209

46026 90480 40172

29

46239 79978 98956 08733

79

89762 70912 90441 42799 |

30

47712 12547 19662 43730

80

90308

99869 91943 58564

31

49136 16938 34272 67967

81

90848

50188 78649 74918

32

50514 99763 19905 97607

82

91381

39523 93716 6S972

33

51851 39399 77887 47&(i6

83

91907

80923 76073 903S3

34

53147 89170 42255 12375

84

92427

92860 61681 65843

35

54406 80443 50275 63550

85

92941

89257 14292 73333

36

55630 25007 67287 26503

86

93449

84512 43567 72162

37

56820 17240 66994 99681

87

93951

92526 18618 52463

38

57978 35966 16810 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

96378 78273 45555 26930 1

43

63346 84555 79586 52641

93

96848

29485 53935 11696

44

64345 26764 S6IS7 43118

94

97312

78535 99699 65963

45

65321 25137 75343 67938

95

97772

36052 86847 76632

46

66275 78316 81574 0741)8

96

98227

12330 39569 41336

47

67209 78579 35717 46441

97

98677

17342 60244 95178

4fl

68124 12373 755B7 21815

98

99122

60756 92494 85664

49

69019 60800 28513 66142

99

99563

51943 97549 91534

50

69897 00043 36018 S0479

100

00000

00000 00000 oomio

Tab. 2. LOGARITHMS TO 20 PLACES, -203

N.

101

Loganthms.

N.

151

Logarithms.

00432 13737 S2642 57428

17897 69472 93169 43687

102

00860 01717 61917 56105

152 18194 35879 44772 54719

103

01283 72247 05172 20517

153 19469 14309 17599 80313

104

01703 33392 98780 35485

154 18752 07208 S6463 06668

105

02118 92990 69938 07379

155 19033 16981 70291 48445

106

02530 58652 64770 24085

156 19312 45993 54461 59693

107

02939 37776 85209 64083

157! 19589 96524 09233 73676

109

03342 37554 86949 70231

158 119865 70869 54422 62321

109

03742 64979 40623 63520

159 20139 71243 20451 49293

110

04139 26851 58225 04075

160 20411 99826 55924 79095

in

04532 29787 S6657 43410

161 20682 59760 )11949 70958

113

04921 80226 70191 61157

162120951 50145 42630 94439

1!9

05307 84434 83419 72280

163 21219 76044 03957 80764

1)4

05690 48513 36472 59405

164 121484 39480 47697 89494

115

06069 78403 £i3611 68365

165

21748 39442 13906 29283

Ilfi

06445 79892 26919 47776

166

22010 80980 40055 09905

117

06818 58617 46161 64380

167

22271 64711 47583 27998

118

07188 20073 06125 38547

168

22530 92917 25862 95365

119

07554 69613 92530 75925

169

22789 67046 13673 53841

120

07918 12460 47624 82772

170

23044 89213 78273 92854

121

08278 53703 16450 08150

171

23299 61103 92153 83613

122

08635 98306 74748 22910

172

23552 84469 07549 91683

123

08930 51114 39397 93180

173

23904 61031 29795 41456

124

09342 16951 63235 07009

174

24054 92482 82599 71994

125

09691 00130 08056 41436

175

24303 80486 86294 44028

126

10037 05451 17562 911052

176

24551 26679 14149 92161

127

10380 37209 55956 86425

177

24797 32663 61806 02756

129

10720 99696 47869 36650

178

25042 00023 09893 97994

129

11059 97102 99219 96370

179

25285 30309 79893 16957

130

11394 33523 06836 76921

180

25527 25051 03306 069S0

131

11727 12956 55764 26081

181

25767 85748 69184 51029

132

12057 39312 05849 86947

182

26007 13879 85074 79513

133

123S5 16409 67085 79225

183

26245 10897 30429 47116

134

12710 47983 64807 62936

184

26481 78230 09536 46451

135

13033 37694 95006 11667

185

26717 17284 03013 80159

136

13353 89083 70217 51418

186

26951 29442 17916 31219

137

13672 05671 56406 76856

187

27194 16065 36499 96929

138

13987 90964 01236 51138

198

27415 78492 63679 85494

139

14301 48002 54095 OS046

189

27646 18041 73244 14260

140

14612 80356 78238 02593

190

27975 36009 52628 96154

141

I492I 91126 55379 90171

191

28103 33672 47727 53764

142

15229 93443 83056 49131

192

28330 12287 03549 60858

143

15533 60374 65061 80996

193

2B555 7S090 07773 76060

144

15836 24920 95249 65545

194

29790 17299 30226 04700

145

16136 80022 34974 89212

195

29003 46113 62518 01129

146

16435 28557 84437 09629

196

29225 60713 56476 05185

147

16731 73347 49176 09972

197

29446 62261 61592 92737

148

17026 17153 94957 38724

19S

29866 51902 61531 11055

149

17319 62694 12274 13S26

199>

29895 30764 09706 65010

150

17609 12590 556SI 24208

200

30102 99956 63981 19521

N. Logarithms.

Logarithms.

60574 2049S fci7144
13694 46623 76949
60379 13212 91805
01674 25898 75626
38610 55754 29930
72203 69153 i
03454 56917 75346
62761 55006
11054 00229
33919 26801
32428 24552 97692 66508
28751 43606
38737 72339
49190 83605
15605 33119

30319
30535
30749
30963
31175
31386 7
31597 C
31806 S
320 14 E
32221 S

32837
33041
33243
33445
33645
33845
34044
34242
34439
34635
34830
35024
35218
35410
35602
35793
359b3
30172
36361
36548
36735
36921
371UG
37291
37474
37657
37839
3S021
3S201
3S3SI
38560
38738
38916

96034 i
37733 4
84599 1
37511 50930 89753
9733S 4H529 51038
64936 046U4 83041
41148 40118 33S3T
26808 22206 23596

22736
29744
48630
80183
25161
84391
58571
48470
54823
78360
19798
79848
59210
58574
78622

70425
53659
62735
98263
60843

85110 6S
50638 6293&
48160 67348
34162 80678
11362 48416
47400 91801
93122 72010
00453 78926
398b7 99413
17592 87887
92144 30876
90899 67297
26018 972
10142 83901
71736 26920
70106 bi
10103 86529
56511 95447
48 137 68500
11606 02294
74969 38408
90431 27671
98312 18648
38729 42431
64532 46621

39967 37214
I 40140 05407
I 40312 05211
, 40483 3716G
I 40654 01804
; 40823 99653
' 40993 31233
I 41161 97059
I 41329 97640
I 41497 33479

41664 05073
! 41830 12913
1 41995 57484
I 42160 39268

> 42324 58739
; 42488 16366

42651 12613
1 42813 47940
I 42975 22800
I 43X36 37641

43296 92908
! 43456 89040
I 43616 26470

43775 05628

> 43933 26938
i 44090 90820

44247 97690
; 44404 47959
I 44560 42032
I 44715 90313

44870 63199
I 45024 91083
I 45179 64355

45331 83400
) 45484 48600
1 45636 60331

45788 18967
I 45939 24877
I 46089 78427
I 46239 79978

16389
: 46538
I 46'iS6
. 46834
I 46982

39093 51071 03379 12702
39269 69532 59665 73074
39445 16SUS 26216 26531
39619 93470 95736 34113
39794 00086 72037 609 57

81039 13934
81544 09573
75817 91962
19938 05946
33955 17062
11849 56171
31294 53716
63230 15891
61251 82752
70817 96442
38280 96198
19745 45602
89757 86897
69S31 06369
36807 S5042
31066 98746
64575 22202
28788 82458
02407 98009
5S9S7 31189
74405 72952
34198 70940
40756 03721
20387 96378
30262 65032
65217 70659
64448 55378
18076 27567
73597 55426
42219 22114
05079 89286
19361 09692
24290 23556
47037 67652
06510 20362
29043 00517
33992 32522
59230 85066
56547 85709
98956 08733
29889 85907 28908
28514 48416 29150
76203 54109 45624
73304 12157 29393
20159 78162 99505
il29 17110 58938 59245
' 47275 64493 17212 35264
i 47421 62640 76255 23347
P 47567 11883 24429 64807
I 47712 12547 19662 48730

TVib. 3. TO 20 PLACKs. 205 1

N.
.ioT

Logarithms.

N.

35l

Lt^rithms.

47856 64955 93943 35712

51530 71164 65824 09109

302

48000 69429 57150 63208

352

54654 26634 79131 01682

309

48144 26285 02305 01157

353

54777 47053 87822 56550

304

48287 35836 OS753 74239

354

54900 32620 25797 82277

305

48429 98393 46785 83867

355

55022 93530 55094 O9098

306

4S572 14264 81579 99834

356

55144 99979 72875 17515

307 1 43713 83751 77186 48475

357

55266 82161 12193 19655

30H 49855 07165 00444 261S9

356

55388 30266 43874 36478

aOQU-iftSS 84794 24834 64247

S59

55509 44185 78319 14782

310 49136 1693S 34-273 67967

360

55630 25007 67297 26502

311

4927fi 03890 2CS37 50555

361

55750 72019 05657 92307

312

49415 45940 1H442 79214

362

55870 85705 33165 70550

313

49551 43375 46448 48481

363

55990 6G250 36112 51980

314

49692 96480 73214 93198

364

56110 13836 49055 99035

315

49831 05537 89600 51009

365

56229 28644 56474 70586

316

49968 70826 18403 81842

366

56348 10853 94410 66639

317

50105 92622 17751 49455

367

56466 60642 52089 33799

318

50242 71199 84132 67814

369

56584 78186 73517 65972

119

50379 00830 57181 12808

369

56702 63661 59060 36910

330

50514 99783 19905 97607

370

56820 17240 66994 99681

321

50650 50324 04872 07S13

371

56937 39096 15045 S7635

322

50785 58716 95830 90479

372

57054 29398 91897 50739

323

50920 25323 31102 89008

373

57170 88318 08687 60551

324

51054 50102 06612 13961

374

57287 16022 00480 16450

325

51188 33609 78874 37878

375

57403 12677 27718 85165

326

51321 76000 67939 00285

376

57518 78449 27661 05006

327

51454 77526 60286 07250

377

57634 13502 05792 85654

328

51587 38437 11679 08015

378

57749 17998 37225 33781

329

51719 5S979 49974 29513

379

57863 92099 68072 34193

330

51951 3939S 77S87 47805

380

57979 35966 16810 15675

331

51982 79937 75718 73861

381

58092 49756 75619 30154

332

52113 80837 04036 29426

382

5820fi 33629 11708 73285

333

52244 42335 06319 S7140

383

58319 87739 68622 74038

334

52374 64668 11564 47520

384

58433 12243 67530 90379

335

52504 48070 36845 23894

385

5S546 07295 09500 67625

336

52633 92773 89844 04886

386

58659 73046 71754 95581

337

52762 99008 71338 62619

387

59771 09650 18911 40100

338

52891 67002 77654 73363

388

59883 17255 94207 24221

339

53019 96982 03082 16009

389

58994 96013 25707 73624

340

53147 89170 42255 12375

390

59106 46070 26499 20650

341

53275 437B9 92497 72042

391

59217 67573 95866 80741

342

53402 61060 56135 03134

392

59329 60670 20457 24707

343

53539 41200 42770 49214

393

59439 25503 75436 69811

344

53655 84425 71530 11205

394

59549 62218 25574 12259

M5

53791 90950 73274 12095

395

59659 70956 26460 23278

346

53907 60987 92776 60977

396

59769 51859 25512 30577

347

31032 94747 90S73 71854

397

59879 05067 63115 06588

348

54157 92439 46580 91506

398

59998 30720 73687 84531

349

hi-?m 51-269 59179 99654

399

60097 28956 86748 22954

3&OJ54406 ,S0443 50275 635511

400

60205 99913 27962 39043

•AHi UIGAHITHMS

Tab. 2. 1

N.

401

Logarithms.

45l

Logaiithins.

603U 43726 201S2 30654

65417

65418 77960 53586

402

60422 60530 84470 06666

452

65513

84348 11382 1IS22

403

60530 50461 41109 44887

453

65609

82020 12831 67416

1404

60638 13651 10604 96470

454

65705 58528 57103 91532]

405

60745 50232 14668 55397

455

65801

13966 57112 40470

406

60852 60335 77194 11326

456

65896 48426 64434 984471

407

60959 44092 25220 03756

457

65991

62000 69850 2223&

408

61066 01630 89879 95148

458

66086

947S0 03869 18934

409

61172 33080 07341 80361

459

66181

26855 37261 24043

410

61278 3S567 19735 49451

460

66275 78316 81574 O740b|

411

61394 18218 76069 20586

461

66S70 09253 89648 14507|

412

61489 72160 33134 59560

462

66464

19755 56125 50397

413

61595 00516 56401 02097

463

66558 09910 17953 13567|

414

61700 03411 20898 94B67

464

66651

79805 54880 86819

415

61804' 80967 12092 70862

463

66745

29528 89953 92175

416

61909 33306 26742 74528

466

66838

59166 90000 16740

417

62013 60549 73757 51775

467

66931

68805 66112 16309

418

62117 62817 75035 19750

468

67024

58530 74124 03422

419

62221 40229 66295 30985

469

67117

28427 15083 26486

420

62324 92903 97900 46322

470

67209

76579 35717 46441

421

62428 20958 35668 30744

471

67302

09071 28396 1T406

422

62531 24509 61673 86030

472

67394

J9986 34087 7759U

423

62634 03673 75042 33900

473

67486

11407 37811 56716

424

62736 59565 92732 63127

474

67577

83416 74085 06050

425

62838 69300 50311 53811

475

67669

36096 24866 57111

426

62940 95991 02718 91860

476

67760

69527 20493 14968

427

63042 78750 25023 86460

477

67851

83790 40113 92022

428

63144 37690 13172 03126

478

67942

78966 12118 68022

429

63245 72921 84724 24725

479

68033

551S4 14563 22010

430

63346 84555 79586 52641

480

68124

12373 75587 21815

431

63447 72701 60731 60075

481

68214

50763 73831 76601

432

63548 37468 14912 09274

462

68304

70382 38849 57929

433

63648 78963 53365 44270

483

68394

71307 51512 14«88

4S4

63748 97295 12610 70559

484

68484

53616 444L2 47193

435

63848 92569 54637 32941

485

68574

173S6 02263 65657

436

63948 64892 68586 02563

486

68663

62692 62293 38169

437

64048 14369 70421 84040

487

68752

89612 14634 3324«

438

64147 41105 04099 53358

488

BB641 98220 02710 eiS^S

439

64246 45202 42121 37063

489

68930 88591 23620 24494

440

64345 25764 86187 4311S

490

69019 60800 2S513 66142

441

64443 85894 67S38 53601

491

69108

14921 22968 4727&

442

64542 22693 49091 69296

492

69196

51027 67360 3222S

443

64640 37262 23069 56023

493

69284

69192 77230 01587

444

64738 29701 14619 82453

494

69372

69489 23646 92596

44&

64836 00109 80931 58951

495

69460

51989 33568 72013

446

64933 48587 12141 86969

496

69548

16764 90197 46u52

*47

65030 75231 31936 47553

497

69635

63887 33332 11681

448

65127 80139 98144 00199

498

69722

93427 59717 53633

449

65224 63410 03323 17492

199

69810

05456 23399 91417

450

65S21 25137 75343 67938

500

69897

0OO43 36019 80479

Tab. 2. TO 20 places

207

N.

Logarithms.

N.

Logarithms.

50l

em^i 773i>4~6724'crTl72fl

55l

74115 15988 51785 04887

502

70070 37171 45019 SS455

552

74193 90777 29198 90180

&0S

70156 79850 55937 39710

553

74272 51313 04698 25871

504

70243 05364 45525 29094

554

74350 97S47 28429 74899

505

70329 13781 18661 37906

555

74429 29B31 22676 23889

506

70415 05168 39799 11483

556

74507 47915 82057 47089

507

70500 79593 S3335 97571

557

74585 51951 73728 90044

508

70586 37122 83919 25467

558

74663 41999 37578 74947

509

70671 77823 36758 74657

559

74741 18079 86423 29561

510

70757 01760 97936 36584

560

74818 80270 06200 41635

511

70842 09001 34712 73179

561

74896 28612 56161 40659

512

70926 99609 75830 75692

562

74973 63155 69061 08808

513

71011 73651 11816 27342

563

75050 83948 51346 22909

514

71096 31189 95275 73238

564

75127 91039 83342 29214

515

71180 72290 41191 00996

565

75204 84478 19438 52758

515

71264 97016 27211 35413

566

75291 64311 88271 43077

517

71349 05430 93942 50516

567

75858 30589 92906 57989

518

71432 97597 45233 02273

568

75434 63357 11018 87173

519

71516 73578 48457 85186

569

755II 22663 95071 17229

520

71600 33436 34799 15963

570

75587 48556 72491 39883

52!

71663 77232 99524 47424

571

75663 61082 45848 05004

522

71767 05030 02262 15714

572

75739 60287 93024 20038

523

71850 16888 67274 23926

573

75815 46219 67389 9749$

524

71933 12869 83726 65124

574

75891 18923 97973 52044

525

72015 93034 05956 87758

575

75966 78446 89630 48844

526

72098 57441 53739 06419

576

76042 24834 23212 04587

527

72181 06152 12546 60821

577

76117 58131 55731 42849

524

72263 39225 33812 25890

578

76192 78384 20529 05229

529

72345 56720 35185 75774

579

76267 85637 27436 19789

530

72427 58696 0U789 04563

580

76342 79935 62937 29255

531

72509 45210 81469 06485

581

76417 61323 90330 73454

532

72591 16322 95048 18268

582

76492 29646 49888 48489

533

72672 72090 26572 26372

583

76566 85547 59014 08638

534

72754 12570 28556 41723

584

76641 28471 12399 48672

5S5

72835 37820 21228 44562

585

76715 58660 82180 44859

536

72916 47B96 92770 01979

596

76789 76160 18090 65146

537

72997 42856 99555 60687

587

76863 81012 47614 47606

538

73078 22756 66389 17530

588

76937 73260 76138 48915

539

73158 87651 86738 70217

569

77011 52947 87101 64120

540

73239 37598 22968 50710

590

77085 20116 42144 19026

541

73319 72651 06569 43688

591

77158 74808 81255 36467

542

73399 92S65 38386 92473

992

77232 17067 22919 77766

543

73479 98295 88846 94758

593

77305 46933 64262 60640

544

73559 88996 98179 90461

594

77378 64449 81193 54795

545

73639 65022 76642 43999

595

77451 69657 28549 56404

546

73719 26427 04737 23243

596

77524 62597 40836 42868

547

73798 7S263 33430 778S1

697

77597 43311 29369 08740

548

73878 05584 84869 15899

598

77670 11639 88410 64329

949

7M57 23444 50091 90848

599

77742 68223 89311 37983

550

74036 26894 94243 84554

600

77815 12503 83643 63251 j

208 LOGARITHMS

Tab. 2.

N.

601

Logarithms.

N.
eTi

Logarithms.

77887 44720 02739 52089

81358 098S5 68191 94767

602

77959 6491-2 57824 55233

652

81424 75957 31920 19807

6(13

78031 73121 40151 30674

653

81491 31812 75073 92143

604

78103 69386 21131 82730

654

81557 77483 24267 26771

603

78175 53746 52468 88629

655

31624 12999 91783 06560

606

78247 2624 1 66286 20678

656

81690 38393 75660 27536

607

7S313 86910 75257 5»096

657

81756 53695 59780 77566

608

78390 35792 72734 93761

658

81822 58936 13955 49034

609

78461 72926 32875 35534

659

31888 54145 94009 8612S

610

7S532 98350 10767 03389

660

81954 39355 41868 67326

611

78604 1210-2 42554 23362

661

82020 14594 85640 23665

612

78675 14221 45561 19356

662

82085 79894 39699 93382

fllS

78746 04745 IB4I5 03774

663

82151 35284 04773 13304

614

78816 83711 41167 67997

664

82216 80793 68017 4S947

615

78887 51157 75416 73659

665

82282 16453 03104 59703

616

78958 07121 64425 45710

666

82347 42^1 70301 06661

617

79028 51640 33241 68205

667

82412 58339 16548 96620

618

79098 84750 68815 83768

668

82477 64624 75545 67041

619

79169 06490 20117 97680

669 82542 61177 67623 110T7|

620

79239 16394 98253 87488

670

82607 4S027 O0H26 43415

621

79309 16001 76580 19075

671

82672 25201 68992 07464

622

79379 03846 90818 70077

672

82736 92730 53825 24408

623

79448 80466 59169 61544

673

82801 50642 23976 84648

624

79518 45896 82423 98736

674

82865 98965 35319 82140

625

795SS 00173 44075 21915

675

82930 37728 31024 92146

626

79657 43332 10429 68002

676

82994 66959 41635 92994

627

79726 75409 30716 43958

677

83058 S6686 85144 316UI

628

79795 96437 37196 12719

678

83122 96938 67063 35530

629

79865 06454 45268 92535

679

93196 97742 80501 68250

630

79934 05494 53581 70530

680

83250 89127 06236 3IS97

631

80002 93592 44134 31302

681

83314 71119 127B5 15740

632

80071 70782 82385 01364

682

83378 43746 56478 91563

633

80140 37100 17355 1023S

6S3

83442 07036 81532 56340

634

80209 92578 81732 68977

684

83505 61017 20116 22655

635

80277 37252 91975 66903

685

83569 05714 92425 57335

636

80345 71156 48413 87336

686

83632 41157 06751 687S5

6S7

80413 94323 35350 43063

687

83695 67370 59550 43142

C39

80482 06787 21162 32330

83758 84382 35511 30726

639

80550 08581 58400 16068

689

83821 92219 07625 81494

640

80617 99739 83987 17128

690

83884 90907 37255 31616

641

80685 80295 18617 42225

691

93947 80473 74198 40758

642

80753 50280 66853 27334

692

84010 60944 56757 90499

643

90821 09729 24222 07249

693

94073 32346 11806 74605

644

80888 58673 59812 10001

694

94135 94704 54S54 91375

645

80955 97146 35267 76849

695

84198 48045 90113 88524

646

B1023 25179 95084 08529

696

84260 92396 10562 11027

647

81090 42806 68700 38446

697

84323 27780 980l» 42305

648

81157 50058 70593 33482

699

84385 54226 23161 09175

649

81224 46968 00369 23101

699

84447 71757 45681 40949

650

8I29I 33566 42855 57399

700

94509 80400 14236 83071

Logarithms.

Logarithms.

1 84571
! »4633
I S1695

I H4757
) 848IS

J5Q64
) 85135
[ 85IB6
I 85iJ47
! 85309
1 85369

> 65430

> 85491
r 85551
i 85Gt2
) 85G72
I 85733
1 85793
! 85853
I 85913
1 85973
i 86033

726 36093
r B6153
( 86213
I 86272

r 86746
i 66805
I S(i864
740 8fi923
i 86981
742 ■ 871140
743j9709«

744 87157

745 87215

746 87273
■ 87S32
I 87390
I S744S
I 87 SOU

80179
71121
53250
26591
91169
47010
94137
32576
62351
834S7
96007

66658 65706
29H05 27631
19823 95834
42112 21203
91398 70650
51R03 7C071
96899 40499
89769 01798
83066 54285
19075 28609
29766 30258
36856 37036
95299 51865 55853
82117 76174 39176
60418 01090 61474
30223 07855 56000
91556 67S0O 12230
44442 42300 34303
98903 62882 60777
24964 31268 46023
52647 19429 03588
71975 69639 11929
82972 94530 92137
85661 97146 90071
80065 70993 69C91
66207 00093 71401
44108 59037 83621
13793 1303? 18556
75293 17974 62377
28601 20455 90107
73769 57860 45495
10910 59391 86161
39746 41127 94317
60599 16070 53320
73390 94194 90351 |
78143 37499 95494
7487S 59051 47490
63618 23041 56431
44383 94925 73669
17197 30976 19202
82079 79328 16S04
39052 79027 07156
88137 60575 29242
29355 45978 702C0
62727 48292 84304
88274 72669 80U72
U6018 15398 77842
15979 64461 35972
18176 99466 47155
12633 91700 04687

1 87563
> 87621
I 87679
I 87737
. 87791

99370
78405
49762
13458
69516
I 17955
) 59795
) 92056
I 17758
I 35922

t 89195
[ 88252
I 8S309

04168 3!
91642 24527
00700 57664
69774 05175
29188 24166
01206 53302
00072 75709
32053 53715
95480 35691
80791 35196
46567 70572 82637
49713 39600 49675
45379 54980 46591
3358f 75689 92806
i 14351 53617 60792
i 87696 32603 93559
) 53639 49980 95947
i 12200 31511 99900
! 63398 01431 03960
) 07251 72481 97146

i 96986
' 89042
) 89097
I 89153
) 89209
1 99265
i 89320
I 89376

i 89542
' 69597
< 89652

I 89982
i 90036
J 90091
J 90145
i 90200
) 90254
J 90308

43780 50956
73003 35736
94939 19324
09606 92992
17025 06310
17212 58199
10198 00914
95969 89689
74576 72564
46026 90490
10338 77300
67530 59348
17620 57943
60626 94438
96567 45252
25460 39407
47323 59064
62174 89555
70032 09420
70912 90441
64834 97676
51815 99493
31873 17603
05024 27096
71286 56470
30677 37669
93213 96112
26913 50729
67793 13991
99969 91943

97446
15102
90897
59621
28924
43743
26492
93146
45605
40172
32694
00262
39922
44229
54155
89332
55847
31790
30627
42799
55351
50098
80309
26109
29771
114053
31727
42476
39295
58564

210 LOGARITHMS

Tab. 2. 1

N.
iol

Logarithms.

N.
851

Logarilnms.

90363 25ie0 §4^37 6aU3l

92992

9b600 84587 b7566

802

90417 436h-2 81163 50I7G

852

93043 95947 66700 1IS82]

803

90471 55452 78680 94182

853

93094 90311 67523 03000,

S04

90525 60487 48451 26187

854

93145 78706 89005 0598l]

sab

90579 58803 67868 51437

855

93196

61147 23172 64091

806

90633 50419 05090 64409

856

93247

37046 77153 22648

807

90687 35347 22070 41738

957

93298

08219 23198 16429

808

90741 13607 74586 15992

958

93348

72878 48705 44247

809

90794 95216 12272 30432

859

93309

31636 31242 30263

810

90848 50188 78649 74918

860

93449

84512 43567 72162

8U

90902 08542 11156 03069

861

93500

31514 53654 76252

812

90955 60392 41175 30847

863

93550

72656 24712 79596

813

91009 05455 94068 16682

863

93601

07957 15209 59266

814

91062 44048 89201 23277

864

93651

37424 78893 28795

815

91115 76087 39976 61243

865

93701

61074 64814 21935

81fi

91169 01587 53861 14669

866

93751

78920 17346 63791

617

91222 20565 32415 48794

667

93801

90974 76210 29438

618

91275 33036 71322 99882

868

93651

97251 76491 90081

619

91328 39017 60418 47451

869

93901

97764 48666 46875

820

91381 38523 63716 68972

870

93951

92526 16618 52463

821

91434 31571 19440 77180

871

94001

81550 07663 20336

822

91487 18175 40050 40107

872

94051

64649 33567 22064

833

91539 98352 12269 83977

873

94101

42437 05569 72637

824

91592 72116 97115 79081

974

94151

14326 34403 03562

825

91645 39485 49925 08762

875

94200

80530 22313 24507

82G

91698 00473 20382 21619

876

94250

41061 66080 72880

827

91750 55095 52B46 67071

877

94399

95933 66040 51823

828

91803 03367 84880 14389

878

94349

45159 06102 56585

629

91855 45305 50273 55312

879

94398

88750 73771 89354

830

91907 80923 76073 90383

660

94446

26721 50168 62639

831

91960 10237 S4U0 99107

881

94497

59084 12047 91274

833

92012 33262 90723 94049

882

94546

85851 31819 73123

833

92064 50014 06787 58996

883

94596

07035 775C8 56562

834

93116 60506 37738 71297

884

94645

22650 13073 08817

935

92169 64754 83602 08477

885

94694

32706 97825 43234

836

92220 02774 39010 39271

886

94743

37218 67050 755441

897

92272 54579 93259 99155

887

94792 36198 31736 39220|

92324 40186 30276 50506

888

94641

29657 78601 01974

639

92376 19608 28700 27500

1889

94890

17609 70213 69496

840

92427 92660 61831 65843

1890

94939

00066 44912 78472

641

92479 59957 97912 17467

691

94987

77040 36874 78993

642

92531 20914 99649 50266

892

95036

48543 76123 06390

843

92582 75746 24742 33016

893

95065

145SS 88546 4259^

844

92634 24466 25655 05551

894

95)33 75187 95917 670771

845

926S5 67089 49692 34320

895

95182

30353 15911 97436

846

92737 03630 39023 53422

896

95230

80096 62125 19721

847

92788 34103 30706 91221

897

95279

24430 44092 08537

848

92839 58522 56713 82649

898

95327 63366 67304 S701S'

849

92890 76902 43952 67285

899

95375 96917 33228 767001

lew

92941 69257 14392 73333

900

95434 25094 39334 87469

930
931
932
933
934
935
936

Logarithms.

95472~47909 ~79062"
95320 G5375 41941
95568 77503 13505
95616 84304 753G3
95664 85792 05203
95712 81976 76813
95760 72870 60095
95808 59465 210S5
95856 38832 21967
95904 13923 21093
95951 83769 72998
95999 48383 28416
96047 07775 34298
96094 6)957 3383)
96142 10940 66448
96189 54736 67850
96236 93356 70021
96284 26S12 01242
II 55113 86111
96378 78273 45555
96425 96301 96848
96473 09210 53G29
96520 17010 25912
96567 19712 20106
96614 173-27 39032
96661 09S66 81934
96707 97341 44497
96754 79762 18862
96801 5713U 93641
9684S 29485 53935
96894 96809 SI 342
96941 59123 53981
96989 16437 46499
97034 68762 30093
97031 16108 72517
97127 58487 38105
97173 95908 S7778
97220 28383 79064
97266 55922 66110
97312 78535 99698
9735S 96234 27256
97405 09027 92877
97451 16927 37328
97497 19942 98068
97543 18085 09262
97589 1 1364 01792
97634 99790 03273
97680 83373 38066
97726 62124 27292
97772 36052 89847

LoCTarilhi

97417
73047 ,
79441 1

25585 ;
110531

44887 I
59992

94458
41757
27597
3S456
09152
43564
26520

05530
69918

60638

HI

62296

3C262

94285

35830

77408

22944

26303

46008

92210

65963

90934

36927

37338

97112

9473S

76237

41875

25572

67028

76632

L 97818
J 97863
( 97909

) 98045
19)
i 98 136
I 98181
1 96227
98272
13)7
I 99362
1 98407
. 98452
I 98497
' 9S542
i 98587

970 i

971 i

972 E

99166
99211
99255
99299
99343

1 99475
I 99519
I 99563
. 99607
! 99651
I 99694
I 99738
) 997B2
i 99825

,ms.

^5169 37413 93185
69483 84474 34489
29006 38326 40853
93747 04095 11544
33715 S3746 34242
78922 7G100 07543
19377 76843 56539
55090 78544 4153)
86071 70663 59938
12330 39568 41336
33876 69545 35933
50720 37812 96)23
6287) 24534 51542
70339 02830 77450
73133 43792 56538
71264 15493 34209
64740 83110) 07360
53573 08393 667)4
37770 50765 32737
]7342 66244 85178
92299 08004 86290
62649 26274 57690
28402 68351 91117
89568 78615 52768
46156 98536 81607
9SI76 66691 81474
45637 18773 07091
89547 87601 44015
26918 03)37 82547
60756 92494 85664
90073 79948 50979
14877 96949 66797
35178 32135 62-275
50984 3134) 51745
62304 97611 73216
69149 41211 21109
71526 69636 73242
69445 87628 12117
6-2915 97179 405-27
5L945 97549 91534

36544 85-275
16721 54178
92484 9538)
63S43 97313
30807 45725
933S4 23699
51583 11655
05412 67371
54992 25982
40774 79316

32S36
65574
17590
31202
45489

213 LOGABITHMS Tab. 2.

N.

1003

Logarithms.

N.

Logarithms-

00130 09330 20418 11880

TTo3

04257 55124 40190

59866

1005

00216 60617 56507 67623

1105

04336 22780 21729

50254

1007

00302 94705 53618 00717

1107

04414 76208 78722

80639

1009

00389 11662 36910 52172

1109

04493 15461 49160

06471

1011

O047S 11555 91001 06349

1111

04571 40589 40867

61503

1013

W560 94453 60280 42845

1113

04649 51643 34708

31364

loia

00646 60422 49231 72283

1115

U4727 48673 84779

4782!

1017

00732 09529 22744 59739

U17

04805 31731 15609

05702

1019

00817 41840 06426 39490

1119

04883 O0S65 28350

04281

1021

00902 57420 86910 24725

U21

04960 56125 94973

15180

1023

00987 56337 12160 15771

1123

05037 97562 61457

78469

102a

01072 38653 91773 10408

1125

05115 25224 47981

28893

1027

01157 04435 97278 19720

1127

05192 39160 46106

54029

1029

01241 53747 62432 93943

1129

05269 39419 24967

86114

1031

01325 86652 83516 54691

1131

05346 26049 25455

293S4

1033

01410 03215 19620 57904

1133

05422 99098 63397

24592

1035

01494 03497 92936 55824

1135

05499 5S615 29741

524S9

1037

01577 87563 89040 96243

1137

05576 04646 87734

77923

1039|01661 55475 57177 41240

1139

05652 37240 79100

36269

1041101745 07295 10^36 155S3

1141

45728 56444 18214

6383i

1043l01828 43084 86530 86897

1143

05804 62303 95281

73884

1045

01911 62904 47072 80707

1145

05880 54866 75906 79892

1047

01994 66816 78842 33384

1147

05956 34179 01267 67648

1049

02077 54861 93557 85991;

1149

06032 00286 88285

17768

1051

02160 27160 28242 22008)

1151

06107 53236 29791

9018i

1053

02242 83711 85486 51839

1153

06182 93072 94699

02164

1055

02325 24596 33711 46987

1155

06258 19942 28163

11353

1057

02407 49873 07426 26758

1157

06333 33589 51749

55393

1059

02489 59601 07485 00279

1159

06408 34359 63595 99543

1061

02571 53839 01340 66612

1161

06483 22197 39573

83830

1063

02653 32645 23296 75697

1163

06557 97147 28448

41139

1065

02734 96077 74756 52817

1165

06632 59253 62037

77699

1067

02816 44194 24469 89253

1167

06707 08560 45370

17354

1069

02897 77052 08778 01749

1169

06781 45111 61840

11069

1071

02978 94609 31855 63385

1171

06855 68950 72S63

12990

1073

03059 97219 65951 03414

1173

06929 80121 15529

24471

1075,03140 84642 51624 13598

1175

07003 78666 0775& 07399

1077;03221 57032 97981 58511

1177

07077 64628 43434

68158

1079

03302 14446 82910 67304

1179

07151 38050 95089

13541

loai

03382 56939 53310 34328

1181

07224 98976 13514

79908

1US3

08462 84566 25320 36037

1183

07298 47446 27930 36912

1085

03512 97381 85148 31517

llSb

07371 83503 46122 67008

1087

03622 95440 86294 53993

1187

07445 07189 54591

22047

1089

03702 78797 55774 95610

1189

07519 18346 18691

58184

1091

03782 47505 88341 87761

1191

07591 17614 82777

50318

1093

03862 01619 49702 79227

1193

07664 04436 70341

87279

1095

03941 41191 76137 14316

1195

07736 79052 84156

48979

1097

04020 66275 747II 13222

1197

07809 41504 06410 66684

1099

04099 76924 23490 5S747

1199

07881 91830 98848 67595

1101

04178 73189 71751 77529'

,

Num.

10 1000

loiooi

101002
101003
101004
101005
101006
101007
101008
101009
101010
lOlOll
101012
101013
101014
101015
101016
101017
101018
101019

101023
101024
101025
101026
101027
101028
101029
101030
101031
101032
101033
101034
101035
10)036
101037

10104U
101041
101042
101043
101044
101045
101046
101047
101048
101049

LfOgarithms.

wr.i-i

00432
00432
00433
00433
00434
00434
00435
00435
00436
00436
00436
00437
00437
00438
00438
00439
00439
00439
00440
00440
00441
00441
00442
00442
00442
00443
00443
00444
00444
00445
00445
00445
00446
00446
00447
00447
0044S
00448
00446
00449
00449
00450
00450
00451
00451
00t5l
00452
00452
00453

1S737
50737
99735
42734
85732

i2a4-2
06721 2352?
88227 02280
27160 77989
23523 34949

2S729 77315 S7458

71726

14723

57719

00715

43711

86700

29700

5S681
01674
44667
87659
30650
73641
16632
59622
02612
45602
88591
31579
74567
17555
60542
03529
46516
89502
32488
75473
18458
61442
04426
47409
90392
33375
76357
19339
62320
05301
48282
91262
34242
77221

57192 36292
83278 61195
66797 88804
07751 03402
06138 89270
61962 30685
75222 11924
45919 17259
74054 30961
59628 37298
02642 20536
03096 64938
60992 54764
76330 74272
49112 07719
79337 39856
67007 53435
12123 34204
14685 6590S
74695 32791
92153 19092
67060 09050
994 1 G 86901
89224 36978
36483 43211
41194 90128
03359 61854
2297B 42614
00052 16627
34581 68112
26567 81283
76011 40355
82913 29537
47274 ^038
69095 35063
4837^ 19816
85120 71496
79326 74302
30996 12430
40129 70073
06728 31420
30792 80660
12324 01980

Differ.

4>!)9!

42998 81505
42998 38933
42997 96362
42997 58792
42997 11222
42996 6S654
42996 26086
42995 83519
42995 40953
42994 98387
42994 55823
42994 13259
42993 70697
42993 28135
42992 85574
42992 43013
42992 00454 44402
42991 57895 89826
42991 1533S

78753
75708
56961
22509

41415
81239
05335
13702
06337

42990 72781
42990 30225
42989 87670
42989 45115
42989 02562

42985 60009
42988 17457
42987 74906
42987 32356

42986 89S07
42986 47259
42986 04711
42985 62164
42985 19618
42994 77073
42984 34529
42963 91966
42993 49443
42983 06901
42982 64361
42982 21821
42981 79281
42981 36743
42980 94206
42960 51669
42980 09133
42979 66598
42979 24064
42978 81531
42978 38998

19508
33447

31637
14079
80769
31704
6668342551 f
86301 1 42550 i
8995ft '42550 1
77851.42549 2
49977142548 4
06333142547 !i
46917 >42546 7
71726142545 G
80760 1 42545 C
74013 1 42544 i
51485! 42543 ^
13171:42542 £
50072,42541 t
89182 42540 i

64301
81299
84295
64294
84290

84258
84257
84251

03501

42540
42539
42538
42537
42536
42585
42534
42534
42533
42532
42531

17272
33073

48874
64678
80485
96296
12107
27920
43739
59558

84225
84225
84219
84219
84214

84205
84204
84199
84199
64196
84193
84189
84189
84187
84181
841R1
84176

•214 LOGARITHMS Tab. 3. j

Num.

Logarithms.

Differ. 1.

Diff. 2.

D.3.

84m

101051)

00453 63178 51322 79561

42977

96467 18023

42530 753SU

101051

00454 06156 47789 97584

42977

53936 42643

42529 91203

84172

101052

00454 49134 01726 40-227

42977

11406 51440

42529 07031

84170

101053

00454 92111 13132 91667

42976 68877 44409

42528 23861

84169

101054

00455 350H7 82010 36076

42976 26349 21548

42527 39693

84167

101035

00455 78004 083.^9 57624

42975

83821 82855

42526 54526

84163

101056

00456 21039 92181 40479

42975

41295 28329

42525 70364

84161

101057

00456 64015 33476 68808

42974

93769 57965

42524 86203

84158

101058

00457 06990 32246 26773

42974

56244 71762

42524 02045

84155

101059

00457 49964 88490 98535

42974

13730 69717

42523 17890

84154

lOlOGO

00457 92939 02211 68253

42973

71197 51827

42522 3373^!

84150

101061

0045S 35912 73409 20079

42973

28675 18091

42521 49586

84149

101062

0045S 76886 02084 38170

42972

86153 68505

42320 65438

84146

101063

00459 21858 88238 06675

42972

43633 03067

42519 81292

84143

101064

00459 64831 31871 09742

42972

01113 21775

42518 97149

84140

101065

00460 07803 32984 31517

42971

58594 24626

42518 13009

84138

101066

00460 50774 91578 56143

42971

16076 11617

42517 28871

84137

101067

00460 93746 07654 67760

42970

73558 82746

42516 44734

84132

10IU6S

00461 36716 81213 50506

42970

31042 38012

42515 60602

84130

101069

00461 79687 12255 88518

42969

83526 77410

42514 76472

84130

lOlOTO

00462 226f)7 00782 65928

42969

46012 00938

42513 92342

84124

101071

00462 65626 46794 66866

42969

03498 08596

42513 08218

84123

101072

00463 08595 50292 754fi'2 +a9li8 60985 00378

42512 24093

84 13 J

101073

00463 51564 11277 75840

42968

19472 76333

42511 39973

84117

101074

00463 94532 29750 52123

42967

75961 36310

42510 55956

84116

101075

00464 37500 05711 88433

42967

33450 80454

42509 71740

84113

101076

00464 80467 39162 68897

42966

90941 08714

42508 87627

84111

101077

00465 23434 30103 77601

42966

48432 21097

42508 03516

84107

101078

00465 66400 78535 98688

43966

03924 17571

42507 19409

84107

101079

00466 09366 S4460 16259

42965

63416 98162

42506 35302

84102

101090

00466 52332 47877 14421

42965

20910 62850

42505 51200

84102

101091

00466 95297 68787 77281

42964

78405 11660

42504 67098

84097

101082

00467 38262 47192 88941

42964

35900 44562

42503 83001

84095

IOI0B3

00467 81226 83093 33503

42963 93396 6I56I

42502 98906

84095

101084

00468 24190 76489 95064

42963

50993 62655

43502 14811

34090

101085

00468 67154 27383 57719

42963

08391 47944

42501 30721

84087 '

101086

00469 10117 35775 05363

42962

65890 17123

42300 46634

84097 1

101087

00469 53080 01665 22686

42962

23389 70489

42499 62547

84083 i

101038

00169 96042 25054 93175

42961

80S90 07942

42498 78464

840801

I010S9

00470 39004 05945 01117

42961

38391 29478

42497 94394

84078 j

lotooo

0O470 81965 44336 30595

42960

95893 35094

42497 10306

84077

101091

00471 24926 40229 65689

42960

53396 24788

12496 26229

34073

101092

00471 67886 93625 90477

42960

10899 98559

42493 42156

84069

101093

00472 10847 04525 S9036

42959

68404 56103

42494 5S0B7

84070

101094

00472 53806 72930 45439

42959

25909 98316

42493 74017

84065

101095

00472 96765 9S840 43755

42958 83416 24299

42492 89952

84063

101096

00473 39724 82256 68054

42958 40923 34347

42492 05889

84060

101097

00473 82683 23180 02401

42957 98431 2M58

42491 21829

84061

10109S

00474 25641 21611 3i|S59

42957

55940 06629

42490 37768

84052

101099

00474 68598 77551 37488

429S7

13449 rms\

424S9 53716

840.^6

' Tab. 3. m 20 places. 215 j

J ^

Num.

Logarithms.

Differ. 1.

Diff. 2

D.3.

UdUm

00475 11555 91001 0G349

42956 70960 )5)45

42488 69660

64050

lOUOl

00475 54512 61961 21494

42956 2847) 45485

42487 856)0

84048

101102

00475 97468 90432 66979

42955 85983 59875

42487 01562

84046

101103

00476 40424 76416 26854

42955 43496 58313

42486 17516

84043

1UU04

00476 83SS0 19912 85167

42955 0)0)0 40797

42485 33473

84040

101105

00477 26335 20923 25964

43954 58525 07324

42484 49433

84040

101106

00477 69289 79448 33388

42954 )6040 5T89t

42483 65393

84034

,101107

00478 12243 95488 91179

42953 73556 92498

42482 8)359

S4035

101108

00476 55197 69045 83677

42953 31074 11)39

42481 97324

84030

101109

00478 98151 00)19 94816

42952 88592 13315

424S1 13294

84028

lOllIO

00479 41103 88713 08631

42952 46111 0052)

42480 29266

64025

101111

00479 84056 34823 09152

42952 03630 7)255

42479 45241

S40ii6

to 111-2

O04SO 27008 38453 80407

4295) 6)151 26014

42478 6)215

840 IB

I011I3

00480 69959 99605 0642)

42951 18672 64799

42477 77)97

S4D20

101114

00481 12911 18277 7)220

42950 76194 87602

42476 93)77

84015

101115

00481 55S6I 94472 58822

42950 33717 94425

42476 09162

84013

101116

00481 9S813 28190 53247

42949 91241 85263

42475 25)49

84012

101117

00482 41762 19432 38510

42949 48766 60114

42474 41137

84008

10111&

00482 S4711 6819S 98624

42949 06292 18977

42473 57)29

84006

101119

00483 27660 74491 17601

42948 63818 61848

42472 73)23

84002

101120

00483 70609 38309 79449

42948 21345 88725

42471 89121

84003

101)21

00484 13557 59655 68174

42947 78873 99604

42471 051)8

83996

101122

00484 56505 38529 67778

42947 36402 94486

42470 21122

83998

101123

00484 99452 74932 62264

42946 93932 73364

42469 37124

83993

101124

00485 42399 68865 35628

42946 51463 36240

42468 53)3)

S3990

10H25

00485 85346 20328 71868

42946 08994 83109

42467 69)41

S3988

101126

004ri6 28292 29323 54977

42945 66527 1396S

42466 85)53

8398S

101(27

00486 71237 95850 68945

42945 24060 2S815

42466 01165

83982

101128

00487 14183 I99I0 97760

42944 81594 27650

42465 17)83

83981

101129

00487 57128 01505 254)0

42944 39129 10467

42464 33202

83976

101130

00488 00072 40634 35877

42943 96664 77265

42463 49224

83978

101131

00488 43016 37299 13142

42943 5420) 2804)

42462 65246

83971

101132

0U4&S 85959 91500 4U83

42943 11738 62795

42461 81275

83972

101133

00489 28903 03239 0397S

42942 69276 81520

42460 97303

83969

101134

00489 71845 72515 S5498

42942 26815 84217

42460 )3334

S3965

10113^

00490 14T87 99331 69715

42941 84355 70883

42459 29369

83964

101136

00490 57729 83687 40598

4294) 4)896 415)4

42458 45405

83962

101137

00491 00671 25583 821)2

42940 99437 96)09

42457 6)443

839571

101138

0049) 436)2 2502) 78221

42940 56980 34666

42456 77486

83956

101139

00491 86552 82002 12887

42940 14523 57)80

42455 935311

83954

101140

00492 29492 96525 70067

42939 72067 63650

42455 09576

83951

101141

00492 72432 68593 SS717

42939 296)2 54074

42454 25625

83949

101142

00493 15371 9S205 87791

4293S S715S 28449

42453 41676

83946

101143

00493 5B310 85364 16240

42938 44704 86773

42452 57730

83944

L01I44

00494 01249 30069 03013

42938 02252 29043

4245) 73786

8394)

101145

00494 441S7 3232) 320.56

42937 59800 55257

424riO 89345

83938

101146

00494 87124 92)2) 87313

42937 17349 65412

42450 05907

83936

101147

00495 30062 0947) 52725

42936 74899 &9505

42449 21971

8iJ934

101148

00495 72998 84371 12230

42936 32450 37534

12448 36037

8393) 1

101149

00496 15935 )6e21 49764

42935 90001 99497

42447 .54106

83929'

LOGARITHMS AND

Tab. 4.

Log.

00000
0000 1
00002
00003
00004
00005
00006
1)001)7
OOOOH
00009
00010
00011
00012
OODIS
00014
00015
00016
00017
00018
00019
00020
00021
00022
00023
00024
00025
00026
00027
00028
00029
00030
00031
00032
00033
00(134
O0OS5
00036
00037
0003)4
00039
00040
00041
00042
00043
00044
00045
00046
00047
OII04M

(P(in4!)

Number.

lomio

10000
10000
10000
10000
10001
10001
1000 1
10001
10002
10002
10002
10002
10002
10003

ooooo

23026
40052
69079
92107
15135
3BI64
61193
84223
07254
31)285
53316

OOOOO
11602
76225

77455
13254
02082
43942

22413 87720
i 45447 41717
i 68481 48750
} 91516 0R823
I 14551 21935
1 37586 88088

OOOOO

68807
57806
89084
84726
6CS25
57474
78767
52806
01691
47528
12421
18484
87829
4257

10004
10004
10005
10005
10005
10005
10005
10006
10006
10006
10006
10007
10007
10007
10007
10008

looiw

I0(H)8
10008
10008
10003
10009
10009
10009
10010
10010
10010
10010
10011
WlOll

60623

29734
52773
75811
9H8ril
21891
44931
67972
91014
14056
37098
60141
83185
06229
29274
52319
75365
9K411
21458
44505
07553
90601
13650
36700
59750
82800
05851

07284
79522
04806
63135
14511

16825
19565
75362
84217
46131
61106
29142
.50241
24405
51634
31929
65292
51725
91227
83802
29448
28169
79965
84838
42788

75222
09653
28651
54360
; 08926
J 14500
t 93233
I 6728
1 58802
89957
82909
59825
42875
54229
16064
50557
79SSS
26242
11803
58761
89308
25639
89950
04443
91330
72787
71052
08328
0682H

23020
23026
23027
23027
23028
23028
23029
23029
23030
23030
23031
23031
23032

11002 6h807
64622 88999
17644 31278
70666 95642
23690 82099
76715 90C49
29742 21293
82769 74039
35798 48885
89828 45837
41859 64B93
94892 06063
47925 69345
00960 54742
23033 53996 62259

23034 07033

23034 60073

23035 13112

23035 66153

23036 19195

23036 72238

23037 25283

23037 78329

23038 31376
23038 84424

91696
43658
17548
13566
31718
72006
34431

23040
23040
23041
23042
23042
23043
23043
23044
23044
23045
23045
23046
23046
23047
23047
23048
23048
23049
23049
23050
23051
23051
23052

37474 05574
90524 78733
43576 74048
96629 91521
49684 31155
02739 92952
55796 76916
08854 83050
61914 11354
I49T4 61835
6B036 34493
21099 29331
74163 46354
27228 85561
80295 46958
33363 30547
86432 36331
39502 64311
92574 14493
45646 86877
98720 81467
51795 9S265
04872 37276
57949 98500
11028 81942

53020 20192

53021 42279

53022 64364

53023 86457

53025 08550

53026 30644

53027 52746

53028 74846

53029 96952

53031 1905G

53032 41170

53033 63282

53034 85397

53036 07517

53037 29637

53035 51 762

53039 73890

53040 96018

53042 1B152

53043 40288

53044 62425

53045 84567

53047 06711

53048 28857

53049 51008

53050 73159

53051 9.5315

53053 17473

53054 39634

53055 61797

53056 83964

53058 06134

53059 28304

53060 50481

53061 72658

53062 94838

53064 17023

53065 39207

53066 61397

53067 835>j9

53069 05784

53070 27980

53071 50182

53072 72384

53073 94590

53075 16798

53076 39011

53077 61224

53078 83442
53080 05661

1 22087
1 22085
I 22093
1 2:
I 2:
1 22102
1 22100
1 22106
1 22104
1 22114
1 22112
1 22115
1 32120
1 22120
1 22125
1 22128
I 221SS
1 22134
1 22136
1 22137
1 32148
1 22144
I 32146
1 32151
1 22151
1 23156
1 22158
1 22161
i 22163
1 22167
1 32170
I 22170
1 22177
1 22177
1 22180
1 22185
1 22184
1 22190
1 22192
I 22195
1 22196
1 2J
1 22202
1 2-2206
1 22208
1 32213,
1 222131
I 2221 -(I
1 222191
I 22224

NUMBERS TO 20 PLACES.

Log.

00050
0005 1
00052
00053
00054
00055
00056
00057
00058
00059
OOOGO
OU061

Number.

00065
00066
00067
00068
00069
00070
00071
00072
00073
00074
00075
00076
00077
00078
00079
«0
•81
000S2
00083
00094
000S5

10011 51955 53HI6
lOOll T5008 17925

10011 9S061 35U5

10012 21115 05388
10012 44169 28744
10012 67224 05186

10012 90279 34713

10013 13335 17328
10013 36391 53U32
10013 59448 41825

10013 82505 83709

10014 05563 78686
10014 28622 26756
10014 51681 27921
10014 74740 82182

10014 97800 89540

10015 2086! 49996
10015 43922 63552
10015 66984 30209
10015 90046 49968

W77(l
76373
91861
57459
95395
27901
77210
65560

61121
45620
47156

10016
10016
10016
10016
10017
10017
10017
10017
10017
10018
10018
lOOIS
10018
10019
10019
10019
10019
10020
10020
10020
10020
10020
10021
00093] 10021
OO0W4, 10021
IMU9bi 10021
00>J96 1 10022
00097 1 10022
0<M9S|1002-i
0U099|l0022

13109
36172
59236
82300
05365
28430
51496
74663
97630
B0697
43765

48797 61011
27870 05299
60049 44800
45337 01798
83733 98580
75241 57436
19361 00661
17593 50550
68440 29402
72402 59518
29481 63203
39678 62763
02994 80510
19431 38756
8S989 59816
11670 6600S
87475 79656
16406 23081
98463 18612

00090
00091
00092

12973
36043
59113
82185
05256
28329
51401
74475 S3647
97549 2 I 96 I
20623 63405
43698 57980
66774 056S8
89850 06530
12926 60507
36003 67620
59081 27S71
82159 41260

8S578
55311
41147
68425
594H4

Differ.

23052 64108 8^603

23053 17190 15488

23053 70272 65598

23054 23356 37936
23054 76441 32506

23035 S

23055 i

23056 S

23056 £

23057 ^

29527 49809
82614 88350
35703 49629
68793 33152
41884 38920

23057 94976 66935

23058 48070 17202

23059 01164 89723

23059 54260 84499

23060 07358 01536

23060 60456 40835

23061 13556 02397

23061 66656 86229

23062 19758 92331
23062 72862 20706

23063
23063
23064
23064
23065
23065

25966 71967
79072 44288
32179 39501
85287 56998
38396 96782
91507 58856
44619 43225
97732 49889
50846 78852
03962 30116

23068 57079 03685

23069 10196 99560
23069 63316 17747

16436 58246
69558 21060

23070
23070
23071
23071
23072
23073
23073
23073
23074
23074
23075
23076

22681 06192
75805 13648
28930 43425
82056 95531
35184 69966
88313 66733
41443 85836
94575 27:i7S
47707 91059
00841 77186

23076 53976 85658

23077 07113 16481

23077 60250 69654

23078 13389 45185
23078 66539 43071

Diff. 2. D. 3.

53081 27885

53082 50110

53083 72338

53084 94570
53086 16803

53087 39041

53088 61279

53089 83523

53091 05768

53092 280(5

53093 50267

53094 72521

53095 94776

53097 17037

53098 39299

53099 61562

53100 83832

53102 06102

53103 28375

53104 50651

53105 72931
!>3106 95213

53108 17497

53109 39784

53110 62074

53111 84369

53113 06664

53114 28963

53115 51264

53116 73569

53117 95875

53119 18187

53120 40499

53121 62814

53122 85132

53124 07456

53125 29777

53126 52106

53127 74435

53128 96767

53130 19103

53131 41442
53133 63781
53133 86127

53135 08472

53136 30823

53137 53173

53138 75531
53i39 97886
53141 20249

1 22238
1 2S
1 22244
I 22245
1 22247
I 22252
1 222.54
1 22255
1 2226]
I 22262
1 23
1 22270
1 22270
1 22273
1 22276
1 22280

1 22295
1 22295

i 22

1 22312

1 22312

1 22315

1 22318

1 22324

1 22321

1 2S

1 23

1 22

1 22^36

1 22339

1 22339

1 22346

1 22345

I 22351

1 22350

I 22358

1 22355

1 22363

1 22362

LOOARITHMS AND NUMBERS TO '20 PLACES.

Log-

00100

ootoi
ootos

00103
00104
00105
00106
00107
00108
00 109
OOUO
00111
00113
00113
00114
00115
00116
00117
OOllS
00119
00120
00121
00122
00123
00124
00125
00126
0012T
0012S
00129
D0130
00131
00132
00133
U0134
00135
00136
00137
00138
00139
00140
DO Ml
00 142
00143
00144
00145
00146
00147
U014S
01)149

Number.

10023 05238 07789 96719

10023 28317 27460 60039

10023 51397 00273 65970

10023 74477 26230 363S0

10023 97b58 05331 95136

23079
28080
23080
23031

10024
10024
10024
10024
10025
1002b
10025
10025
10026
10026
10026
10026
10026
10027
100*7
10027
10027
10029
10023
10028

10029
10029
10029
10029
10030
10030
10U30
10030
10031
10031
10031
10031
10032
10032
10032
10032
10032
10033
10033
10033
10033
10031
10034

20639 37579
43721 22974
66803 61516
89886 53211
12969 98055
36053 96052
59138 47202
82223 51506
05309 08967
26395 19585

63112 i

63182

17724

49118

79747

31997

29258

90922

423B2

05036

23082
23083
230S3

51431 83361 01264 i
74569 00296 53529 ;
97656 70392 84178 i
20744 93651 15638 i
43833 70072 70321 i

66922
90012
13103
36194
59-285
62377
05469
26562
51656
74750
97945
20940
44036
67132
90228
13326
36424
59522

99658 70642
82410 39017
18328 97867
07415 69614
49671 76683
45098 41504
93696 86507
95469 34126
50414 06799
5S535 26964
19833 17064
34308 99545
01963 96855
22799 31444

24U1G 02279 i
04399 83439 '■
37968 91712 i
24724 49561- !

05720 64667 79455 :

28820 57800

51921 04122

75022 03636

9S123 56342

21225 62242

44329 21333

67431 336-29

90534 99119

13639 17(100

36743 8%94

45260
26122
68927

0924'
9904
b5712

n»(i;(i (ia:t-;;Li

72613 05931

25956 70910

79101 58256

82247 07976

85395 00070

36543 54542

91693 31394

44944 30629

97996 52250

i 51149 96261

) 04304 62664

» 57460 51460

> 10617 62654

i 63775 96249

r 16935 52245

r 70096 30649

i 2325S 31460

) 76421 54663

) 29586 00321

23089 92751 68375

23090 35918 58850

23090 89086 71747

23091 42256 07069
23091 95426 64621

46598 45003
01771 47619
54945 72673
08121 :^0165
61297 90100
14475 82491
67654 97310
20835 34589
74016 94822
27199 76512
80383 61161
33569 08273
86755 57849
39943 29894
93132 24408
463-22 41397
99513 80862
5-2706 42905
05900 27231
59095 34140
12291 63533
654S9 15416
18697 89T94
71897 86671
250ti9 06049

23093
23093
23094
23094
23095
23095
23096
23096
23097

23100
23100
23101
23102
23102
23103
23103
23104
23101
23105

Diff. 2.

53142 42611

53143 64979

53144 87346

53146 09720

53147 32094

53148 54472

53149 76952

53150 99235

53152 21621

53153 44011

53154 66403

53155 89796

53157 11194

53158 33594

53159 55997

53160 78404

53162 00811

53163 23223

53164 45636

53165 68054

53166 90475

53168 12897

53169 35322

53170 57752

53171 80182

53173 02616

53174 25054

53175 47492

53176 69985

53177 92381

53179 14829

53180 37279

53181 59733

53182 82190

53194 04649
53165 27112

53196 49576
53187 72045
53I8S 94514
53190 16939
^3191 39465

53192 61948

53193 84426

53195 06909
58196 29393

53197 51883

53198 7437S

53199 96877
53201 19379
53-J(t2 41881

D. 3.

1 223tii»
1 22867
I 22374
1 223T4
1 22378
1 :

1 22400
1 22403
1 22407
1 22407
L 22412
1 22415
1 22416
1 22421
1 22422
1 224251
I 22430 !
1 22430'
I 22434 I
1 22439
I 22439
1 2-2443
1 22446
1 22448
1 22450
I 22454
1 22457
1 22459
1 22463
1 22461
1 22469
1 22469
1 22475
1 22476,
1 2247si
1 22483
1 22493
1 2-_'494
1 22490
1 22495
1 224991
1 22501 I
1 22503 j
1 SSri'lfli

Tat

). 5.

HYPERBOLIC

LOGARITHMS.

219

N.

l-Ol

Logar.

N.

1-51

Logar. ^

N.

2-01

Logar.

N.

2-51

Logar.

0-0099503

0-4121097

0-6981347

0-9202828

102

0-0198026

1-52

0-4187103

202

07030975

2-52

0-9242589

103

0-0295588

1-53

0-4252677

2-03

07080358

253

0-9-282193

104

00392-207

1-54

0-4317824

2-04

07129498

254

0-9321641

105

0-0487902

1-55

0-4382549

205

07178398

2-55

0-9360934

106

00582689

1-56

0-4446858

206

0-7227060

2-56

09400073

107

00676586

1-57

0-4510756

2 07

0-7-275486

2-57

0-9439059

1-08

00769610

1-58

0-4574-248

2-08

0-7323679

2-58

0-9477894

109

00861777

1-59

0-4637340

209

0737 164.1

2-59

09516579

110

00953102

1-60

0-4700036

210

0-7419373

2-60

0-9555114

111

0-1043600

1-61

0-476-2342

211

0-7466879

2-61

0-9593502

112

1133-287

1-62

0-48-24261

212

07514161

2-62

0-9631743

113

012-22176

1-63

0-4885800

213

0-7561220

2-63

0-9669838

114

0-1310-283

1-64

0-4946962

214

0-7608058

2-64

0-9707789

115

01397619

1-65

0-5007753

215

0-7654678

265

0-9745596

116

01484200

1-66

0-5068176

216

0-7701082

2-66

0-9783261

117

0-1570037

1-67

0-5128236

217

0-7747-272

2-67

0-9820785

118

0-1655144

1-68

0-5187938

2-18

0-7793249

2-68

0-9858168

119

0-1739533

1-69

0-5247285

2-19

0-7839015

2-69

0-9895412

r-20

0-1823216

1-70

0-5306283

2-20

0-7884574

2-70

0-9932518

1-21

0-1906-204

1-71

0-5364934

221

0-7929925

•2-71

0*9969486

1-22

0-1988509

1-72

0-54-23-243

222

0-7975072

2-72

10006319

1-23

0-2070142

1-73

•0-5481214

2-23

0-8020016

273

1-0043016

124

0-2151114

1-74

0-5538851

2-24

0-8064759

2-74

10079579

1-25

0-2231436

1-75

0-5596158

2-25

0-8109302

2-75

10116009

1-26

0-2311117

1-76

5653138

2-26

0-8153648

2-76

1-0152307

1-27

0-2390169

1-77

0-5709795

2-27

0-8197798

277

10188473

1 28

0-2468601

1-78

0-5766134

2-28

0-8241754

2^78

1-0224509

129

0-2546422

1-79

5822156

2-29

0-8-285518

279

1-0-260416

1-30

0-2623643

1-80

0-5877867

230

0-83-29091

2-80

1-0296194

1-31

0-2700271

181

0-5933268

2-31

0-8372475

2-81

1-0331845

132

0-2776317

1-82

0-5988365

2-32

0-8415672

282

1-0367369

1-33

0-2851789

1-83

06043160

2-33

0-8458683

2-83

1-0402767

1-34

2926696

1-84

0-6097656

2-34

0-8501509

2-84

1-0438041

1-35

0-3001046

1-85

0-6151856

2-35

0-8544153

2-85

1-0473190

1-36

0-3074847

1-86

06-205765

2-36

0-8586616

2-86

1-0508217

1-37

0-3148107

1-87

0-6259384

2-37

0-8628899

2-87

1-0543121

138

0-3220835

1-88

0-6312718

2-38

0-8671005

2-88

1-0577903

1-39

0-3293037

1-89

06365768

2-39

0-8712933

289

1-0612565

1-40

0-3364722

1-90

06418539

2 40

0-8754687

2-90

1-0647107

1-41

0-3435897

191

06471032

2-41

0-8796-267

2-91

1-0681531

1-42

0-3506569

1-92

0-6523252

2-42

0-8837675

2-92

10715836

1-43

0-3576745

1-93

0-6575200

2-43

0-8878913

2-93

1-0750024

1-44

0-3646431

1-94

0-66-26880

2-44

0-8919980

2-94

10784096

145

0-3715636

1-95

06678294

2-45

0-8960880

2-95

1-0818052

1-46

0-3784364

1-96

0-67-29445

2-46

0-9001613

2-96

10851893

1-47

0-3852624

1-97

0-6780335

2-47

0-9042182

2-97

1-0885619

1-48

0-3920421

1-98

0-6830968

2-48

0-9082586

2-98

1-0919233

1-491
l-50»

0-3987761

1-99

0-6881346 2-49

0-9122827

2 99

10952734

0-4054651

2-00

0-6931472 2-50

09 16-2907

300

1-0986123

220

HYPERBOLIC LOGARITHMS.

Tab. 5.

N.

3^
302
303
304
305

3-06
307
308
309
310

311
312
313
314
315

316
317
3*18
319
3-20

3-21
3-22
3*23
3-24
3-25

3-26
3-27
3-28
3-29
3-30

331
3 32
3-33
3-34
3-35

3-36
3-37
3-38
3-39
3-40

3-41
342
3-43
3-44
3-45

3-46
3-47
3-48
3*49
3-50

Logar.

1-1019401

1052568
1085626
1118575
1151416

1184149
1216776
1249296
1281711
1314021

1346227
1378330
1410330
1442228
1474025

1505720
1537316
1568812
1600209
1631508

1662709
1693814
1724821
1755733
1786550

1817272
1847900
1878434
1908876
1939225

1969482
1999648
2029723
2059708
2089603

2119410
2149127
2178757
2208299
2237754

2267123
2296406
2325603
2354715
2383742

2412686
2441546
2470323
2499017
2527630

N.

3^
3-52
3-53
3-54
3-55

3-56
3-57
3-58
3-59
3-60

3-61
3-62
3-63
3-64
3-65

366
367
3-68
3-69
3-70

3-71
3-72
3-73
3-74
3-75

3-76
3-77
3-78
3-79
3-80

3-81
3-82
3-83
3-84
3-85

3-86

3-87
3-88
3-89
3-90

391
3 92
3-93
3-94
3-95

Logar. N.

1-2556160
1-2584610
1-2612979
1-2641267
1-2669476

1-2697605
1-2725656
1-2753628
1-2781522
1-2809338

1-2837078
1-2864740
1-2892326
1-2919837
1-2947272

1-2974631
1-3001917
1-3029128
1-3056-265
1-3083328

1-3110319
1-3137237
1-3164082
1-3190856
1-3217558

1-3244190
1-3-270750
13-297240
1-3323660
1-3350011

1-3376292
1-3402504
1-3428648
1-3454724
1-3480731

1-3506672
1-3532545
1-3558352
1-3584092
1-3609766

1-3635374
1-3660917
1-3686394
1-3711807
1-3737156

3-96 1-376-2440
3-97 1-3787661
3-98 1-381-2818
3-99 1 1-3837912
400 i 1-386-2944

401
4-02
4-03
4-04
4-05

406
4-07
4-08
4 09
4-10

411
4-12
4-13
4-14
4-15

4-16
4-17
4-18
4-19
4-20

4-21
4-22
4-23
4-24
4-25

4-26
4-27
4-28
4-29
4-30

4-31
4-32
4-33
4-34
4-35

4-36
4 37

4-38
4-39
4-40

4-41
4-42
4-43
4-44
4-45

4-46
4-47
4-48
4.49
4-50

Logar.

N.

4-51

1-3887912

1-3912819

4-52

1-3937664

4-53

1-3962447

4-54

1-3987169

4 55

1-4011829

4-56

1-4036429

4-57

1-4060970

4-58

1-4085450

4-59

1-4109870

4-60

1-4134-230

4-61

1-4158532

4-62

1-4182774

4-63

1-4-206958

4-64

1-4231083

4-65

1-4255151

4-66

1-4279160

4-67

1-4303112

4-68

1-4327007

4-69

1-4350845

4-70

1-4874626
14398351
1-442-2020
1-4445633
1-4469190

#

1-4492692
1-4516138
1-4539530
1-4562868
1-4586150

1-4609379
1-4632554
1-4655675
1-4678743
1-4701758

1-4724721
1-4747630
1-4770487
1-4793292
1-4816045

1-4838747
1-4861397
1-4883996
1-4906544
1-4929041

1-4953488
1-4973884
1-4996230
1*5018527
1-5040774

4-71
4-72
4-73
4-74
4 75

4-76
4-77
4-78
4-79
4-80

4-81
4-82
4-83
4-84
4-85

4-86

4-87
4-88
4-89
4-90

491
4-92
4-93
4-94
4-95

4-96
4-97
4-98
4-99
500

Logar.

1-506-2971
1-5085120
1-5107219
1-5129270
1-5151272

1-5173-226
1-5195132
1-5216990
1-5238800
1-5260563

1-5282-278
1-5303947
1-5325569
1-5347144
1-5368672

1-5390154
1-5411591
1-543-2981
1-5454326
1-5475625

1-5496879
1-5518088
1-5539252
1-5560371
1-5581446

1-5602476
1-5623463
1-5644405
1-5665303
1-5686159

1-5706971
1-5727739
1-5748465
1-5769147
1-5789787

1-5810384
1-5830939
1-5851452
1-58719-23
1-5892352

1-5912739
1-5933085
1-5953390
1-5973653
1-5993876

1-6014057
1-6034198
1*6054299
1-6074359
1-60943791

Tab. 5. HYPERBOLIC LCG\RITIIMS.

221

N.

501

Logar.

N.

5-51

LogaT.

1

N.

6-01

Logar.

N.

651

Logar.

1-6114359

1-7065646

1 -7934247

1-8733395

502

1-6134-299

552

1-7083779

6-02

1-7950873

6-52

1-8748744

503

1-6154200

5-53

1-7101878

603

1-7967470

6-53

18764069

504

1-6174061

5-54

1-7119945

604

1-7984040

6-54

1-8779372

505

16193883

5-55

17137979

6-05

1-8000583

6-55

1-8794650

506

1-6213665

556

1-7155981

6-06

1-8017098

6-56

1-8809906

507

1-6233408

5-57

1-7173951

6-07

i-8033586

6-57

1-8825138

5-08

1-6-253113

5-58

1-7191888

608

1-8050047

6-58

1-8840347

509

1-6272778

5-59

1-7-209793

609

1-8066481

6-59

1-8855533

510

1-6-29-2405

5-60

1-7227666

610

1-8082888

6-60

1-8870696

511

1-6311994

5-61

17-245507

611

1-8099-268

6-61

1-8885836

512

1-6331544

5-62

1-7263317

6-12

1-8115621

6-62

1-8900954

513

1-6351057

5-63

1-7281094

613

1-8131947

6-63

1-8916048

514

1-637053.

564

1-7298841

6-14

1-8148247

6-64

1-8931120

515

1-6389967

5-65

1-7316555

6-15

1-8164521

6-65

1-8946169

516

1-6409366

5-66

17334239

6-16

1-8180768

6*66

1-8961195

517

1-6428727

5-67

1-7351891

6-17

1-8196988

6-67

1-8976198

518

1-6448051

568

1-7369512

618

1-8213183

6-68

1-8991180

519

1-6467337

5 69

1-7387102

6-19

1-8229351

6-69

1-9006139

5-20

1-6486586

5-70

17404662

6-eo

1-8245493

6-70

1-9021075

5-21

1-6505799

5-71

1-7422190

6-21

1-8261609

6-71

1-0035990

5-22

1-6524974

5-72

1-7439689

6-22

1-8277699

672

1-9050882

5-23

1-6544113

5-73

1-7457155

6-23

1-8293763

6-73

19065751

5-24

1-6563215

5*74

1-7474593

6-24

1-8309802

6-74

1-9080599

5-25

1-6582281

5-75

1-7491998

6-25

1-8325815

6-75

19095425

5-26

1-6601310

5-76

1-7509375

6-26

1-8341802

676

1-91102-29

5-27

1-6620304

5-77

1-7526721

6-27

1-8357764

6-77

1-9125011

5-28

1-6639261

5-78

1-7544037

6-28

1-8373700

6-78

1-9139771

5-29

1-6658182

5-79

1-7561323

6-29

1-8389611

6-79

1-9154509

5-30

1-6677068

5-80

1-7578579

6-30

1-8405496

6-80

1-9169226

5-31

1-6695918

5-81

1-7595806

6-31

1-8421357

6-81

19183921

5-32

1-6714733

5-82

1-7613003

6-32

18437192

6-82

1-9198595

5-33

1-6733512

5-83

1-7630170

6-33

1-8453002

6-83

1-9213-247

5*34

1-675-2257

5-84

1-7647308

6-34

1-8468788

6-84

1-92-27877

5-35

1-67IP966

5-85

1-7664416

6-35

1-8484548

6-85

1-924248T

5-36

1-6789640

5-86

1-7681496

636

1-8500284

6-86

1-9257074

5-87

1-6808279

5-87

1-7698546

6-37

1-8515995

6-87

1-9271641

5-38

1-6326884

5-88

1-7715568

6-38

1-8531681

6-88

1-9286187

5-39

1-6845454

5-89

1-7732560

6-39

1-8547343

6-89

1-9300711

5-40

1-6863990

5-90

1-7749524

6-40

1-8562980

6-90

1-9315214

5-41

1-6882491

5-91

1-7766458

6-41

1-8578593

6-91

1-932&696

5-42

1-6900958

5-92

1-7783364

6-42

1-8594181

6-92

1-9344158

5-43

1-6919391

5-93

1-7800242

6-43

1-8609745

6-93

1-9358598

5-44

1-6937791

5 94

1-7817091

6-44

1-8625285

6-94

1-9373018

5-45

1-6956156

5-95

1-7833912

6-45

1-8640801

6-95

1-9387417

5-46

1-6974488

5-96

1-7850705

646

1-8656293

6-96

1-9401795

5-47

1-699-2786

5-97

1-7867469

6-47

1-8671761

6-97

1-9416152

5-48

1-7011051

5-98

1-7684206

6-48

1-8687205

6-98

1-9430489

5-49

1-7029283

5-99

1-7900914

6-49

1-870-2625

6-99

1-9444805

b'bO

1-7047481 1 600

17917595

6-50

1-8718022

7-00

1-9459101

222 HYPERBOLIC LOGARITHMS. Tab. 5. I

1

N.

701

Logar.

N.

7-51

Logar.

N.

8-01

Logar.

N.

8-51

Logar.

1-9473377

2-016-2355

2 0806908

2

•1412419

7 02

1-9487632

752

20175661

802

20819384

8-52

2

•14-24163

7 03

1-9501867

7-53

2-0188950

803

20831845

8.^3

2

•1435894

7-04

1-9516082

7-54

20202222

804

20844291

6-54

2

•1447610

7-05

1-9530276

755

20215476

8-05

20856721

8-55

2

1459313

7 06

1-9544451

7-56

20228712

8-06

20869136

8-56

2

1471002!'

7 07

1-9558605

7-57

20241931

8;07

2 0881535

8-57

2

•14S2677

708

1-9572739

7-58

2-0255132

8-08

2-0893919

8-58

2

•1494340

7-09

1-9586853

7-59

2 0268316

8-09

20906287

8-59

2

1505988

710

1-9600948

7-60

2-0281482

810

2-0918641

8-60

2

1517622

711

1-9615022

7-61

20294632

811

2-0930979

8-61

2

15-29244

7-12

1-9629077

7-62

20307764

8-12

20943301

8-62

2

1540851

713

1-9643112

7-63

20320878

813

2-0955609

8-63

2

1552445

7-14

1-9657128

7-64

2-0333976

814

2-0967901

8-64

2

1564026

715

1-9671124

7-65

2-0347056

8-15

20980179

8-65

2

1575593

7-16

1-9685100

7-66

20360120

8-16

20992442

8-66

2

1587147

717

1*9699056

7-67

20373166

8-17

2-10046S9

8-67

2

1598689

7-18

1-9712994

7-68

2-0386195

8-18

2-1016922

8-68

2

1610215

719

1-97-26912-

7-69

20399208

819

2-10-29139

8-69

2

1621729

7-20

1-9740810

7-70

2-0412-203

8-20

2-1041342

8-70

2

1633230

7-21

1-9754690

7-71

2-0425182

821

2-1053529

8-71

2

164471f?

7-22

1-9768550

7-72

20438144

8-22

21065702

8-72

2

1656192

7-23

1-9782390

7-73

2-0451089

8-23

2-1077860

8-73

2

1667654

7-24

1-9796212

7-74

20464017

8-24

2-1090003

8-74

2

1679102

7-25

1-9810015

T-75

20476928

8-25

2-1102125

8-75

2

1690537

7-26

1-9823798

7-76

2-0489823

8-26

21114246

8-76

2

1701959

7-27

1-9837563

7-77

20502702

8-27

21126345 8-77

2

1713368

7-28

1-9851309

7-78

20515563

8-28

2-1138430

8-78

2

1724764

7-29

1-9865035

7-79

20528409

8-29

2-1150500

8-79

2

1736147

7-30

1-9878743

7-80

20541237

8-30

21 162555 8 80

2

1747517

7-31

1-9892433

7-81

20554050

8-31

21174596 8-81

2

•1758874

7-32

1-9906103

7-82

20566846

8-32

21 1866-23 8-82

2

1770219

7 33

1-9919755

7-83

20579625

8 33

21 198634! 8-63

2-

1781550

7-34

1-9933388

7-84

20592388

8-34

2- 12 10632

8-84

2

179-2869

7-35

1-9947003

7-85

2-0605135

8-35

212-22615

8-85

2

1804175

7-36

1-9960599

7-86

20617866

8-36

2- 1234584

S-66

2-

1815468

7-37

19974177

7-87

20630581

8-37

21-246539, 8-87

2

1826748

7-38

1-9987736

7-88

20643279

8-38

2-1258479; 8-88

2

1838016

7-39

20001-277

7-89

20655961

8-39

21270405! 8 89

2

1849270

7-40

2-0014800

7-90

2 0668628

8-40

2128-2317 890

2-

1860513

7-41

2-0028304

7-91

20681-278

8-41

2-1294215

8-91

2

1871742

7-42

2-0041791

7-92

2 0693912

8-42

2- 1306098

892

2

1882959

7-43

20055259

7-93

20706530

8-43

2-1317968

8-93

2-

1894164

7-44

2-0068708

7-94

20719133

8-44

2-1329823

894

2

1905356

7-45

2 0082140

7-95

20731719

8-45

21341664

895

2

1916535

7-46

20095554

7-96

20744290

8-46

2 1353492

8-96

2

1927702

7-47

2-0108950

7-97

20756845

8-47

2-1365305

8-97

2

■1938857

7-48

2-0122328

7-98

2-0769384

8-48

2-1377104

8-98

2

1949999

7-49

20135688

7-99

20781907

8-49

2 1388890

8-99

2

•1961128

7-50 120149030

800

2 0794415

8-50

2-1400662

900

21972246

1 ab. 5. HYPERBOLIC LOGARITHMS.

223

N.

901

Logar.

N.

9-36

Logar.

N.

IjOgdLT.

2- 1983351

2*2364453

9-71

2-2731563

902

21994443

937

2-2375131

9-72

2-2741856

903

2-2005524

9-38

2-2385797

9-73

•2-2752139

904

2*2016592

939

2-2396453

9-74

2-2762411

905

2-2027648

9-40

2-2407097

9-75

2-2772673

906

2-2038691

9-41

2-2417729

9-76

2-2782924

907

2-2049723

9-42

2-2428351

977

2-2793165

9 08

2-2060742

9-43

2-2438961

978

2-2803395

9 09

2-2071749

9-44

2-2449560

9-79

2**2813615

9-10

2-2082744

9-45

2-2460147

9-80

22823824

911

2-2093727

9-46

2-2470724

9-81

2*28340-23

912

2-2104698

9-47

2-2481289

9-82

2-2844211

913

2-2115657

9-48

2*2491843

9-83

2-2854389

914

2-21-26604

9-49

2-2502386

9-84

2-2864557

915

2-2137539

9-50

2-2512918

9-85

2-2874715

916

2-2148462

9-51

2-2523439

9-86

2-2884862

917

2-2159373

952

2-2533947

9-87

2-2894999

918

2-2170272

9-53

2-2544446

9-88

2 2905125

9-19

2-2181159

9-54

2-2554935

9-89

2-2915241

9-20

2-2192035

9-55

2-2565411

9-90

2-2925348

9-21

2-2202898

9-56

2-2575877

9 91

2 2935444

9-22

2-2213750

9-57

2-2586333

9-92

22945529

9-23

2-2-224590

9-58

2-2596775

9-93

2-2955605

9-24

2-2235419

9-59

22607209

9-94

2-2965670

9-25

2-2246-236

9-60

2-2617631

9-95

2-2975726

9-26

2-2257040

9-61

2-2628042

9-96

2-2985771

9-27

2-2267834

9-62

2*2638443

9-97

2-2995806

928

2-2278615

9-63

2-2648832

9-98

2-3005831

9-29

2-2289385

9-64

2-2659211

999

2-3015846

9-30

2-2300144

9-65

2-2669579

10*00

2-3025851

9-31

2-2310891

9-66

2-2679936

1000

4-6051702

9-32

2-2321626

9-67

2-2690283

1000

6-9077553

9-33

2-2332350

9-68

2-2700619

# 10000

9-2103404

9-34

2-2343062

9-69

2*2710944

100000

11-51292546

9-35

2-2353763

9-70

2-2721259

224

HYPERBOLIC

LOGARITHMS.

Tab. 6. »

N.

Logar.

N.

51

Logar.

101

Logar,

N.

151

Logar.

1

0000000

3-9318256

4-6151-205

5-017-2798

2

0-6931472

52

3-951-2437

102

4-6249728

152

5-0238805

3

10986123

53

3-970-2919

103

4-6347-290

153

50304379

4

1*3862944

54

3-9889840

104

4-6443909

154

50369526

5

1-6094379

55

4-0073332

105

4-6539604

155

5-0434251

6

1-7917595

56

4-0253517

106

4-6634391

156

5-0498560

7

1-9459101

57

4-0430513

107

4-6728288

157

5-0562458

8

2-0794415

58

40604430

108

4-6821312

158

5-0625950

9

21972246

59

4-0775374

109

4-6913479

159

5-0689042

10

2-3025851

60

4-0943446

110

4-7004804

160

50751738

11

2-3978953

61

4-1108739

111

4-7095302

161

5-0814044

12

2-4849066

62

4-1271344

112

4-7184989

162

5 0875963

13

2-5649494

63

41431347

113

4-7273878

163

5-0937502

14

2-6390573

64

41588831

114

4-7361984

164

50998664

15

2-7080502

65

4-1743873

115

4-7449321

165

5-1059455

16

2-7725887

66

4-1896547

116

4-7535902

166

5-1119878

17

2-8332133

67

4*2046926

117

4-7621739

167

5- 1179938

18

2-8903718

68

4-2195077

118

4-7706846

168

5-1-239640

19

2-9444390

69

4-2341065

119

4-7791235

169

5-1298987

20

2-9957323

70

4-2484952

120

4-7874917

170

5-1357984

21

304452-24

71

4-2626799

121

4-7957905

171

5-1416636

22

3-0910425

72

4-2766661

122

4-8040210

172

5-1474945

23

3-1354942

73

4-2904594

123

4-8121844

173

5-153*2916

24

31780538

74

4-3040651

124

4-8-202816

174

5-1590553

25

3-2188758

75

4-3174881

125

4-8283137

175

5-1647860

26

3-2580965

76

4-3307333

126

4-8362819

176

5-1704940

27

3-2958369

77

4-3438054

1-27

4-8441871

177

5-1761497

28

3-332-2045

78

4-3567088

1-28

4-8520303

178

5-1817836

29

3-3672958

79

4-3694479

129

4-8598124

179

51873858

30

3-4011974

80

4-3820266

130

4-8675345

180

5-1929569

31

3-4339872

81

4-3944492

131

4-8751973

181

5-1984970

32

3-4657359

82

4-4067192

132

4-8828019

182

5-2040067

33

3-4965076

83

4-4188406

133

4-8903491

183

5-2094862

34

3-5263605

84

4-4308168

134

4-8978398

184

5-2149358

35

35553481

85

4-4426513

135

4-9052748

185

5-2203558

36

3-5835189

86

4-4543473

136

49126549

186

5-2257467

37

3-6109179

87

4-4659081

137

4-9199809

187

5-2311096

38

3-6375862

88

4-4773368

138

4-9272537

188

5-2364420

39

36635616

89

4-4886364

139

4-9344739

189

5-2417470

40

36888795

90

4-4998097

140

4-9416424

190

5 2470241

41

3-7135721

91

4-5108595

141

4-9487599

191

5-2522734

42

3-7376696

92

4-5217886

142

4-9558271

192

5-2574954

43

3-7612001

93

4-5325995

143

4-9628446

193

5-2626902

44

3-7841896

94

4-5432948

144

4-9698133

194

5-2678582

45

3-8066625

95

4-5538769

145

4-9767337

195

5-2729996

46

3-8-286414

96

4-5643482

146

4-9836066

196

5-2781147

47

3-8501476

97

4-5747110

147

49904326

197

5-2832037

48

38712010

98

4-5849675

148

4-9972123

198

5-288-2670

49

8-8918203

99

4-5951199

149

50039463

199 5-293304S

50

3-9120230

100

4-6051702

150

5-0106353

200 5-2983174

Tab. 6.

HYPERBOLIC LOGARITHMS.

2'2o

N.

20T
202
203
204
205

206
207
208

Logar.

5-3033049
5-3082677
5-3132060
5-3181200
5-3230100

N.

251
252
253
254
255

5-3-278762 256
5-3327188 257

5-3375381
209 1 5 3423343

210 5-3471075

211 5-3518581

212 5-3565863
213 '5-3612922
214 5 3659760
215 '5-3706380

5-3752784
5-3798974
5-3844951
5-3890717
5-3936275

5-3981627
5-4026774
54071718
5-4116461

216
217
218
219
220

221
222
223
224
225

226
227
228
229
230

231
232
233
234
235

236
237
238
239
240 i

241
242
243
244
245

246
247
248
249
250

258
259
260

261
262
263
264
265

266
267
268
269
270

271
272
273
274
5-41610041275

5-4205350
5-4249500
5-4293456
5-4337220
5-4380793

276
277
278
279
280

281

5-4424177
5-4467374 j 282
5-4510365 283

5-4553211
5-4595855

5-4638318
5-4680601
5-4722707
5-4764636
5-4806389

5-4847969
5-4889377
5-4930614
5-4971682
5-5012582

5 5053315
5 5093883
5-5134287
5-5174529
5-5214609

284
285

286

287
288
289
290

291
292
293
294
295

296
•297
298
299
300

Logar.

N.

301

5-5254529

5 5294291

302

55333895

303

5-5373343

304

55412635

305

5 5451774

306

5-5490761

307

5-5529596

308

5-5568-281

309

5-5606816

310

5-5645204

311

5-5683445

312

5-5721540

313

5-5759491

314

5-5797298

315

5-5834963

316

5-5872487

317

5-5909870

318

5-5947114

319

5-5984220

320

56021188

321

5-6058021

322

5-6094718

323

5-6181281

324

5-6167711

325

5-6204009

326

5-6240175

327

5-6276211

3^8

5-6312118

dri9

5-/5347896

3S0

5-6383547

331

5-6419071

332

5-6454469

333

5-6489742

334

56524892

335

5-6559918

336

5 6594822

337

5-6629605

338

5-6664267

339

5-6698809

340

5-6733233

341

5-6767538

342

5-6801726

343

56835798

344

5-6869754

345

5-6903595

346

5-6937321

347

5-6970935

348

5-7004436

349

5-7037825

350

Loj»ar. N.

5-7071103 351
5-7104270 352
5-7137328 353
5-7170277 354
5 7203118 355

5-7235851 356
5-7268477 357
5-7300998 358
5-7333413 359
5-7365723 360

5-7397929 361
5-7430032 362
5 746-2032 363
5-7493930 364
5-7525726 !g65

5 7557422 366

5-7589018 367

5-7620514 368

5 7651911 369

5-7683210 370

371
372

5-7714411
5-7745515
5-7776523 1 873
^-'374

5-780743U
5-7838252

5-7868974
5-7899602
5-7930136
5-7960578

375

376
377

378
379

5-7990927 380

5-8021184 381

5-8051350 382

5-6081425 383

5-8111410 364

5-8141305 385

58171112 386

5-8200829 387

5-8230459 38S

5-8260001 389

5 8289456 390

5-8318825 391
5-8348107 392
5-8377304 393
5-8406417 394
5-S435444 395

5 8464388 396
5-8493-248 397
5 8522025 398
5-8550719 399
5-8579332 1 400

Logar.

5-860786-/
5-863031-2
5-8664681
5-869296J)
5-8721178

5-8749307
5-8777358
5-8805330
5-8833224
5-8861040

5-8888780
58916442
5-89440-28
5-8971539
5-8998974

59026333
5 9053618
5-9080829
5 9107966
5-9135030

5-916-2021
5 9188939
5-9215784
5-9242558
5*9269260

59-295891
5-9322452
59348942
5 9375362
5-9401713

5-9427994
59454206
59480350
5-9506420
5-9532433

5-9558374
59584247
59610053
5 9635793
5-9661467

5-9687076
5-9712618
5-9738096
5 9763509

5-9788858

5-9814142
5-9839363
5-9864520
5-9889614
5 9914645

2-2(>

HYPERBOLIC LOCAIUTHMS.

Tab. 6.

N.

Logar.

401 5-9939614

402
403
404
405

406
407
408
409
410

411
412
413
414
415

416
417
418
419
420

421
U22
423
424
425

426
1427
428
429
430

431
432
433
434
435

436
437
438
439
1440

441
442
443
444
445

446
447
448
449
450

5-9964521
5-9989366
60014149
6-0038871

60063532
6-0038132
60112672
60137152
6-0161572

60185932
60210*233
60234476
60258660
60282785

60306853
60330862
60354814
60378709
60402547

60426328
60450053
60473722
60497335
60520892

6-0544393
60567840
60591232
60614569
60637852

N.

60661081
60684256
60707377
60730445
6-0753460

60776422
60799332
60822189
60844994
60867747

60890449
6-0913099
60935698
60958246
6-0980743

6-1003190
61025586
6 1047932
6-1070229
6-1092476

451
452
453
454
455

456
457
458
459
460

461
462
463
464
465

466
467
468
469
470

471
472
473
474
475

476

477
478
479
480

Logar.

6-1 1 14673
61136622
61158921
61180972
61202974

61224928
6-1246834
61268692
61-290502
61312265

N.

50T
502
503
504
505

506
507
508
509
510

Logar.

61333980 511
61355649 512

481

482
483

484
485

486
487
488
489
490

491
492
493
494
495

496
497
498
499
500

61377271
61398846
61420374

61441856
6-1463293
61484683
6-15060-28
6-1527327

6-1548581
61569790
6-1590954
6-1612073
6-1633148

61654179
61675165
61696107
61717006
61737861

61758673
61779441
61800167
61820849
61841489

61862086
61882641
61903154
61923625
61944054

61964441
6-1984787
6-2005092
6-2025355
6-2045578

6-2065759
6-2085900
6-2106001
6-2126061
6-2146081

513
514
515

516
517
518
519
520

521
522
503
524
525

526
527
528
529
530

531
532
533
534
535

536
537

538
539

540

541
542
543
544
545

546
547
548
549
550

6-2166U61
6-2186001
6-2205902
6-2225763
6-2245584

6-2265367
6-2285110
6-2304814
6-2324480
6-2344107

6-2363696
6-2383246
6-2402756
6-2422233
6*2441669

6-2461068
6-2480429
6-2499752
6-2519039
6-2538288

6-2557500
6-2576676
6-2595815
6-2614917
6-2633983

6-2653012
6-2672005
6-2690963
6-2709884
6-2728770

6-2747620
6-2766435
6-2785214
6-2^03958
6-2822667

N.

551
552
553
554
555

556
557
558
559
560

561
562
563
564
565

566
567
568
569
570

571
572
573
574
575

Logar.

6-2841342
6-2859981
6-2878586
6--2897156
6-2915691

6-2934193
6-2952660
6-2971093
6-2989492
6-3007858

6-3026190
6-3044488
6-3062753
6-3080984
6-S099183

576
577
578
579
580

581

582
583
584
585

6 3117348
6 3135480
i6-3 153580
6-3171647
6-3189681

6-320768a

6-3-225652

6-3243590

6-3261495

63279368

0-3297209
6-3315018
6-3332795
6-3350543
63368257

6-3385941
6-3403593
6-3421214
6-3438804
6-3456364

6-3473892 '
6 3491390
6-3508857
6*3526-294
6*3543700

586

587
588
589
590

591
592
593
594
595

596
597
598
599
600

6S5610T7
6-3578423
63595739
63613025
6-3630-281

6-3647508
6*3664704
6*3681872
6*3699010
63716118

6-3733198
6-3750248
6*3767269
6-3784262
6-3801225

63818160
6*3835066
6 3851944
6-3868793
6*3885614

6*390-2407
6-3919171
6-3935908
63952616
6*3969297

Tab. 6.

HYPERBOLIC U)GAR1THMS.

227 i

N.

602
603
604
605

606
607
608
609
610

611
612
613
614
615

1616
617
618
619
620

621
622
623
624
625

626
627
028
629
630

631
632
633
634
635

63o
637
638
639
640

641
642
643
644
645

646
647
648
649
650

Logar.

63985949
6-4002574
6-4019172
6-4035742
6-4052285

6-4068800
6-4085288
6-4101749
6-4118183
6-4134590

6-4150970
6-41673*23
6 4183649
6-4199949
6-4216223

6-4232470
6-4248690
6-4264885
6-4281053
6-4297195

6-4313311
6 4329401
6-4345465
6-4361504
6-4377516

6-4393504
6-4409465
64425402
6-4441313
64457198

6-4473059
6-4468894
6-4504704
64520490
6 4536250

6-4551986
C45G7697
6-4583383
6-4599045
6-4614682

6-4630295
6-4645883
6 4661447
6-4676987
6-4692503

64707995
6-4723463
6-4738907
6 4754827
6-4769724

N.

651
652
653
654
655

656
657
658
659
660

661
662
668
664
665

666

667
668
669
670

671
672
673
674
675

676
677
678
679
680

681
682
683
684
685

686
687
688
689
690

691
692
693
694
695

696
697
698
699
700

Logar.

6-4785096
6-4800446
6-4815771
6-4831074
6-4846352

6-4861608
6-4876840
6-4892049
6 4907235
6-4922398

6-4937538
6-4952656
64967750
6-4982821
6 4997870

6-5012897
6-5027900
6-5042882
6-5057841
6-5072777

6 5087691
6-5102583
6-5117453
6.5132301
6-5147127

6-5161931
6-5176713
6-5191473
6-5206211
6-52209-28

6-5235623
6-5250-297
6-5264949
6-5279579
6-5294188

6*5308776
6-53-23343
6 5337888
6-5352413
6-5366916

6-5381398
6-5395860
6-5410300
6-54-24720
6-5439118

6-5453497
6-5467854
6-5482191
6-5496507
6-5510803

N.

TOT
702
703
704
705

706
707
708
709
710

711
712
713
714
715

716
717
718
719
720

721
7-22
7-23
724
725

726
727
728
729
730

731
732
733
734
735

736
737

738
739
740

741
742
748
744
745

746
747
748
749
750

Logar. N.

6-5525079 751
6-5539334 752
6-5553569 753
6-5567784 754
6-5581978 755

6-5596152 756
6-5610307 757
6-5624441 758
6-5638555 759
6-5652650 760

6-5666724 761
6-5680779 762
6*5694814 768
6-5708880 764
6-5722825 765

6 5736802 766
6-5750758 767
6-5764696 768
6-5778614 769
6-5792512 770

6-5806891 771
6-58-20251 772
6-5884092 778
6-5847914 774
G-5861717 775

6-5875500 776
6-5889265 777
6-5908010 778
6-5916737 779
6-5980445 780

6-5944185 781
6-5957805 782
6-5971457 783
6-5985090 784
6-5998705 785

6 601-2301 786
6-6025879 78T
6-6039438 788
6 6052979 789
6-6066502 790

6-6080006 791
6-6093492 792
6-6106960 793
6-6120410 794
6 6138842 795

6 6147256 796
6 6160652 797
6-6174030 798
66187390 799
6-6200732 800

<|3

Logar.

6*6214(157
6 6227368
6-6240652
6-6253924
6 6267177

6-6280414
6-6293633
6-6306834
6-6320018
6-6883184

6-6846334
6-6859466
6-6872580
6-6385678
6-639^758

6 6411822
6-6424868
6-6437897
6-6450910
6-6463905

6-6476884
6-6489846
6-6502790
6-6515719
6-6528680

6-6541525
6-6554404
6-6567265
6-6580110
6-659-2939

6-6605751
6-6618547
6-6631327
6-6644090
6-6656887

6-6669568
66682282
6-66949«l
6-6707663
667203-29

6-67^2980
6-6745614
6 6758232
6-6770835
6-6783421

6-6795992
6-6808547
6-6821086
6-6833609
6-6846117

228 HYPERBOLIC LOGARITHMS.

Tab. 6.

N.

Logar.

N.

851

Logar.

N.

901

Logar.

N.

951

Logar.

801

6-6858609

6-7464121

6 8035053

6*«575141

802

6-6871086

852

6-7475865

902

6*8046145

952

6-8585650

803

6-6883547 j 853

6-7487595

903

6-8057226

953

6*8596149

804

6-6895993 854

6-7499312

904

6-8068294

954

6-8606637 .

80&

6-6908423 855

6-7511015

905

6*8079349

955

6 8617113

806

6-6920837 856

6-7522704

906

6-8090393

956

6-8627579

807

6-6933237 857

6-7534379

907

6-8101425

957

6*8638034

808

6-69456211858

6-7546041

908

6-8112444

958

6*8648478 .

809

6 6957989 1 859

6-7557689

909

6-8123451

959

6*8658911

810

6-6970342 860

6-7569324

910

6-8134446

960

6-8669333

811

6-6982681

861

6-7580945

911

6-8145429

961

6-8679744

812

6-6995003

862

67592553

912

6-8156400

962

6-8690145

813

6-7007311

863

6-7604147

913

6-8167359

963

6-8700534

814

6-7019604

864

6-7615728

914

6-8178306

964

6-8710913

815

6 7031881 865

67627295

915

6-8189241

965

6-8721281

816 6-7044144 866

6-7638849

916

6-8200164

966

6*8731638

817 6-7056391

867

67650390

917

6-8211075

967

6-8741965

818 6-7068623

868

6-7661917

918

6-8221974

968

6-8752321

819

6 7080841

869

6 7673431

919

68232861

969

6*8762646

820 6-7093043

870

6-7684932

920

6 8243737

970

6-8772961

821,6 7105231

871

6-7696420

921

6-8254600

971

6-8783265

822 '6-7117404

872

6-7707894

922

6-8265452

972

6-8793558

823 '6-7129562

873

6-7719356

9-23

6-8276*292

973

6*8803841

824 6-7141705

874

6-7730804 ' 924

6-8287121

974

6*8814113

82516 7153834

875

6-7742239

925

6-8297937

975

6-8824375

82616-7165948

876

6-7753661

926

6-8308742

976

6-8834626

827 [6-7178047

877

67765070

927

68319536

977

6-8844867

828

6-7190132

878

67776466

928

6-8330317

978

6-8855097

829

67202202

879

6-7787849

929

6-8341087

979

6-8865316

830

6-7214257

880

6-7799219

930

68351846

980

6*88755*26

831

6-7226298

881

6-7810576

931

6-8362593

981

6-8885725

832

6-7238324

882

6-7821921

932

6-8373328

982

6-8895913

833

6-7250336

883

6-7833252

933

6-8384052

983

6-8906091

834

67262334

884

6-7844571

934

6-8394764

984

6-8916259

835

6-7274317

885

6-7855876

935

6-8405465

985

6-8926416

836

67286286

886

6-7867170

936

6-8416155

986

6-8936564

837

6-7298241

887

6-7878450

937

6-8426833

987

6-8946700

838

6-7310181

888

6-7889717

938

6-8437499

988

6-8956827

839

6 73-22107

889

6-7900972

939

6-8448155

989

6-8966943

840

'6-7334019

890

6-7912215

940

6-8458799

990

6*8977049

841

6-7345917

891

67923444

941

6-8469431

991

6-8987145

842

6-7357800

892

6-7934661

942

6-8480053

992

6-8997231

843

67369670

893

6-7945866

943

6-8490663

993

6*9007307

844

6-7381525

894

6-7957058

944

6-8501262

994

6*9017372

845

67393366

895

6-7968237

945

6-8511849

995

6-9027427

846

6-7405194

896

6-7979404

946

6-8522426

996

6-9037473

847

6-7417007

897

67990559

947

6*8532991

997

6-9047508

848

6-7428806

898

6-8001701

948

6*8543545

998

6*9057588

849

6-7440592

899

6-8012830

949

6-8554088

999

6*9067548

850

6*7452363

900

6 8023948

950

6*8564620

1000

69077558

Tab. 6.

HYPERBOLIC LOGARITHMS.

229

N.
fool

1002
1003
1004
1005

1006
1007
1008
1009
1010

1011
1012
1013
1014
1015

1016
1017
1018
1019
1020

1021
1022
1023
1024
1025

1026
1027
1028
1029
L030

1031
1032
1033
1034
1035

1036
1037
1038
1039
1040

1041
1042
1043
1044
1045

1046
1047
1048
1049
1050

Logar.

6-0087548
6-9097533
6-9107508
6-9117473
6-9127428

6-9137374
6-9147309
6-9157234
6-9167150
6-9177056

6-9186952
6 9196838
6-9206715
6 9216582
69226439

6-9236286
6-9246124
6-9255952
69265770
6-9275579

6-9285378
69295168
6-9304948
6 9314718
6-9324479

6*9334230
6-9343972
6-9353704
6-9363427
69373141

6-9382845
6-9392539
6-9402225
6*9411901
6-9421567

6-9431224
6-9440872
6-9450511
6-9460140
6-9469760

6-9479371
6-9488972
6-9498565
6-9508148
6-9517722

6-9527286
6*9536842
6-9546389
6*9555926
d-956M54

N.

1051
1052
1053
1054
1055

1056
1057
1058
1059
1060

1061
1062
1063
1064
1065

1066
1067
1068
1069
1070

1071
1072
1073
1074
1075

1076
1077
1078
1079
1080

1081
1082
1083
1084
1085

1086
1087
1088
1089
1090

1091
1092
1093
1094
1095

1096
1097
1006

Logar.

69574974
6-9584484
6-9593985
6-9603477
6*9612960

6-9622435
6-9631900
6-9641356
6-9650803
6*9660242

6-9669671
6-9679092
6*9688504
6-9697907
6-9707801

6 9716686
6-9726063
6-9735430
6-9744789
6-9754139

6-9763481
6-9772813
6-9782137
6*9791453
6-9800759

6-9810057
6-9819347
6-9828628
69837900
6-9847163

6-9856418
6-9865665
6-9874902
6-9884132
6-9893353

6-9902565
6 9911769
6-9920964
6-9930151
6-9939330

6*9948500
6*9957662
6-9966815
6-9975960
6-9985096

6*9904225
7-0003345
7*0012456

i . W .tSl

10901 V*tt091 160
*008065^

N.

1101
1102
1103
1104
1105

1106
1107
1108
1109
1110

nil

1112
1113
1114
1115

1116
1117
1118
1119
1120

1121
1122
1123
1124
1125

1126
1127
1128
1129
1130

1131
1132
1133
1134
1135

1136
1137
1138
1139
1140

1141
1142
1143
1144
1145

1146
1147
1148
1149
1150

Logar.

7-0039741
7 00488-20
7-0057^0
7-0066952
7*0076006

7*0085052
70094089
70103119
70112140
7*0121153

70130158
7-0139155
7*0148144
70157124
70166097

7*0175061
7*0184018
70192967
70201907
7-0210840

7-0219764
7-0228681
7*0237590
70246490
7-0255383

7-0264268
70273145
7-0282014
70290876
7-0299729

7-0308575
70317413
7-0326243
7-0335065
70343879

7-0352686
7-0361485
70370276
7 0379060
7 0387835

7 0396603
7-0405364
70414117
7-0422862
7 0431599

7-0440329
7-0449051
7-0457766
70466473
7-0475172

N.

1151

1152

1153

1154

1155

1156

1157

1158

1159

1160

1161

1162

1163

1164

1165

1166

1167

1168

1169

1170

1171

1172

1178

1174

1175

1176

1177

1178

1179

1180

1181

1182

1183

1184

1185

1186

1187

1188

1189

1190

1191

1192

1193

1194

1195

1196

1197

1198

1199

1200

Logir.

7-0483864
7-0492548
7*0501225
7-0509894
70518556

7*0527210
7 0585857
7*0544497
70558128
7 0561758

70570370
70578979
7*0587582
70596176
70604764

70618344
7*0621916
7-0680482
7*0689040
7-0647590

70656134
7-0664670
7-0678198
7-0681720
7 0690234

7 0698741
7-0707211
7 0715734
7*0724219
70732697

7-0741J68
70749632
7*0758089
7-0766538
7-0774931

70783416
7-0791844
7-0800265
7-0808679
7*0817086

7 0825486
7-0833878
7 0842264
7-0850643
7-0859015

7-0667379
7*0875737
7-0884088
7 0892432
7 0900768

«i

4

2-30 LonisTic uiGABiTHMs. Tab."7,

I

2

3

4

5

6 7 8

9

W

11

ir2

^

-!L.

HO

ISO
1-477

IHU
1-3010

340
M7fil

300

1-070

360 4-^0 480

BOOO 9331 B76

am

600
7782

6.-.|780
736816990

i-7Hia
l'77lfl

3-6683

1-473S

1-2986

1-1743

1-077

9988 9330 8742|833

7774

736

6984

3- 8553

l-7«3S

h469S

1-2962

1-1726

10763

9978,9310 873.

8223

7767

735^

6078

3-0792

1-7671)

h4684

1-2939

1-1707

1074a

9984 0300 872

S3I6

7760

7348|«l7a

2-9542

1-750

1-462D

1-2916

I-16B9

10731

0982 0389 8714

820

7703

34

6966

2-Bfi73

1-7434

1-4504

1-2891

I- 1671

I-072C

B940|887» 870t

619tl

7745

733816960 )

3-7782

1-73GB

1-456D

1-2868

!■ 16541 1 -070c

9028,9269 8097

819

7738

7326

6954

8-71IS

1-7308

l'462S

1-2845

i-l03610e92

9916,9369 8688

8183

7731

7322

6MH

2-W3S

l-783fl

1-449

1-2821

1-1619 1-0678

09O5 92J9 8679

8175

7724

7315

6IM3

3W21

1-7175

1-4467

1-2798

11601

10663

9893 0838 8670

8167

7717

7300

61I36

3-5883

1-7II2

1-4424

1-2776

1-1584

1-0649

9881 93S8 8661

8160

7710

7310

6938

2-5149

1-7050

1-4390

1-2753

1-1566

1-0636

986919318 8662

8162

7703

7Me

ises4

2-4771

1-6090

1 -4.-157

1-2730

11549

^0621

B858|9808 8643

8144

7'i98

7889

69IS

2-4424

1-6930

I -4328

1-2707

11633

1-0608

8136

7608

7283

6913

2-4102

1-GB7I

I '4292

I '2686

1'I515

\-06M

8128

76BI

7-276

6906

23802

1-C812

1-4200

1-2663

1-1498

1-0880

98339178 8617

8120

7674

7870

6900

2-3622

1-6766

1-432S

1-2C40

11481

1-0666

98119108 8608

8112

7667

7364

G3»4

2-3269

1-6698

1-4196

1-2618

11464

1-0562

9800'9158 8599'B104

7600

7257

6888

2-3010;i0642

I-41C6

I-2S96

11447

1-0639

9788|9 148, 8591

8097

7663

7251

6883

2-2776 !■ 6687

1-4133

1-2674

11430

1-0626

9777 9138 8582

6089

7646

7244

6877

20

2 2663

1-6632

1-4102

1-2863

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2028

1913

1801 1693 1587

1484

3D

3310 3061 l2i)l7

3776

2643

3612

2384

3361 13141

3034

1910

1700 16U|ll586

1483

40

3208

3060

aoia

3776

2640

3510

2382

22693138

2038

1008

1707

1689 1484

1481

41

3806

30fi6

S912

3773

2638

8507

2380

2257

3137

2028

1906

1704

16B7ll482

1479

43

3203

21110

3771

2506

2378

3136

9018

1904

I7W

168li 1480

U77

43

3300

2W)t

3760

2634

8503

2376

235^

3133

2016

1903

1782

1884,1578

1476

44

3188

3786

2632

2501

2374

2201

3131

9014

IU81

1700

18821577

1474

4S

3196

3047

290!

2784

2620

249912373

2241)

3189

9012

1889

1781.

1880:1576

1472

4(

3183

3044

2W1

8762

2627

2497!2370

2947

31=7

2010

1887

1788

1878

1573

1470

*:

3100

3043

2888

2780

2636

2404 3368

2346

3136

2009

1896

1785

1677

1571

1469

31SH

3039

2806

2J67

363:1

34i>8 12360

3343

3)33[2UU7

1893

179:1

1076

1570

1467

4!

3186

3037

28j»4

3746

2400

3364

3241

3131

2006

1881

1781

1673

1568

1466

3183

3034

3801

8763

3818

2488

2362

233;

3110

8003

1889

177s

1071

1506

1464

ni

31B0

3033

2680

2760

3616

2488

3358

2237

3117

2001

1SB8

1777

1670

I6G6

1463

S3

31 8

3030

2687

2748

2614

2484

3367

2236

3116

1099

1R86

1775

1668

1563

1460

R3

31 a

3037

2884

2748

2813

3482

2366

3333

3113

1997

1884

1774

1660

1561

1459

G4

31 3

3036

2883

3744

2810

2480

2353

3331

3111

1U96

1883

1772

1664

1559

1457

fiS

31

3033

9880

3741

2607

2477

2361

3339

2100

1003

1880

1770

1663

1666

1455

SI

3168

3020

2877

2739

2605

2476

3340

2327

3107

1001

1878

1768

1661

1066

1454

s;

3166

31)18

2876

3737

2603

2473

3347

3326

2105

1U80

1876

1766

1650

1654

1453

SH

3183

3015

3873

3736

2601

2471

2346

3223

2103

1087

1876

1765

1667

1652

1440

W

3160

3013

2870

2733

260S

2468

2343

2*20

2101

1088

1873

1763

1656

1541

1449

OU

3ISB

30)0

3888! 37311

36U8

24Ci7l2:i4l

3318

2<I!IU

1984

1871

1761

1664

1649

1447

Tab. 7. LOCiaTic logarithms. i;33|

'

43 1 44 1 45

46

47

48|49

5U

bl

b2

!i3

tii

ii

56

57

-^

2680j2G40 2700

271iO

2B-20

28(10 2940

:t(N)0

3OG0

312(1

J180

3240

(^78

3360

3420

1447

1347 1249

1164

Toel

OBBO

0792

0621

DS39

04dB

0300

0223

1

144G

1345 1248

1162

1059

0B78

079O

0620

0837

0456

037-,

0398

0221

1443

1344 1246

1161

1057

0877

0789

0619

0536

0456

0378

0397

0230

!

1342 124^

1149

lose

0875

0787

0617

0635

0434

0374

0396

0219

1440

1340 1243

1148

1054

0903

0874

0786

0700

0816

0533

0152

9373

0394

0218

a

1438

1339 1241

1146

1053

0063,0872

0786

0609

0615

0633

0451

0371

0393

0216

6

1437

1337 1340

1145

loai

0960 OB7I

0783

0697

0613

0631

n460

mo

0393

0310

7

1435

1335 1238

1143

1060

0782

0696

0612

0639

0448

9360

0391

0814

8

1433

1334 1237

114!

1048

0760

0694

0610

0028

0447

9367

0380

0313

9

1432

1333 1235

1140

1047

0966,0866

0779

0693

0609

0620

0446

0366

'1288

0211

in

1430

1331 1333

1138

1046

0964.0866

07;7l«I93

0608

0620

0444

0360

0387

9810

11

1428

1329 1233

1137

1044

0953,0863

0776

0690

0606

0634

0443

0363

0286

9309

13

1427

1327 1330

1136

1042

0901 0862

0774

0689

OBOB

0633

0443

0363

0384

13

1426

1326 1220

II34

1041

0960,0860

0773

0687

0003

0631

0440

0361

0SB3

14

1423

1334 1227

1133

1039

0948,0868

0772

0686

0603

0830

0430

0389

0282

0306

Id

1422

1X13 1225

1130

1037

0947,0857

0770

0686

0601

0618

0438

0358

0280

0304

16

1420

1321 1324

1120

1036

094s!o8S6

0769 0683

0590

0517

0436 0387

0379

0303

17

14IH

1319 1323

1127

1034

0707:0683

0598

0616

0435 0356

0278

0301

18

1417

1317 1321

1126

1033

0942 0853

0766,0680

0598

0314

0434 0354

0276

0300!

19

1415

1316 1319

1134

1031

09410862

0764! 0679

059S

0613

0432 0383

0275

0199

20

1413

1314 1317

1133

1030

0930,0850

0763|067B

0594

0512

04310352

0274

0197;

21

1412

13131316

1131

1028

O938'084fl

0702 Ofi7(.

0592

0610

0430 0350

0273

0196!

22:1410

1311 1314

1119

1037

0936 0847

0760,0675

0591

06O0

0428 0349

0371

0195

23ll40Ii

1309 1313

lllfl

1025

093B;084(.

0789,0673

0590

0507

0427 0346

0370

am

24 1407

1308 1311

1116

1024

0933 0844

0767,0672

0588

0306

0428 0346

0369

0192

2611405

1306,1309

Ills

1022

0832 0843

0750,0670

0587

0306

0424 0345

0267

9191

26 1403

1304

1208

1113

1021

0930l0B41

0784 0660

06S5

0803

0433 0344

0360

0190

27ll4l)2

1303

1306

1112

1019

0B29 0840

0763 0668

0664

0602

0432,0343

0366

0109

28|14ao

1301

1205

1110

1018

0937,0838

O751I0666

0683

»0I

0480 0341

0364

0187

S9 1398

1300

1303

1109

1018

0826,0837

0766 0666

0661

0419:0340

D303

0186

30 1337

1298

1201

1107

1015

0924 0836

0749,0663

0680

049f

0418,0339

9361

01 BS

31 1390

1296

1200

1106

1013

0933 0B34

074710663

0»7»

0407

04180337

9860

0184

32 1393

1205

1198

1104

1012

093l'oe33

9746,0861

0677

041B03S6

9388

0182

33 1392

1393

1197

1102

10 in

09'.M:0831

0744 0659

0578

0414,0336

0257

0181

34! 1390

IZUI

llUfi

1101

1008

09130630

0743 0658

0S74

0412 033:

9286

0180

35I3B8

1290

1193

1099

1007

09170S2H

0741 96E6

0873

9491

0366

0179

361307

1288

1192

1008

1006

09150637

0740 0C8S

0572

0490

0410,0331

0353

01 7

37 1385

1287

1191

1000

1004

09140S25

0739 0684

0670

0489

0408 0329

0352

01 6

:UI'I383

128.-.

1131

lOikS

1003

0913 0824

0737 0653

0669

0487

0407 0338

0351

01 6

3» nu2

13K1

1187

1093

1001

U911 nU32

0736,0661

0568

0486

0406 0327

0360

01 4

40|138«

1283

1186

1091

0999

0909 US2I

0734 0649

0568

O46lj0404^O336

0348

0178

41,1378

13B0

1184

1090

0098

0908 9819

0733,0646

0665

0483 i 0403 0324

0347

9171

42,1377

1278

1182

1038

099r

090610818

0731 064710663

0482 (0402 0323

0316

0170

43:1375

1377

1181

1087

0996

0906

OHIO

0730 0646.0662

0480 0400 ;0322

0344

0169

44 1373

1275

1179

1086

0093

0903

0616

0729 0644 0661

0470 0399.0320

0343

0167

45 1372

1374

1178

1084

9992

0903

0814

0727 0642 0559

04780308 0319

1)343

0166

4611370

1272

1176

1082

0090

0000

0812

0726,06410558

0476 0398 0318

9341

0166

4711368

1270

1174

1081

0989

0899

OHll

07m'064o!o557

047G'0396 0316

0339

0163

48,1367

1269

1173

1079

09S7

0S97

0809

0723 0636,0665

0474 0394,0315

9338

01 62

49;i3ti.';

I2H7

1171

1078

D9(Mi

U69G

060810721,0637 0554

0473 0392 0314

9837

0161

50

1363

I2UC

1170

1076

0984

0K94

0806

0720^0635 0562

0471,03910313

9336

0160

51

1362

1264

1168

1074

D983

0693

nao5

0719 06340561

0470 0390 031 1

9334

0158

52

1360

1263

1167

1073

9981

ouai

0803

0717 0633 0650

0468,0388 0310

0333

0167

sa

1359

12B1

1165

1071

9080

0890

0002

0716 06.11,0648

046710387 0309

0238

9160

54

13.^7

1259

1163

1070

0978

OBBlj

0601

0714 0630,0547

0466,0386|0307

0330

OlSfi

55

1355

1237

1103

1068

0977

0387

0789

0713 0628 0546

0464 0364

0306

0329

9103

56

1354

1356

1160

1067

0975

068G

0798

071 1' 0627 (»44

04630383

OMS

0163

67

1353

1254

1159

1005

0974

0884

0706

0710 0028,0643

0463 0383

0161

68

1350

1253

1167

1064

0973

0883

0795

0709 0624 0641

0460 0381

nijw

59J1349

1251

1166

1062

0971

0881

0793

0707 0623,0540

046a;0379

Ul48

60

1347

1348

1154

1061

\om

0880

0792

0706

0621

o.'.3n

0468

0378

0300

W88

0147

LOGISTIC tXlGAItlTHMS.

0147 W

1 0U6 (N

5 OUb W
3 0I43IH

6 0U1 n

>GS7S7

■&9786
F4 9785
>3 9784

97SI)9I
9719 9<
9717 91
9716 91
97U9(
97U9<

3 0131
.4 0130
9 0129

6 0127

7 0126
e012S
0124
!0 0I22

lb' »914 9
a »913S
13 9912
13 9910 9

iB 9779

17 977B
[6 9777

i5 977a
14 9774
12 9773
119772
10 9771
19 9770
17 97*17

,6 9A79i9:
.S 9570 9J
,3 0577 ft
,2 9576 W
I 9I>75 9i
,0 9:-7* 91
19 9573 9<
18 9972 91
U 9671 91
16 9970 91
15 9969 91
13 9967 91
12 9966 9j

13 0119

14 0117
19 0116

13 9764 9{
12 9763 91
II 9763 W

3810112 IH
29 0111 CH
aojOllO 01

31 0109
320107
1 as 0106

I4 0105 <
16.0104
160103
37 Oil

ia oiof)

lUOOiK)
40 0098
41 '0096
43 0095

46 0091 (K

46 0090 01

47 oiinu W
4yiKiaeo(

49 OU87 0<

50 0085 01

36 9816

BS'l'BlB

4 »883iHS13

13 9X13

9877 91

9S76 0i
0875 Ul

9758 91

9757 ff

9796 91

9756 H

9754 91

9753

97SI

9750

9749

0748

B747

0740

B74S

9744

9742

9741

9740

0739

973H

9737
14 9736
39734
129733

n 9732

I1M27
10 9436
18 9425
17 9434
16 9433
16 9431
14 9430
13 9419

907991
9678 9(
9077 91
9676 91
9675 91

16 94»<1 04
15 9480 94
14947994
13 9478 94
11 9477 94
10 9476 94
19 9475 94
W 9473 94

17 9473 94

51,01
53 0083

53 0083

54 0080
95.0079
560078
57:0077
6SIKI7d
K9 01174

100 0073

0010 91
(HMS9!
U0D7 9I
0000 91
0009 91
IKXM OS
0002 9!

17 9797 a:
)e9796o:
)5 9796 a;
1397949;

3 9863 9;
Z0S6I y,
I 9860 9;
aBlb9 9;
KOBd^li;

9369 91
9368«
»»7»

9248 9
9347 9
9346 9
9245 9

•8 9197
7 9196

•esigc

i5 919i
■4 9193

1311183
11 »I81
10 9I8D

15 9179

I8S17B

179177

16 9176
15 917s
14 9174
13 9173

10 9170
I9 91S9

tsttiea

9157
9156
9155
9154
9153

73 74 I 75 76

* i300 4440 4500 4S(W 4<

LOGISTIC LOCAItlTHMS.

7s j7rpS(r~81 82~ "

9140
IBUT

2 0146

3 9146

4 9144
6 9143
G 9142 W

1XI89'1H>31
0088 9030
9039
9086 9028
908S|9027
908l'9O36

6973 8!
S972U
60718!

6971 8<
6970 81

2 90S3'902a

7 914ll90BZJy024

U 9140 9081 9023^696)!
;!t 9080

a 9079

:0 9136 9<
119137
12 9136

3 913a

4 9134
la|9l33

!l 6904

16

9133

!8 9121
!9 9130
10 9119

9078 9020 01

9077 00I9 61
9076 9018 6!
9076 9017 6!
907e 9016 6!
9074 9019
907390IS
9072 9014
9071 9013
9070 9013
9009 9011
906819010
9067i9U09
0068 9008
9065 9007
9064 9006
9063'900S
9063 9004
9U61r9003
■""■■" 9002 81

5 9009 9001 8
7 90&8 9000 8

6 9057 R999 8
G 9056 8998 8
4 9055 8!n»7 81
3 9054 8996 8!
2 9053 8!
I 9053 8!
9051 8993 81
19 9050 8993 81
n 90408992 8!

17 9048 8991 81

18 9047 9!
16 9048 B989 8!
14 9045 61
13 9044 6987 8!
r2g043ffl

It 0042 8!
M) 0042 6!

6957 8!
895l<m
6955 8)

6837 ;876-j|U738' 6674

6589 '8537 6468

";Ba36 ■

658718536
8588 8534
a'lH.I 8634
0686 8533
8S84S532
8683 8531
8582 8630,

8621

8630

8837 878118727:8073
6838 8781 67i!6 6073
8836 8760 8725 6873
0834 8779 8724 6671 8616
— " 8617

8616

8833 8770.6734 6070
8832,8777 8723 6600

6631 8776 6722 0068
8330 8776 8721 '6007
6629 8774 8730 18668

8773 6710 6665

6837 8772 6716 B''66
8826 8771 1717 0064;
6825 877l'67l6 6003,8610
6836 8770!87I5 6602 6609

8834 8769 0715 066l{6808

B760!S7I4'B660!8607
6622 8767 6713 0050 " "
6821 8766 8713 6658 0806

8765:8710 6057;
0819J87e4 8710 0057 0604
8818 8763 8709 0G58 00O3
8617 87ir2 fl706 6C55;6002
876118707 8054 8*101
8815J87Cl|0706 6053 8600
8814 8760 8706 6653 6599
13I8789 8704 '0051 8699
681318768,8703 6650|Q6g6
6612 8757:8703 6650 6597
8611 8766 8702 6640 6596

-l!0B7a6'8701 6040

10!( 11764 0700 0047'flS94

.!ii;it7S3 86!l9a(H6'

■■'■1 6762 8(B18 80*3
.iP'i 6753 8607 6044

iil,-.'675l mrjiwKi

!9 6176 6
:8 8477 !l
16 6470 6
!7 8475 II
\e 847S U
!5 8474a
8624 8473 Ik
8623 6472 jl-
e6->2 8471
8322 6470
8621 8469
8620 6460
65 19 '6406
6407
8517,8406
R610B485
8616JOI64
86160484
J6I40-
16 8613,8462 &i

:l 8380
«8380
19 B:i70
8 8376

7 8377

I9S370

9 8309
636U
7 6387
6 0306
6 0306

6414 6:
8413 0:
8412 6:

8411 8:
:i8410 8:
» 8410 6!

9 8408 8;

0457 8^
6559 8607 0456 84

6556 8606 8455 8i

6557 8605 '8454
0650 8604 '8463
6S55 8604 8463

8503 6463
8553
6553 8501 6460
6653 8500 6449
[;65l|3499 8146
6650 '8496 0447
I549JR406 6447

8496 8444 6:
8494 18443 O:
8493|8442 8!
8*03,8442 0:

i

*■:■

.

TABLE VIII.

LOGARITHMIC

SINES AND TANGENTS

TO

EVERY SECOND

IN THE FIRST TWO DEGREES.

«
i

1 240 Peg.

9'

IC

7 »GliB167

3 7'368fl2l.

3 7'369i3l6

4 7H7« -

s 7'a;i3i62
07-37MI07

7 7'373I034

8 73739943

9 73748832

10 7'37fi77afi
"1 7'37«GS59
18 7'377&39G

13 7-3784ar

14 7-37930 1 ■
IG 7:^801 7U(i
1S7381U66I
17 7'3SI930R
I8,7'3B3B038

7-4179(181 7«07iM
74187716,74644487
7-4196737 ;-4Ml 707
T420374al7-4eS8fll6
7-421 1733I7-4606112

7-4236617
7-4243549
7'425I467
742S9370
7-4207260

7-4s;si34

74aa299S
7-4890841
7-4298673
7-4a0G4»l
74314290
7-4322086
7-4320861
7-4337624
7-4346372
7-4363106

19 7-3836760

20 7-3846444

21 7-3SS4I22
23 7-3862782

23 7 3871424

24 7-3f

2«'7'3f

26 7-3B97249 T

27 7'390fiS94 7<
18 7-39143d1 7

39,7-3922922 7-4406866

7-4687620
7-4604776
7-47019 16
7-4709041
7-47161 S4
74723267
7-47303*7
7-473742d

7-4744403

7-4751649
7-4768694
7'4'766627
74772649
7-4779669
7-4786668

7-6064331 7-6441112
7 6070871 7 6447123
7-6O7742S 7-6463126
7-6dS39S8 7-6480120
7-6090483 7-6466106
7-6006999 7-647IOS4
7-6l033(W T5477C53
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38 7-31

39 7-4007418
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6 7-4139282
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LOG. SINES.

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8-1763681

8-1764084

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LOG. SINKS. I 1 Deg.

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2-J71335
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8 2373830
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LOG. COSINES. 89 Deg.

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83506715
83600655
8 35076fM
83508533

530047;

3GI04I1
8 351 1 ^.V)
835IS2S8
83513326
8-36UI64
83515103
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83516077
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8-3518851
83510788
83520725
8-3531061
8-3522507
8-3533333
83524460
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83181313
83482158
0-342ea.f3 831 83103
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3127005 83484091
3438032 83486036
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8-3433740^8:1460710
3433702 B 3400853
3I34657'B 3401500
8-3435012 8-3492530
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3^01

83565448
3568373
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8-3571004

8-3571 oati

83673855
8-3673780
8-3674705
8-3675030
B-3676555
8-8377470
83678493
B-3S79327
8-3580351
8-3581 1 76

3537375
3338310
8-3529145
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8-3648720
8-3649000
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8-3630783 41
8-3631676 41

8-3587635
8-3688567
8-3580470

83306937

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83697787

8-3599607
B-3B0O527
B3C01440
8 3002365

83007076
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1-3G14297
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83617046 5;
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83018877 51
" 3619793 6*

3644438 Z
3845348 21
8-3648258 2i
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8-3654439 1<
8-3655347
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3862605
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8 3884417 '
8 3665323 '

8';(6n6329 :

8 3li67>36 :
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LOG. COTANGENTS.

88 Peg.

IDeg.
" 21'

!A a :i7 23(103
ra a'3T:f3i9fi

15 8 3394389

16 8373K!II3

Ml »ymn4
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17 8-37a7»59
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11 Bam*ia

13 83733309
15 8 37:U2oa
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12 8-3737762
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18 8-37SIW73

14 8-376BIU0
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17 83761739

13 8 37636IS
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18 a 3767922
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15 8-376968D
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M 83771466
IB 8-3773339
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8-3774 1 06

83774
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83776670

8-3776763

-3777636
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8 3780280
8 378IIC1
83783042
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8-3783804
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8-3780963
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8-3791734
83793603
83703483
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8 379623S
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83796996
83707874
83798761
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03800607
8-3801384
S-3802S6I
3803138
B380J0I6
83804891
6-380:1768
B'3BU6(U4
3BO7S30
83B08398
8380927)
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83811022
3811807
3812772
83813647
'3314522
3BI53yR
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83B17I4Q
B38I80I9
83818892
83810766

LOG.

8-38^112(1
-383^4!- -
83839364

83831 106
83831078
83833848

83838940
83839810
3840679
3841548
8 3842417
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83844166
83846033
83846802
8 3816760
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83848496
8 3840363
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8 3861008
3861966

8382387'i
83838748
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, 83881346 83932710
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.83883067
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8-3890807

83831(i06

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8 3896B1B|8 3948002

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83864951
8 3866816
83866680
8 3867644
8-3868408
8-386037 1
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8-3871861
3872734
83B73u87
83874466
83875312
8387G174
83B77037
83877698
83870760
8^879623

24'

83083476
839843IG
83986167

83036113
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8-39037I8
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8-3994397
8 3996336
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8 3997761
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8 3976436

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34'

35^ I
LOG. COSINES.

Tab^a.
~2iV~ '21'

8-4033663 68
8-4034485 67
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8403614766
B 403C976 5(

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19 51
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8 4040300 50

8-4041 n

8-4041 WW :48
8-4042790 47
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8 4048 I U
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8 404S594!40
84049423 39
84050361 38
840S10Bo!37
8-4061908,36

84007801
84008637
B-4000473
"4010309
84011146
4011981
4012816
84013662
840U487
84015392
84016157
84016992

1-4033831
1-4023664
14034407
1-4026331
1-4026164
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4037820
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8-40634S4 32
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8 4067611,17
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8407685S 7
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84070146 !
840799G8 !
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3-^
88 Peg.

8S(.7U(U
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8-3104103

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8-9705007
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8-3713071
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8-37iee&:i

B-»7t7a48
B-371B443
8-3718336
83730232
8-3731137
S-373'W3I
8- 3723315

LO(J. TANGENTS.

-22'" 23' 24'"" 25'

3777 106

837779B0
8-3778B78
8-3770764

fl3829TS8
8-3830031
83831503
83832374

8-3736304
fr3737l03
8 373U08G
83738970
8-3739807
83740757
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83743938
83743437
' 3744317

8-374S3<J(i
83746006
8 374608S
83747874
8 374B763
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8-37S0A39
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8-375-2.-II6
8-3753^03
8-3754001

a-37e4a7»

8 3753RC6
837SG763
8-37S7G40

8 37X0449
83700320
8-3701209
8-3703089
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'3793SJII
3704728
37O06O7
8-370ftl86
' 37073(i3

83836860
383G73I
8 88:17001
B3838473
83830343
8 3840213
8 3641083
3641093
364SU22
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B3D4A43D
8 3846299
3847168

83840774 asooiGse

83600879
8 3801 7^7
8-3S02G34

6-3806144
8-3807021
8-3807B08
8-3808774
8-3800630
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B3764729
B376G614
8376649!

6-3814030
8 3614!)
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S- 381 7530
1-3816404
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6-3773574
83774457
8-377534U
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838-i8208
8'»H-27I4I

K:itHiOOiB 8 393:f:i3li
8 3681760 B3933IB7

8-3882642
8-3683504
83864365
8-S88S237
83886088
83886049
83687809
83388070
83S89S30
8 3890391
8 389 1 35 1

31 II

83S93970

83631510
3832378
3B53349
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8-3864080

8-385M47
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" 3657561
6 3856446
83850314
)|-3B6D180
8-3861046

3IHI1012
8-3062778

3863613
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63865374

83670503
S3871430
8-387-2290
8-3873163
8-3874017
8-38741180
8-3B73743
6387660G
63877469
6 3878333
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83034801
83a367'IS
83936003
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8-3984835
8-3965677
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63967360

83910K48
83941696
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83900723
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3003244
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8-3996704

J-389554e fr3D46794
83896408 8-3047643
8-3697300 83048493
83808139,83049340
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8-389984318 3001037
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l'830a3733

8 30034 IG;8 3053581
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8-3aOA84e 8 3056971
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83006417 83050511
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83010130 8-3061204
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8-3012607 »39G3742
8 3013553 8-3961660
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8-301611983067124
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6-3035516:6-39704

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63937221
13928074

63928927
1-3929770

6 30780U7
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8 3970783

63961467

63983310
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84037641 »i
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6 4014103
64U15031
84013667
B 40 1 6702
6 4017538
84016373

401 92
84030043

4030076
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84033617

8-4024316
81035060

4036884
81020717
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84028384

4039217

37

84030623

4051604
84052463
8405331 1
6-4054140 :u

4054968 .-«
6 4056790|33
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84057153 31

10 30

84050107 «
8105903B2I
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84061589 2(
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8 4061693 Si
840637'22'3I
84066348 20
84067374 19
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84069035 1 7
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8-4070676: 15
8407l60l|l4
84072326 13

4073161 13
8 1073975 II
8-4074800 10
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84076440 6
81077273 7
61078097
6-4076020 5
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8 408056^ 3
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1082214 I

4083037

LOG. COTANGENTS.

IDeg.

LOG. SINES.

•2^y I m I 3V I 3-^ \ 3-S' I 34'

fl'408W30
BVtBiOOS
8-4084723
8'4086M&

8-41331

8-4I33S27

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8-4I3S66S

8-4136304

8-4137170

84I379B8

8-4130000

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8-4188421
8-4IS7-233

84092201
8400;illl
8-40!K)»3l

40»47ai

8-4n05J7l
■40lKa»l

8-4IOSIS4
a-4102942
8-4103700
84104978

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4 142U4a
4143850
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4144477

04145*87
414CO08
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8-4147:

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8-414^337

8 4IJUI47
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841o3

30

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8-4i&fMU:~
8-4169B&0
8 4100057

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841 02273
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Ili8-411!t278:'

17 84120003 1

18 8-4120008 I

41O701O
4108725
4100531

17 B-4171

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84227903 8 427^408
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84229553 84270980
84277700
84278502
84279330

84230348
8-4231141
8-4231 U37
8-4232731

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8432-J33.1
84.123117

4234319
8-4235113
84233907
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84237404

4338287

84337004
4.137781
8-4338550

84280134
84200900
842814194

4282480

428320G
8-4^84050

_ 84331 M5

84285010 84332441
8 42S0404 18-43.132 17
84207lfi8j843339a3

8'41»4441
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8-4108443
8-4ld!)243
8 4200040
8-4200046
84301848
8-4202446
8 4203245
8-4204045
8-4204S44
84203644
8-4206443
84307242
8-4208040
8420SB3D
8-4309038
84210436
8 4211234
8-4312032
8-4213030
8-4213021
84214431
843I5S23
8 4216020
8-4216813
U-4S1701£

8-4Z44B38

145420

8424621

1-4250 ino

1-4250959

84367090
04366708
8-43ti9538
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84372616
8-4373384
8-4374 153
84374921
84375(90
84370458
B-4S772S7
8-4377095
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6-4289AI0; 84336330
ff4SI>0324 84337005
B 4201 108 8 4337071
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f^ 4 2958071 8-434 25 19
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H 4446820 18

84261239,8 4^08313 8 43fi4892l8 440007'!
84203918 843O9093'84355U64i84401740
8-42628Mi's 431KJO73 8436643G 84403503

II4320R0I
8-42213911
B-4232394
8'4233l»0
842-23900
842247(12
" 423S677
■422037:
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29'

8 4203303 |B 4310034
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8^4203172.8 4312313
8 43r>59«l!8-43IS993
8 420074818 4313773
8^4207336 8-4314553

84268324
IN'209111
8-4200899
ff4270«Bfl
8^4271474

■ !72281
B-437304B
4273034

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■28'

8'4aiA333
8-4310111
8 4316890
B 4317069
84318447
4310230
4.320004
84320783
4321561

8 4337207
843571170
"43.18701
84369.122
4300303
8-4381064
8-4:t01833
84362006
:Hi»377
304 148
8-4364018

844U403I
8-4404704
B-44Ki557
84406331
4407083
84407846
8-4408000
8-4409372
10134
lOHOU
8-43fl3euH 8-4411(15!
8-43U8459 84412421
a436732!*84413l83
B-43679U0 84413914

444a<i76
B-4447332
" 444H087

444U843

17

9 11
5 10
8445362ft' 9
8^4453375 8
84454129 7
8 4454BU4 6
8 4135638 5

LOC. COSINES.

24'

880^.

1 Deg. LOG. TANGENTS. 261 ^

"

28'

:iy' 1 aty

ai'

32'

SS' 1 34'

36' 1"

"o

8 4083037

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8 42211690

6 4276176

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8441f.003 60[

S-40a38SU

B-4l32B4S'«4iai4H:i

84WM4HS

8 427'a6:!

8 4323929 B 4370393

84416366 69 1

2

84084683

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B 42302H1

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8 4324707 8437 lie

8 4417127 58

3

8'40a5(>06

8-4 13467284 1 a30U2

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8 427H537

6 4325486,8 4371033

B-i4]7aeu57

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8^4086327

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B-4326264 '84372703

0-4418051 66

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8-4087140

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U 4327042 8 437;t473

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8

840B7071

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8 4233402 8 4280897

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8 4420174 64

7

8-4088703

84137823 8-4186307

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B-4235051 8 42824liO

8-4329375184875781

8 4421697 52

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84I3!I44U,84187!JI4

B433584684383255

B-4 330 153 '8-4376550

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841411261 B41UU717

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B-4141073 84189520

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8-4331707 8-4378089

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8 4230239 B-4.'85642

84332484 8^4378857

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8-4333201 8-4370626

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47

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R 433403818 43S0395

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8 4 144319: fr4 192731

8 4240610 8 4307968

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46

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8 41451111 8-4193633

8-4241 404' 8-4288752

8433S5918 43BI931

84427783

44

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8 4145942 8 4194338

842421971 8-4369637

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84428543

43

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8-4242GaO 8-4300.122

84337144 8-4383468

8-4429303

43

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8-4243783 8-4391100

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8-4149186 8^4107543

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B-4339472 8-4385771

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32 84101103

8 4140903 8-4198344

84346163 8-431)3459

8-4340248 84380538

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8-4394243

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84433i0i'.'l7

S4 8-4102741

84I&161G84199947

84247747

8-4295027

84341799

84388073

84433BU0 36

«s' 8 4103560

8-4I5242S

R-4200748

8-4248530

8 4205S11

84342574

84.188840

8-4434610:35

!6»41043;a

84153235

8^4201549

8-4249331

84296694

84343349

8 4389B07

B-44;ia37Bl34

57:B-410510e

8-41B404S

8-4202349

8-4360123

8-42973J7

8-4344124

8-4390374

844301 37 1;43

28,8 4108017

84154854

8 42D31M

84260BIJ

84298161

84344899

B 4391 140

84430896

sa

Sa>4l(H(83fi

84155604

8-4203960

84261706

8 4208944

84345674

8 43M1007

84437654

31

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8-4156473

8-4204760

B-4252498

84299737

8-4346448

B-4392U73

8-443B4I3

30

al '8 4100472

84157282

8-4206560

84263289

84300510

B 4347223

8-4393440

8 4439171

30

S2 8-4IOB-ifjO

84158001

a-4206350

84254080

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B4347097

8-4394206

8-4430929

98

33 8 41 10107

8-4158000

84207150

84*34872

843O2075

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8-4394973

84440CB7

37

34 8'4il09-2S

8 4158708

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B-42a6U6'2

84302B57

84340545

84305738

84441444

!B

3fi»4lll;i3

8-4160517

84208749

B-435(M53

84303039

8-4360310

0-4396503

84443202

!S

3884112560

8-4161325

a4209a49

a-4307244

84304422

84351003

8 4397269

8-4443960

34

3784113377

B4IR2133

8-4210348

S4S6W34

84306204

8-435 ia67!8 4398034

84443717

23

3UK'4INI'J4

84l0ii94l

8-4211147

8-4268835

84306965

84352640 B 4398800

8-4441476

23

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84163740

8-421 1948

8 42600 15

84306767

8-43634)3 84309505

8-4445232

31

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8-4212746

8-4260405

84307549

8 4354I87IB44O0330

0-4445089

20

41 8 4ll(W4d

8 4165364

84213543

8-4261 lOS

B-430R.'13a[8'43641J60;a-4401Og6

H-444C746

42^B41I74(>1

8416U17I

8421-1342

84261985

B 430011 118-4355733 8 4401U60

8-4447503

43ff41IB27S

84166079

8-4216140

^4262774

8-4300092'B-435R5fl6 8-4402024

8-4448259

44 1i41IIHK)4

8 4IU17U6

B-4363564

»4310«73; B 4357278 8 4403389

B-4449018

4GU41I09IO

8-4160593

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84264353

Jl-43 1 1464 iB-4388U51 ;8 4404 153

8 4449773

4ll84liiU726

BAiimon

8 4217534

8 4265142

B 431 2235'B 4358823

8-440491 B

844S0529

47 '8 41^1641

8 4170206

84218332

8-4266032

B4313U16J8435»d9fi

8-4405682

8 4451286

48 84123367

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8-421S130

B-42G6720

B 4313796

8436036J

84452041

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a-4171819

8-4219027

84267609

8-4314676

8-4361139

a-440720fl

84462797

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B-4 172025

8-4220726

84268398

84316356

8 4361911

a 4407973

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8-41734318-4221532

B 4269080

84310136

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84408737

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8-4174237 8^232319

84269875

8-4310916

a-440950<l

8-4466063

63 8-4126432

8-4176043,8-4223116

84270063

84317606

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8-4410263

84466819

6418 4127247

8-4175848

8-4223012

B427146I

84318476

8 4364097

8-4411027

84466574

6584128082

8-4176654

84234709

8-4372239

84310355

84366768

84411790

84467329

S8l84 128876

84177459

84225605

84373037

84330034

8-4366640

8-4412553

844680S4

fi7|8 4iaofl!IO

8-4178264

8-4226302

B-42 3814

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8-43G7310

844I331S

8445BS39

68 8-4130504

B-417!I060

0-4227008

8'42T4(»I3

B43-JI503

8-4368081

B-44 14078

B-4459594

61ti8'4l313l8

84170874

e-4237BlM

842 5389

B-4323372

84368863

B-44NB4I

B446034B

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8 42-2B6SO

8-4276176

8^4323150

8-4369623

8-4415603

B-44BI103

-■'\-^v

30-

2i^

28'

27'

26'

~2T

^T'

LOG. (OTANCENTS, &S Deg. |

»44«aiG3

8-4461070
844624S3
»44U»l7t)
B-44S1939
II-4464BB3
fl'44ft5430
S-446tilaj
8-446G94I)
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B'4jria44a
8'44(»I97
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K-44707OI
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8'4SI>738S

(l'4JM)H13I

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a 8 4473707
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S (<'4475MI

13 844707 12

14 8''l4774e2

£ 8-4478213
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10 8-448 1 W;4

11 8-4482714

12 84483463
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14 8-4484982

15 B'4480712
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17 8-4487210
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It) 8-4488708
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41 8'44U020£
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43 8'449I70I

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Mi|a-4ani4i7

97|I> 4602164

ssltMstiaiio

JH4a03C38
, 60|»U044U2

23'^

I Peg.
37'

LOG. SINES.

8-4S4BU34
»4M9«72
8-4300410
8-4UI1 ~
8^4061886
8^4561684

4SI4090
40148.14
45I6A78

8-4&M099 fr4Q9SlS0
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8 4fiaU3l I 84800310

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8 4659369l»4tf03334
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H 4500733 8-4604692
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8 4519207
8-4S20040
8^4520784
8-4021527
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84523013
84523750
H-4524498
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8-4 .'•3; 84 4
84538584
8-453S3Z4
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0-4543023
4643702
8-4544501
84.t40S4a
64540970
6 4546718
4;i47467
45461 IIS
4546034

38' 39'

845M3013
8-4083744
4594474
tt45ftj:iOO
ft45!15H30
840g6GGC;
8-4S973U6

4066826
64069660
a- 4070205
64071020
84571764
8-4672408
8-4573233
8-4.>73»67
8-4S74701
8-467M30

8-4636649
8-4637372
8-4C38II9G
8'48383I0
8'4631t042
4640205
4640988

464171
a 4642434
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8 4643B79
84644801
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4660376
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64661818
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84611248
4611076
64612703
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84614166
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8-40IM13
8 4818340
8-4617067
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8-4G18520
8-4619247

84577630 tf 402 1 426
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84025761
8^4026506
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84682708
84583000
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8-4884965
8-4586697
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8'4e8716l
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84688625
8-4569357
84590088
8'4;^Iin8l9
8-409 1 55 1
4592262
8-409.1013

84671962
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840733117
8 467411"
6467483-^
84676040
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64676003
8-4677700
■4678417
4670134
8 4670800

LOG. COSINES.

8-4079800
8-46«l6«7

4681283
8-4681900
8-4682716
8' 4633431
8-4684147
8 4884862
8 4G80076
8468629:'
64087000
64687724
64686439
8-4680154
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4690084
8-4891298
8-4692013

8-4G93441
84694106
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64603981
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84066422
8-4066143
8-406686'J
84057583
8'4e58303
8'4G5»D23
6'4S5g743
8'4G60463
8-4661 182
84601002
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8'4G04O09
8-4604776
8 4005407

8 4097720
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8 4699I0I

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8-406UOIMJ

41'

U 4702003
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64703429
6-47U4I41

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6-4709126
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8 471 1266
8^4711971

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8-4714104
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4713526
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8 4710947
8-4717657
8-4718367
8-4719077

■47I97S7
8-4720497
8-4721207
fl-4721910
84722626

4722626
64723330
8-4784044
8-4734703
8 472fi4S3
8-4726171
8-472(1880
8-472758»
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47-i900G
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8 4730422
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8-4731638
8^4733046
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847»3982
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8-47360B4
8-47387BI
8-4737498
0-4738205
8-4738913
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8-4740325
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474-2444
6 47431uO
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8-47402C8
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8 4747380
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8-47495011
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8-476332U
4703024
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U-475SI37
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64766645
8-4707349
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11 8-4484426

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14 8-4486870

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16 8-4488176

17 8 4488935

18 8-4489075
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10 8-4401173

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10 H'45a«ini

LOG TANGENTS.

B4S0GI3I
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U-45D7G24
1.508371
8-45119117
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8-4513840
8-4513301
8 4514336
8 4515081

8 45l73l(j
8-45IW)01
8 4518805
8 4519549
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84531038
8-4321783

23'

11438
84532178
84333915
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S-4555130 8-4S993UI

8-4556807:8-4600602
8-4557344l»4e0i3»3
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84339556 8-4003584

1-4360295 8 46043!

1-4561033 8 4005013

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84584717
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8 43-34013
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8-4623390
84528243
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S 453847:
8-4329EI6
8-4539957
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8-4531442
8-4532184
8-4532026
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84534410
84535153
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84336635
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84369870

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41081
8 4341822
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84544043
B-43447S3
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8-4546382
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8 4548481

8-4395546
84590277
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8-4840059
4841382
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84645723

84646440
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B 4849336
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8-4608691
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8 4905304

8-4945924

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8 4005984

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8-4900664

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8-4973357 8 5012317

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8-61303381 1

60|84850505

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13'

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8'

■'

LOG. COTANfiESTS. 88 Dej^. 1

266

1 Deg.

LOG. SINES.

Tab. 8.

"o
1

2
3
4
6
6

7

8

9

10

11

12

13
14
15
16

17
18

19
20
21
22
23
24

86128U73
&5129319
8 5129966
8-6130611
8*5131256
&6131902
fr 61 32648

26
26

27
28
29
30

31

8-6133193
8-6133838
8-6134484
8-6136129
fr6136774
fr6I364l9

8-6137064
&6 137708
8-6138363
8-6138997
fr6139642
8-6140286

8-6140931
fr614l676
8-6142219
fr61428G3
8-5143607
8-6144160

53'

86144794
8-6146438
&6146081
8-6146726
86147368
8-6148011

8-6148664
32 8-6149297
S3'86149940

34
36
36

37
38
39
40
41
42

43
44

46

46

47

48

49
60
51
62
63
64

66
66

67
68
69
60

8-5 150583
8-6151226
8-6151869

86152611
8-6163164
86153796
86164438
8-6156080
8-6165722

85156364
8-6157006
8 5157648
85158290
8-6168931
8-6169673

8-6160214
85160866
8516U97
8-5162138
8-5162779
85168420

&6164061
8-5164701
8-5165342
8-5166983
8-5166623
86167264

85167264
&6167904
86168544
8-5169184
86169824
86170464
86171104

86171743
86172383
8-5173023
8-6173662
86174301
fr6174941

fr5175680
86176219
85176868
86177497
86178136
86178774

86179413
85180051
86180689
8-5181328
86181966
8 6182604

54'

86206514
8-5206148
8-5206783

fr5207417
8-6208052
8-5208686
8-6209320

86209964
86210588
8-5211222
8-6211856
8-6212490
8*6213123

8*621 3767
8-6214390
8-5216024
8-5216657
8-6216290

55'

6261601
5252229
6252857
5253485
5254112
8*6216923|8 6254740

r

86183242
8-5183880
8-5184618
8-6185166
8-6185793
86186431

8-5187068
8-5187706
8 5188343
85188980
8-5189617
8^6190264

85190891
86191528
86192164
85192801
86193438
85194074

85194710
8-5195347
86195983
85196619
8 6197255
8 5197891

fr6217566
8-6218189
86218822
86219465
8-5220087
8-6220720

86221362
8-5221985
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86223249
8-5223881
8*6224613

8*6225146
8*6225777
86226408
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86227672
8-5228303

8-5228934
8-5229566
86230197
8-6230828
86231459
8-6232090

fr5243430
8-5244059
86244688
86245317
85245946
86246574
8-5247203

8-5247832
86248460
86249088

86249717
86260346
fr6260973

8
8
8
8

56'

85256367
8-5256995
86256622
8-6257249
86267877
8-6258604

fr62d9131
8-6259767
85260384
86261011
8-5261637
8*6262264

8*5262890
8*6*263517
86264143
8-6264769
862663JI6
86266021

86281017
8-6281641
86282264
8-6282888
8-6283511
8-6284136
8-6284768

85285381
85286004
86286627
85287250
86287873
85288495

8-5289118
8-6289741
8-5290363
8*6290985
862916081
86292230

57'

58'

8*5318281 8
86318900,8
863195188
86320136 8
8 6320754 8
8-6321372'8

6355228
6366842
6356465
63570G8
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86393079
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86:i94295
86394902
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8 6326313
8-5326931
8-5327648
85328165
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85364416
8 5365028
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58!

57
56
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86396117 53
8639672553
86397332 51
86397939 50
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8 6399163 48

85292862;8

86293474|8

8529409618

85294718 8

85295339

86295961

5330015,85366863
5330632,86367474
6331249 8 5368086
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85332482 8 5369308
86333098 85369920

85399700
86400367
85400974
86401681
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47
46
45
44
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8-d296583;8
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8-6402794 42

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8 6404007 40
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8 6406826 37
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8-5233351
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8 5198526 8-5236503
8 5199162 85237133
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8-5240912
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8-5267273
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85268524
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85270400
8 5271025
8 5271651
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85273525

8-6274150

85274776
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85277273

85277897

8 5278521

85279145

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8-5281017

86300310
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8-5337410|8
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8-6307756
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5385170
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5386997
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5388822
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9
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7
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88 Deg. i

1

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33'

54'

66'

06'

57' 1 5a'

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87 DCff

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I,OG. SINES, &C.

273

Sine.

Dift.

8 5o:i5:Mw;i:fl,.
8-5(;or,404 :"^f,;^,

fr36:WI>94lJ]3*jf:

Cospc.

ll-4d7inOH

ll-4.'iaa7»*2
I r4r>()00.V2
11-440'46*14
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ll-4:«)45»0*

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11-4002791

« 8740714

ll4(H)0;.l7i(;8«7034O
M -4023483 8 81):«4a4

8 (J00a3l7io -J'o 1 l-3J>i»U68:V6 8!W80:)J>

8 C0348^(;|^|^';;

8r»fH)827«ii:,,:..'^
8oC42912l'**''''^'*

0^0000220

1139(;5ll4i6!K>(>I221

85877275
857113(;8

8-5745197
8-57787C(;
8 5812077
8-58451.%'

85877945'
8 5910509
85942832
8 5974917

34383

34093
33829
3:i589
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33059
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325^4
32323
32085
31850

8 8008707 1'ifiio
8 0038380 '

S W)i)73Jl IjiJi^ 1 1 3902859 9180183

«-6i2C2;j5,i!!!!2f
8 6i6«9io'^5;!;;;

862196161:12557
5"5xi??5? 29831

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1 1 393377410 9123927 B 0009777

86100943
8 0I3I889
8-6102010
8 0193127
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8 0253518

113871705:0-9247990
11 384 1090'6 9309372
11 3810031 !0 9370317
Il-3780384|0-94:{08:i7

11-3750347.6 94905)39

1 1 372051610-9550027 8 0283402

80313083
81)342503

J

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i

I (8 6425634',,«p.p! 1 1 35743fW; 984:^03 18 0429825
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8-6:1091 1 1 ijojo/. 1 1 309988910 90(»9907

8-6:438537'o«|.4t* * *^''*^'*'*^'^ 6 9008780 80342503
H-«367764ir>rtx',- * *^*'32230 9727208 8 637 1 846

8-63!*6796:.Vy j^I 1 1 3003204.0 9785:^59 1 8 0400931

I 8-64W-282,f> "7°
1 18-6482/42 o;..,-.

I is 6511018 r,2r>/>i

il 1-3517258 9957334
11 3488984 T00I391I

8-0487044
80515375

8-rN539l07 o^IJyA 1 1 3400893' 7 0070121 j8 654:^22

31391

31160
30940
30727
30511
30300
30091

29884
29081
29480
29282
29080
28894

28703
28510
28:^31
28147

8-6587017 .™V, 111 3432983:7 0125909 '8 0571490 "'''"J

27C12
27440
27207
27099
20931
20705

26003
20441
20282
20125
251/09
25810

2500:1
25514
25:t00
25218
25075
24930

-24700
24049
24511

24374
24239

11 •4509102
11-4533091

114497317
11-44018.34
11-44200.38
11-4391724
11-4357088

114322725
11-4288032
114254803
11-4221234
114187Q23
114154804

11-412-2055
11-4089491
11-4057108
1 1-4025083
11-399.32.33
11-3901014

11.3.930223
113899057
11-3808111
11-38373W
1 1-3800873
11-3770573

Covers.

9-984572.»

9-9844417
.0-9843108
9-904 17.99
9-9840490

Secant.

10-00(»2046
10 0002091
1000027:^)
10 0002780
10'0(M)2826
9-9839 180.- 1^0002872
9-9&37809' 10-0002918

86594748

8-662

fr6649684

8-6676803

8670393

86730804 .^..^,e

86757510 „«.,.,!l 1 3242490170507101 ,80702,393
867W052 .,;S„,;l I 3215940 7 0560270 8 0788996
8-68lfM.33L,,!:J!: Ill 3l89507'70(U3()08:808l,54:i7

1 1-3740482
11-3710598
11-3080917
11-3057437
1130281.55
113599009

11.3570175
113541472
11-3512.050
113484025
113450473
113428510

99830559;

9 9835248

998.339.30!

1^98.32024'

9-9831312

99830090

9-9828087:

9.O827373

99820000

9-.0824745

9 9823431

99822110

9-9820801
99819485
9-9818109
99810853
9 9815530
9 9>)I4219|

100002964
10-000.30] 1
10 0003058
10-0003106
100003164
10-0003202

10 0003261

10 0003300
100003350
100003399
10 0003450
I0000:i500

10 0003551
10 0003002
10 0003054
10 0003706
IO0003758
10 0003811

0-9812901
9 9811583
9^9810-205
998089401

99807(»*27"
998003081

9-9804988'
9980.3068;
99802347
99801020,
9-9799704

!9979o:v;3i

10 0003804
10 0(H)3918
10 0003972
10 0004020
10 0004081
100004135

10 0004191
10-0004247
10 0004303
10 0004359
10 0004416
100004473

11-.3400721 9 9797061; 10 0004531
1 1 3.373109 9 9795738 100004589
1 1-3345609 9-97944 15 10 0004647
1 1-3318402 .^9793092' 10-0004705
1 1-3201303 9-9791768! 10 0004764
1 1 3204372 9 9/90444 1 0004824

11 -.3-237007
113211004
11-3184503

9 9789119
9 97877i>5
99780409

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86939980 *

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8-6990734

87040899|.-,4jj^.y
8 7065760 ., ,72 .

8-7O9O490 r^l*^;^

8 7115075 25']^^
8713!l5-20f;^fj
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Il-.3:)8i^021i7082l052, 8 0919629

1 1 -:*OW)020 j 7-08723 1 180945292

ovioi' * 1 3034569'70923249 8 0970800

^,..'1 1-3009200 70973885 ;8 09901 72

Cosine.

Diff.

l|-29JMllli71024-2-28
11-2959101 71074280

11-29,342.34 71124045
Il-29095l0i7- 1173527
11 -28849-25 '71222728
ll2fJOO48O|7*1271052
U-28:<6171 71320302

112811998

Secant.

7- 1368080

8 7021390
87046406

87071395
8 7090185
87120834
8 7145345
87109719
8 7193958

Covers.

11-3158-281 9-9785144
113132150:9 978.3818
11-3100187 9 9782491

11 3080371

9 9781104

11 3054700:9-9779837
11.3029194 9 9778510

ll-:i003828
11-2,978010
1 1 2953535

.9 97771^2
99775^^3
99774525

n-29-28605 9 9773195
1 1-2903815,9 9771«60

Cotang".

Diff.

11 2879 100
11 2854 W5
112830281
11-2800042

Tanj?.

99770530
9 9769-200
99707875
9.0700544

Verseds.

10 0004884
100004944
100005004
10 0005005
10 0005120
10 0005188

100(K)5250
10 0005312
10 0005375
l0-0<(05438
10 0005502
10-0005505

10 0005030
10 0005094
100005759
1000058*24
10 0005890
10-00()5956

Cosec.

D.

45
44
45
46
46
46
46

47
47
48
48
48
49

49
50
49
61
60
61

61
62
62
62
63
63

64
64
64
65
54
56

66
56
56
57
57
68

68
68
68
69
60
60

60
60
61
61
62
62

62
03
63
64
63
66

64
05
05
00
60

Cosine.

9 9997354 00
9 9997309 59
9 9997265 58
9 9997220 67
9-9997174 56
9 9997128 66
9-9997082 64

9-9997036 63
9 9996989 62
99996942 61
0-9996894 50
99996846 49
9-9996798 48

9-9996749 47
9^9996700 40
9-9990660 46
999fKi601 44
9^9996550 43
9-9996600 42

9-9996449 41
099.96398 40
9-9996346 39
.99996294 .38
99990242 37
99996189 30

9^9996130 35
9 9996082 34
9 9996028 33
9-9995974 32
99995919 31
9 9996865 30

9 9995809 29
9-9995763 28
99996697 27
9 9996641 26
99995684 25
99995627 24

9-9996469 23
9^9996411 22
9-9996363 21
9^9996296 29
9^9996236 19
99995176 18

9-9995116 17

99995056 16

9 9994996 16

999949:i5 14

9-9994874 13

9-9994812 12

9^9994760 11
99994688 10
99994626 9
99994562 8
9-9994498 7
99994436 6

09994370 fi

9 9994306 4

99994-241 3

99994176 2

9 9994110 1

9^9994044

D. Sine.

De^. 87.

d

274 3 Dtfg.

0Uli233(i0

I Obsusnt

9DG3gi60
SIU3E074
4 0034979
AOMTBSS
0640788

7 DM3693

8 0S4f{&97

9 0MI1S08
IOI)SS34U(i
.1 DGSOSll
13 DfiaSSlS

9 067e&M
» 0501448
II 0fifl43a2
Ri DSB7ISC

13 osDoisn

tfi D99&0(t7
lU 0698871
:7 0601779
!H 0604^78

15 0607683

16 0610166

i:i:u6^''.o

16 0617905

17 063080d

ui (h;:i37I i

19 Wt36HI4

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I 0043420
i 00411323

3 0648228

4 0851129
6 0864031

18 0866934

47 01

18 0082739

19 966J841
50110686-14

il 0071446
52 0674349
>3 110773^1
•4 D6S0ia»

18 0801761
i»0GfM66»
10 0897666

NATUllAL SINES, &C.

0476G4U
9473736
M701O1
9467038
946S02I
!M6S1I7
8469213

^,9447684
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1 0898226

18102619

IB 0U7"37 10566 189

17814213 05A9n87

I7'549O30
17460016
17371960

™'' H383708
;™:j9377!»l
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9380192
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,^9318871
jj^* 9316089
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9524078

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19 081137
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18U71068
18 707764

iB-r

0561823
0587841
0570769
0573678

I6'77!M39
16898082
1661'.

16-837717

16-362873
16226080
I6 1409S7
IS 074617
lS'99fKI4S
15 025971
16862678
16*780951
15708008
ie'636793
15-66613
16496 1 14
16-426721
16357!M0
t&2807«8
15^222231
15156270
1 1 1601
16-023103
14-957382
14893226
14829128

0602887
0606787
0608706
0611628
0614646
061746S
0620388 :

183G5537
18 3ft7654
1^170807
18-074977

■ 7-980160

■ 7-886310
■7793112
1770 1S23
17610550

17-265809

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0013867 ,,
001 101 I
0014166 \;

06108291
064376O
0646671
0G49593
0652513
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0887121
0670043
0872066

0675887

10^19723
1-W»13877
I-0014030
1-0014185
1-0014341
1-0014407
1-0014655

1-00I1RI30014T9I ,,
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1-00 15132'0015 109 I'
100 15393 OOI62eK:^

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16 687398' l'nniU156|001U^23
16-507468 1-0018332 0018290
■ 6'428279' 1*0018509 0018475'
16-319655 10018687 0018652:
16 272174 1-90188660018830
16-196225 I 0019016W1900g'
16116908 19010226!OO^OIKI
16 013482 1 OU191P7l90)9369
16 988667I l-9010689i00t96a0
■6-804646: l'O01O773|M19733
16'R21106'l-0glO868
16-71B337:l*O02O1 "
16-876233 l-0n2at
15804784,1-00305
16'6.13!l81>l'0l)2069g
I6 463814J1-0020SH7

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9UB5050

9084881

9984731

9984670 _

9084408148

, 9984246
0084061

l00839^7

I 9983751
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' 99834 ■B

' 9982913 3!
"IB9B2712 31
, 8983570 3^
,8982398 31
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^ 99S2052 31
,.9981877 3;
" 998^701 39
^ 0981625 31
^ 9981348 3C
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47

16-304276 1-0021076
lfr325358 1 0021266
16 2570521 1 002 1467
16 immsll 0021618
15-12221211002184
16-0557231-0022031
14-989781 1-0023330
14-8214 17 10022423
■4S5a«^6 1-0032019
14795372 1-0022811
■ ■l-73^b79 1 0023013
I l<:'iS52U 1-0023311
I n;<l,->OI8 l'00234^0
I 1 ->j:I033 ■0023610
lllHa273 1-0023811
11-1->1S30 IOU24013
111360886 ■0Q313IG

0020470

0030657

0020841

0021032,.

0O21221 [

002^1l^

00216011 J;

oo2^783 ;

002^985 j;
0022178'
(W22373
003256?'
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0022860
9023157
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0023756 ^,
0023966 f.
0034157 a
9 0021360 "

!67'4

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[j it8788O0i22

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^ )W7B530 21

i 9979313 I!

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9978779 II
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9977821 1:
89776*7 "
,89774331 9
; 89772371 8
,98770101 7
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.9078646 I
9976445 ■
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, B97«145 1
; 9076843 1
'9976611 I

.

Dif. Vgrs. [SfCBnt |Cntan.| Tanff.

I Cosec. CoversI D.

86Deg.

Ueg

•■7313IM0J:

8-73M78>

B-730flH83

1-7333635

^7■J-•.' "
^7jt!uuls
h7490ja3 -,

h7si«»73 ^;

i7ft3627B»
^7»57JeB *

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r 77iM»4o 1^

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r 7836niB "

t7«S<i763 ^

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I-7W88U"
fr7W8B4l^

i7!M8a74
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t80R87fi1
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t8n7SI92
Ilt0ff7773
1-81 1 7i»

^8I3>

I'&1J)5JBS

^817(217

18194363

l'a3l34U

LOG. SINES, «:

IB37U113:

h328e844

18307400

iHSauoei ,
f«4I77»l

18(35845 '

CiRcc-, Versed s. Tbii^.

I-Stll 11^8 7

I :i7BTM0 T

l-a7M054 T
1-27*0278 7

1 i-^imn T

11-9693118 7-
1 l'3UaE)78B T

ii-aetr>i6.i 7

11-2531085 7'
I I-25IW447 7'
■ l'I4K702; 7
II 2444722 7
11-2442631 7
1I-24204M 7'

12;

1-337fiG34l7324M»71
l|-S3MgK9i;iZli3S»7

I l-33a33S3i7'23»i0M
ll-23ll725t7'23700Dfl

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11-2206680 7-2582317

112tlU7»e|7-2024l6(

I|'21(U9S3|7-26«SS1U

Il-2l«3247l7-2707a5a

tISI2a«4r727<<H50fl

II2IU2133 7'37B05«I

tI-2U«17tS "

112081406

n-HI4nS6

112021060

n-eooiostt

) 11081086
U'luei23«
111041477
l'IU2ia0B
11-11)02228

II 188273017-3228707
II ll)«EU3.il7-32C7S4f;

-330<i332
11 lS24TU3l7-3»MS37
ll'IH05e377-lU'l31«l
lM786675i7-34213J7

7-29SIHI»8'7Da76I&

7-2991 97i
7-303IBO7
7-:M)7I830

7311"
3IWI572
3I80773

I-I711l60i7»572-1M

1-168350,^(7 3609678
1-1673934 1736<-

I-IS37U3I
I leiSfilMi

!'IU004:ijl
I I6B33SJ

73r20757

737S74Ca

7 .t;ft4027
7-3830431

7193(I5'I
8'72I80»3
8-7242035
8-7285877
8728961)11
8-73191 7<«

7336631
87360964
87383172
1^7466258
a-7429223
87-IS2(Ni7
8'747-17D2
8-7497400
8-7610802
87642260
8-7584631
B7S8688I
8-7608719
8'7I]30647
8 76524C5
8-7674176

87«9f.777
87717274

87738066
77S9962
7781 130
7802218
8-7823109
S'7844070
8-7864861
87665644
8-7908)30
^7926620
879470U
&7UC7313

fr8007«33
8-8027853
-' 8047583
3&067423
"81187173
0106834

88126407
~8146U»4
H^I652IM
8181608
820383H
'8223084
8242O40

nS547l3
H3732I I
ftHj!llf>3:i

IH00977
8-12)124;
K446437

SKtiiit. Covers. | Coluug.

1 1 3806042
1 1-2781037
11-8757305
11-2734133
1I-S7I041]
ll-2r

ll'2t

12670778
13547933
1 1-2526208
1-3!
1-2480108
1-246773 1
11-2435409
112413310
11339I2B1
11-2360353
1I'2»1753S
II2325U25
1 1-2304223
ll'22«272U
11-3361335
ll'324mU8
112^1086
1 1 2107762
1121768UI
113165921
11-3135139
1 1'Sl 14458
1 1-3003870
11-3073380

11 1873603

II 1B64I0U

11-1034708

1I'1H153»3

11179611

111777018

111757054

111738074

II 1720078

II I7OI250

IMG4S388
111616780
111608367
1 1 15U0U23
1 1 1571 756
111553563

Diff. Tang. Verseds.

0706644
0-0765313
9-9763881
9W625J9
9-9781210
9-9769883
0-9768660
»97573I6
9766883

9764647
9 {176321 2
9^0761877
0-9750641
»9749205

9747U6U
0-9746532
0-9746194
0743867

9742610
0741180
0730841
00738603
0O737I82
9-9736833
9-0734483
9-9733141
OO73I6UO
»g730458
91*729117
90737774
OU72643I
997250S8

'97^3745
0^9723401
00731057
9^9719712
»D71H367
9^0717921
907 15075
9-9714320
997I3UB2
9 9711636
097IU2K8
0^9768040
9O707S02

0706343
9-9704804
09703645
0703105
O070D346
9-0609494

9808143

'0696792
90695440
1 1' 16</3866 9-9694080

99093735
9-9861:182
0-9690029
0-9608675
9-9087321

100006051
1»0006032
1O000608U
10-0008156
IOOOO61I24
10-0006293
IOO0063O0

lo-oomuss

1 06006497

10«008667

IO00U0836

I90008707

100000777

100<

10 OU'ltiOlO

lOOOOUOOl

10 9007083

100007135

10-0007207

101»072fl0

1O0007364

100007430

100007602

10iW07676

1O000T651

10-0007726

ltfOlMI780-J

1O000767H

IO0O07964

lOOOOUOSI

109008108

100008185

ia«(HI8363

10-000834 :

100008430

10-0008499

I0'0ou8a7e

100008738
IOOOOSSI8
10-0008809
100008080
10-0000062
1O0009U4
10-0000226
1 00009309
10'll0a9392

100009643
10 0009737

160009813

lOOOIl

IOOOIO-.242

10-00103:

lU-OOIOJiU

10 0010504

10-0010592

COBC

. 9 0994044 6

', 0090:1078 5

, 9 9993911 6

, 9903844 6

00993776 6

09993708 6

9^0993640 5

99993433 6

89903364 6

. 0-9903293 4

9-9993323 4

' 9-0993600 4
, 9-3003938 4
I 9 0002806 4
; 9 0093793 4
9 9902730 4
99902646 4i

■ 9-9ira357a a
9 0119-2498 3

I 0-9992349 3<

, 9-0992274 3

; ff99[J3lua 3

! 'JOiBHi-i S

: 9-0992046 3

. 9-909 lOffit 3

, 0-9!l9l892 31

9 0991500 2
99091601 3
99991433 3

9900118
9 9091101
90901020 I

I 9 99n044l I

, 9-0n!IO3!57 I
; U9990-J73 I
^ 9 0900180
I I0 9990III3
I !9*J0OOI7
' 9 0989931
, 9 9980815
' 00697.18
' 999a!Hi7l
' 0-9089584

SGDep.

' 9l6 4 Deg-. NATURAL SINES, &c.

30700270
4070SI71
G[G7I3073
00714971

7(i71J87e

Bmtom

lOlOTIMSO
II0731MSI

13 or ■ ■

13 0735383
14|07381«4
l3 07dI0Sa

19 ii7a3ssa

1\'07oBi8a
'.'-2I07C13UO
S» 0704300
S4 07'(71UU

36 0770001
B8 0772B9I
27l077SBal
88,077B7BI

■■ 07Hiiiai

078J&U1

»1 0767^01
a2'H7UU3al
:iaii793«Ki

?4, 07001 00

:i£ 0700000

:W OS01B80

37 0R04ft89
00077118

30 OR1U4IS7

"■ OK13iH7

41 OH1(I480

0RJ!)3Ha

■IHI00:»U81

-<7|l)833880

Otl3U778

nil4357U
0640474
0B48373

oonis7i

0854 1(I»

0837007

ooamm

D8t:2RU4
0lin6763

oGseeeo

m 0871067

Cosi

Dif-C

^0302436
3001]

U393730
™*'^9SB7827

8373420
EKI7DGI9
D2S7(ilH

33IM7t7

uaoioie

0368016

0247313
034441
034 IS II
OSSMIO
9236710
9233010
923900S
9227000
9234100
9331300
0318909
9316409
8313609
9309609
930N7I0
9303810
9300910
9198011
BI961I
9103311
01SU3I3
1 861 13
9183614
9180816
9177710
9174817
9171918
91G0OIO

139!

13873013

13-818391

IS'7G3116

13708379

13GG4077

13S00306

13-640798

13403731

I3'44I118

13 388014

13-337110

13-386719

13334717

I3-|B41(JU

131338112

13 UB4040

13434&78

13-1

m37i3«

01342.18
0131340
III3U443

UH36dU7
14370200
14-317304
14-168804

14'inooes

14-043604
(3986614

13-8084 10
840416
13-793779
I274S496
13^008960
13-061071
13-006734
2 660816
12-614340
13-468905
1»43407H
18-379404
13-336310
12-291362
13-247(iOtl
12^304374
13-161340
12-IIBB22
13070098
033970
110031.17
11-060696
1 1 000340

Tanp.

Secant

V.^rs.

14341134

-0034H39
0036036
0036341
14007866 1-0035440
, 13-9507 10; l'00-J6668
i>/iif/j^ 13-S94U<iai I'ui/aiuu/
0722667, 13837827 10026078
0736681 ' 13 7B20BW I 0036289
U738606 13-720730110026501
0731 430, 13 671856! I 00-J67 14
07343S4 1SU1T400 1-0036038
0737279 13 5G339lll-D(l37l43
0740303 1350S799, 10027368
0743138 1345UU36 1 0027574
0740063 13 403H67i 10037791
0749979' 13 361318, lWI21HM)g
07519O4 13299574'l-

ll9iDU24360
002466J
0024767
0034972
0036178

0754820'l3-24803l' 1-0038448
0757755 13- I9GBU3I I 0020669
0760680' 13 UOI27 10026800
O7O36O6' 13 U96757 10020113
U7nfl533'l304576u! 1-0020336
0760468' 12 yjOlUU 1 0029560

I(j'l9

0789944
0793U7I
0795798
O7OU72O
0801853
45S1
0807509

ou 10437

OS 1X0)3

:>8 n

1 3-649657 i 1-003U337
1 3^(101 417i 10030404

12^7538341-

13 706205 1-0030033
12 653126 10031162
12G13390 10031383
l»(>(tS997'|-
12519042 1-003)847

12-474231.) 0032l)8i:(>031978,o;^':
12-4263311 003231510032311 Ijj

1 1-787274
11-747141
11707283

I I-««0n33
I'QIIOOO
11-478713

0833150

08260:

0828007

0830038

0833865

oa:ui784

0839733
0843663
0u45583
0848513
0051443
0854373
OSS7303
0860233
0063163
086603
086VO-.i5
0K7I96G
U874887

12 260503 1-0033261
1220ti71U 1-0033900
121 63338 1 0033740

0036866|:
0O370fl0[
0027383';
0027498,:

002771l'5

0037931,,
0030149 .

9974033 3>
9974815 61
9974408 61
9974190 6:
9973S90 3:
9973780 61
U97360UK
9973357 4!
9973145 48

0039038
0029360
0020472^

"•^
*M6

0U30146 "^^

0030372

0030699

003082?:^

0031055ij3^

0031515 ^

00324451.
0032e7!»|i;
0032015^
0033151 1^

13 077103,1-0034:
13 034623 '10034463

11 092:14'). 1-0034706

l'Ua0370, 1-0034050
11900683 10033105
106728210035440
1026167:1-0035007
I '7lt53.H3ll -0036934
11-744779 1-0030)82
-704JWn )-00aB43)
11064496 1-003668)
11-634761 1-0036933
11-585294' 1-0037 183
11-646003 1-0037436
11607164)0037689
1-46U474 1 0037^43
11-430053 1-0038198

9972931
9973717
9972602
8072380
9073069
997 1861
9071633
0071413
9971 1S3
9070972
9970760
9970tS8

47

0035071
0035116
0035660

0030947
0036796
1)037040
0037290
0037648
0037800

9967789
8967653
U967321
9907086

9965414
9966171
tl»64R3U

SeCBiil, (.:o(8n. Tang,

Coverti D. Sine,
80 be^.

4 Deg-.

LOG. SINES, &C.

277

1

2
3

4
A
6

7
8
SI

1
2

%
I

1

i

I

)

I
>

If

I
1

7

9
(I

1
2
3
I

Sine. iDifi:

8 84718271 i;^*

«-84h;)707!

17805

8 8507512' 1"^"
8 8525245! }4/.*{
8 85420U5 r.„

8-8560403 1... I-
8-8578010, 7;Jj7

8-85.%457!ji«i'
8 8612833 ''

Cosec.

»8630]3.9
88647370

a8664545
»8681646
a8688680
8 8715640
887325461
8-8749381:

17300
17237
17169

I7I01
17034
16966
16900
16835
16769

11- 1564155
111540126*
111528173
11151 0293
111 492488
111474755
11 1457095

11 1439507
11 1421990
II- 1404543
1113H7167
111369801
11 1:^52624

11- 1335455

II 13UI354
111301320
IM 284354

III 207454
11 1250019

lM233a'>0

Versed s.

7'3««(;6«3
7-390-2785
7393^1730
73974539
7-4010190
74045700
7-4081071

74110293
7-4151372
74106311
7 422110J>
7-4-255707
7-4290288

74324«?73
7-4358921
7-4393035
7-44*27015
7-4400862
7 4494578

7-4528103

Tanpr.

8 8446137
88464554
88482597
88500560
88518461
88536283
88554034

88571713
88589321
88000859

880243-27
88641725
8-8059055

88076317
886.93511
8871063/J
88727099
8-8744694
88761023

Dilf.

11-1217140:74501619

88778487
88795286

10576

16512

1 10450

16387

16325'

11 1200507 74594946 8 8812022

8-881606*91
8883*2581!
8-8849031

88865418
8-8881 743
888fM)007
8-8914209
8-89:<0351
8*8946433

8-897841 8' '•'•'*'•*

11 1183931

'II 1167419

1 11 150909

7-4028146
74661219
74694166

74720989

100221

8-8i)94322
800101f;8

11 1134582
1 Iwfij ' ^ ^'^ ^ '«'257 7* 4759688
i«-l»o J *• * ^0\90:i 7 4792264
filj9;*'*'<*«5791 7 4824719
uu\^\ ^ 11009049 7*4857052
innoo! 1 11053567;7 4889205

1 11-1037545
1I-10215H2

15904,
15846

88828694
88845303
8-8861850

88878334
88894757
8 8911119
8*89274-20
88943660
88959842

I8II7
18043
17969
17895
17822
17751
17679

17608
17538
17408
17398
17330
17262

17194

17127
17001
10995
10929
16864

CJotancf.

8*9(V259;w!{^?!!7; J 10974045,7 .V
8 9041685'J*';r 'ill 095831517 5

89057358
JMW172975
89088535
8-91040:19
89119487
8-9134881

8-9150219
»9 165504
8-9I8(»734
8912^911
8 92110:i4
8^9226105

15617;
15560

7 4921359 88075903

7 495333518 899*2026

1 1 -1 005678 7-4985 1 93 1 8 .9008030

1 10989832 7-5010934 ■« 9023977

mum) iwmnHiHi

8-9055097
8 9071472

!1 1 094*2642

15504
15448
15394

110927025
IKK) 1 1405

5080071
75111408

7 5142751 8 90871.90!
7 5 1739*23 !0 9102853
! 1 1 0895901 7 5204.9821891 18460

15338;

1 1 0880513 7 5235931 89134012
1108651191/ 520076918-9149509

15177
15123
15071
15018

1 10804089 7 53<W038 8 !»2 10957
11 0788900 7'5419:i:{8l8 9220180
1 1 0773895 : 7 5449532 , 8 924 1 :Ui3

14966
14914

8*924 1123

89250089

8-927100;

8-9286»66;i^,

8*9300678: ,1!:if

89315439jj*Jjj

8;)330150|,,«-,

8 0344811! i2i I
8 93594*22!;*?;.!

»-937:W83 Ij?,.\

8938349/»:^!!;.^

8-940*>960r'*^ *

11-0758877 7 5479621 :8 9250487
1 1074391 1 7 5509607 i8 9*271500

3 iTo/.^;!! 1 0728997 7 5539489|8928658l
^iuftl? 110714134 75569268 89:501552

("osiiie. ; DilK

I l-(Ni99322l7 55.98946
1106845617 5628522

11066985017-5057998

II 0655189 7 5687:^73
110640578i7-571»»650
1106*2r;017 75745Jr28
110(ni504 7 577t}K)8
ll-0.'>97040 7 500:i«191

Swaiit.

89316471
89331:^0

8 9:il6100
89300929
89375f»50
89390321
89404944

16799
16736
10672
10609
16547
16484

16423
16362
16301
16240
16182
16121

16063
1001)4
15947
10889
15831
lt'»775

15718
15fi63
15007
15552

15497
15443

15:{88

15:j:j5

15*282
15-2*29

15177
151*24

15073
15021
14971
14919
14869
14820

14769

14721

114071

1140-23

1115535(^5
1M535440
111517403
1M499434
1114815.39

111403717
111445960

11- 1428287
11- 14 10079
1113.93141
11-1:575073

II i:i58275
11-1340945

11-1323083
1113064 89
IM 289:562

III 272301
11-1*255:^00
11-12:^8377

11 1221513
11-1*204714
11-1187978
111171300

Il-ll54/i97
111138150

Covers.

SecuiiL

10 0010592
100010681
100010770
100010859
100010948

9-9685967

9-9084012

9-9683256

9-9681901

99080544

9 9679188' 10 001 1038

9-9077831|l0 0011129

99076474 10 0011220
9 967511610 0011311
9907:^758 100011402
9 9072;H99 10001 1494
10 0011586

1).

9 9671041

9 9669681 10 0011679

9^9608:52-2 100011772
9 9660901 10 0011805
9 9005001! 10001 1959
9 9604240! 10 0012053
9-9002879' 10 00121 47
9^9001517 100012*242

89419518

14574

Covers. \ Cotaiij?;.

Ditf.

11 1121066
11-1105243
11-1088881
11 1072580
11 I056:il0
11 1040158

11 1024037
11- 1 007974
110.9919/0
1109760-23
LI 0.9001:54
110944303

110928528
110912810
11-0897147
110881540
110805988
110850491

110835048
110819000|9 9625974
1108043-25 9 9024602
ll-07W)043i9 90-23229
11077:<«14l9062li556
11075803719 9020482

11074351319 9019108
11072844019 961773:5

89
89
89
89
90
91
91

91
91
92
92
!)3
93

93
94
94
94
95
96

m

06
96
97
97
97

98
98
98
99

loo

99
9 904:5779,10 001,35081 '
9 964*2412 10 001:5008;™

99041044 ioooi:^7wii;; ,

9 90:59670 10 00138i»9 JJ!
9 9638308 lOOCM.iOlO [",
9 90369:59 10 tW 1 40 12 ""

Cosine.

9 9<i60155
9-9658793
9^96574:50

10 0012337
10^0012433
iO-0012529

9 9656067 10001*26*25
9 9614703; 10-0012722

9^9653339
99651974

10-0012819
10 0012916

9 90506lO>iaO013Ol4
9 9(>49244 10 00I3I12
9 9647879 10 0013210
9 9046513 10-001:5:109
9 9645140 l<HN)i:5409

9-9635570 100014114
990:54200|lO00I4216
9 90:52830,10 0014318
9 9031400' 10 0014 121
9 9030089 10 0014525
9^9028718.10 0014028

99627346

102

102
102
103
104
103
104

110713419
llOf;98448

99010:559
1^9014983

110<»5:55*29 9 9013608

ll-0008<'>00

990122:52

1 10653840 9 9610855
110(W9071 9900947a
11-(M>*24:550 9-!)608101

1 1060907:) 9^.9(100723

110595056 9 9005345

1 1 0580482

9900:5907

Tanp;*. iV'erseds.

10 00147:i2 ,^.
10 0014837 ^?

100014942
10 0015047
10 0015152
10 0015258

10-0015364
100015471
100015578
10-0015685
10^0015793
10^0015901

100010010
lO^OOIollO
10 00102*28
100010:5:57
10^0010447
l0O0l(;558

Cosec.

105
105
106
106

107
107
107
108
108
109

KHJ
109
109
110
111

1).

99989408
9 9989319
99989230
9 9.989141
9998.9052
.99988.902
9^9988871

99988780
9f)988689
999885.98
9 .9988506
9 9988414
9 9988321

9*9988228
9 9988135
9 9988041
99987947
99987853
9 9987758

99987663
9 9987567
99987471
9 9987375
99987278
9 9.987181

99907084
99980986
99986888
99900790
9!)980091
9 9980591

9 9980492
99986:592
99980292
999150191
999800!M»

9-9:/85980

9 0985880
!^9.9{55784
9 9985082
99985579
99985475
9-9985372

9^9985208
99i)8516:5
99985058
99984953
99984848
9 9984742

99984630
9^9.984529
999844*22
99984315
9!I984207
9^9984099

9^9983990
9^9!)03881
9 998:5772
99983663
9 9983553
9998:5442

60
5!)
58

67
60
55
64

Sine.

I

53
52
51
50
49
r48

47

40
45
44
43
42

41
40
39
:58

37
36

35
34
33
32
31
39

2J)
28

27
20
115
24

23

21

20
19
18

17
16
15
14
13
12

II
10

9

8

7
6

6

3
2
1

8:5 r)ea-.

27G

4 Deg.

NATURAL SINES, &G.

Tab. 9.

Sine. Dif.

0G97665
1,0700407
20703308
3| 0700270
4:0709171

2902
2901
2902
2901
2902

Covers

6;0714974

7i071787G

8 0720777

90723678

10:072(;d80

nj 0729431

120/32382

13 0735283
1410738184
15 0741085
10 0743980
170740887

18 0749787

19 0752688
20,0755589
21 0758489
22.0761390
23;07(i4290
24,0707190

25'0770091
26 0772991
2710775891
28,0778791
29;0781691
300784691

31!0707491
32; 0790391
33 0793290
:<4|079(JI90
:<5.0799090
30:0801989

37
38

39
40
41
42

0804889
0807788

0810687
0813587
0810486
08l(»385

2902

2901
2901
2902
2901
2901
2901

2901
2901
2901
2901
2900
2901

2901
2900
2901
2900
2900
2901

2900
2900
2900
2900
2900
2900

43:0822234
44 '08251 83
45! 0828082
46 i 083098 1
47|08:i3880

2900
2899
2900
2900
2899
2900

2899
2899
2900
2899
2899
2899

2899
2899
2899
2899

9302435
9299533
9296632
9293730
9290829
9287927
9285026

9282124
9279223
92763*22
9273420
9270519
9267618

9264717
9261816
9258915
9256014
9253113
9250213

92473)2
9244411
9241511
9238610
9235710
9232810

9229909
9227009
9224109
9221209
9218309
9215409

Cosec.

48

49
50
51
52
53
54

55
56

57
58

0836778!

0839677
0842570
0845474
0848373
0851271
0854169

0857067
0059JHj6
0862H64
0865762

12898

59:0868060
60 0871557

Cosine Dif.

2899

2(,*99
2898
2899
2898
2398
28J8

2899
2898
2898
2898
2897

9212509
9209609
9206710
9203810
9200910
9198011

9195111
9192212
9189313
9186413
9183514
9180615

9177716
9174817
9171918
9169019
9166120
9163222

9160323
9157424
9154526
9151627
914872f^
9145831

9142933
9140034
913713(5

9i:j.12:j8

9131.340
JM 28443

Vers.

14:^35587
14-276200
14-217304
14158894
JU100963
U043504
13986514

13929985
13873913
13818291
13 703115
13 708379
1.3654077

13 600205
13546758
13 493731
13-441118
13 388914
13-337116

13-285719
13 234717
13184106
1313:i882
13084040
13034576

12^985486
12 936765
12-888410
12 840416
12-792779
12745495

Tang:.

0699268
0702191
0705116
0708038
0710961
0713885
0716809.

0719733
0722657
07255811
0728505
0731430,
0734354

Cotang^.

14300666
14241134
14 182092
14 123536
14-065459
14 007866
13950719

13 894046
13 837827
13-78*206(k

Secant Vers.

1-002441910024369
10024623 0024663
l-0024829!0024767
1 0025035 0024972

10026241
10025449

0026178
0026386

1-0026668 0026692

D.

10026867
10026078
10026289

0737279
0740203
0743128
0746063
0748979
0751904

0754829 13 248031 10028448

1 3-726738' 10026601
13671866:10026714
13617409 10026928

13 663391 10027142
13509799,10027358
13 46662511 0027574
13 403867 1 00-27791
13 351518.10028009
13 299574; 10028228

0025801
0026010
0026220
0026431
0026643
0026855

204
204
206
206
207
207
209

209
210
211
212
212
214

Cosine

9976641160

9976437
9975233
9976028

59
68
57

9974822 66

65
64

0757755,
O7OO68O
0763606,
07W;532'
0700458

214

0027069
0027283 t\l

0027498,; 2
0027714!;};

0027931.;; J

0028149^ **

0029028
0029-260

12698560
12-651971
12-605724
12569815
12614240
12^468995

12424078
12-379484
12-335210
1*2-291252
12*247608
12204274

12-161246
12118522

218

0028367'ooA
13 I9688:ri 002866910028587 i^oft
13 U6I27 1 0028890 00*28807 ^j"
13 095757 10029112
13 045769:10029336

12 996160 10029660

I

07723iM; 12946924 1 00*29785
12 898058 10030010

1 2 849557 1 0030237 .„^

1 2 80 1 4 1 7 i 1 0030464 0030372 ™
12^7536:<4 10030693 0030599 t^t
12 706*205 10030922

0775311

0778237
0781164
0784090
0787017

0789944
0792871
0795798
0798726
0801653
0804581

0807509
0810437
0813365
0816-293
0819221
08*22150

0825078
0828007

221
222

0029472|5|[

00-29696'

0029920

0030146

•224
226
226

9974616
9974408

997419916?
9973990,52
9973780161

9973569
9973357

6(1
49

0030827;^a
0031055

12 659125:10031152
12 612390 10031383 0031285
12565997 1-0031615 0031515 J^
12519942 10031847i0031746i».5
12 474221 1 0032081 (H)31978 ^.4
12 428331 10032315 0032211 ^^

!230
230

9973145 48

9972931 47
9972717 4G
9972602 46
9972286 44
9972069 43
997I86I 42

9971033 41
9971413 40
997119339
997097238
9970760 37
9970628 36

9970304 36
9970080 34
9969854 33
32

12 076098 (J8:^936
12-033970! 0833865
11 992137 J0836794
11-950595 10839723

1 1 909340
1 1868370
11-827683
11-787274

11-747141

11 707282

11-667693
11628372
11-589316
11550O-23
11-511990
11473713

Sfcant. C'otan.

0842653
0^45583
0848512
0it51412
0854372
0857302

0860233
0863163
08(;6(V' i
08690-^5
0871956
0874887

1 2 383768 1 003255 1 0032445
12 3390-28 1 003-2787
12 294609 10033024
12 250505 10033*261
12 206716 10033500
12163-236 1 0033740

234
234

0032679 %^

0032915: ;;:J!: 9967085

0033151 !;^;!9966849

0033:^8 o^!' 19966612! 19
238 jg

9969628
9969401 31
9969173 30

9968946 29
9968716 28
99G8486 27
9968254,26
9968022 25
9967789 24

996756623
9967321 22
21
20

0033626 ^jjj9966374

12120002 l-0033980i003:V865lojo 9066135
12 077192, 10034-221 ;0034105;o,!! 9965R95il6

17

1 1 908682, 1-O0:i5195,0035071

11 867282 1003344010035316
11 0*26167, 10035687 00:«560

11 785333' 1-0035934
11744779,10036182
11-7045W 110036431
11 6(i4<H>5 10036681

11 624761! 1-003^1932
11-585294 10037183
11 546093! 10037436
11507154 10037689

00:^805
0036052
0036299
0036547

0036796
0037046
0037296
0037548
1 J 468 174 1 1 (K)37943 0037800

ll4:i(K)52

Tan jr.

KMKM] 198 0038053

Coscc. Covers

244

245
246
*247
247
248
249

250
250
252
252
253

9964929

II

10

9

9964686
9964440
9964196
99(vK)48
9963701
9963463! 6

8

7

D.

9963*204

996-2954 =

9962704

9962452

9962200

9961947

Sine.

4
3
2
1

85 Ue^.

4 Deg-.

LOG. 81N£S, &C.

277

1

2
3

4
A
6

7

8

'J

10

11

12

13
14

15
16

17
18

19
21)
SI
22
23
24

25
2«

27
28
2U
30

SI
32
3:i
34
Xp
36

37
38
3!)
40
41
42

43
44
4h
40
47
48

Sine. iDifi:

H-84;i5n4:)i

J18t)20

8'84f'i')874 > I <^nf>u

8 84710-27 i";;;

a84«f)707l '2S.5
8 8o07r>i2;Jirx:'

8a-i42005i ZV''"
•i/j88

8-85e04J)3!,,-,-

8'8678010 ;• ji

Cosec.

I

88o!»457!

I737«

8 8612833:,-^.,.
8-8C30130; 4?!^-
8 8647376' jjfj;;

88664545L-,„,
8-868 1 G46 }:",!
8-86f>8680|;/,5^

16835

88732546
»874936l jg-jj^lj

8-876G150!,g.^,^
8-8782ft^4 2«:j

8 87JW493' «?:*;;.!

8-8«lC0«!)i p^JSl
8 883-2581 ,7., in

8 88854 18;, !>«.>,
8-88817431 2.>«4:
88898007' Sn^l

889:«)3ol,^J|

»f^«3;|S)22
8lb62465!,™»
8-«97H418|}-;j7
»-8!WI322' I' ";.

80<Hoir;«ii?";;*

«<io-25f).v,! ^;'L*7

80041685- '•

111584155
1M548120
11- 1528173

II 1510293
11*141)2488
1 11 474755

III 457095

11 1439507

II 1421990

III 404543

11-13»71«7
lM3h'98(;i
11 l:i52G24

111835455
11 1318354
1M:{01320
111 284354
11-1267454
11 1250619

Versed s.

7'38()(;683
7'39()-2785
739:W73rj
73974539
7*401 01 98
74046708
7-4O8IO7I

74118293
7-4151372

Tanrr. JDilf.

.1

8 8446137
88484554
88482597
88500568
88518481
8-8538283
88554034

88571713
88589321

7 4186311 8880G859
7 4221109 88824327

7-4-255787
7-4290288

74324««73
7-4358921
7-4393035
7-4427015
74480862
7 4494578

1 11-233850, 7-4528183
11 l217U8i74561619
11 I20O6O7
11 1183931

88641725
88859055

I8II7
18043
17969
17895
17822
17751
17679

17608
175:i8
17468
17398
17330
17262

Clotancf.

17194

17127
1 7061

J

88676317
88693511
88710638

8 87'27899i;;.x«;

88744894 ^.1^^'j^

8 8761823! i;;:^^:;

88778487
88795286

7-4628146
11 1167419 7 4661219

7 4594046 8 8812022

1 11 150989

11 1134582
111118-257
11*1101993
111085791

88828694
88845:i03
8-8861850

4R
60
61
52
53
54

55
56

57
58
59
60

80057358
8-9072075
80088535
8-OI040:UI
89119487
8-9134881

j^91502l9
80l(;5504
8*91fm734
89I!KV)11
8 02II0:i4
69226105

8-02411-23
60256089

151,73

15617

15560

15504,

15448

15394

153:i8i

152/)5
15-230

151771

15123,
15071'
15018

74694168

7 4726989 888783;U
7-4759688 8 8894757
7-4792-264 8 8911119
7-4824719 8-89-27420
1 1 1069649 7*4857052 8 8943660
11-1053567|7 4889265 88950842

1 1 1037545 7 4921359!88975963
1 1- 10215«2!7 4953335 18 899'2026
1 1-1005678 7-4985193|89(K)80:i0
1 1 0989832 7-50169:W « 9()231>77
110974045 7oOI8;V;0l890398t>6,,. p..,
11 0958315 7 5080071 8-9()55697l,;|S-5

1 1 094-2642 751 1 14fi8;8 907U72| , . «, „
11 0927025 7 514-2751 18-9087190!, *'.!:
11 09I1465 7 51739-23|89IO-2853 t^**

16799
1673<i
16672
16609

16547
16484

16423
16362
1(1301
16-240
16182
16121

16063

16004

15947

'. 15889

11-1553583
11-1535446
11*1517403
11-14994:^
111481539

111463717
111445966

11-1428287
11-1410679
11-1393141
11- 1375673
11-1358-275
11-1340945

11-13-23683
111306489
111 -28936*2
11-1272.301
11 1255306
ll-12:i8377

111-221513
11-1-204714
11-1187978
11-1171306
ll-ll54r;97
1 11 138150

Covers.

I
I

14986'

8-»27l003iH^li!
8-02&i866i J,7;;

8-9300678. 1!:;.:

603154391 jj'j I

iT:!?!!?!!::!' 14513

60:188498 ]"'•
69402960;****'^

Cosiiif. ; DitK

1 1 0895961 7'5204982'891 18460
1 1 0880513 7 5235931 i89i:U0I2
1 1 0865119.7 526676989149509

1 1 0819781 75297498 89164952
1 10834496,7 53-281 19 89180340
1 1 08l92f;6!7 5:r»8632:8 9195675
1 1-0804M89 7 5:<89038;8 9210957
1 1 0788966 7 5419338'8 9226186
110773895 7 5449532|8 9241363

1 1 07588777 5479621 H 9256487
1 1 074391 1 i7 5509607 89-271560
11 0728907 75539489 8 9286581
1 10714134 7 5569268 8 9301552

110699322 75598946
11-0684561 75628522

1 1 066*985ol75657998
II 06551897 5687373
110640578!7-571<'650
I I0<;-260I 7 75745828
11-061 1504,7 5774iM)8

1 1-0597040
St»c:iiit.

89316471
89331 :U0

89346160
8-936lH)29
89375650
89390321
89404944:

15607
15552

15497
15443

15388
15335
15282
152-29

15177
15124

15073
15021
14971
14919
14869
148-20

7580:i4191 89419518

14769
14721
1 16*71
1 4623
14574

Covers. I Cotana*.

Dilf.

11 1121666
11-1105243
111088881
11 107*2580
Il-I056:i40
11 1040158

II 1024037 9

III 007974 9
110991970 9
1109760-23 9

11 o.%'oi:m 9

1 1 0944303 9

110928528 9
11-0912810 9
11-0897147
11-0881540
11 0865988 9
11-0850491 9

9-9685967
9-9684612
9-9683256
9-9681901
99680544
99(i79188
0-9677831!

9 9676474
9 9675116
9 9673758
9-9<»723!)9
9SKJ71041
09669681

Secant.

10 0010592
10 0010681
100010770
100010859
100010948
160011038
100011129

10 0011-220
100011311
10 0011402
10 (N) 11494
10 0011586
100011679

D.

Cosine.

09668322
9-l>666961
9 9665(M)1:

100011772
10 0011865
1O0011J>59
9 <KJ64-240; 100012053
9-966-2879' 100012147
99661517 IO0012242

9 9660155
9-9658703
996574:iO
99656067
09654703
09653339

09651974
9 9850610
09649*2441
9 9647879;
9 9646513
09645146'

100012337
100012433
16001-2529
10001-26*25
10-001-27*22
10-0012810

10 001-2916
100013014
100013112
10 0013210
l(h0(»13309
100013409

9643779 10
.964-2412 10
9641044 10
!M,*:J9676 10
9638308 10
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89
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89
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91
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91
91
92
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94
94
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11-358070 1-003871
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9-96d5967
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10(M)10502
100010(;81
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11-1410670
111:103141

17608
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16

15

14

13

12

U
10

!l

8

7

6

6
4
3

T

8.) Deo.

280

6 Deg.

NATURAL SINES, &C.

Tab. 9.

I

2
3
4
5
6

7
8

10
II
12

Sine. IDif.

1045285
1048178
1051070

2803
'J892
2893

Covers

8954715
8951822
8948930

10539C3;"":',8948037
1066856;^Sooi«->-1^144

1059748
1062641

I2892i

13
14

2893

2892

1065533 «„,vn 8934467
I (uiRAoa. '*'**'^ : HiVA I A7r»

8940252
8937359

Cosec. I Tang"

1068425

2893

8931575

1071318 ;r"i 8928082
10742lUo«j)2|8925790

2892
2891

1077102
1079994

1082885
1085777

15 1088669

16 1001560
17! 1094452
18.1097343

19 1100234

20 1103126
21' 1106017
22)1108908
23 11117.99
241 11 14689

25; 11 17500
26' 1120471

27 11233*;i

28 1126252
29.1129142

8922898
8920006

8917115
8914223
8911331
8!K>8440
8905548

30l 11 32032

31 1134922
32' 1 137812

33 1140702

34 1143592

35 1146482
3611149372

37 1152261

38 1155151
39' 1158040
40' 1 160929
41,lUr3818
42 1168707

43,1160^
44'll7Jlb5

45 1175374

46 1178263

47 1181151

48 1184040

49 1186928

50 1189816

51 1192704

52 1195593

53 1198481

54 1201368

55 1204256'

56 1207144
5711210031
58! 1212919

2892
2892
2891
2892

-JJy'J 8902657

!8899766
8896874
8893983
8891092
8888201
88{t5311

9-5W»7722
95403686
95141110
948799<t4
9 4620296
9-4362033
9-4105184

2892
2891
2891
2891
2890
2891

oon, 8882420
oftun «879529

o«^>873748
^"^"'8870858
8867968

8865078
8862188
8859298
8856408
8853518
8850628

2890
2890

2890
2890
2890
2890
2890
2889

2890
2889
2889
2889
288!)
2889

2889
2889
2889
2mm
2889
2888

8847739
8844849
8841960
8839071
8836182
8833293

8830404
8827515
8824626
8821737
8818849
i88159r>0

o„„« 8813072
-""8810184
•' 89i«"''729«

;""•'' 8804407
^^**^ 8801519
8798632

2887
2888

59
60

12158U6
1218693

Coaiiie

2888
2887
2888
2887
2887

Dif.

8795744
8792.J56
87^9969
8787081
8784194
8781307

tfts.

93849738
93595682
9-3343006
9 3091699
9-2841749
9 2593145

9 2345877
9 2099934
9 1855305
9*1611980
9 1369949
9 1129200

90889725
90651512
9 0414553
9 0178837
89944:^4
8 9711095

8 9479051
8 9248211
8-9018567
8 8790109
88562828
8 8336715

8 8111761
87887957
87665295
8-7443766
87223361
8 7004071

8 6785889
86568805
86:^V2812
8-6137901
85924065
8 5711295

85499584
852WJ923
8 o07I»304
8 4870721
84603165
8 4456629

8 4251105
8-4046586
8384:^065
83640534
83438986
8 3238415

8 3038812

8 2840171
8-2642485
8 2445748
82249952
82055090

1051042
1053983
1056925
1059866
1062808
1065750
1068692

1071634
1074576
1077619
1080462
108340^
lt)86348

1089291
I0f)2234
1095178
1098122
1101066
1104010

1106955
1 109899
1112844
1 1 15789
lllf^34
1121680

Cotang.

9-5143645
94878149
9 461 4 116
9^4351531
9^4090384
9-3830663
9-3572355

93315450

Secant, i Vers.

D.

305

1-0055083 0054781
10055391 0055086 ,4^
1 0055699 0055591 i^.

1 0056009 0055697
10056319 0056004
1-005663110056312
1-0056943'005(S621

Cosine'

307
308
309
,:109

10057256.0056930
9^3059936' 1 0057570 0057240
9^2805802 l-0(»57885, 0057552

S>;M521960
9944914-59
9944609I58
!liM4303,o7
9943996 5fi
994:i688j5S
1>943379,54

310

994307053
""'9942760 52
, !;.l>»42448i5l

994213(ii50

^!:: 994 1823149
JJ? 9941510,48

92553035 1 0058200, 00578(M
9^2301627 1 00585 1 7 '0058 177
92051564 1 0058834'0058490 ^J

9-1802838^ 1 0059153 0058805
9 I5554:i(;! 1-0059472;0059120 .*:;:^ 9940880
9 1309348' 1 00/.9792I0059437 :!j;;994a663
9 10645(>4 1 (H)60113|0959754 ^{.'^'9940246
9 0821074; 10060435i006lM)72 «}5;i9939928
9l»578867, 1 0060757|<>06(»390 ^^^19939610142

9941195 47
40
45
44
43

9 03.379:« 1 0061081 •OO6O7IO «^, ;90.'{9-290 41
9 0098261 roO6l4O5!0O61031 l]^ -!)9:i8969,40
8 98598431 1 0061731 i«H»(!1352 V.f,,,\*J*J'6mi8 39
8 962266811 006*2057'006]674 ?,%' 9938326=38
8 9386726; 1006-2384'0061J»97 iT? 9938003137

i:

3-24

1124625
1127571
1130517
1133463
1136410
1139356

1142303
1145250
1148197
1151144
1154092
1157039

89152009|10062712:0(»6232I i.": 9!l37679'38

8 8918505: 1 0063040 0«)62645 «oij 993735536
8-8686-20611 O063370'0O6-2971 l^^! 9937029 'S4

8 845510311006:
8 8225186' 100640:
8 7996446; 100643fM!

8-7768874 I-0064697I0064-281 33|ji993d7l9j30

87542461
87317198

1 00(h'%031 1006461 1 VII !993o389,20
1 0065366j0064942,5. 1 J9935058'2H

8 709:^077 l(M)65702l006d273.»L;!9934727r-?
8 687OO88 1 006603910065605 o|^v!»934395!20

Ot)66376|0065938 »«; 19934062.25

0066714 0066272 o«t [9933728 24

8-66482*23
86427475

1159987 8 6207833 1-0067054 0066607 33«'99:i3393 23
1162936 8 5989-290;! 0(»67:^94i0066!M3 ^^^^j 9933057! 22

1165884
l]688:i2
1171781
1174730

Secant.

85771838 1 00677:^5 i0067279 .^.,7
8 5555468 1 ()06«W77'0(Ki7616 'joA
8 5:^40172 1 00684 1 9 0067955 l^n
8 5125943 I 0068763 0068294 «.,«

1177679 8-4912772 10069108.0068633 3^j

1 189478:8 4070515 1 0070494 0070001 -m.
119-2428!8:i862519 1 0070843 0070345 j^^g

9932721 |2I
9932384120
99320451 19
9931700118

I

9931367 17
92)31026 16
99:i(H;85|l5
!>930:{42 14
99*29999113
9929655'I2

1207182 8 2837579 1 097-*601 0072078 .^0-9927922 7
1210133 8 2635547 1 0072955 0072427 a^y J»9-27573| 6

12I30R5
12160:W
1218988
1-221.041
1-2-24893
1-2-27846

Cotan.

8i8:i704i 1 oo74:i80 007:i8:ii

8 16:J9786 1-(M»747:*9 m'J^UiV'.^-'
8 I44:i464 l-JM»7if(»!>8'O0745:«j

Tan^. i Cosec. .Covej*.»| 1).

9927224

9926873;

99*2652 li

9926169

99-25816

9!»25462

Sine.

5
4
3
2
1

83 DofT. I

e D.T^

iMKiitaia

V02S8U4

<M)2H7'>-t2

9IKI2JAII7
»-0334Xld

( IM>35;4U7
I B0361S5II
t IH0UIM77

LOG SINES, &C.

V-044nili<li I

laBH07t>d4
I0'[I7UAMS
ll>'!)7f06SJ
ln-97717«
IOS7fiBIH3
l(IH747B7S
IDDTMISS

I0-0724331
1«

7 73mi3u:.
y;* 10376

7' 74341180
7'74SH3I9
7'748aiai

7-7AOad!if
77S2S'7«
77afiUlD
77677031

9-047 laSH
»1UJI37'KI
»0494IW.i

»0al(!J54

!Hin4!r<ai
»0A71713

!fO«46IIJ7

rawseiu
t Mesoann
I ;HteuiuT4
( V«7<)I70I
r »07ia42i
I iHt72:t»6a
I »0733eO3

»U77a83S
" 1310

l»071M)7<)3
i »0807ti
I Bi)SI7SW

r >-oi»7f c(i

t »iwfi»l7
I 9-o8tse4:

*[! H)Bftft!H;

^..,„7-7B241)«

I uiW77'i:t3 77047409

1000651811 r7li10»*3

i»'»Sfi4i7B iieonsn
UKteiasiiSi? 7717371

1UII«31043 7-7740641

iosKiar,33\Ti7«aa4a

IO!)COKa34|77786tiIH!

lUtU!HU70 7-7inD6ss
100M5148 7'78S!607
IU837376I 7'7a6ft47:i

iiitooimuM-mBno

I»U5A1MC,7'7»0I(I2U
10W139739 7-7!«3706

iaU6iiiie-J|77lHKPl

1011517314 770C8007
IB6llflW«77«ll406

..ib4imhu<i7>'<)i:»ia:>

l094S3U4li 7ai3«34«

io»i;^jU 7 si>6»asu

100461412 7(lt)WB96
10-0450.13.1 7BI03079
I0043U2II4 71126837
IO'942e277 7B147345
lftlM17J89 7'al<»39J

iao4ueiau 7 biuissb

in^WJSOWe 7 8213334
1^9384401 '7B235306
i»9373814 7B26703i
10-lt3627US|7»27«r~-
10-836 1 043 7B300I
10-0341148 70123 —
IO833O3alj78343704
1 n-flSl 0640,7 R3e.>34B
10 1t:<0802U;7 1306851

Tnntr.
8-0-iilU^
309:2 B33H
irU24U44l

unasuio

&a-JB4S48
fr0270A62
!1 0-288534
ff0»ia484
0313373
9032434a
»U33li093
9-II3470O6
9U350681J

»0383160
!I'03!»4B48

»04412!ia
ftri452H36
1^0484343

10028707917 A421'69a
10S27tm45!7 8461037

lo^anHiaan 7'»4;23!7

10 0266740
t01|-i463nl
10'Bf3487l

lfl»l!l3Bll
10 111 (134 1
ltl-!a73IIH.
JU'»1(I16R3
1IKUI6I357
lll-tlUHViS

7'8a770!KI
7'BG08!lRO

78(il»'J10
7'8(M<)7SU
TBtHIItilR
ZHtiSiXn
7-87U3l3ti
78733806

KecBiit. Cover*.

0^0510078

~>3I 438

9 0332771

0614074

U 06(18685
9 0577813
9'0J8»003
90600164
9-061 1 SU7
9'06334ai
00633482
9 0644633
»06S6666

0-0877632
O06H8483
0-0090381

9-o7ios;n

U7I 1 133

9073 i»e»

0-0743779
90763663
90764321
0-0776063
907B67SU
0-0706441
9 08(17086

3-08l77afl

9-0828331

!)-087UA01
1I88UU81
O-nWIU.'lB

lO 0733798
10-H77I882

1007£

10fl7474»l
10-8736452
10-8723448
l»87 11476
1OBR0R63G
101MI87K27
■-9675761
IIMW039O7

9-9620518
8^9619111
8-961771
-9516307
-9514902
8-0613497
9-9613092

9-9510686
9-U509280
9-8507874

' 06064(1 7

12
10-062S561

oiffiieaii

100806163
10 9603494
I0B681I -
10-0570208
10 8668701
10-9647164
10-9336657
10 0694179
109612730
l»a6013)|
1O8480932
0-0478661
11^04 07329
10-84SS02U
10 8444051
10 943340&
0-0422187
09410998
10S399836
10 8388703
10 9377607
10-S36(;S18

1»83S6467
109344444
108333447
10 9323478
1 831 1636
9:iU0U19
00SI10730
I002788(J7
-0268031
10B28792I
10[t2464U7
19 823667!)
10 8324047
10-0214240
10-0303660
10 0183904
0<01R-^J74
08171608
100161089
109150334
10 9140004
1 00120490
1O9I10OII
109108662

9-9603G52

g-a'i02243

8-9500636

9 9480430

fr94860l

9-04DH«07

90406196

9U41»6S1
90488139
9 0486726

9483486
»H481071
9-9479666
9-047824:
(►0476825
0476408
98473993
0^8473676
0-9471169
994ffi)74l
08468.193

9^9401226
90469806
9 94683(15

99463690
90461273
084411860
0-0448426
90447001
9U446S77
9-9444161
9-0442728
9-9441:100
0-943087i
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0^943701
8943flS8

0O023il67
1000-23889
1Q-U024123
mn024267
IOO02430I
100024536
100024660
lfr0034796
1000249:11
1OO02AO67
1U0023303
1 0002634(1
10 0026477
lfr0O3Sni4

0036762
10 0036890
10 1)02602»
mo02K167
100026307
100026446
10-0026506
10-0026737

— leaoo

lD^M)2700g
1 00027 150
IOD027393
100027434
■ 0097577
10-0027720
100027683
10O02U0U7

RISl

100028441

100026586

IOO02B733

10-0026878

100029024

1000-20171

IO0028318

100098466

100028613

100028701

10-0020910

10003006)1

IOOII3O208

100030358

100030508

lOOO

100030800

D. CoHine. '

TT 90076143 60
!2f 9^9976011 69
?* 99976877 66
?* !»9B76f«3 67
,^ 9 9876B09 66
1^ 9^9876475 66
[^ 90875310 M
,^99076205 63
:??fr 9976069 63
Jil? 9-9974933 .11
*J 9-8974797 60
,1' 3 8974000 49
!^^ 99974623 46
,,„999743B6 47
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?? 9-0974110 46
™ 00873971 44
, j„ 9-8973833 43
J^ 9 0973693 42
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!:"!^y9734l4 40
J J 9973273 3D
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[* lt91(72MI 87
1^380972860 36
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Ij^99979.->B0 34
[I' 00979423 S3
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[j"i!H)071268
jlj^ 11-8871 1 ■-•■'

10-0031112
100031364
100031416
100031663
100031723
1OO03IS76
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10-0032183
10 0039338

10 0(

9403

147

,.,8 8970076
jil8 0870H-a
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V907O:t87 19
110^8970230 '■
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|:8986!I!I41

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;9-g908643

190968403

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,|90D(i9101

:°' 90968(140 10

!„9006808a 9

!"l9096ft736 8

\" 90068584 7

!°^'90968431 6

,.„;9006n97B 6

?Jo09«Bm 4

■'O886707I 3

"*'99967817 2

;i?9-00670«9 I

'"'J 9 9967507

D. I Sine.

•39 i,
14 36
"" 96
34

iwuo 17

!I!I41 16

NATUBAL SINES, &e.

D I'iima „,
I IJ-JISRI ^

3 122U68 g|
9 122735ft J

4 IS.W34I *'

5 1133138;!

6 1236015 ^

7 1238mi ,

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D 124407* "

12475(10 *^

1 12504 (« '^

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3 12B0318 „,

4 1259104^
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6 1204875 ^

7 1287761 ?^

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1286071*

4 1287858 ^
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17 139(ieOU -
8 lS»!MiH Z

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a 13.11213 t

13340i;6;

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3 1338863

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I. Covers Cosec.

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" 6778419 a-
' 8776633 8-

' H772046 8'

, B7na7ao b-
' a7G(i87a e-

' 8783986 8

122784C

7 1230708
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8 1330705
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, 8781099
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„ 8743783
"8740898
I 8738010
» 8735126
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* 8789304

80716081 IS
80639062 IS
80342331 IS
8-OI6«4aO)lS
70971 44S; 12
7-9787208 IS
79604003
0421558
7'923»050
79050179
7'8B79-;38
7-8700 1 20

ISG

128

1272181

I27S117

1278073

■1348071
'1053600
0860043
0667304
■0475847
80384790
80094835
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14 705:10334
19 7')'343758
~ 9158161
7-8073396
787«tM89
7-8000433
7-8434191
7-8343790

, Secant. | Vers. I
I 0076098 0074538 ~
1-0075459 0074893*
1-0075830 0075249^
1 O0781B3 0075608 i,
1-0078545 0075963^;
1-0079008 007II!I2 1 .'
1-0077373 0076681 ^
1-0077039 0077041 -.
1-00711006 IW77W1 Z
1-0078372 0077703 X,
1 0078741 007U138 T,
1-0079110 0078489 r^
1-OO79480 0078863 |J
1-O079861 D079SI8 ^
1-0080232 U0795B4 %.
10080595 0079951 %.

ooaatiH?

. 9U3546-J A
! 0925107 M
I 9924751161
9S34394l5i

11343 0(

" 8730698 7 8167050
™ B717814'7-790I778
^ 8714929,7-7alG(ttl7
|;|a712O4477«42JO0
,,18709159 77*68001
^ B706373 7-720OI76!
™iB703391 7-7124227;
^18700506 ,7-6053047
2| 8697822 7-67828311
T 8694738 7-6612078:.
,,18601854 '76444075
^ 8GR8970 7-627B023
~|86BGna7 7 6106518
^!8I;B3303 7-5041849
"8080310 7-5775910
~8r.77 436 7-5810713
„l8674653 7-5446238
"8671670 7-5282478
~86BB7S7|7-5I10437
~ 88650047*057108
~ 8603021 ]7-4705483
^8880138 7-1634660
,_l8057356 74*7*336

™I8(J54373T "

™l 8851491 7-* 155B69
~|Be4UKO8|7-390770B
„ 8845728 73840318
^ 8642844 [73683512
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Ul 8837081
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,: 8628436
j^ 8625665
„ 8023073 7-
:J 8619793 7-
, 8016911 '
" 8814030 7

138103a|7-8063312|l DOSI7I8 0081056
10083094 0081428
1-0082471 008I796;.„,,
1-0082849 00821681^^
10083228 00825411"
1 00B3607 O0B2O14|

1 383986 '7-7883453'
1388943' 7-7703506
1389900177536366
1292858 7-7*10038'
12!)5ai6 7-7171486:
1298773 7-6'J0573a
1301 731 17-6820769'
1304690 7-1^8465841
1307648 76J73I741
1310607 7-6300633'
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284 8 Deg.

NATURAL SrNES^ &C.

Tab. 9.

1

2
3
4
6
6

7
8
9
10
11
12

Sine.

1891731
1394U12
1397492
1400372
1403252
1400132
1409012

1411892

Dif.

2881

2880
2880
2880
2880
2880

Covers

8008269
8005388
ooS! 8002608
8599028
8590746
8593808
8590988

Cosec.

71852J05
71704650

Tanp.

1405408
1408375

Cotang.

8588108

1414772:^552 8585228

141705lj;"'^'8682349

^^^^ 8579409

1420531
1423410 ^^^^
1420289

13 1429108!

2879
2879

2879

8570590
8573711

8570832

71550704 1411342
7 1409687 1414308
71203019 1417270
7-1117059 1420243
Of>71700 1423211

70820941 1420179
70082777 1429147
70539206 1432116
7 0390220 1435084
7 0263820 1438053
70112001 1441022

7-1163097
7-1003820
70864673
70705934
7-0567905

Secant Vers.

10098276i0097319
10098089{ 0097725
10099103;0098131
10099618:0098638
1-0099934 009^945
0099364'

D.

7 0410482 10100361
70203002 10100709

09970700 1443991
14| 1432047 Jo4o «507963: 9830092 1440901
16 1434920 ;°;^ 1 8605074 jo 9089994 1449931
ie|l437806„o:Xi85e2195 09550404 1452901

17 1440084

18 1443502

19
20
21

1440440
1449319
1462197

28791
2878
2878

23
24

26
20

27
28

29
30

31

2879

2878

2878

2878 ___

1400830^8^18539170

22; 1465076

1467953

8559310!0 941 1490 1466872
8550438:09273089 1458842

6 9135239' 1401813

8553600
8550081
8547803

70117441
0!>971800
9820781
9082335
09538473
09395192

0-9252489
9110359
08908799
8827807
08087378
8647608

08408190

10101187
1

0099703
0100174

406
400
407
407
409
409
411

411

Cosine

9902081

OD

0101007j0100686.JJ2

9902276169
9901869 68
9901462:67!
9901066,601

10102027 0100997:

413

10102449 0101410;.,^
10102871!0101823***

10103294 0102238

416

415
10103718,0102663.' ,-
10104l430103009 ::S

10104668,0103480

417

090064666
990023754

9899826163
989941 6 J53
9899003|6I
989fr>9u!60

9898177 49
9897762 48

8997942 1404784J0 8-209437
0-8801196 1407750 8131227

8544925 8724995 1470727

8542047

8589338 1473099
84542*22 1470072

07993505
7856440
7919807

1403708
1460585
1409403

8530292
^77185334,5

1472340 l^l

1475217
1478094

2877
2877
2877

0-8319642 1479044 7583820
08185597 14820170 7448318
8062082 1485590,0 7313341
852700010 7919095 14«050:J 71 78891
8524783 778()032 1491530 7044900

8530537

1480971. „p„
3211483848;";/

33: 1 480724 ;:j;iU

34| 1489001
35: 1 492477

8621900;07054091
851902910 752:^208

I OI04995'0103904li}2
10I05422'0104323*;;;

10106851 0104742!J2!J

1-0100280 0105162\.oo
1 0100710 0106584 *"^

1010714l|oiO(i'000^.^

425

1 0108875;0107702kor
1 0109310 0108128,!l:

0108566|:5*
0108983 '^

1 0109747
10110184

8507523

2877
2876

30 1495353 ,^222 8504047

1 2077 1

l498-230!^o.,.!8o01770
1501100

1494510!0 0<)11502

1497484'C 0778077
851015210 73923001 1500458 0040307
8513270'67201905 1503433 0514449
8510309 07132079 1500408,0 0383100

37
38
3911503981

7002fi99 1509383 0252258
60873822 1512358 00121919

42 1512008

43 1515484
44,1518359
4511521234
40| 1524109

00745440
8498804 0017508
8490019 60490184
00303293
00230890
601 10973

2870
2875

40| l50C857|^«Z^i8493]l43

4 1 i 1 509733 ;°' '; 18400207

-«72|8487392

^ 1 84845 1 : (;-5985540

.7H7^ 8481041 10 5800587

4-o„Z;.8478700!0-5730112

-.,.^-,..,9 ^„';?i8475891 05012113

47;i5209H4i„„i'J 84730K> 05488580

8470142 5:{65d28

8407207

48

49
50
51
52
53
54

55

1529858-2W

532733'

153

65242938
5120812

57
58

59
00

15:«007i?JZf 8404393
1538482|;^(;J!8401518'0 4999148
15413501 ,„;;';«458044 04877944
1544230 ;"'] 8455770 4757195
^"'■* 8452890 64030901

1547104

1549978
1552851
1555725
1558598
1501472
1504345

Cosine

2874

2873
2874
2873
2874
2873

8450022
8447149
8444276
8441402
84:i8528
8435055

Dif.

Vcis.

0-4517059
04397000
0-4278719
4100210
64042154
3924532

Secant.

1 5 153:{3 6 5992080
151 8309' 65802739
1521285'65733892
1524262 65005538
1527238 05477072
1530215 05350293

1533192 5223390
1530170:65090981
1539147 4971043
154212504845581
1545103 4720591
1548082 4590070

155100110 4472017
1554040|6-4:U8428
1557019,0-4225301
1559998 4102033
160'2978|0-.3980422
1505958 63858005

10110022
I 01 11001

10111501
1-0111942

0109412
0109841

0110272
0110703

1-0112384:01 11 1:{6
101l2827i01 11508
101132700112002
0113715

I508939;o:<737359
1571919,0 :i(;i0502
1 5749(m 63490092
1577881!63;i70120
1580IU>3 3250001

1583844 3137515

'

Coti;n.| Tanjf,

1

10114100
10114000
10115054
10115502
1-0115951
10110400

10110851
1 Oil 7303
1-0117755
10118-209
10118(M>3
10119118

10119575
10120032
1012a489
10120948
10121408
10121809

10122330
10122793
10123250
10123720
101-24185
10124051

Cosec.

01 12430

0112872
0ll3:i03
0113745

429
429
431

431
432
433
434
434
430

9897347 47
9896931 46
9896614 46
9896096:44
0896677 43
9896268!4S

D894838;41
9894416:40
9893994 39
9893673!38
9893148-37
9892723:36

989229835
9891872 34
9891446133
9891017 '32
9890588,31
9890I59|30

9889728 '29
9889297 128
9888866 27
9888432j36
9887998125
9887664 '24

9887128123
98<i6692!22

0114022
0115001

0115502
0115943
0116385
0116828
0117272
OII77I6

0118162
0118608
0119055
0119603
0119962
0120401

0120862
0121303
0121766
0122-208
0122662
0123117

Covers

436

4^3 9886265 21

'"""^—"20

19

^4l|9884939jl8

44.9884498:17
9884067:16
9883616 15

0114183 :^"|988d817

442
443
444
444
446

446
447
448
449
449
451

461
462
463
464
455

D.

9883172
9882728
9882284

14
13

IS

9881838 II
9881392 10
9880946 9
9880497 8
9880048 7
9879699 6

9879148

9878697
9878246
9877792
9877338
9876883

Sine.

6

4
3
S
1

^1

SI Dpp.

8D.-K

LOG SINES, Sic.

1 »■ 1444932

s t-usaisa

2 9-1482435
A frl«l3S8

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7 rifssoiB
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a B-|al5()»4
4 HSUhfn
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4 Haaoiii
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7 »l58MIVi
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B g-lflOMKU
n SIGUOSO
:l 916203114
3 9'1628fl93
9 U 1637434

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t » 1663074
7 S 16713(10

a 9-n;aooiii

IU-II5GI447 7 91
Ifrfl5S54IHI|7-91
l(MU4«>5n7 7S910947
10 m:i756.^ 7-8936020
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Ill-Hal 97311.7 91171653
iaiUIWI3a'7!K<B»713

i(iflani3B3»ooo7n37

lUH4!i:il»0,8'<HI233<a
,,,,,, 10«4M4;M)B.UU<M307B
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9-1705103
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o-i7as»u5;j5i;

lH730(iIIU,- -
0-173307;

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B I7U7B4
» 170411 J
91772436
9 1700(21
917KKNI1
917S7XC5

B B-iao»i2

91813744
01BJ19UU
91830160
91638344
9l846fil3

043li

B313

8247

9ia62R0-J
^1670023
9-IB7&03!!

9i687120[^^
«-1927343l»l7.

Coficc- Verseilf

10ll4(IUti9U H007UII!>I

lU'B4S7tti4'i;00lMIllU

m-U44!)i6c onii37i<;

10-DI404*^a6UI3l2r;7
10H4317U4 S0I48B>!
lU-84:f3UIH)B0WH13L'l
10 8414314 UaiU37tU<
ll>B4Ulitf4a B02U|->13
lOBSOCnOS 8-02IBni)7
l<^a3Btl3Ml BOJSii'JtM
10-0.17:1746 S02S32HII
llhB371147 B-lli7'»J7M
10 BMIJAGU 8 0287B3.1
10-8354011-3 Br

I0 83454S6 8 032223S
10 83mi2n 8033!I3»1
IOB3:.>a4U BOSAOaOH
IDS319Ul9IIO:i73a:)2

10U3IU41 8 0311064:
I0-B3U^>'J79BU407(>3I
10 e-ja4:>35 6-0424642
ID B31Hil07 8-044139^1

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13034634 6

: 00034181 3

!h0033369 9

; 99933737 1

99033616

80 Deg.

NATURAL SINES,
L'otHiig.

., fl2JS160

L, B3M7742
;^B23*B7B

~ 8Z3»4a7
^B320WU
B 88177112
" B2l41Mn

.„ BBnSltl

,, 8l»t!

: Biaooin

'.] GISIi2»l
|!Hltt33«6

ffl335 aSiO BI77C4a
«ai6l5u«nBI7*785

18079^8171933
10835 SS^i HIOWMIB

Cospc. ] Tanp.

.V76a77i>a l7'Kl27t>

i4 a 74iMeiiM7Ufl2(m

IS (r73U8:i-'i3 I7G9389
5'73MI3lll7722(»

sTSloaa 1775870
;i 1069111778270

6-70233'iO 17S1371
5 C!)30R93 1784273

5tiU377:t* 1787S74
ey^B-iso 17S027«

6-eGSU:i31 I7S327S
SC5(tlS84 I79G3BI
5K470N0 17UU284

'(i.178S9Ii 1802287
5{i-i6aiie 1805291
SGIU753a 1808295

'010T34a 1811209
56017386 I8I43US
55H277I9 1817308
S'G83d343 1820313
5-ST40258 1823310

51160400 1820334

•5571S5I 11

'54S3726 1832337

'5300786 1835343
S-63081S9
5 5220764
fr5l3

-504S843

4060306

'487 4043

Secant. Vers. D. Cosioel

1811358
18443GS
1847373

-ejiaviBi

5B6IU509I
5G530S18;

64248:18
363294741
S 623443 1 1

'6139680

a'6D45347.

19511311

56857303

576:1786
'5670574
5-5577063
S54H005S
53037 4U
53007:i4

'4Q3S604
3*484dUa4i

a*47e47BB:

a'4G648l2
a'4S79l31
6-44857 IG
S'4306fi93
G'43077aa
6' 4210188
S'4130»06
6 40439U1
m 6'39dai73

BIS7827
„ M134768

^ Bisison

n 6140(161
'" B1461H2
„ 6143334

44 1)163383 S™

45 1665240 a^H

40 1668090 SHsh'
47 1670950 ^« I
4tl 1873813 ^J I

49 1B76070 aasH '

50 1879628 ^"
611882385^

.02 I88B241 ^

S4 IBJOINUS

' Cob

20187
8123330
BI20472
Bl 17615
8114760
11111902
8160040
.8108169 5
" 8103333
~. B 1 00477
^ 8097621

;r, W1M780

"' 8001910

5 4768056

4709343
5-4610001
5 4531731
5-4446831
112 199
5'4S7783.1

4103737
5' 4 109003
54020333

3943028
63SS0070
6-3777109

361M6C4
53612303
5-3530370

3446630
5-3367114
53285861
5 33II4B60
S-3124109 li
63043606 1!
6'jlOCi:i54 1!
e':8S3347 I!

1065438
18GB4!t8
1871440
1874460
1077471
1880483
1883405
1886507
1680630
1892533
1695546
I ■196559
1061573
1 904587
1007602
1910617

63520636
53434527
S'33486aG
3263131
317783(1
S 3IIH2703

'264470HIIU3474H
6 2565718 1937760
5 S486!t79 1940764

■2408431 liM386 3

Secant. I Cutsn.

S-27 55266

- -171517

0-2588036
53W48(I
5-3421 B!
6-23301iei
5-2J.ibti47
ft 2174436
S2U024S9
'3019736
3 1929204
1S4B03S
i;«706l
1686311
3 1C058I3
51526561

0154366 :0 1519221
'OI54787|0162428 *
'0156310 0162034 ~
0165833 0153442 %
0166357 0163650 %
1-0166882 0164468 ^
1'0I5740B'0164968 °
10la7934|oie6470'.
1-0166462 0156000 ?
1-0166991 101606113°
Hli59620 0157016°
1-01611066 0167620°
1 01CU6tt2 013B044 ^
10101114 6138350'
10161047 0139076 °
1010:1181 0139593°
10162716 0160111 °
10163263 0160630°;
10163789^0161150^;
10104337 6ieiB7o',!
10164865 11162102°;
10169405 6162714°:
10165046 0183337',:

10166487 0103701 r:

10167039 01 G4Ua3^
10167573 0164811 .,
0168117,0166337°;
10168663 0163864°:
10169306,0160392°:
10ie0756|0l66!l31 °:
I 0170303 0107461 °:
1 0I70B51 0167981 ..
101714010108613^
10171958 0160045 1:
I 0172503|0I6U678 t
101 73636 0170112°:
1'nl73609 0170647 J
I'fll74163 0171182 „
10174719 0171718?
1-0176276 0172266°:
1017383210172704 ^
l'017('3B0 0173333 T,
1 0176949 0173072 ^
10177609 0174413,,

i'Oi7nofi9 0174954 .

I 01 78631 0176406 ^
1-0170194 01760%) <,

. 01766635,

017J187 0.

0177673 ,.

1788191.
0178766 .,
0179314?;
0170B83ji,
0180413^

9847373 61
9847066 6S
984«55S.37
0S4G06A|K
0IU5342 6a
9tt45032lU

1-0100887
1-6181463
1-0182020
1-0182688
1018!
10183738
10184398
10184870
10186443
■0186017
I'OlMSOr

e 1-0187107

UIBl
0102067 1
01112620 f.
0IB3174I'
0183728

ms^_

Conec. Cover» 1

51

0843498
9843985
S84S471
9841956
9841141 17
9R4aD34 ~
9646407
9839Blt9
9830370
»83lia5«U>
9BS8330 41
9837608 41

0837rad:a

9836i3&|37
IIB3671SM
9835189

0833019
1431497

OBStutt

&6S0I3I ;

BB103B7 *

9619037 5

0H1848A 4

9817033 3

9817380 1

9tll0B3a 1

0816372 J

Sin*. '

10 Deg.

LOG. SINES, &C.

289

Sine.

2^2403861

9-2411007
0-2418141
9-2425264
9-2432374
9-2439472

9-2446558
9 2453l>32
9-2460695
9^2467746
9-2474784
!^248181l

Dif.

3 9-2488827
9249583^1
9-2502822
9^2509803
9-2616772
9-2523729

9^530675
>] 9 2537609
9-2544532
9-255U44
92558344
9-2565-233

» 9-25721 10

93578977
9-2585832
1^2592670
9-2599509
9-260^330

9-2613141
^2619941
9-2026729
9-2633507
9-2640274
9-2647039

9-2IM775
9-26605U9
l|9^2667233
>|9*2673945

9-2680U47
92687338

9^2694019
9-2700689
9-2707348

S|»27139!)7
92720635
9-2727263

»2733880
9^2740487
927470H3
92753660
S|9276<»24d
92766811

I

7159
7146
7134
7123
7I1U
7090
7086

7074
7063
7001
70:i8
7027
7016

7003
699-2
6981
6969
6957
694G

6934
6923
691-2
6900
6889
6877

6867
6855
6844
6833
6821
6811

6800
6788
6778

«767
6756
6745

6734
6723
6713
670*2
6691
6681

6670
6659
6649
6638
6628

r;6i7

Cosec.

107603298
10^7596139
10-7588993
1^7581859
107574736
107567026
10^7560528

Verseds.

6607
6596
6586
6576
6566
6555

9^2786445
»2792!I70
l{»27»9484
i 92805988

i

iS^

me.

6514
6504

8 1816*2-20
8 1830648
81845051
81859431
8-1873786
8 1888118
8 1902426

10-7553442 8
10 7546368 8
10-7539305
107532*254:8
1075252168

Dif.

107518189

1^7511173
1^7504170!

10-7497 17«
107490197:
107483228

107476*271

10 7469325
10 7462391
107455468
10-7448556
10 7441656
10^7434767

1&7427890
107421023
107414168
107407324
1^7400491
107393670

10^7386859
107380059
1(^737327I
1&7366493
ia73.»9726
107352970

10-7346225
107339491
107332768
10732(U)55
107319353
10731-2662

10 7305981*
107299311
10 72926,v2
10 7286003
10 7279365
107272737

8

1916710

1930971
1945208
1959421
1973611

1987778

Tuiljr.

Dif.

8 2001921
8 2016042
82030139
82044213
820582fM
82072293

82086298
82100-281
8-2114-241
8-2128179
8 214-2094
82155987

8-2169857
8 2183705
8 2197531
8-2211334
8 22*25116
82238875

8 2*252613
0-22663*29
82280023
8 2293695
8*2:W7345
82320974

82334581
8 2:i48l67
8 2361732
8 2375-275
8-2388797
8*2402*297

8-2415777
824*29235
8 2442073
8 2456089
82409485
8 2482860

10 7266120' 8
10-72595138
107252917 8
10-7246331 8
10723:1755 8
10 7233189 8

107-2266.34
10 7220009
107213555
107207030
107200516
10-7194012

Secant.

•2496214
2509547
2522860
2536152
2549424
2562675

82575906
8 25H9117
8-2602307
8 2615477
820'28627
8 2641757

Covers.

9*2463188
92470569
92477939
92485*297
92492643
92499978
92507301

92514612
9*2521912
9^*2529*200

9 2536477
92543743

9*2550997

92558240
9*25f»5472
9*2572692
9 2579901
92587099
92594285

9-2601461
9*2608625
9-2615779
9*26*2-2921
926:^0053
9*2637173

92644283
9 2651382
92658470
9 2665547
9267*2613
9-2679669

9-2686714
92693749
92700772
92707786
9-2714788
9-2721700

92728762
927:i5733
9 274*2694
9 2749644
9-2766584
9 276:1514

92770434
92777343
9 2784242
9-2791131
92798009
92804878

92811736
9-2818585
928254-23
9 2832-251
92839070
9 2845878

92852677
92859466
9 2806245
9*2873014
92879773
928865-23

7381
7370

7:i58

7346
7335
7323
7311

7300
7288

7277
726(i
7254
7243

7232
7220
7209
7198
7186
7176

7164
7154
7142
7132
7120
7110

7099
7088

7077
7066
7056
7045

7035
70-23
7014
7002
6992
6-982

6971
6961
6950
(;940
6930
6920

6909
6899
6889
6878
0869
6858

6849
6838
6828
6810
6808
6799

6789
6779
6769
6759
6750

Clolanjj.

Cotang.

Dif.

10-7536812
10*7529431
10 7522061
107514703
107507357
10-7500022
10 7492699

1^7485388
IO7478O88
107470^100
10 7463523
107456-257
107449003

1 0744 1760
107434528,
10 7427308,
10 74-21)099
107412901;
10 74057 15|

107398539
107391375'
10 7384221 1
10-73770791

10 7309947!

10 736-28-27

10^7355717
10 7348618*
10-7341530
107334453
1073-27387
107320331

107313286
107306251
10 7*299228
107292214
107285212
10 7278220

10 7271238
10-7204267
10 7257306
107250356
107243416
10 7236486

10-7229566

10 7*2226.-»7
10 7215758
10 7208869
107201991
lO-71fi51*22

107188264
107181415

107174577
IO7I67749
10 7160930
10 7154122

10 7147323
10 71405:W
10713:^755
10 7126986
1071*20*2*27
10-7113477

Tan-

Covers.

9 9171650
9-9170144
99168638
99167131
9 9165624

99164117
9 916*2609

99161100
9-9159591
9 9158082
9 9156572
99155062
9-915:^51

99152040
991505*28
99149016
9^9147504
9 9145991
9-9144478

99142964

99141450'

9-9139935,

99138420

99136904

9-9135388

9 9133872
9913-2355
9 9130837
991-29319
9-91*27801
9 9126282

99124763
9^9123244
9-91217*23
991-20-203|
9 9118682
99II7I6I

9 9115639
99114116
9^9112593
9-9111070
9-9109547
9 9108022

9 9106498
99104973
99103447
99101921
99100395
99098868

9 9097341
9 9095813
9 9094285
9^9092756
990912-27
9-9089697

99088167
9 9086637
9-9085106
99083575
99082043
9 9080510

Secant.

Verseds.

10 0066485
10^0066708
10-0066932
100067155
100007:179
10-0067604
10 0067829

100068054
10 0068280
10006850(i
10 0068732
10-0068959
10-0069186

100069413
10 0069641
10(K)69869
100070098
1000703*27
1O0070556

10 0070786

100071016
100071-247
100071478
100071709
10^0071941

100072173
10-0072405
10007'26:)8
10^0072871
100073105
100073339

100073573
100073808
100074043
10-0074278
10 0074514
10^0074750

100074987
10 0075224
100075461
10 0075699
1 00075937
10-0076176

10 0076415
100076654
1O0076894
1000771:^

10 0077374

1^0077615

10 0077856
100078098
10 0078:^40
10 0078582
100078825
IOOO79O68

10 007931 1

100079555
100079799
10 0080044
10-0080289
10 0080534

Cosec.

D^

223
224
223
224
2*25
225
225

226
226
226
227
227
227

Cosine.

99933515
999:13292
99933068
9^9932845
9^993-2621
9-9932396
9-9932171

9^9931946
99931720
9-9931404
99931268
.99931041
9-9930814

228
228
2-29

^;i!i 9-9929673

230

60
59
58

57
56
55
54

53
52
51
50
49
48

9 9930587 47
9 9930359 46
9 9930131 45
9-9929902' 44
43
9 99-29444 42

««.l99929214
^^"99928984
,^:;} 99928753
;^ 999-285*22
oXii9^9928*291

232

232
233
233<
234

99928059

99927827
9-9927595
99927362
99927129
19 99*26895

41
40
30
38

37
36

234!
234

235
235
235

5^>99925486
23^ 9 9925250

9-9926661

99926427
99926192

99925957
99925722

237
237
238
238
239
239

239
240
240
240
241
241

242
242
242
243
243
243

244
244
245
215
245

99925013
9-99-24776
99924539
9 99-24301
99924063
99923824

9992:^585
99923:^46
9-9923106
99922866
999-22626
9-99-22385

9 9922144
9 9921902
9 9921660
99921418
9 9921 175
99920932

i) 99*20689
9 9920445
999-20201
99919956
9^9919711
99919466

D.

35
34
33
32
31
30

29
28

27
26
25
24

23
22
21
20
19
18

17
16
15
14
13
12

11

10

9

8

7

6

5
4

3
o

I

Sine.

79 Ueff.

u

! 290

1 1 Deg.

NATURAL SINES, &C.

Tab. 9.

1

2
3

4
5
C

7
8

9

10

11

12

13
U
15
16

17
10

bine.

19
20
21
22
23
24

25

l!M>8090
1910945
1913801
191C856
1919510
1922365
1925220

1928074
1930928
193:^82

Dif.

2855
2856
2855
2854
2855
2855
2854

Covers

1936(;36,,

1939490!

2854
2854
2854
2854

1942344

2854
2853

8091910
8089055
8086199
8083:M4
80804rf0
8077635

Cosec. I Tans:. Colanjr.

5 2408431
5-2330121
52252050
52174216
5-2096618
52019254

8074780 51942125

8071926 5 1866228
8069072,5 1788583
8066218 5 1712128
8063364 5 1635924

Secant. Vers.

I0187167i0l8:i728
1018774310184284
10188:^21 0184840
10188899l0185397
10189478;0185955

1943803 5 1445540
1946822 5 1365763
1949841 5 1286224
1952861 5 1206921
1955881 5 1127855
1958901
1961922

1964943
1967964
1970986
197400815 065835211 0192973;0I89320

D.

556

Cosine

9816272 60
9815716.59

^^^19815160 58
558

5 104902411 019005910186614 '??2
50970426 10190640 0187073:^1

6-0892061 10191222 01 87634 Lp,
50813928 10191805 0188195'^^
5 073(»025'l 0192389 0188757 ^^

564
564

8060510 5 1559948I97703I!5 0580907 1 0193559 0189884
8057656 dl484]99: 1980053' 5 0503690 I 0194 146|0 190448:^

981460357
9814045 56
9813486 55
9812927:54

9813366 53
9811&05'52
9811243 51
9810680 50
9810116 49
9809552 48

1953756|;"""j

iaA«#mo.*o^^l804339i!5 1l08«35J1995172'60120984!l0197093j0193284;™
t^% 8040539 5 1034431-1998197, 5004511i;i 0197686:0193853;™

1956609
1959461

2852
2852
2852
2852

2853
1962314
1965166
1968018
1970870
1973722 ZZI
1976573 ?«?^

1979425l„«-,
26 1982276 ook!
2711985127 nj?
20 1967978 ^2?*

1990029 ^^^

1993679

8037686

S7l

980898647
9808420 Hi
9807853 45
9807285 44
9806716 43
9806147:42

29
30

31

I
2860
2851

1996530

2850
2850

32 19U9380

33

34 2005080 ^,._ .

.•15 2007930 ;^I:

'^ 2010779 ^^2
2013629'
20164

86 5 0960248 2001222 4 096945911 0198279 0194424' ., 9805576 41
34 50886284J2004248 4 .90040271 10 198873:01 94995 e^Al 9805005 40
82:5 0012539 2007274'4 9018013 1 01994680195567 ?;f 9804433 39

8034H34

8031982:5 0012539 2007274

802913015 0739012 2010300 4 9743817

8026278
8023427

8020575
80 I 7724
8014873

50665701 2013327 4 9669037
5 0692606 2016354 4 9594474

5 0519726 201938r4f»620125
50447060 2022409 4 9445990

5 0374(K)7 2025437,4 9372068
8012022 5 0302367 2028465! 4 9298358

8009171
8006321

8003470
8000620

36

37
38
39
40
41
42

2002230 ;«"^'7997770

7992070
7989221

7986371

2849

5 0230337 203 1494 1 4 92:?48d9
5 0158517,203452314 9151570

5-008l)'907'2037652 4 9078491
5 0015505 2040582 4 9005620
4 9944811 2043612:4 893295(

10199468 0195567^;: J
I0200064|0196l40?;,'l

574

9803860!38

1 0200661 01967U ^'"9803266 37
1 0201259:0197288 ^i^ 9802712,38

10201858 0197864'e7|.'9802136 33
1-0202457,0198440 ^i!:;980l560 34
10203058 0199017 g:^l9800983 33

1 0203660,0199595 .-^
l-0204262'0200173?i2
10204866|0200753 r^

9800405 32
9799827SI
9799247130

9703667|29
9798086 28

20193:

1 0205470,0201333' p,
) 1 0206075 0201914 ^"i
ill 0206682 0202496 ?«f 1 9797504 '27
4 9873323 2046643 4 8860499|l 0207289 0203079 r„j|979eS921 26'
4 9002541 2049674'4-8780248 10207«!*7.0203663 i^:'9VJ6'S%t.5ti
4-9731964 2052705i4 8716201 1020850G 0204248 ^^979575224,

4 9661691 '2055737'4 8644350 1 020911 6 0204833 .«« 19795167 23!
478 $0^1117903522 4-959 1421, 2050769 1 4 8572719 1 0209727 1 02054 19 ^J!!: 9794 58 1.22 i
327 ;o,;;'7900673 4-9521453 2061801,4 0501282 I 0210339,0206006 "J' 9793994:21

20491

2022176 284a!7i>77024

2025024

2049

2027873 --^

43 2030721 'oojo

44 2033569 oC]^

45 2036418 «2l7

46 2039265 ^^ii

47 2042113;°;^°
48:2044961 ^^j"

49l2047808Lo_,,
•-" 2050655 o„j'

20535025":;

2056340 'nHTi

2069195 oflin
2062042 ^^7

60
51
52
63
54

56
66

57
58
69
60

2064888
2067734
2O7O68O
2073426
2070272
2079117

Conine

2846
2846
2846
2846
2846

Dir.

7974976
7972127

7069279
7966431
7963.-i82
7960736
7957887
7955039

7952192
7949345
7946498
7943651
7940805
7937968

7935112
7932266
7992420
7926574
7923728
7920883

Vers.

4 9451WJ7 20648344 8430045! 10210952;0206594 ™
4 9382120 2067067i4 8359010 1021 1566 0207182 i^

4-9312754 2070900 4-8288174

4-9243586 2073034 4 8217536
4 9174616 2076968 4 8147096
4-9106844 200(KM)3 40076854
4-9037267 2083038 4-000»;800
4-8968886 200607314 7936957
4-8900700 2089109 4 7067300

4 8832707 2092145 4 7797837
4 8764907 209518114 7728568
4-8697299 2090218 4 7'>594 90
4 0629003 2101265:4 7590603
4-856'2657 2l04293'4-752l9O7
4 8496621 2107331 4 7453401

1-0212100:0207772

^^^9793406 2f»
9792818, 19

590
590

4-8428774 2110369
4 8362114 2113407
4-8295043 211(5446
4-8229357 21 19406
4 8163258 2122525
4 8097343 2125566

Secant. ICotan.

4-7385083
4-7316954
47249012
47181256
4 7113686
47046301

Tang.

9792228 18

o-ji-.i7Jiii w.suzKiCiX-Qi 9791638 17
02134l3i0-208953 JJU 9791047' 16

9790455; 15

1 0212796 0208362

1

1 0214M30;0209645

592i
593

102146490210138 r;:;;; 9789862 14
102152680210732 ?:!: 9789268 13

10732
10215888 0211326

10216510 0211921
10217132 0212517

694
595

596

I 0217755:02131 14|52J!9786886

1 0218379 0213712
1-0219004:0214311

10219630

1-0220267
10220085
10221614
10222144
10222774
1-0223406

Cosec.

0214910
02165101

■598
599
599
600

9789268
9788674:12

9788079' 11
9787483' 10
9
8

7
6

9786288
9785689
9786090

g^. 9784490
02161111^; 9783889
0216713|S^- 9783287
0217316j^;9782684
0917090 ^19782080

0217920
0218524

Covers

604

9781478

6
4
3
2
1

D. Sine, i'

78 Deg.

II Peg.

'I Sine. iDir.l Cn>.ge. VtrMttl-

"ofraawttwl^^ iii;ii)-ioi^>H-2fiii7J
I »«Bia4«3j™'; iii7ia;ji;Mw-ifl«-

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O. Sine, i '

:i

2i)2 12 Deg-

NATURAL SINES, &C.

Tab. y.

1

2
3
4

5
6

7
8

a

10

II

12

13
U
15
Ui

17
18

19
20
21
22
23
24

25
26

27

20
29
30

31
32
33
34
:^5
30*

37
38
39
40
41
42

43

44
45
4(i

47

4U

49
50
51
52
53
54

55
56

57

68
59
60

Sine.

2079117
2081962
2084807
2087652

2090497
202)3341
2096186

2099030
2101874
2104718
2107561
2110405
2113248

2116091
2118934

2121777
2124619
2127462
2130304

2133146
2135988
2138829
2141671
2144512
2147353

2150194
,2153035
2155876
2I587I6
2161556
2164396

Dil.

2845
2845

Covers! ('osec. | Taii^. ' Cntanpf.

7920883 4 8097343 2125566 47046301
7918038 4 80316132128606 4 6979100

;"^"!7915193 4 7966066 2131647 4 6912083
,„J;i79l2348 4 7900702 2134688 4 6845248
1>uj'79095(»3 4 78:i5520 21377:W'4 6778595
ooiil7906659 4 7770519'2140772;4 6712124

Secant.

2845
2844

2844
2843

2843

10223406
10224039
10224672
10225307
10225942
10226578
7903814 4*7705699 21 438 14' 4-6645832 1 0*227216

1 0227^4
10*228493
I 02*29133
10229774
10*230416
1 0231059

„„. ,17900970 4 7641058 2146857 4 6579721
ooi"! 7898120 4 7576596 2149900 4 6513788
7895282 4-7512312 2152944 4 6448034

SrtJj 7892439 4 7448206 2155988.4 6382457
9Hj^ 7889595 4 7384277 2169032'4 6317056
fr,t 7886752 4-73-20524 216*20774 «251832

Vers.

o«ii 78S3909 4 7256945 2165122 4 6186783
ou'Jq 78810W 4 7193542 2168167,4 6121908

2843
2842

78782*23 4-7130313 2171213 4 6057207
SIu? 7875381 4 7067256 2174259 4 5992680
9«Io 7872538 4 7004372 2177306 4 69*28325
.Iq^o 7869696 4 6941660 2 180353' 4 5864141,

9nAo'7866854 4 6879119 2183400,4 58001*29
!:«:7 7864012 4 6816748 2186448 4

*2841
2842
2841
2841!:

5730287

7H61171 4 6754548i2]89496 4 5672015

7858329 4 6692516 2192544 4 56091 11,

7855488 4 6630652,2195593 4 5545776

2^JI786*2647 4 65689562198643 4-5482608

9ftji 178498064 6507427'2201692'4 5419608
ooli 17840965 4 6446064 2204742 4 5356773
i7844l24 4 6384867:2207793 4 5294105
7841284 4 6323836,2210844 4 6231601
7838444 4 626*29(i7 i 22 1 3895 4 5 1 6926 1
7835604 4 6202263'2216947 4 5107086

2841
2840
2840
2840
2840

2840
2839
2839
2839

7832764 4*6141722.2219999 4 5045072
7829924 4-6081343 2223051 44983*221
7827085 4 6021126 2*2*26104 4 4921532
7824246 4 5961070'2229157 4 4860(HM
7821407 4*5901174 2232211,4 4798636
7810508 4 5841439 2235265 4 47374*28

2167236
2170076
2172915
2175754
^2178593^
2l614J-2y.^j^

2184271 „„..„ 78157*29'4 5781862 2-238319 4 4676379
2I87IIO ^";:;; 78I289O 4 572*2444'*2'241374 4-4615489
;2I89948;; ::"i7810052 4 5663 183 1*22444*29 4-4554756
!2l9-2786!,^":!!|7807214!4-5604080 2*247485'^
21956241,^;:^" 7804376 4 5545 1 34 225054 1 4 4433762
2198462 -;;:,., 7801538 4-5486344;*2253597 4 4373500

7798700 4 5427709'2256654 4 4313392
7795063 4-5:if;9229 225971 1 ,4 4*253439
77930-26'4 5310903'2-262769 4 4193641
771J01 89 4-5252730 2-265827 4 4133996
7787352 4 5194711 2268885 4 4074504
4 5136844 2271944 4 4015164

10231703
10232348
10232994
10233641
1 0234288
1 0*234937

10235587
10236237
1-0236889
10237641
10238196
10238849

10*239604
1-0240161
10240818
10241476
10242135
10242793

10243456
1-0244118
10*244781
10245445
10*246110
10246776

2201300

2838
2037

2*204137, -
2206974^^7

*2-2098ll '^"**'

2212648
2215485

2218321
2*221158
22*23991
2226830
'2229666
|223*2501

2235337
2*238172

2837
2837
2836

10247442
10*248110
10248779
1 0249448
10250119

02185*24
0219129
0219735
0220342
0220960
0221568
02*22168

0222778
0*223389
0224001
0224613
02*25*227
0226841

0226456
0227072
0227689
0228307
0228925
0229644

0230164
0*230785

0231407
0232030
0232653
0233277

0233902
0234628
0235155
0236782
02364 U
0*237040

0237670
0238301
0238932
0239565
0*240198
0240»32

D.

Cosine

g 9781476
SS. 9780871 59

607

9780*265

^^ 9706098 35
^.j? 9765472, 34

^gj97642l8

0*241467
0242103
0242740

0243377

0-244015

1025079010244655

10-251463
10252136
10*252811

0245294
0245935
0*246577

2837

7784515
7781679

1 0-253486,0*2472l9
10254l62i0*247862
10254839 0-248506

4-5079120 2275003 4 3955977

oiiir 7778842 4 5021565 2278063 4 3896940
*•"•*' 777600(J 4 4964152;2*281123!4 3838054

2836 m^m.t I »»

9fl./v7770334
2836P7«7499

10*255518
10256197
10*256877

4-4906889 '2284184 4 3779317
4-4849775 -2287244 4 3720731
4 4792810 2*2903061 4 3662*293:

0249151
0249797
0250444

10*257558 0*251091
10*258*240|0251739
10258923,0252388

::,.';77618-28|4 4679324 2*2964*29'4 3545861

•2249511

' !C()s

iiie

7750489

4 4735993*2*293367 4 3604003 1 0259607 1 0253038

10260292 0253689
10ie;0978 0*254340
1 026 16r>5 0-254992
1 026*2:552 10255645
I 0*2f;:i041 0256*299

610
610

611

^' 977fi658
^""^9779060
'^'*'9778442
9777832

9777222

«J2:W6611
gl5 9775!)99

614
614
615

60 i

r
58

67
56
55
64

53
52
61

616

617
618

9776387 60

9774773

9774159

49
48

47

619
620

9773544

9772928 46
45
44
43
42

9772311

^Iq 9771693

9771073
9770456

nqx 9769836 41
gi> 9769215 40
l:,^ 9768593' 39
«oH 9767970 38
024»767347[S7

625

9766723! 36

629
630

631
631

9764845' 33
32
31
30

9763589
9762960

9762330

976169d
^^ 9761068
,.^i97<i0435
^;9759802 25
.-^9759168124

O.f.l Vers.

4-4454115*2308682

St'caiil. Colaii.

43314759

(
6*35

636
637
637
6:i8
640
639

641
(^12
642
643
644
645

646
647
647
648
649
650

651
651
652
653
654

29
28

27
26

9758533 23
9757897

Tanir. I Cosec. Covers

9757*260 21
975(i623 20
9755985 19
9756345 18

97547O6' 17
9754065' 16
9753423J 15
975*2781 1 14
97521381 13
9751494' 12

9750849,11
9750*203 Ifl
9749556! 9
974890!) 8
9748*261' 7
97476I2! 6

9746962 5

9746311 4

9745660 3

9745008 2

9744355 I

9743701

D.

Sine.

77 Deff

2'J4 la Deff.

natuhat. sines, &c.

S8UI79

sssaois

2SeiHM8

22731 Tit
227H13
2277844
2280077

lit

111 £IIIUI.VI I;

ujeaiisiy-

*( .2ai4flJB ;

:aii74;a i

4 i*!S!«i7i
3u[S3W4h|;^,

.tu' sswiioiS;
■M ■JS4.17fiU !S:

sB'sBnai:™-;

3; ^3.14248
wi i:«7ii7-''

Co«ec. Tang. Cotiing.

1 •JSti-JTHf

.38;;, i,

III

77iM4H'J
77476M
7744811

7741887
77981U
7736320

7733487
773l>f;M

j7-.i7Bai

7734DB8

77i2ltc
771932S
7711491
7713669
77l)U2ll,
77<'7»liu
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77<t233i'
7li9ilSU3

' maim

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: iiiiiiiitj

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' 7fll 748(1

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tl33l4ail
4*42ea731,S317lliG
'4-J3ISS4ls3Z0!Ml
'417^839 ^324007
'41 20C37 233707s
-4IK>SS5e 33.tOI4(
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3901168,2339343
3846Kt8 2S4341U
4 3782367 334A479
4 3738niS 3348S4S
'3C839I0 S3filHI7
3fHin43 33S4887
4 3»76113 23I77S8
4'3e22nit

43357347
4-330007^
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4'2n 131903
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4'S7470AG
4'3«gl{t73
4^835318
42570501
2A23033
■liliMBS
id4l3l77
,'23»100(*

Secant. Vprs.

Mrju:i04l
1031137:11

1-U2IU42I
I-03G3113
1-0285806

1-0387I1M

036O9fi4
0257110
D2S8266

4-3^08081 £)0!KM) 4 23U->977
4 U1S43C Kthra?! 4-^2tmm
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27847.16 34D3BG4'4'15{)96»5
4'3733U29 34V(!t>42,4'tMe501,
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4-S3274;4 3419205 4-I33S046
4-347(;402'3433334 '4'IS83490
4-342.'i457 242J4t4 4'lS30fl7!l
4 3374637 3438104.4 1 177784
4-23Sl!l4» 2431575 411^614
4-3373373 2434h56'4'lo;3M9
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4'3l334ltS 24431102 4-0918178
4-i:07233.-| 2448iHt4 40888627
- KM»4'08lnl98

1 0369983 03G3884'
1 (hiTOeSI 0963547
10271381036421
1 0273083 0Sei»T6
10273786 0265541
1 0273488 038G207
I 0274103 0-20C«75
10274897 0267542
10275803 036831'
1'027'ntlO 026888
It);if701U 0360591

io2J7rJ7iK7lW3s;

10278437 0270303 .
1'0STII148 U27I56B f
l'l)270II60 0272241 J
I 0S80.'>T3 0273018.
10281287 0273591 Z
i'tl21l2<HJ3 0274-267 f
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4 t!)2284a^245(l23«'4 07127117
4- 1873352' 243!l3Sn'4-n(H;iB43
41823785 24ll24ll.->'4-lriillt;iHI
4-1774438 2485401 '4-85591(77

41725210 2468977:4'

4-16T0P0-'-.'47l'i'f3 4'
4'IVJ7H4 ;n:i7J".4

0384871 0276980'.,
0265500 0-277661 ,t
02683110278342^
'0287833 0270034 ^
0287766 0-270708 u,
l'0288478'02b0390 ^
0380303,02811)74 „
'02fl9a2» O2H1780 "
l'02!HI8a6 0283448
1'02!I13U3 0263133
1'0-J921II 0283830
lilS9-iB40 0384509
|-0-29357llo3S.Vl!l8
l-0S!l4n02'028.'>SB8
1-02»5034;0286679
- >«7271
|-0-J»6riU2 0287864
10;a(7337D-288657
I-O307!t73 0289351
I-G20li711 OS90IM7
l'l>S)944a 0-290742

4M0 •8,0311 4U
1^130011280282137
1-0301669 0292835

I75IMS90
7.WJU73

7.^in-24n'

7588426,
7.-|83UD4

^^a■2^^.l■■l^llH■:^ll■2\^■n-•l}^u6

'4-13B3!):Kl'24IHnfl) 40187S70;
4-1 335«iW.24^(32Wl4«l07^

I'll3024ll|021>3534
I 03)131 64 0294-2:14
l'l):Ut.-||l[IU,0294935
l'»3iM643'02n5C37
HI305389'03IKi33!>
l'fl30(tl3C'0297043

9743701 flO

™»74SM«M

^il>74SSeO 56

™lB74lt*4 57

- '9741077,66

»74Mlt'' 56

9739788 54

9739100 53

»73A43g 33

0737778 5

19737116 M

|D738453 49

^19736780 48

g_.!»;35124'47
'^l97S445!» 48
[9733793 46
[9733135 44
,.j 97324M 43
^9731788 42
«J973HH4I
K74'9730449 40
T, 97*9777 W
Z IT2fllUd 38
3 97211432 37
J:»7277M 36
.(in37084 35
,.'9726409 34
. It7a57:» 33
„ 11726056 X
2 11724378 31 !
° 9723698 30
, 9733020 39 I
! 97S2339 SH I
I 9731&)ff 27
; It72fl!l70 26
J 9720394 a
^9719810 21 I
n U7 189-38 2S I
H 0718240 SS (
SS|87'7WM 21 I
Si 9716867 20 :
™' 97161110 19 i
,'971MU1 18 I
«J9714802 17;
^,,,f7l4ll2 16
™.',971312I U
""V'"-"'*' 14
9712830 13
||U7II343 M
.WliVMO 11
''97099.13 I«
^-19709218 9
:S:.'.|9708361
9707863 7
9707165 6
a7l>846G .
!i;057«6
9705005 :
9704303
970:)6«l

704;:;

Isi-t-iiiit, jfiitiiti.! 'I'uiijf. I CohOt:. H'l

■J!U7

7() IVff.

LOG. SINES. &:

9 Jfi jniHH)
t w-SsMSju

S It 3U?2S4
4»3U'j;tO
E»-3MRI3«

no-sat;! 130

to 93a7-~>i4l

iiaauoer,
It o-asawu;

uaasotrjei
13 S'Jsmioj
IS ff-auTfiifi
l7tf3>llSS7D
l8 9-3aiB:i7

SI 0-3631319
*S f)'36393:i!)
EI»3flMS3l
84 B3BM1S8

SH 9-387131.1
t9 9-387G3a7
SOHSettlSM

3S»3IKI7BnB

a4a370M«i

Sa 9-3708979
S(]B-37l33a4
37 9-37IR3Zt
34 9-3783735
U,fl3;il»40
4S,»373«I39
4l|lh3}il0381
t!ff3744J17

44»a7U>i68
4>»37lia(Kt4
41 B-RlSAIiH

TTIiDS

Mini

W»3|BI

«,w7«ir67„,.

11 B-37INI<il)4 ? -

«l9SBI»IlV)>li L
Wjl»-38U«3:i7!y
«,»38113."W' .
mUHB33 I
ma-aaaififOfl.

W9MW7M

D>r.

Cos ec.
11)- (14711 1:2

10 lillWltlU
IIHM(U736

iD'e4»72»<i

10-644099318-4164741
10-W»S6;4l8-4I7S7W
1<l-a4»»l64!8-41Baa-J(l

1061'.>47IHt
0(t41Wlffil
10-U413973

107044
8'430flfiB3
»4319fiUB

Tung.

0-31133041
l>-36394(l)
9-304SI6fi
93651)001
9-3G96U41
U-3SI>!374
»3668I00
93Q73SI9
9-3U7im3
9-SnB.<)23B

a-amoitsj

, \&r,Sit7IHIi\B-*2ril2Dt
' 10-e3a24S3'«-4au3073
l063«713»:A4a73»iB
lo-ioawsi »4!84770
loe37fU42»4ZauiMI
10(07110884300414
10 63637RI '04317216
'0(l36l>461 »l3280a4
10<K).'>nl48,a433877R
0-0349843 8 43195311

10-6344543 4360380
1003:t9i50 B-4371()M
I0-C:i33»04 8-43RI74a
IO63J80&'>ft43!)3447
in-&')33413 0-44(13141
100318147 4413021
10 6312:18964124480
106307637 8-4435142
IO03n£3n2 84443783
t0«297l^ 8 44604)0
106291921 84467IH4
106286806 8 4477035
IOR-2314;;i8-418B3l:
76205, 8-44111 r70R
IO-0271(>f]0| ff45lffl330
IOII26.i8Gl.fl4S1!INf
"IMKiH9|«'4:i3ll4:
lDG2U483fl4^4<i:<.-

iaii25n304 a4.i5ni
fa4.'ii33;a45Gi:ji

I06339'H;g 8-4573440
1 0^33 jmN!' tUMsaw

l0 632UnB»U^4603;<7H

10'H2245D7|a-4Ull3(f34
Ifl..:' i:::.:

-37U331S
37O7D04
0-3713667

0-3734 90S
3730645
9^3736301
3741830
9-3747563
»375H1»0
03758810
9^3764433
93770030
9-377sn3l
937B132S
9 3700813
9-3702354
9'37»79f9
038U3537

g-.teooinv

Ittfl 4655
9^383031)5
»882A74e
9-3831805
9 38368IV

to (tioitjfn

lOfilOHfVl
1001 "
I Ih 0170177
100173399
10'(ilU831U
10 01fl.W4B

d-ll»i6233
8-467rh'i90
a-4600[t35

n 4n:i7j«7

8-47l"75«7
4717604
ff 47201 1"

C..lH...r.
10-83(HJ350
iOIKVIthVJH
I0-6354H5
IO-e340<l9»
I0«343359
ln-fi'33762R ItSKR.'UU.
10 6331900 9868375-
10 6336181 9-888316!
10 6330460; 9-800057 1
10 631 4763' 9-8878076
10«301«W3U«8773H6
liri»0337 119 8875793
10'62U7'>8:»>f"I74199
lOG->9200(t'9-887260.'i
IOU28l»33'9-H87191U
10636nW7i9886»4l5
IO-63;3008 9-8867819
106209355'»8B'h;3£I
106263709 9-H664637

1062*8070!>-
10-6353437 988GI4331I1:
16-634«810l9-8H59K34ilC
106341 190-9-8858236' 11;
10633»ii77;98n5»(>37jl(
l0633B970,9'8n55038;l(
10-6334369' 9-8853130' IC
10-112 18775.0 68511)37, IC
1063131 67'!1 88311336 IC
106207606 9-BH4INi3a I(
IOi>2tl203l|fM«t47033 It
l06IfHU63.]l-SlM543i;i(
IO-RI909in'9-Rll43ft>8! ][
|IHI1U5345{9'HR43226 U
IO«1797l»'9-884iHI31.U
10r.l743.-i3 9-ni3IIO171l
10-KI6U71S 9-BS37JI3 1(
10 0183164 O-803MO71(
10 6157ff6o'!)-S834302 K
100152143 9-KU335IH),K
»-6»3!)ll89'l(
U-882il302 U
0-8037775 l(

0-8R34AAr'I(
D-8822JI4U K
0-88-ii:i40 1<'
BBl!l7:iO l(
08R18119K
U-8816308 l<
9'ft8l4R!l7<ir
D-SaiajKJ-K
6-»ll1673 1(
0-RRllhHn U

I. I Cnsiii.

"19-08872:1.. ™

"9ltR8S947:ri9

",9-9BII66.W;fi8

, '*;«08l!n363'57

I *~'»98»0070|56

' "10960377656

jJ^iO 9885468. 64

' 199885108' 63

^:9<9H848.'>4.62

™'9-9«8489!)!61

r!.';9J)«84303.'»

Hi: U-9UH4008 40

;^":9»883712 48

8-81101986 II
H8003T3. ll
»-R7007iHI, II
0-8767l4Q| ll

-_ B-M743S9 I
J2ff0874031 li
™9 9«737J3 '■

I i!!i;l^!lo;i54!l| n|

I *4^ 990712361 7
Pi ^[^;fr9870924l «

II " "J9-n870«ll! 31
i Ij j'o-0B7«l2!»Hi 4!

296 14 Deg

NATURAL SINES, &C.

Tab. 9.

1

2
3
4
5
6

7
8

9
10
11
12

Sine.

2419219
2422041
2424863
2427(>85

2430507
2433329
243GI50

2438971
2441792
2444613
2447433
2450254
2453074

13 2455894

14 2458713

15 2461533

16 2464352

17 12467171
18!2469990

19J2472809
20 12476627

21 12478445

22 12481263
23:2484081

24 2486809

25 2489716

26 2492533

27 2495350

28 2498167

29 2500984

30 2503800

31 2506616

32 2509432

33 2512248

34 12515063

35 12517879

36

2520694

37 2523508

38 2526323

39 2529137

40 2531952
41 '2534766
42 j 2537579

43 ! 2540393

44 12543206

45 2546019

46

47
48

49
50
51
52
53
54

55
56

57
58
59
60

2548832
2551645
2554458

2557270
2560002
2562894
2565705

2568517
2571328

2574139
2576950
2579760
2582570
2585381
2588190

Dif

2822
2822
2822
2822
2822
2821
2821

2821
2821
2820
2821
2820
2820

2819
2826
2819
2819
28l!l
2819

2818
2tn8
2818
2818
2818
2817

2817
2817

2817
2817
2816
2816

2816
2816
2«J15
2816
2815
2814

2815
2814
2815
28 1 4
2813
2814

2813
2813
2813
2813
2813
2812

2812
2812
281 1
2812
2811
2811

2811
2810
2810
2811
2809

Covers

7580781

75779511
7575137

7572315
7569493
7566671
7563850

7561029
7558208

75553i<7
7552567
7549746
7546926

7544106
7541287
7538467
7535648
7532829
753U010

7527191
7524373
7521555
7518737
7515919
7513101

7510284
7507467
7504650
7501833
7499016
7496200

7493384
7490568
7487752
7484937
7482121
74793O6

Cc»sec. I Taiifr.

1335655
1287487
1239435
1 191498
1143675
41095.%7
4- 1048374

2493280
2496370
2499460
2502551
2505642
2508734
2511826

4 1000893;25U9I9
4 0953526 2518012
4 090627212521106
4 0859130:2524200
4 0812I00;2527294
4 0765181:2530389

CotanfT.! Secant

40107809
40058165
4000863^)
39959223
3 9909924
39860739
3 98116^9

39762712
3 9713868
39665137
3 96I65I8
3 9568011
39519615

4 07 1 8374 '2533484 3
4 0671677i25:%*580 3
4 062509112539676 3
4 05786151254 2773'3
4 0532249 2545870 3
4 0485992,2548968 3

4 0439844
40393804
40347872
40302048
40256332
40210722

; 2552066 3
'2555 1 65,3
12558264 3
2561363 3
3

12564463
i 2567564

40165219:2570664
4 0119823;2573766
4 0074532 2576868
40029:i47 2579970
3^984267 2583073
3 9939292 2586176

3-9894421
3 9849654
3 9804991;
3 9760431
39715975
3 9671621

2589280 3
2592384 3
2595488'3
25985933
2(;01699 3
2604805 '3

9471331
9423157
9375094
9327141
9279297
9231563

9183937
9136420
9089011
9041710
8994516
8947429

8900448
8853574
8806805
8760142
8713584
8667131

8620782

8574537

8528396

8482358'

8436424

8390591/

7476492 3 9627369 260791 1 ,3 8344861
7473677 3-95832 1926 1 1018 3 8-299233
7470863|3 9531*171 126I4126'3 8253707
74 68048 = 3-9495224 i 26 1 7234 j 3 820828 1
3 945 1 379 1 2620342 j 3 8 1 62957
3-9407633 2623451 :3 81 17733

7465234
7462421

7459607

17456794

74531)81

7451168

7448355; 3

7445542|3

Cosine

Dif.

12626560 3 8'>72609
J6296701 3 80-27585 1
1-2632780 3 798-26611
263580113 79378351
'2639002 3 7893109
'2642114,3 7848481

7442730
7439918
7437 106
74:i4295
7431483
7428672

7425861
7423050
742024(^
7417430
74I46I9
741I8IO

9363988
!l32tM43

9276997
9-233651
9190403
9147-254

9 1 04203' 2645226 , 3 780395 1
9061250 2648339 3-7759519
9018395|2651452|3 7715185
8J»75637|2654566;3 7670947
893-2976 2657680 3 7626807
88904 1 1 ^2660794 ,3 7582/63

38847943
3 8805570
3-8703293'
3 8721112,
3 8671)025:
3-86370:wi

Vers.

26^3909 3
•2667025 3
•2670141 3
•2673257,3
2(;76374 3
2679492 3

!>ecant. j Colnn.

75:^5815
74941)63
7451207
7407546
73<J3980
732(^508

TaniT.

03U6136
(KH16884
0307633
030832t3
0309134
0309886
0310639

0311393
0312147
0312903
0313660
0314418
0315177

0315936
0316697
0317459
0318222
0318985
0319750

0320516
0321282
0322050
032*2818
0323588
0324359

03251.30
0325903
0326676
0327451
0328227
0329003

0329781
0330559
0331339
0332119
0332901
0333683

0334467
0335251

0336037
0336823
0337611
0338399

0339188
0339979
0340770
0341563
034-2356
0343151

0:{4394f;
0344743
0:i45540
0346338

0347i:^«
0347938

0348740
0349542
0350346
0351 150
0351955
0352762

Vers.

0297043

0297747
0298452
0299158
0299864
0300572
0301280

0301989
0302699
0303409
0304121
0304833
0305547

0306260
0306975
0307691
0308407
0:M9125
0:^J843

031056*2
0311281
0312002
0312723
0313445
0314168

0314892
0315617
0316342
0317069
0317796
0318524

0319252
0319982
0320712
0321443
0322175
0322908

0323642
0324376
0325112
03*25848
0326585
0327322

0328061
0328800
0329541
0:i30282
03310*23
0331766

033*2510
0333254
0333999
0334745
0335492
0336239

0.336988
o:«7737
0338487
0339238
0339989
0340742

D.

Cosec.

704
705
706
706
708
708
709

710
710
712
712
714
713

715
716
716
718
718
7ISI

719
721
721
722
723
724

725
725
727
7-27
728
728

730
730
731
732
733
734

734
736
736
737
737
739

739
741
741
741
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Dir. Vers. Secant. | Cotaii.

Coiec. I Covers '.

'25 Deg".

LOG. SINES, &c.

319

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2682
2679
2678
2675
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10 3740517

Verseds.

8 9717035

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10 3735103 8 9728424
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10-3681409
10-3678745
10^3676084

49
50
51

9 f;384585
fH;387199

96389812
9-6392422
96:i9d030

2610
2608

52 9 63!)7637 S

53 9 6400241 oS!-i
5^1:9 6402844

2657
2656
2653
2652
2650
2647

2646;
2643

26421
2640
2637
2636

2634
2632
2630
2628
2625
2624

2623
2620
2618
2616
2614
2613

10^367:U24
10^3670767
10 3668111
!l03(;65458
10-3662806
103660156

55l!»6405445
56 9 6408044
5796410640
58 964132:15
5019 6415828
61)9^6418420

Cosine.

2603
26U1

2599
2596
2595
2593
2592

Oir:

10^3657509
10-3604863
10 365-2220
ia3(i49578
103646938
10-3644301

10^3641665
1036:19031
10-3636399
10-3633769
10 3631141
103628516

103625892
103623269
10^3620649
1^3618031
10^3615415
10:i612801

10-3610188
10^3607678
10-3604970
1^3602363
10-3599759
10^3597156

103594555
10:i591956
10-3589360
10 3586765
103584172
10^3581580

8 9802073
89807711
8 9813346
89818976

8 9824603
8 9830226
898:15845
8 9841460
8 9^147072
89852679

89858283
8986*3883
89869480
89875072
89880%*!
89886246

89891827
89897404
89902978
89908548
8 9914114
8-9919676

89925235
89930790

96729468
9-67:ii715
96736020
9-6739294
9-67425r»6
96745836

9-6749105
9-6752372
9-67556:18
9-6758903
9-6762165
9-6765426

9-6768686
96771944
9-6775201
9-6778456
9-6781709
9-6784061

96788211
96791460
96794708
9-6797953
9-6801198
9-6804440

9-6807682
9-6810921

Secant.

8 9936341 9-6814160
89941888 9*6817:196
89947432

8-9952972

89958508
8 9964041

96820632
9-6823865

96827098
96630328

8 996956919-68:13557
8-997509519 68:{678d
8-998061619 6840011

89986134

89991648

8 9997158
90002665
9-0008168
90013667
9^0019163

90021655
900:10144
a00:i5628

9 0041109
90046587
90052061

Covers.

96843236

9-6846459
96849681
9 6852901
96856120
9 68593:18
96862553

3298
3296
3294
:1293
3291
3289
3288

3286
3285
3283
:1282
:i280
3278

3277
3275
3274

:i272
3270

3269

3267
:i2(i6
:i265
3262
3-261
3260

3258
3-257
3255
3253
3252
3250

3249
:i248
3245
3-245
3242
3242

Cotanj^.

IO:i313-275

103309977
10-3:106681

1033r)33«7

Covers.

97614630
9-7612647
9-7«10663
97608679

10:1300094 1. 9 7i;06693

10 3296803
103293514

10-3290226
10 3286940
10:«8.3655
10 3280372
10-3277090
103273810

103270532
10.T267255
10:i263980
10 3260706
10:«57434
10 3254164

10.3250895
103247628
10:i244:i62
10:1241097
10 3237835
103234574

103231314
10.3228056
103224799
10 3221544
103218291
103215039

96865768
9 6H68981

3239
3239
3236
32:16
3233
32:13

3230
3229
3228
3226
3225
3223

3222
32*20
3219
3218
:1215
3215

3213

96872192::{;^!.1
968754021'^-'"

96878611
9 6881818

3209
I3207

Cotanj?.

DIf.

10.3211789
10 .3208540
1/) 3205292
10 3202047
10 3198802
103195560

103192318
10 3189079
10^3185840
103182604
10-3179368
103176135

10-3172902
10-3169672
10-3166443
103163215
10 3150989
10 3156764

1031.5.3541
10 3150319
103147099
10 3143880
1^3140662
103137447

10 3i:i42:i2
1^3131019
10 3127808
10 3124598
103121:189
10 3118182

976O4707
9 7602721

9-76OO734
97598746
9-7596758
9-759476O
9-7592779
9-7590789

9-7588798
97586806
9 7584814
9-7582821
9-7580827
97578833

97576838
97574843
0-7572847
9 7570850
97568852

Secant.

1004-27243
1^0427832
100428422
10 0429012
10 0429603
10-04:10194
10 0430785

10 0431.377
10-0431970
10-04:12563
190433156
100433750
10-0434344

10 0434939
10 0435534
100436i:i0
I9043672(J
1004:17322
100437919

100438517
10 0439114
1004:19713
10 0440311
100440911
9-7566854110 0441510

D.

9-7564856
97562856
97560856
.9-7558856
97556855
9-7554853

10^0442110
100442711
10-0443312
190443913
10^0444515
100445118

10-0445720
100446*324
10-0446927

9*7552850
97550847
97548843
97546KI9; 10 0447531
97544833,10 0448136
9-7542828 10-0448741

Tang^..

9 7540821
9-7538814
97536806
975347O8
97532789
9-7530779

9-7528769
97526758
97524746
97522734
97520721
97518708

9*7516694
9 7514679
97512663

9-7510647
97i">08630
9*7506613

9-7504595
9 7502576
9 750055(5
97498536
97496516
97494494

Verseds.

10^0449347
190449953
100450559
10 0451166
100451773
10-0452381

10-0452989
10^045.3598
10*0454207
1^0454816
ia0455426
100456037

100456648
100457259
100457871
10 0458483
100459096
100459709

10-0460323
10 0460937
10 0461552
ia0462167
190462782
190463398

Cosec. D.

689
590
590
591
591
691
592

5.03
693
603
594
594
695

695
596
696
50(J

597,
598

Cosine.

60
69

9 9572757
99572 168
99671678|58
99570988|67
.99670397166
9 9569806 56
9 95(;9216 54

9 9568623 53
9-9568030 ! 62
61
60
49
48

995674.37
99566844
99566*250
9^9565656

99665061
9^95644(;6
9-9563870
9956.1274
99562678
99562081

697
600
598
600
699
600

601
601
601
602
603
602

604
603
604
605
605
606

9 9561483
.99560886
9 9560287
!)9559689
99559089
99558490

99557890
99557289
99556688
99556087
99555485
99554882

99554280
9.0553676
99563073
99552469
99561864
99561259

9 9660653
99550047
99549441
995488:14

606
(U)f;
607

J!!!^ 9 9548227
'*"" 9^9547619

608

609
609
609
610
611
611

611
612
612
613
613
614

614
615
615
615
616

9-9547011
99546402
9*9646793
9^9546184
99544574
99643963

99643352
99542741
9*9542129
99641617
9^9540904
99540291

99539677
99539063
9^9538448
995.37833
9-95372I8
9^9536602

Sine.

47
46
45
44
43
42

41
40
39
38

37
36

35

:u

.33
32
31
30

29
28

27
26
25
24

23
22
21
20
19
18

17
16
16
14
13
12

11
10

9

8

7
6

5
4

3
2
1

04 Dcg.

NATURAL SINKS,

S430lliS»
41394101!
6 43lW77a

^ 56nB447
^ AGOSRSJ
' 0003231
^5G0DG08
, afi979i)fl
- B5M773

3 44176811

4 4420278 I'i
fi 4422887 i,,

6 442M9{I ^n

7 442BKM j^"

8 4430712 ^

9 4433319 ^
1(1 4438927 ™
■ -38634 1.

l.UO^

W 44(11978 J
II 44043SI q.
It 44C718J S

13 44fln7(lfi ^

14 4472368 ; '

15 4474U90 ^

16 4477691 5;

17 4480192,

18 448^792 J

19 44S»392^

10 4487y82 i

11 44.10591 .,

42 4493190 t

43 4405789 „,
14;4498:«7 t
in 4a0U0U4 t'

4(1 4B
4745OCI79

18 4M8T7a

19 451 1372
M 4513907
>1 4510603
19 45I9I5G

13 4521753 ;

i4 4524347
i0 4S2(mi
iQ 4529635
i7 4532128
IH 4534721
>'Ml'45373i3
1I)|45^0S

' I Cosine

,fia8Z332

1557972:
557711:

'i5S74.-<(li
5557181"

3-2798124
3-2784648
2-2770987
2275744s
29743921
2-3730416
23716997
J27034S7
i2l!!KHI05
32070571
22663156
2-JG4D7»l
2 2636376

Tani:.
48773ai
488U9S7
4884530
48B8I33
4891737
4805.^3

1909775
4913380
4910997
192U010

Ci.iHng.

20503U3U
20187919
2 017280(1
2-0457 7' W
30443(134
3-0427578
3'(M 12540
30307519
30382517
20367532
g0.tS25(IS
2 0:t3701

20307769

"5568800
^5556264
«^563e4a
,, 5561013
"~ 5548138
?^554S«33
^ 554322!)
Z 6.%40e-M
'-15538022

„ 55 1980S
"6517208
jJ^SSIiaOB
^6513008
!^ 5509409
™A506819
,-8504311
?^ 5501613
J; 9490016
^ 5196418

J5 6-19121

an 618881
?^ 5186033
|!? 5183437
" 6180842
JT 5178247
^ 5176653
ru 5473069
" 6I7OI65
ll 6IO7B72
" 5463279
^ 5402087
"" 6400095

ii: V*ra.

3 2543204
32529961
32516711
32503536
2-3190318
2 2177178
33104035,
2-2450889
2 2137770|
2 2124Cf!lt,
2-341 ISSiS
33398517

2385168
22373135

23591 1 9
22310121
22333138

22330171
22307526
2^2304595
2 2281081

l!liW2i
1U19549.
4953171

4056794
111601 1 8

1964U43

.■iij:t316i

M (I31H651
j3020;iB(;

20180088
[8-0) 71331

20139592
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4Q67(W9l 2^01301 CI

,4U71297|20]1

4974925;2-OII

|497S651'2'0'M

1983185'20(r

|4U85810 2 00;

19 2-0042295
12 20027719
L7i2'O013ll2

2^2230192
22217302
22201518
22191762
22176971
221G6308
22163160
22I1073U
321381)16
3311531.
3-2108637
3-2089972
22077:^3
2-2'>64»9l

2 2052075

3 2039476
2202<»93

6007037 jl
50il3C6|l

III1906
50l8.;47
5022189
6035833
6029176
5033131
5030768
6010115
6011063
6OI77I3
5061363

1-9940554

19936087
1-9911637
1-9897201

"■98U-.'7e7
1-9868.187
l-9mi0O3
1'983!W36

6006977
6009033
6073290
6076948
5O80(i07
6084267
SOB7929

1-0783334
1-97U8050
19753782
1-9739531
1-97353MJ ;
I 0711977
I-960C874
19683088
1-0668618
1-9654364
1-9640337
19026105

1024819
1026133
10274 16

I03I373
I0325S0
1033817
154C59 1036130
1D3S125
1037715
103DU06
1010297
101I5B9
1042882

1011176
1015471
1016766
1018063

210061
311663
2133II8
211903
210620
2i827«

1014011
1016888
1017166

™l697<i43S
I™;e97S15l

,2;89738»«
;^^ 887*584
,3j8»7ir

;i2«7

1387

.1289
138D

|™[ll9«a98»

laoi ;89TO994

^8969703

10S1561

10568ol
IO57I66

1059760
10U1064
1002368
1063671
1061979
106(U86
1007594
1068902
1070-31 1

1076151
107(1760
1078080
1079394
1080709
1062935
ID8334I
1081658
1085976
108739.^
1088615
I0B9935

H-MtTMB "O
'. HiiWiGOa 50
""53WI68
1112 67

,89816U

8078996 U
18977716 52

J;!8!I70«14
Jill(9(«7«7«

'.jH»«744a *4
SBMOISX 43

"!89S0994»
;;^ 18969703 38
I H^ a96B41li3T
I J^|8057N8
I ,„,!89SSSS4 K
S:;a9S4M» 34
i !^ 8953231 31
! ;£;,B95I938S»
) \^l 8950G11 31
i 1^^,8919311 30
> ,,,-„l8!M8<H5 39
I .^18916716 28
1 ,™|8915440 37
1 ^™!8944ll0 8«
I ;J^l8912»ll 35
I j^ 8911513 34
,„, 8910240 33
""l893S!»36 22
f^8937CS2 3l
™| 8930320 20
JS 8935031 19
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'8933106 17
8931098 IB
8939789
89381B0

jgj J 89*5858 12
, S93I54«|II
^ ;80232S1|I9
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^ ;89SiWI6 «
'* 8919201 7
;^1>I7975 6

,,.,||EI1H859 6
I , ';89I6»12 1
I , "8911021 a

' ii4n 691 1383 1
; """ , 8910083 _0

Difi Si ne. '
63 Deg.

•M Peg.

9-64210K9
IU36la3

1^0431 ;i47
9-6433tl3»
B'G43r!5(M
»613»0St>

9-04-14326
9-0446796
8-6449365

3 9-6431931

4 &«4o449a
S9-«»70M
B»»iS06\a

7 IMH<al78
8B-04R47M

8 »S 147900

B-rHGuB14

1 'J-W73:HI.-t

5 ff<H7't«A
23 9-647;JI'i

31

U9-G4833B3
M b-aill5li4
87 B-64e7ni»

3» 9-n4il9740
39 9-6496374

D-MarsD?

S4 9<6IHIB3»5
U9-A5079SO

36 »6AIIM44

37 9-6613966
3B9 6al94IW
3it 9-6318004

]Mi3!l3»7»
U-eMUUtl
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l»4SRa4
[»6M8nSI

B(isav>;s

!F63Siesa
9K>aa6S9
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I06<>S»II
KSAMSI
SMM06
»-6M1»»7

lO'.ViNIAKI)
lll3.t7tlUlll
103676404
10-3673618
IO-3A7ia36
10-3666863
1^366(1074
103663406
1 ((-36001(20
10-3668346
Ifr3.'>li6774
I»3a63-^II4
10-3560635
lfr334HI)na
10-3646504
10-3643913
10-3640381
10-3637832
10-3639366
103633710

90008460 1 1)-6a0143U
9>aO739SO,0^68ft463l
9-007937619-6897631
9-0084837:0 6901030

I IJU5753I CBft'iOffl

aswi, ])

Uif.' C'lmiip-.

SWl

io3iiuin-j

,^|10:ilI4!l77

10-3108676
10-3106309

^Jj™llOa09097»

.1103006774
", 11^30!I267K

9-0133S91 9 nOa3378
90128316 9fl»^
901337369 «W!I76«:
90IS916I 9GU3SUU

9-9149973,1

-|3I

[<■' l«HS537B;9-e94317B!-,.„
166 9-0llin7Kl !^C94r>U.'Wi I' i^'
1 0-3337606 U-D 1 66 i 79 V U94 8B3:i ' ), . i .'.
1O3636066 9-0171 074j96g630im:^l''[
10-3688606 9-01 76966 !9fl95.Me:il^|'^
1036191)63 9-016339:1:9-0956366 ..^'-^
lOSTilTJ IS 90107738 9- 69G16S7
n 3.->l 41176 9-01931 19'9-ri964697
1(I:15H:i:).'>9-019K49U:!)-G967H<!u
10 3.1tHi7!)7 9-020387n'»fi!17l03a
10 ;l607«io|9-D209S10 9 (1074)96
10-35947--!G'9-a! N6a7|9-6977363
10-3502193 9-OSI0D7o!9(98a;>36 ..,-, 10-30194',
103499862 a-0336330.»D9B3Ga7 ~;^l IO30I63I3
lO3497l32V0330e87;fffl9fl'!lM7!^ S ;'0™l"*l«
103494606 9-03:161139 9-609U0U6 J JU< 10- StHRKH'
10»492ll8lt&n34l389'9«9!l3l64-'™ 10 300083

1(^3489660 9^^^^6735 o-ouiwaaOiJ j^i K^soosuw

10-34 a7034'9-0333ll77'9-SII99J7-ti«,-,l"'3™*320
10-3484614 9113.17116 9-70(l2(i36^^ l(^2!«)7373
103181996 90363763 »-7«*''7IM'ls <« 1<I-2«M330
1n.v1Tn1.7n nn.ii:nnai u^linHriVl "^ I n-9<|i| 1 11TII

103076622
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10 3I>67I>6H
1O306:Ut83
1 03060703
10-30:i7332

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1030.11 1«7
10304:
10-3044617
10S04ir "

10-3038173
1(^303.1.393
103032136
1930-^0968
1030:

103179479 ff030noa4 .
103476965 9-0373413 9-70*-"™ 3. .,
103474452 »037M7M9-70l6'a7 3ijJ 10^84773
10347l94lVo21Hn69'!»-7'>IB374'. 192901036
IOS409432 9-0389376 OiO^lolO ^\™ 10-39784B1

3NJ

I03466!I35 90394693 9-7034603 ''l" 102H76337
103464419 9-0300004 07'>871IOa ~\" 10-3973135
■n-iiniiiiii o-Avnitqia a.in<in<UII .'* lO-tMUMfLvi

Covi
9-74^-^94

9-7492472

97490449

974H0426

9-748(1402

U7481377

»74ll3:i62

97160336

9747'>-S)9

9747'i.;73

9^7474J44

9 7-17j!2r

9747011

9^74^1158

9-7-ieai36

0-746 ing.-<
9'74n3nO»
9-74niNi:Hi
9-7457997

07-1 36963
U 7-1531128
9^7451693
97449857
9 7447621
9 7445784
9-7443740
97441707
9-743960H
9 7437638
97435588
974S3:i47
9-7431606
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9-74274I!
97436376
0-7433331
9742I8H6
97419340
97417193
97416146
97413099
9741)060
9-7409001

10-0404016
10 04ti463l
]IHI4IU24!
10^0465866
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10 0407193
109467723
1094l>8,'i42

i094fmn63

1904611683
(HM7(I303
10-0470036
I0fl4'
100472069
10-9473(93
10-047.^316
lt>«473n3!
10-0474683
19047S187
100475813
10 0176438
10 0477l)64
1O04776WV
100478317
100476941
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10(UW12UI
100460839
10-0461

9-74(14901
07403660
9 7400796
9^7398746
la-3g(»l914 97396693
0-73M63B
'07393581

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516053B
5156903

154448 20637404
5151964 20636863

VerH. Setant.

20724606
■0713670
207DS740
20691830
3-0680940
067UU56
2O650IS6

'8215026
1-8302473
8169932

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1-8161802
18152391

5527800
5531688
5535488

1 1403135
11401243
1140'>063
1-1407883
1-1409706
1-141" "

ll4i:

11415163
11117013
1 1418612
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1-1430179
4 1-1438017
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8763067 li
8701065 11

87574A6 1

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8749016 i
8747607 I
B746197 I

33

61 Deg.

I »67IUII8

S 9-8723913
4»fi7a>S8a

6Ih673a31»

10

0-0736047
8 l)'673740g
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10-3270139
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10-3267316
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10 3262391

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10 335311

10-3360806

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10-3-2387 1 !>

103234377

10-3232037

10-3229698

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10 3206721

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10 3151133
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9-0701M6
90709090

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0-7296263 ^

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0-7333508
0-7336527
9-7329517
0-7333566
0-7336661
0-7336601
0-7341618
7314631
9-7M7814

9-0639380 0-7350666

0-0641356197353607

0-0619322 9-7356677

0-0864386 9-73696R6

9^0659247

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90869169

9-UH71111

O 067 0069

90681005

1^0688948

9-0831413

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9-7247087

9-7314984

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9-7310770

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0-7238966
9-7231469
9-7232353
9-7230241
9-722Hir'
9-7226037
9-7923017
0-7231Ba7
9- 7319696
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9-0928381
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Cotanp.
103713356
10 3710209
10-3737183
10-37%4n9
10-2731076
102728033
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10272105!
I027IR913
10-3715876
IO-27l2r-
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102706770

102703737

1 02700705

1O2S97075

102691616

102691617

102688500

1026S6561

102662540

102879516

103070491

103673173

IO2870463

102667434

102684416 971921:

102861390! 9^7 1 90066

103658364 9-7187041

I0266S369'b-7I65R2I
3!loa66333e|9-71fl3B08
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10 2577391 '0713039a

102574406 07128260

103571423 07128198

102668441 071

102665480 07I3IR22

103583180 07 110877 1

Tanp. |V eri.eHH.|

Secant.
ioOMOOSl
1O0S4I323
100641906
19^06426811
100513341
100511016
106544 000
100516364
100646040
100646715
10061739 r
1 00516068
IO0646745
100549133
100550101
IO056076O
IO0551460
100662136
10066:
10a^634!)9
100664179
100664(161
100655643

0-7207014 1 ■
9-7301898
9-7303781 {
9-7300663 '
9-7103646':
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9-7194307110-0567501

" 100.M6275

100556959
16-0559644
100580329
1O05V1D16
IOO68I7OI
1O056:>368
IO06C3U75
100563762
100564451
10-0566139
IO0583B26
IO06665I6
1O05O7206
10 0567808
1005G85U9

1O0569072
10-0670666
10-0571367
IOO57-JO6I
10 0573746
100573139
1O0674134
100571639
IO0676634
1O0576321
100676917
1O0677614
100676313
100679010
10 0679709
100680406
IO050I107
1O05H1607

M 66

9 9157332 57
90466650 66
"^ll 0465985 56
glj 9-9465310 5
p.„ 9-9451638 61
^i" 9 0463911

gni533a„ .

9 0162609 5<
OU161932 41
a'9461266 4

47

, 9 9450577

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90140320

09446511

9-9147682 —

9-9447182 43

90116601 41

19446821 40

J9146I39 39

™ 9^9141467 »«

«??OB113775S7

™ O0443093]36

994124091 35

90411735-11

9 9111041 33

' O91103ii6 33

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l^ 39138985 30

„ 99438299 39

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^9 0416693
''^199118193

61 Ueff.

:i■^^^ ■2'j Des.

NATURAL SINES, &C.

4S48aiHI

1 4«iD«40
■ UUUllM

S43a3n7
4UI68IT0

S4660Sla

Dir. Cdvera Cosec.

!) 4870977

10 4B73GI7

11 4S7ei»7
1S4878S07
[3 48B11H

14 4883074
'1 4086213
d 4888750
7 4BS1SSS
18 4ffi

» 4011673
« 4SUlaf
17 4918638
!S 4610171

SN»3fl0 3-nftlA830
BI4SBI6|S-080503I
lll44373:a'0684Sd9
ltU1730;9'OISS3460
SI30IBB2-(»73Oa6
M36646 »U66I»43
GIMIOG 9-0601303

6I3I5U4 s-ouojye

GI2SN>S330a397in

SI364a:t2-0SI(MHi1

St 33943 -2050837-1

SI21403 3'0497(m8

&118B64 2-0487036

51 I632(i 2-047(080

Gll3788 2-040a750

&lll250 2-OUJl2e

5108712 2-044431.

GiUGI73 2-04X)Ul'

51 D3030 2-04233.11

SIOII03 3-O4127S7

5088587 20408107

MIH)032 303UI84U

5003497 2-0381114

aODOiWa 3-0370592

9088-128 2-0300083

aDB689J 3-0340S8;i

5083302 3 0330100

q.,o 5OIIU82!i;3-0:i2IHI2H

M^|M7a3!)0 3 03IMI

^j,|50757O4»030778O

„-, 5073233*0297280

",| 5O7O7O2,*0a8e8B3

5?SA6O6817ll»0S704*3

2530

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5500739
5573551
55773S4
5A8II7!)
5584994
558881

2533°'

A6374M8
5030879
M1347IO

5838513
5U43378
5046313

17 4941048
Ul 4944478
10 4947005

10 4940533

11 4»5soeo

■3 4954587
■3 4907113
14 4909630
■5 4982105
in 49C4C90
■7 40(;7215
IB (9liD740
ID 4973364
M 4974787
il 1977319
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U tDBS35S
U 1984877
U 4987309
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If 43D3441
iS 4004901
^» 4997481
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J50U311I
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5058052
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^5045413

|r042S87
2520:

5035310
6a')2785
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: 5025213
.5023690

3-0334937
3-0334589
2'0314353

5013001
50100BU
6007550
500503II
5003510

l)if. Vers. Setaiit.

2^173031
3-0102756
3-0153494
3-0142343
2-0133005
3-0131779
2-0111564
30101363
30001178
50301673-0080004

3^0040403
2-0030383
0030177

5688488
6093339
5600191
5700045
570389H
570775S
57M612
57 ■5471
5719331
5723193
5727064
5730018
5734783
6738640
6742516
6746380
675095G
5754136
57S7999
5761873
5705748
5700631
5773503

Cntan.

Cntang.

I8U4U478
1-8038108

■ '8015751
1 '8003408
■'7901077

■ '797876!'
1-7960464

1-7954163

■ '7941883

■ 702U610
•7" ■7302

7905121

r. Cosine I '

1-1437231 i:
1143907'i a
I' 1440027 I!
I'I44277» I:
■ 1444030 1!
I-144G484 IS

1-71

17880678
I-78U847&
1-7850285
1-7844107
I-783I943
l'7819700
1-7807851
1-7705524
1-7783409

17771307

1-77311218

17747141

'7735070
■ '7733034
'7710086

'76:18058

7086943
'7674940
'7003050
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I-76390U7!
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1-7603) 83l

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1'7620033
1'7608^U1
1740637 1
17484MI4
17473708
17460984
l-74Jll-il3
1-7437453
1-7435705

■1408863
l'I47073C
1-1472003
1-1474470
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1- 1478339
1480131
1482005
■1483890
11486777
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■ '1480555
I 1491447
1' 1493:140
1-1495336
11497 133
I-I4U9030
■1500930

1207943

13IW360

1870778

187SIW

1873610

1375040

1376463

1377884

1379307

1380731

1382106

1383681

1386007

1286434

1387862

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1390710

1393149

, «74ei97 W

{ 8744786 50

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1300744
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8S73314
_„„ 8671888 I

: 8864614 :
J 8683161 :
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:. iC.

60 Deg-

29 Deg.

LOG. SINES, &e.

908S7!)!ir

D-(UKS642

n-GHUSIG

b!HISI!7068

o-enioss
u-esTiioi

9-(ieT8435
!l-(ieHWtH8
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62 9-697SI1B
53;»lt9;4347
'4 90D7V54S
A 9-0978741
■fi U-e980!KiF

'7 otfflaiisn

Dif. Cosec. Versed !

IO'3144SR8
lfr3142009
I&3130733
lD'3i374S8
ID-313S164
MI3
10-3I30C4I
llhSI 18373
193136105
l&3l33fiM
l(h3l31S7a
10 31 1331:
10-3117051
103114701
10-3113533
Ifr3l 10377

loaiouoss

IO-31U67(>a
10-310351 S
lOSlOlEW
10-3009017

iD-3o»a7eo

10-30946E4
IO3093I7H
10-3090036
IO3007705
103085555
10-3083317
10-3081081
ia307884S
10-3073613

10-3074380
10-3073149

™"ilfr30fi7l»2!0-ll40700

0-U!l83«!l3
9-1)987176
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0-1006681
0-1011349
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9103137S
91D36138
9- 1030996
9-103SS50
9-1040701
9-1045560
9-1060396
9-|05S'238
9-I0B0078
0-IOG491S
9-1009749
0-1O74SSO
9-1079408
0-1084334
9-1089OS6
0-1093876
9-1098603

Tang. Dif.

97437fiM~
»7440493 ~?°
97-443476 SI:
0-7446463 ^l
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»743a403 ^.°
0-7465378^^
9^468340
9-7461320 ?.^'
9 746*300 f^"
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97470227 SS?
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9-74B3089;r^
0-74B6052[^'
9 748801 3^-^
97'130974,^
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9-1117932
9-1122735

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9-1133331
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9-II4I9I7

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10-3054338 9 1175377
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2217
2215
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10-31143288 9-II99I93

10-3030063
10-3037863
10-3026053
10-9033465
10-3031359
1(1-3019064
I030I8R71 91250068
10 3014679 9-1300790
In-.'»I12489 9-1365608
10.^1030019 1370233

0-751 I6GO!,
0-76 14823:;

9-7617673 ;

0-7690623 ;
9-7693473 :
0-7626420 ;
9 7629388,
9-7632314 :
9-7633369 ;
9-7538203 ;
9-7641140;
9-7644088 ;

7547039 '.

7549069 ;
97663908 ;
9-7666846 ;
9-7668783 ;
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9-7564053
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103562480
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102656594
10-9663647
19-9560679

9-7 i 19677
9-7117633
9-7115387
7113340
9-71 1 1093

10-3547697 9-71FSa46

10-9644624
10-2641651
10-2538680
10-25367 10
10-2532741
10-2529773

lose

103533840

10-2317011

10-3514948

103511087

103300026

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1(^3303108

1&S500160

103497104

109404238

102401984

103479177
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97980957
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LOG. SINES, Sic.

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2 9499407a

3 9-69962^8

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6 9-7002802

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9-702S357
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B-7026687
9-7028849

19 9-7031011

20 9-7033170

21 9-7835329
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25 9-7043B17

26 9-7U4U099

27 9-7048248
26 9-7050397
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30 9-70M680

31 0-7056833
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33 9-7061110

34 »7il6J2SS

35 9-7D653B4

36 97067S3:

37 9-70G96fi7
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40 9-7075064 ^

41 9-7078194 ,

42 9 7080323 ^J

43 9 70824.')n

44 9-708457^
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19 9-7093063
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10-2980319
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10-2232315 19-6872688
10-2229448 9-6B704S0

10-2226582
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10-2217988
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9-6866002
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10-0656512

100657263
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NATURAL SINES, &C.

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5215061
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5224986

5227466

32 522994S

33 5232424
5234903
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5247290
5249766
5252211
5254717

5263139
52G46I3
5367085
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52S6S53
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4849619
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4832176
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4827196
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4809781
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1-9416040
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4799839

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13147
4710678
4708210
4705742
4703274
4700807

C0086UG
G0H566
6016527
6020490
6024454
6028419
6032386
6036354
6(140323
6044294
6048266
6052240
6036215
606019
60641 7
6068149
6073130
6076112
6030095

-9370344

-9267009
-9257784
-9248570
-9239366
-9230173
-92-20990
•9211817
'9202655
9193503
'9IS4362
-9175230
-91661;
'9156999
-9I47S99
'9138809
■9139729
l-gilOeSS 6136013

6088067
6093054
6096043
6100034
fil 04036
6108019
"2014
611601

'9111600
■9102551

'9093512
'9084183
■9075464
■9066456
■9057457
■9048469
■9039491
'9030522
'9031564
'9013616
'9003678
'6994750

-8959138

'8950259
-S94I391
-8932532
'8923684
•8914915
■S906016
■8897197

6140018
61440-24
6I18D12
61 52041
6156052
6161)064
6164077

6188188
6192211

G196'23G
6-200263

62133;

6216383
6320417
62-24452
62-28488
13-2527
6236566
6-240607
6314650
6348694

1-6577189
1-6566293

-6555405
1-6544539
1' 6533 6 63
l'6522aoq
1-6511963
1-6501 I2B
1-6490304
1-6479490
1-6468687
1-6457893
1-64471!
1-6436336

■6435576
1-6414824

'6404U82

71919

I'636I2I:
.6350528
'Hai9847
■fi329l77
■6318517

1-0275977
1-6265368

1-625476S

1-6191380
1-6180850
1-6170330
'6159820
1-6149330
1-6138839
■6128349
■6117B78
■6107417
■6096966
.■608652J
'I6076094
■6065672
I ■6055360
16044858
■60344G5
■6024082
-6013709
■6003345

Ta»g-

Vers.

666234
IG68374
1670416
[672459
1674504
1676551
1678599
1680649
IC8270I
1684755
168(1810
1688867
1690926
1692986

1699178 1'
I7DI2J5 1'
1703314 1-
1705385
1707457
1709531
1711607
713685
.715764
.717645
.719928
72301
734099
726187
728277
730368
.7^2462
734557
736653
73B752
740S52
742951
74505S
7471 63
749270
751379
753490
755603
757717
7398:!3
761951
764070
766191
.768314
770439
.77-2566
.774094
776824
778956

1439826

1431335

1432825

1434326

I43SS27 I

1437329 I

1438832

1440336

1441840

1443345

1444851

1446357

1447865,,

1449373 ;

1450881 '■

1456923 ,,
1458436 |;
1459949 ,;
1461462 :
1462977 ;
1464493 j;

466008 ,i
14675-25 [;

469043 ;

470WO ;

1472079 ;
1473598 [;

■1751 19
I476»40
147S16I

479684
1481-207
1482731
1494255 ,,
1485781 ;
"487307 ;

1501073 J;

1502606 ,,
1504140 :
505675 ;

1507210 ;

1508746 ;

15I02S3 :

i: Cosini
„ H57l673le0 ■
" 8J70l74j59
„ 356S67S 5S
?! 85671 75 1&7
8565674 fr
" 8564173 fr
[^ 9362671 5
^8561166 5,
" 8559664 *
[l 8558160 5
H 8556655 51
^ 8555149(49
ll 8553643 4
„, 6552135 4
™ S.'>S0627 4'
^BM9II9 4
„ 8547609 ■i
, 8546099 4
j 85445B8 4
- 8543077 4
° 8541564 4
''8540031 3:

. 8533992 35
' 8532475 |:M
'8530956 33
I 85294'Id'32
^ 8527921 131
r 89:ift402 31

1 29

.783225 i;

785362 i;
7«7.'>01 1'
769642 i:
791784 i;

' 8521839 K
i 6520316 21
" l'il87Ma
] 8517269 2.
515745 2;
"8514219 21
^8-.1269-
"8511167 8)

"8501991 U
\T, 8500459 l;
1^ 8499937 li
,,8497394 11
ll S4958(HI U
"9494323 1
™ 8492790 I
:° 8491254 3
"8489717 (

^8486641 J

"S48il02 :

"6483562 !

ys4«30iS I

" 84tt048l I

58 Di-g.

31 Deff.

LOG. SINES^ &C.

331

1

2
3
4
5
6

Sine.

F7Ti8393
9-7120495
9-7122596
9-7124695
9-7126792
9-7128889
9*7130983

7:9-7133077
89-7135169
9 9-7137260

10 9-7139349

11 9-7141437
9-7143524

Dif.

12

13
14
15
16
17
18

19
20
21
22
23
24

9-7145609
9-7147693
9-7149776
9-7151857
9-7153937
9-7156015

9*7158092
9-7160168
9-7162243
9-7164316
9-7166387
9-7168458

25 i 9-7 170526

26 9-7172594
27.9-7174660

28 9-717672.')

29 9-7178789
30.9-7180851

31 9-7192912

32 9-7184971

33 9-718703^)

34 9-7189086

35 9-7191142

36 9-7193196

37 9-7195249

38 9-71973U0

39 9-7199350

40 9-7201399

41 9-7203447

42 9-7205493

43 9-7207538

44 9-7209581

45 9-7211623
46
47
48

49
50
51
52
53
54

55
56
57
58
59
60

9-7213664
9-721570.1
9-7217742

9-7219779
9-7221814
9-7223848
9-7225881
9-7227913
9-7229943

9-7231972
9-7234000
9-7236026
9-7238051
9-7240075
9-7242097

2102
2101
2099
2097
2097
2094

2094
2092
2091
2089
2088
2087

2085
2084
2083
2C81
2080
2078

2077
2076
2075
2073
2071
2071

2068
2068
2066
2065
2064
':062

2061
2059
2059
2056
2056
2054

2053
2051
2050
2049
2048
2046

2045
2043
2042
2041
2040
2038

2037
2035
2034
2033
2032
2030

2029
2028
2026
2025
2024
2022

Cosec.

10-2881607
10-2879505
10-2877404
10-2875305
10-2873208
10-2871111
10-2869017

10-2866923
10-2864831
10-2862740
10-2860651
10-2858563
10-2856476

10-2854391
10-2852307
10-2850224
10-2848143
10-2846063
10-2843985

10-2841908
10-2839832
10-2837757
10-2835684
10-2833613
10-2831542

Vereeds.

9-1548276
9-1552831
9-1557382
9-1561931
9-1566477
9-1571021
9*1575562

9-1580101
9-1584637
9-1589171
9-1593702
9-1598230
9-1602756

9*1607280
9*1611800
9-1616319
9-1620835
9-1625348
9-1629859

9-1634367
9-1638873
9-1643376
9-1647876
9-1652374
9-1656870

10-2829474:9*1661363

Tanp^

9*7787737
9-7790599
9-7793459
9-7796318
9-7799177
9-7802034
9-7804891

9*7807747
97810602
9-7813456
9*7816309
9-7819162
9-7822013

9-7824864
9-7827713
9-7830562
9-7833410
9-7836258
9-7839104

9-7841949
9-7844794
9-7847638
9-7850481
9-7853323
9-7856164

9-7859004

Dif.

2862
2860
2859
2859
2857
2857

2856
2855
2854
2853
2853
2851

2851
'2849
2849
2848
2848
2846

2845
2845
2844
2843
2842
2841

2840

Cotang.

10-282740G;9-1665854,9-786I844'^^

283S
2837
2836

10-2825340 9-1670342
10-2«23275|9-1674828
10-2821211 19 1679311

Cosine.

Dif.

10-2819149

10-2817088
10-2815029
10-2812970
10-2^0914
10-2808858
10-2806804

10-2804751
10-2802700
10-2800650
10-2798601
10-2796553
10-2794507

10-2792462
10-2790419
10-2788377
10-2786336
10-2784296
10-27S2258

10-2780221
10-2778186
10-2776152
10-2774119
10-2772087
10^770057

10-2768028
10-2766000
10-2763974
10-2761949
10-2759925
10-2757903

9-1683791

9-1688269
9-1692745
9-1697218
9-1701689
9-1706157
9-1710623

9-1715086
91719547
9-1724005
9-1728461
9-1732914
9-1737365

9*1741813
9-1746259
91750703
9-1755144
91759582
9-1764018

9-1768452
9*1772883
91777312
9-1781738
9-1786162
9-1790584

9-1795003
9*1799419
9-1803833
91808245
9-1812655
91817061

9-r864t>82
97867520
9-7870357
97873193

Secant.

9-7876028
9-7878863
9-7881696
9-7884529
9-7887361
9-7890192

9-7893023
9-7895852
9-7898681
9-7901508
9-7904335
9-7907161

9-7909987
9-7912811
9-7915635
9-7918458
9-7921280
9-7924101

9*7926921
9-7929741
9-7932560
9-7935378
9-7938195
9-7941011

9-7943827
9-7946641
9-7949455
9-795-2268
9-7955081
9-79'>7892

2835
2835
2833
2833
2832
2831

2831
2829
2829
2827
2827
2826

2826
2824
2824
2823
2822
2821

2820
2820
2819
2818
2817
2816

2816
2814
2814
2813
2813
2811

Covers.

Cotan^.

Dif.

10-2212263
10-2209401
10-2206541
10-2203682
10-2200823
10-2197966
10-2195109

10-2192253
102189398
10-2186544
10-2183691
10-2180838
10-2177987

10-2175136
10-2172287
10-2169438
10-2166590
10-2163742
10-2160896

10-2158051
10-2155206
10-2152362
10-2149519
10-2146677
10-2143836

10-2140996
10-2138156
10*2135318
10-2132480
10-2129643
10-2126807

10-2123972
10-2121137
10-2118304
10-2115471
10-2112639
10-2109808

10-2106977
10-2104148
10-2101319
10-2098492
10-2095665
10-2092839

10-2090013
10-2087189
10-2084365
10-2081542
10-2078720
10-2075899

10-2073079
10-2070259
10-2067440
10-2064622
10-2061805
10-2058989

10-2056173
10-2053359
10-2050545
10-2047732
10-2044919
10-2042108

Covers.

9^6857076
9-6854843
9*6852609
9-6850374
9-6848139
9-6845902
9-6843665

9-6841428
9-6839189
9-6836950
9-6834710
9-6832469
9-6830227

9*6827985
9-6825741
9-6823498
9-6821253
9-6819007
9-6816761

9-6814514
9-6812266
9-6810018
9-6807769
9-6805519
9-0803268

9-6801016
9-6798764
9-6796511
9-6794257
9-679200*2
9*6789747

9-6787491
9-6785234
9-6782976
9-6780717
9-6778458
9-6776198

9-6773937
9-6771676
9-6769413
9-6767150
9-6764886
9-6762622

9-6760356
9-6758090
9-6755823
9-6753555
9-6751287
9-6749017

9-6746747
9-6744476
9-6742205
9-6739932
9-6737659
9-6735385

9-6733110
9-6730835
9-6728558
9-6726281
9-6724003
9-6721715

Secant

Tanff.

V'erseds.

10-0669344
10-0670103
10-0670863
100671624
10-0672384
10-0673146
10O673908

10-0674670
10-0675433
10-0676196
10K>676960
10-0677724
10*0678489

10-0679254
10-0680020
10-0680787
10O681553
10-0682321
10-0683089

10-0683857
10-0684626
10-0685395
10-0686165
10-0686935
10-0687706

10-0688478
10-0689250
10-06900-22
10-0690795
10*t)691568
10-0692342

10-0693117
10-0693891
100694667
10-0695443
10-0696219
10-0696996

10-0697774
10-0698552
10-0699330
10-0700109
10-0700888
10-0701668

10-0702449
10*0703230
10-0704011
100704793
10-0705576
100706359

10-0707143
10-0707927
10 0708711
10-0709496
10-0710282
100711068

10-0711855
10-0712642
10-0713429
100714217
100715006
10-0715795

D.

Cosec.

759
760
761
760
762
762

762
763
763
764
764
765

765
766
767
766
768
768

768
769
769
770
770
771

772
772

Cosine.

9-9330656
9*9329897
9-9329137
9-9328376
9-93-27616
9-9326854
9-9326092

9-93-25330
9-9324567
9-9323804
9*9323040
9*9322276
9*9321511

9-9320746
9-9319980
9-9319213
9-9318447
9-9317679
9-9316911

9-9316143
9-9315J74
9-9314605
9-9313835
9-9313065
9-9312294

9-9311522
9-9310750

^li 9-9309978

773
773
774

775
774

776
776

9-9309205
9-9308432
9-9307658

9-9306883129
9-9306109 28

60
59
58
57
56
55
54

53
52
51
50
49
48

47
46
45
44
43
42

41
40
39
38
37
36

35
34
33
32
31
30

9-9305333
-.^ 9-9304557
;^y 9-9303781
''' 19-9303004

JJft '9-9302226
^^^ 9-9301448
9-9300670
9-9299891
9-9299112
9-9298332

778
779
779
780

781
781
781

9-9297551
9-9296770
-a^ 9-9295989
Hi 9-9295207
;2ii9-9294424
'^|9-9293641

7 Ad'

;2: 9-9292657
;2J 9-9292073
III 9*9291289
;~ 9-9290504
:?2 ^9289718
'«>«* 99288932

527,9-9288145
is; 9-9287358
7M 9-9286571
^^ 9-9285783
9*9284994
9*9284205

789
789

D.

27
26
25
24

33

22
21
20
19
18

17
16
15
14
13
12

11
10
9
8
7
6

5
4

3
2
1

Sine.

58Deg.

332 32 Peg.

NATURAL SINES, SiC.

Sine.
i299193
»Ula59
S3D412S
3306^91
U090S7
531 1521
i3t3SSfi

7 !>31G4S(I

8 &31S913

9 S331376

9 534S982 X;
a) 5348440 *
[1 S3ft0898 "

a 5:153355 ■;

3 S355S12 Z,
!4 535B26S "
!S 5360724 t
S 5363179 ?
7 536563<I ^
!8 5368089 ,.
■S 53705-13 ;"
ID 537^998 *

11 5375.14!!^

12 5377902 :;"

13 53*IU35J X

N .'ia.yisofi :r

4700807
4698341
4695875
4693409
4690943
46B8479

4eseoi4

46S3550

4681087

4678624

4676'

46731

4671237

:[ 4668776

!' 4666315

!" 4663855

'" 166139:

?" 4658935

*" 1655477

46540)8

4651ifi0

4649102

4G46S45

4C441BU

4641732

4639276

4630821

4634366

463191

46-29457

4C27004

i 4624551

' 4I12-J098

K 19646

fil.-19-l

.614743

Cosec. I

^8570799
-886:2019
1-885324S
1-8844489
1-BB35738

Tang.
6248694
6252739
G2SG786
6^60834

17 5390158
IS 5392608
19 539:10!
10 5397507

12292
460384s
„ ,„ 46073U2

8818266 6'.
-8809545
■8800833]
-8792131
1-8793438'
1-8774755
l-B766082|
1-875741 9'6:
1-8748764 6,
■874lH^06:
1-87.114S5 6:
1-8722859 s;
■■87I4Z44|6:

[■8705637
"■8699040
■8688453;
■8679875
■8671306-
■8662747
■8654197
8645657
-8637] 26
1 '8628605
■8G2II093
■8611590
■8603097
■8.5946)2
1-8586138
1-8577672
) -856921 6
■856076U
'8552331
1-3513903
'8535483
■35-J7073

6277042
16281098
6-285155

Cntang.
1-600:1345

■5992991
1-5982647
I-597-231!

'5961987
5951672

-594)366
)-5931070
I-59207S3
1-5910505

1791704 )l
'17939:S8 11

1-1796074 II

1-1798222 i;

1-1800372 11

1-1!
•1804676 II
'1806631 11

1-5869491 I

4 1-5959-261 1

l-5i:(4y041 I

1-11
l'1811)46 11
1-1813307 11
1-1815469 II
1-18)7633 11
1)819798
I'18'2lg66
1' 1821135
I' 1826306

1)738 !■
'6325810
'63-29883
'63339:i9
G33S035
'6;M21
'6346)93

541170 :

is427-i2 !;

1541274 ;
1545^28 :
1547382 ;

,6370703

6371793

6378885

6382076 1'

6387073 1-

6391)69 1'

6395267 )'

6399366

6103467

6.107569

641)673

)'S80S253
) '5798079

Ki787915
1-5777760
1-57676)5

t-57J74;H
1-5747353
l-57.)7-234
1-5727)26
1-571 70-26
1-5706936
1-5696B56

■184U739i)53672) J

10307 15G 1400:
)-)852500 156-296)1
185 l(,D4i) 51345-23

l<5:i)6540
1-5606542
1-5596552

1)870)07
)8723)G

1-1874527
1-1876740
1-1878954
1-1881171

ISGi!
15S6086[}f^

1569213,^
1570778 '^^
1572343
1573909
1575476

1577044
1578612
158UI8I

1568

13 540.1851

14 3407299

15 5409745

16 5412191

17 5414637

18 5417082

19 S419S27
rt) 542197)
•1 54^1415
>2 5426859
i3U293D!t
<4 5431744
15 5434187 '
i6 54.16628 X,
\1 5439069 *
p8 5441510 ;*
i9 544.395) %
iO M46390

1587809 !■;
458536 :
4:iS29IS )<
4-5SD47'(
4^78029

.:)75585
4573].!)

1570698
4568256
4iB58l3
4363372
'<6U93)
4358490
4>3()04'J
135361(1

'8426666
'8418574
1-8410292

1-8-
1-8.193753

l-a'iSJ498
■8377251

6-148678
8452797
64561
6461041
64G5163
G4G9290
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6177546
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10-0511557

10 0309013

9-5325925
9-53-23137
5320349
9-5317559
9-5314768

10 0498838
100496295
100493752
10 0491209
10-0488666
10-01861-24
10-0483581
0481039
10-0478497
100475955
10-0473113
100470872
lO'O'l
I0U4G5789
100463248
I0'0460707
10^0456166
100455626

'5364839

■5303594
9'5300797
~5298000
9-5295201
9'5'292402
95289601
9 5286799
9-5283997
95281
9'5278388
95273582
9-5272774

5269906
9-5267157
9-5:!64346
9-5261535
9-5258722

5255908
9'52530<14
9- 5 250 2 7.-;
9'5217461
9'5244fi4,!
9-524182 :.
95239003
9-5236182

D.| Cosii

101222201
101223600
101224399
I0'12'i54g9

10-1226509
1O1227700
101228802

1099

18777799 61

1099,0.

Ifrl233215

10-1234320
10'1235426
ID'S 23653:
10-1237639
101233747
101239855
10 1 240964
101242073

'76700|59

'8775601 59

'|9-8774:.01 157

;9'B773401j56

, g-6772300l55

;9'877 11 96:54

,""''i9'87700J6.S3

,,"■9-8768993^2

IX ss^fi'S-fa 51

1105

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9-8765680 4t
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"°.9'876I213 4;
, I "° 9'87a0145 4.
j "o 9'87S90)6 4;
J, jj, 9-6737927 4i
,,,.'9873681
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6 41

lO'l 246.51 8

Itl- 1247631 :

10-1248744,':

10-1249858

lO't 250973

10-12520B8

101253205

10-1254321

1&I2J5J39

10-1256557

10-125767.'

101268795

1012- "

10-1261035

10-1262156

101263278

10-1264401

10-12fi5524

■3754594 3(
9-8;53482 3>
9-8752369! 37

.9 3751-256136

'9S75OI42I35
9-3749027 '34
9'3747912 33

I9'8746795 3i
9'8745K79,3I

■ 9-87445613

9-5230536
9-5227711
95224885

■5222058
95219230

■S2I6401
95213571

5210739
95207907

'5205073

'5202239
9-5199403
95196566

Versed s.

101273406 j:
101274534 j:
10-1275663 j:
10-1276793 ,.
10-1277924 ,
101279055 }.
10 1280187 }
10-1-281319 I
10-1232452 {:
10-1283586 ,
10-1234721 }.
10-1263856 j.
101236992,:
101233128 j:

,,,„' 98743443 !29
j '^9-874-2.t-25|;i!
i" 93741-205 2:
''-"■9-a7400s5i26
'iV,93738965|25
jjj^. 93737344 24
,,.,„J9'87367i2 23
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!{7;'9'S734476i21
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, , . ■ ■.■■2L'0;6'17
, ,-'- ■■■ -.■2-!M4U'16
ya727722l:
3726594 1'
■° 9'8723466 l;
1^9 6724337 1;

98723207

9-6722076 II

:9^67209I5 1

9'3719S13 I

11

. 9-3716414 I

^98715279 ■

; 9-8714144 ;

713006 :

lO^i

Cusec. D. Sine.
48 Dej;.

_35^_42De^.

natukaL sines, i

3 fi6!J77as

4 116999-18
b 67U2ID8
6 67(M2G6

330437;^

3302:

33UUa3-i

i\ll\329573A
,1^293576
'329141

;; -2158;

1'4S447B;
1-4939940
1-4935118
l-493o;iOI
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I492II6HU
1-491 S87H
1-4911076
l-49UG:fB0
1-4991 4Sj9 I

9994940 1
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9U145HU 1'
SU19M:)4
y9^ai.'il
9930411

yoascga

HW(;6.>3
19^0171
197369.1

.1067219

Secant Vers,

1-3456327 2S6«552
I'345g853l2570498
'2446
25743<M
2->76342
2578292
>»802l;

I'346li9l4
1-3470449

1*347.1987
1-3477528

'22-.82102 „

9104(1 1 9
UI091I4U
9lln265

9120392
'.'125922
'il:!l2:i5

1-D9S4201

1-09.»7(M7
109S1397

1 l-094300ii
'9 1 093861U
"I|-(m:l2223

I Iiau6714
109U0W7
1-0893984

I-0B74918

1 1740-20
B 179379

9IB4740
|tll9Ula4

9193471

9200S4I 11-0863571
9206214 1'0H622^
9211590 10855889
19216969 1-U849554
92^2350 II-0B432S)
922773411-0836896
9333122 1-0830573
92;i8Sl:f 10824254
9243U05 1-UH 17939
9^9301 1-0811621
4700 l-0aU532[
926010-2 1-0709018

06 '] 07927:

9Z7U914{10 8 4.

92 6124,10780 32

9iS 718110773845

I 675E1

82

■.JU-254 2(
523834
1-3527417
1-.WHI0(>3
1-3534593
1-3533185
1 ■3541789
1-3545379
1 '3518980
1 ■355258;
1-3556193
1-3559803
l'35<i3417
1-3567034
1 ■3570654
1 ■3574277
1-3577903
1-358153:1
1.1583 164

i 1956
^1957

" 1938

9125151 0723687

1-3592438

l'339G0Sil
1-3599725
1-3603372
1-3607023
1-3610677
l-3fil4334
1-3617993
1-3621658
1-3625324
1-3628994
1 3632667
1 3636343
~ 364U023
1 3tl4 704

3U7389
1 3651078

365477ol

36 84

3 62162
1 3665863
" 3069 67
1 36 i 75

2611525

26134B5
2615447
2617408 ,,

■ 19371
2621331 {:
2(i23297 {;
2625262 ;
26272'27 {;
2629192
2631158
2633125
2635092
:ia37O60
2639029
26409'(8 I,
26429n8 ;
2644939 ;
2646910
264Bt)B2 j;
!650834

-431448 M

74295U2r>}

7427^54{»

7435Se65;

74^654 SS

74817IH|:i5

7419738154

, -4lr808ls3l

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* 74I39l)r.|;

II19'>3!»I
J 7410
74U8(M6 4f
7406092 4J
7404IJ7 U
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7-100325 14
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, 7378666
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; 7374738
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33

2658750 ,;
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2670612 '
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{[ 732:.4-29| t,
, 73JH49I i
7321467 J
' 7319486 3

42 Peg.

1 9-8256S12

2 9-8M7913

3 9-82^9314

4 9-8260715

5 9-826SII4

6 9-8263S12

7 9-S264910

8 9-8^66307
g 9-82G77U3

8273279
9-8274671
9-8276063
9-B2774ft3
9-827S643
9-8280231
9-8281619

24 9'e2lib!i47

25 9-8289930
2e'9-6291312
27|9-S2926y4

38 9 8294075
29:9-8293454
30|98^9GS33
31 9-8296212
32'9-8299589
33|9'S3(Wge6
34 '9 8302342
35 1*83037 17
3C'9'830S091
37 9-8306464
3g.983078;f7

39 9 8309209
4olo-63io:ieo
4l'9 8311950
42198313320
43 983I4G8S
44,9 83160 16
45 9-8317-123
45 9 8318789
47|9-8320lJ5
48 9-8321519
49:98322883
50 9-8124.i46
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53 9-B32H331

Si 'J ■. ,
56 'J ^ . -

S9;9833C-i;8|l'
60|9-a33;B33|

Dif. Coaec. Verseds

10-1744891
10-1743488
10-1742087
10-1740686
10-1739285
10-1737986
I0-173G488
10-1735090

'40968^3
9-4100174
9-4103462
g-4106750
9-4110036

'4113321
9-4116604
9-41 19885

10-1733693 9-4123166
10-1732297|9-4U6445
101730902 94129723
i0-1729507j9-41S2998
10'imil3 94136273
10-1 726721 (9'*1 39546
10-1 7-25329' 9'414-J818
10- 1723937: 9-4146088
10-172W47|9-4i49357
10-1 721157' 9-4 1 52625
10-1719769.9-4155891

Tang.
9-9544374

'954691!
9-9549455
9-9531993
9-9SS4S35
9-95S7073
9-95S9615
9-9562154
9-9564634
9-9567233
9 9568772
9-957231
99574850

10-1718381 8-4159156
10-171699419^4162419

10-1715607,9-4165681
10-1 714222,0-4168942
10-1 71 2837 19-4 1 72201

10-1711453 9-4175459
I0-I7l007ol9-4I78715
101708688 0-4181970
10-l70730e'9-4183:iii3
10-1705925 9-4188475
10- 1 704546 1 941 91 726
10-1 7031 67 jO-4 194975
10-1701798 9-4198223
10-I70U4I1'9-4'201470
10-16991134 94-204715
10-l697659|9-4207959
10-l696283,9-42n201
10-1694909.9-4214442
10-I69.15.^6|9-42I7681
101692163 9-Jl'20U20
10-l6;iOrH11!)'422JI56
IOI6^U42oy-)-J-^73y2
10-lfi9S0.5lJi9-4230h2S
■ ' ■ ■■ 'ISiSSS

10-1685312

,10-1677117
''!lO-1675754
;|10-I67439I
110-1673030

','10 16711

7"a09

Ciisine. |l)ir.| Secant.

9-42370S9
9-4240319
9-4243548
9-424677:
9-4JftOOOI
9-4253225
9-4256447
94259669
94262889
■4266108
9-4269325
9-427:1541
9-427,i756
9-4278969
9-42S2181

99S85D04
9-9587542
9-9590080
99S92618
9-9595155
»9597693
9-9600230
■9602767
■960S305
9607842
■9610378
■9612915
■9615452
99617989
9-9620525
99623061
96255B7
99628133
9-9630669
99633204
■9635740
9-9638275
"964081
9643346
■9645881
9648416
9650951
9-9653186
9-9656020
"■9658553
9661089
9-9663E23
■9666157
'9669692
9-9671225
9-9673759
9-9676293
■9678327
9-9681360
9-9683893
9-9686427
9-9688960
"9691493
9691026
9 9696359

CiituDf;.

1004

^0-0450345

10-0448003

10-0445463

10-04429-23

10-044038:

i 95196566
I 9-5193728
9-5190889
9-318B049
9-5185207
'3182365
■3179521

10-1^89265
10-1290403
10-1291542
10-1292681
10-1293821
10-1294961
10< 1^96 103

10-04:i:-'
10-0.1 1-1 I .

10-04:i(IJ-:-
lO-04276fl9U51C3'.'H7,
10-0425150 9-5102430:
10-0422611:9-5139585:
10-0420073 9-5156733
10-04)7535 9-3153879
10-0414996:9-3131024
10-041-^58 9-5148168
10040992095143311
10-0407382 9-3142453
100404845.9-5139394
10-0402307 9-5130734
100399770 9-3133872
10-0397233 9-3131009
100394695 9 3128)46
10-0392158,93125281
10-0389622 951224 15
10-0387085;9-3tl9548
10-0384548:9-3116679
10-0382012,9-5113810
10-0379473,9-51 10940

I0B74
10130!
10-13U2963
10-1304109
10-1305256
10 1306403
10-1307351

I0'03r6939 951
I0'O374403|9-5IO5195l
10-0371 g67|d'51 02321
10-0369331 9-5099446

10-13(1

IO13l09e8

lfrl3)214g

10-13)3300

10-1314452

10-]3I5604

10-1316758

10-)31791

10-1319066

10-132022!

10-1321377

10-1322534

10-1323691

10-1324849

10-0361725 9-5090814
10-0359189 9'50S7934|
10-0356634 9-5085054
10-0334119 9-50821 72
10-0351 5g4'9'5079399
10-0349049

10-0346514
10-0343930

10-0311415
10-033991 '
10-0336377
10-0333843
10-0331308
101)328775
10-0326241
10-0323707
104321173
10-03)8640
10-0316107

loosisr

10-031 )(

100308307
100303974
100303441

9-5073319 II
9'5070633ll(
9'506774rJli
9-5064--.; 1 1

1D-I331811

10-1332974
1 0-1.134 137
10-1335301
10-1336466

50764031 lO'l 337631

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9'869U132

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9 8686700
9'8695548
9'8684396
9-8083-242

'?:9'86B0''34 3<
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9-5047500
9-5044603

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10-13481511
10-1349323

0-1350496

.,,iiaDDDifi9 23
^ 9-8667026 22
2,9-8665863 21
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19-8661203 17
:''98S600,t6 16
'":9-e6J8.S69 )5
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, ■i.-f;J6531 U
, ■^.■i(iJjJ62,12
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,.;l9-8G4833r 6
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4 IO-13J872-i i

1. CoKeC. I D. j

47 Uejr.

304 43 Deg. natural sines, &c. Tab. 9. |

1

.Sine.

Dif.lCov.,^

Cosec.

Tanft.

Cot«nK.

SecunL

Vera.

Dif

Cosine

G8I9984

,,„ 31801)16
; ;^31778S9
^Hi? 3175763

1-4662792

9325151

i-0 7-2368 7

1-J673275

268646.1

19S4
1985
1985
1936
1987
1987
19S8

7313537

SO

1

68221 1 1

l-46r>B22n

9330591

10717435

1-3676985

2688447

7311553

3

m-i'\i37

1 -465:1^52

933603*

1-0711187

1-3680699

2690432

7309S6S

M

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b92f,.m

■H*3173637

14649089

9:i41479

1-0704943

1-3684416

2692417

7307593

57

M'iSib'i i'if^'amhu

1 -4644529

934692S

1069870-2

1-36SB136

2694403

7305597

56

fia3{Hil3* -7:1169:187

14639973

9352380

l-0£g-2466

1-369 1859

2696390

7303610

55

f

e83ur3H.:;|*;J 3167^62

1-4635422

9357834

106H6233

1-3G95586

2698377

7301623

54

7

69.W8f,l''" 13165139
6*16984 ;;.^:3I630I6

1-4630875

9363292

1-0680001

1-3699315

2700365

1989
1989
1989
1991
1991
1991

7299635

53

t-4B2633l

9368753

1-0673779

I-370304S

2702354

7297646

52

(i839107 .„,:;; 3161)89.1

1-4621792 9374316

1-0667558

1-3706784

2704343

7295657

51

ID

BSnrii!3.; -- J15877I

1-461725719379683
1 46 [■27-M 9385153

10661341

1-3710523

2706332

7293668

50

11

6843350; ;|31S66ilJ

1-0655128

1-3714266

2708323

7291677

49

ll!

68454/1. ]j^l31545m

1-4608198 9390625

1-0648918

1-371S01I

27I03M

7289686

48

684-591' ., '3152109
6849711 ;;^" 315^289

1-4603675

9396101

1-0642713

1-3721760

2712305

7287695

47

U

1 4S99156

9401579

1-0636511

13725512

2714297

!"!!- 72^,V0.1

15

e85l(t3U; ^,3148170

1-4594611

9407061

l-063o:ji:! 1 ;r'j'i.-.- jri'.j'Mi ;■' ■':,-■ .no 4j|

16

685:1948; "13146052

14591)130

9412545 l-06-2.in- i ,. , ■' ;.-i:i,;44

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6858184.^1 {«

3143934

1 458:.62:j

9418033 1061-^'-J- ■-■-.-■-■: .:^243

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9423523 1-061 1.- -1. : ..".i ■.■ ■ :.JJ.,_ |,,,^.; ::::7^>t^i2

19

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3139700

1-457662 1

9429017 1-06055601 l-;i"44:>21 '27-il26Si,„„r

7275732 41

ao

3137584

1-4572127

943451310599381

1-3743092

27-26-264

1996
1997
1998
1998
1999

7*73736140 1

21

313S4G8

14567636

9440013 1-0593206

1-3751867

2728260

7271740

39

22

3133353

1-4563149

94456161 1-0587035

1-3755645

2730257

7269743

38

23

3131230

1-4S58666

945 lOSl 11-0580867

1-3759426

2732255

7267745

37

24

3129125

1-4354187

94SG530' 1-0574704

1-3763210

2734353

7265747

36

2

6872988 „,,„
*7 101^ ^

31' 012

1 4549712

94620421 10^68^44

1 3766998

273625"

'OOO
2000
2001
2001
2002
-003

263'48

35

2B

31 4899

1454 ^1

9467556110562388

1 3770789

2738252

7261748

14

J J 4

4 3 ihu J

1 45SJ

740252

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33

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742253

7257747

32

9

744234

7255746

31

3U

1,

746456

72S3744

90

31

6WS 1

748259

2003
20M
2005
2005
2005
2007

7a.'il741

29

3i

bBM7 , „ 1

4 H4J8 10

J »3b02

27S02S2

7249738

28

33

ft8S987J na'1'1'" '
GBJ1981 7^3108019

145 14055 |950t> 245

10319401

1 3797416

2752366

7247734

27

3.1

1 4509616 9"il 1784

1 0513275

13801233

2754271

7245729

36

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14505181 195173 fi

1 0507153

1 3805053

2756''76

72437i4

25

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' j Cosine.

1308
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1301
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1298
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10-1582287
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DIK

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Secant.

9-46.33468
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Covers.

Tanff.

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9-9858484
9-9861012
9-9863540

9-9866068
9-9868596
9-9871123
9 9873651
9-9876179
9-9878706

9-9881234
9-98a3761
9-9886289
9-9888816
9-9891344
9 9893871

9-9896399
9-9898926
9-9901453
9-9903981
9-9906508
9 9909035

Dif.

2528
2528
2528
2528

2528
2528

2528
2528
2527
2528
2528
2527

2528
2527
2528
2527
2528
•2527

2528,

2527!

2527|

2528

2527

12527

Cotan^.

10-0151628
100149100
100146572
10-0144044
100141516
10-0138988
100136460

Covers.

9-4847860
9-4844883
9-4841905
9-4838926
9-483594fi
9-4832964
9-4829981

Secant.

10 1430659
101431879
1014.33100
10*1434322
10-1435545
101436768
10-1437992

1001314049
10-012887719
10-0126349:9
r00123821 9

10-01 33932; 9-4826997J 1 0- 1 439216
4824012 101440442
48210-26 101441668
4818038 10-1442891
4815049 10-1444122
4812059 101445350

1).

100121294'9

9 9911562
9 9914089
9-9916616
9-9919143
99921670
9-9924197

99926724
9 9929251
9-9931778
9-9934305
9-9936832
9-9939359

9-9941886
9 9944413
9-9946940
9-9949466
9-9951993
99954520

99957047
9-9959573
9-9962100
9-9964627
9-9967154
9-9969680

99972207
9-9974734
9-9977260
9-9979787
9-9982314
9-9984840

9-9987367
9-9989893
9-9992420
9-9994947
99997473
100000000

|2527
{2527
I2527
2527
2527
2527

2527
2527
2527
2527
2527
2527

2527
2527
2527
2526
2527
2527

2527
2)26
2527
2527
2527
2526

2527
2527
2526
2527
2527
2526

2527
2')26
2527
2527
2526
2527

100118766
10 0116239
10-0113711
100111184
100108656
10-0106129

10 0103601
10 0101074
100098547
10009r>019
100093492
100090965

10008S438
10 008'>911
10 0081384
100080857
10 0078330
10-0075803

4809068
4806075
4803082
4800087
4797091
4794093

9-4791095
9-4788095
9-4785094
9-4782092
9-47790S8
9-4776083

94773078
9 4770070
9-4767062
9-47ii4052
9-4761042
94758030

Cotanjf.

Dif.

10-0073276 9
10 0070749 9
10 00682221 9

10-0065695
100063168
10-0060641

10 0058114
10 0055587
10 0053060
10 0050534
10-0048007
10-0045480

100042953
100040427
10 0037900
100035373
10003-2846
10-0030320

100027793
10 00252S6
1000'22740
10-0020213
100017686
100015160

10 0012633
10-0010107
100007580
10-0005053
10-0002527
10 0000000

4755016
4752002
4748986
4745969
474-2951
4739932

9 4736911
9-4733889
9-4730866
9-4727841
9-47-24816
9-4721. "89

9-4718761
9-4715732
9 4712701
94709669
9-4706636
9-4703602

9-4700566
94697530
9-4694492
9-4691452
9-4688412
9-4685370

9-4682327
94679283
9-4676237
9-4673190
94670142
9-4667093

101446579
10-1447808
10-1449039
101450270
101451501
10145-2734

101453967
101455201
10-14)6436
101457671
10-1458907
101460144

10-1461381
101462619
101463858
101465098
10-1466338
10-1467579

101468821
10 1470064
101471307
10 147-2551
10-1473796
10-1475041

101476287
101477534
10 1478782
101480030
101481279
10148-2529

1220
1221
1222
1223
1223
1224

1224
1226
1226
1226
1228
1228

1229
1229
1231
1231
1231
1233

1233
1234
1235
1235
1236
1237

1237
1238
1239
1240
1240
1-241

1242
1243
1243
1244
1245
1245

r246
1247
1248
'1248
1249
1250

Cosine.

60
59
58

9-8569:«l

9-8568121

9-8566900

9-8565678|57

9-856445556

9-8563232155

98562008154

98560784'53
9-8559558 ,52
98.558332'51
98557106*50
9 8555878-49
9-8554650 48

9-8553421
9-8552192
9 8550961
98549730
9-8548499
9-8547266

47
46
45
44
43
42

9-8546033 41
9-8544799140
9 8543564*39
9-8542329 38
9 8541093 37

9-8539856

36

9-8538619 35
9-8537381 34
'J-8536142 33
9-8534902 '32

9-8533662
9-8532421

31
30

i

J1251

1251
1252
1252
1254
1254

Tanp:.

Verseds.

101483780
10 1485031
101486283
10 1487535
10*1488789
101490043

1255

10-1492554 ;Sfi
1014938IO,i.727
10-l495067!!r,?o
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9-8531179 29
9-8529936 28
9 8,528693 27
9 8527449,26
9 8.526204 25
9-8524959 ;24

9-85237 13123
9-8522466 22
9852121821
9-8519970 20
98518721 19
9-8517471:18

9'e516'22o'l7
9-8514969 16
98513717.15
9-8512465 14
9-8511211 13
9 8509957,12

9 8508702 11
9-8507446 10
9-8506190 9
9-8504933 8

101498843
101500103
10 1501363
10-1502625
101503887
101505150

Cosec.

1260
1260
1260
1262
1262
1263

D.

9-8503675
9 8502417

9 8501157
9-8499897
9-8498637
9-8497375
9-8496113
9-8494850

Sine.

7
6

5
4
3
2
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4 63S1

3 8064

541U

4440B

6 184

M

40

15963

3 8567

5 3623

44991

61284

23

44

604 5

41

1-5283

3-9363

&-2830

4-5924

603

246

6 24

■■

42

4-4689

4-0148

4-6839

5-9J

53

6 83

1 4

31

4-4457

4-0294

5-1867

4-7009

592

6-668

04

^

43

J-3881

4-0920

5-1196

4-7740

585

80

4

44

43160

4-1680

50354

4-8626

5754

23

34 4

ih

4-2426

4-2426

4-9497

4-9497

5-6519

4

4

~

?

D=|,.

Ul.

D^

-uC

TT'

De

U g

a

£

C

Di..6, 1

D. . 7.

"

i

Q

0.

360 LLNGTHS OF CIRCULAR ARCS. Tab. 1 1 . |

D Arc

Del Arc

I|D,I Arc_ 1

' Ai-.-

,"|A..

l!li^

I ■U\TihS

6lll064H5Us||l'Jl|2-lUW484|

1 -2909

1 4

2 -03-1906

1-082104

122 2 1293017

2 5818

2 9

3 ■o.vja.-.Fi

f

l-099,->57

12.1 2-14K75.-10

3 8727

3 14S

at 2

4 ■Ofigsis-'

1117010

12-1 2-1642083

4 11636

4 194

4 3

5 -oernees

I]341fi4(l

125 2-181(1616

5 14544

5 242

5 4

6 -iiwnas

6

1-151917.

lar. 2^1991149

6 17453

6 29

6' 5

7 'laairao

G

1-1693706

127 2-2165682

7 20362

7I339

7) fi

6 -I396gb3

R

11868239

128 ^■2340214

8 23271

8, 388

8 6

9 ■ir.70796

6

12042772

129 2-2514747

9 26180

9 436

9; 7I

ID -ly^SiU

7

1"Z31730S

130 -2-2689280,

29089

10 485

10.8

11 -1S19S6-..

T

1-2391838

131 2"2863ai3

1 31998

U .533

11 9

12 '2094395

72

1 '2566371

U-i 2'303S.'!46

2 34907

12 582

12 10

13 -SaGBgiJS

73

1-2740904

T33 2-3212879

3 37815

13 630

13 11

14 -24434'il

74

1-291S43G

134 2-3J87412:

4 40724

14 679

14,11

IS -2617994

75

1-3089969

135 2-3561945

5 43633

I5I 727

15 12

IB 'i7Sr-i7

76

l'3264502

136 2-3736478'

6 46542

16 776

16 13

17 ■29670(10

77

1-34:19035

137 2-3911011:

7 49451

17 821

17,14

18 -3141593

78

l-36l35fiW

138

2-4085544,

8 5-2360

18 873

18 is

l!l -33]G]'JG

79

1-3788101

139

242li0077

9 55269

9 921

19,15

20 -3490659

80

1'396263J

140

2-4431610,

» 58178

20 970

20 16

21 -38GS1U1

81

1-4137167

141

24609143

1 G1087

ariois

21 '17

22 -3839724

l'431i700

142

2-4783675

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23 -4ai-l2>7

83

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23 19

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84

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85

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36 -4537856

86

I-aU0983j

146

2-5481807, -

37 -4712389

87

l'S18J364

147

2'5656340l '■i

38 -4B8692;J

88

1-5358897

148

2 5830873' '-

29 -506 [455

89

1-5533430

149

2-6005406' 2

30 -5235988

90

1-5707963

150

2*179939 3

o7-2,;Y"'i'^-'i

fU-21

31 -Ml 052)

91

1 '5882496

151

2 6354472' 3

90175

1 1.503

31I35

32 -5585054

92

l'6O57029

152

2-65290U5 3

2 93084 ;

a 1,551

32 26

33 -5759587

93

1-6-231562

153

2-6703538 3

3 95993 ,

13 1599

33 27

34 '5934119

94

1-6406095

154

2-6878070 3

4 98902 1

14 1648

34 27

35 -6I0BG52

95

1-6580628

155

S705a603 3

J 101811

5 1697

35 28

36 -6283 IS5

96

1-6755161

156

27-227136 3

6 104720

G I74S

36 29

37 '6457718

97

1-6929694

157

2-7401669 3

T 107629

7 1794

37 30

38 '6632251

98

1-7104227

158

2-757620-2 3

B 110536 :

S 1842

3831

39 '68067S4

99

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159

2-7730735 3

9 I 13446 3

IISSl

3H32

40 -G9SI3I7

100

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ICO

27923268 1

116355 4

19.19

4032

41 '7155B50

101

-7627825

161

28099801 4

119264 |4

1 198S

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■12 '7330383

102

■7802358

162

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43 35

44 '7679449

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164

2-8623400 4^

127991 !4

4 2133

44 36

45 -7853982

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165

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46 '8028515

ion

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166

2'897240U| 46'13380g 4

6 22.i0

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47 -8203047

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167

2-9146999! 47 1.36717 ■*

7 2279

47 39

43 -8377580

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-8849556

168

2932I531 48ll3962fi '4

9 2327

48 39

49 -a.-.52113

09

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9 '2376

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10

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170

2-9670597 5

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171

2-98-15130 5

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1 2473

141

52 -9075712

12

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172

3-0919663 ,5

151262 |5

2^521

2 43

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13

■97-i'2iiO

173

1-0194196 15

!l54l71 i5

3 2570

3 43

54 '942-1778

14

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174

J-0368-29 5

157080,5

4 2618

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55 '95ug311

15

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75

30543262 5

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5 2666

544

56 ■977:<&I4

16

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76

J-0717795 5

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6 2715

6 4S

57 '99)8377

17

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177

J 0892323 5

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7 -2763

7 46

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18

78

3-1D6B861 5

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8 47

59 i-oiynin.

19 ^-076^118

79

M241394 5

171624 15

5 '2860

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(to;3-U15q27|i6

174533 ,6

2909

048

i) Arc 1

Del Art Del Arc || '

Arc 1

A.c

"Ia

Tab. 12. COMMON and hyp. logarithms. 361

CL
•01

HYP. LO.

CL
•26

HYP. LO. 1

CL
•51

HYP. LO.

CL
•76

HYP. LO.

•02302585

•59867212

117431840

1-74996467

•02

•04605170

•27

•62169798

•52

119734425

•77

1-77299052

•03

•06907755

•28

•64472383

•53

122037010

•78

1-79601637

•04

•092103-40

•29

•66774968

•54

1^24339595

•79

1-81904222

•05

•11512925

•30

•69077553

•55

1-26642180

•80

1-84206807

•06

•13815511

•31

•713801381

•56

^28944765

•81

1-86509393

•07

•161 18096

•32

•7368-2723

•57

1-31247350

•82

18881 1978

•08

•18420681

•33

•75985308;

•58

1-33549935

•83

1-91114563

•09

•207-23266

•34

•782878931

•59

1358:)25-20

•84

1-93417148

•10

•23025851

•35

•80590478

•60

138155106

•85

1-95719733

•11

•253*28436

•36

•82893063

•61

1-40457691

•86

1-98022318

•12

•27631021

•37

•85195648

•62

1-42760276

•87

2-00324903

•13

•299336061

•38

•87498234

63

1-45062861

•88

2-02627488

•14

•32236191

•39

•89800H19!

•64

1-47365446

•89

204930073

•15

•34538770

•40

•92ia3404;

•65

1-49668031

•90

207232658

•16

•36341362

•41

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•66

1-51970616

•91

2 09535243

•17

•39143947

•42

•96708574

•67

1-54273201

•92

2-11837829

•18

•41446532

•43

•990111591

•68

1-51575786

•93

214140414

•19

•43749117

•44

1013137441

•69

1 58878371

-94

216442999

•20

4605170::

•45

103616329;

•70

1-61180957

-95

218745584

•21

•48354287

•46

1059189141

•71

1-63483542

•96

221048169

•22

•50656872

•47

108221499

•72

1-65786127

•97

2^23350754

•23

52959457

•48

1- 10524084

•73

1-68088712

•98

2-25653339

•24

•5526-2042

•49

112826670.

•74

1-70391297

•99

2-27955924

•25

•a7564627 50 M5129255! 75 |

1-72693882

100

2-30258509

Tab. 13. — A TABLE of Rumbs, showing the Degrees,
Minutes, and Seconds, that every Point and Quarter-point
of the Compass makes with the Meridian.

North.

NbE

NNE

NEbN

NE

NEbE

ENE

EbN

Ea^t

NbW

NNW

NW b N

NW

NWbW

WNW

WbN

West

Pls.qr.

0.

1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

6

6

6

6

7

7

7

7

8

1
2
3

1
2
3

1
2
3

1
2
3

1
2
3

1
2
3

1
2
3

1
2
3

2 48

5 37

8 26

11 15

14 3

16 52

19 41

22 30

25 18

28 7

30 56

33 45

36 33

39 22

42 11

45

47 48

50 37

53 26

56 15

59 3

61 52

64 41

67 30

70 18

73 7

75 56

78 45

81 33

84 22

87 11

90

45
30
15

45
30
15

45
30
15

45
30
15

45
30
15

45
30
15

45
30
15

45
30
15

Pu.qr.

1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8

1

2

3

1

2

3

1

2

3

1

2

3

1

2

3

1

2

3

1

2

3

1

2

3

South.

SbE

SSE

SEbS

s;-:

SEbE

£SE

EbS

Etst

SbW

SSW

SWbS

SW

SWbW

wsw

WbS

West

362

TABLE XIV.

Eqotvalknt ExpasssioNs for Sin. A» Cos. A, and Tan. A.

1.
2.
3.
4.

5.
6.
7.

8.

9.

10.

11.
12.

13.

14.
15.

VALUES OF SIN. A.

FoKMULA. . . • COS. A tan. a.

COS. A

cot A

^(1 — COS.* a).

1

:. or

1

^(1 + cot.' a)' cosec. A
tan. A

V(l +tan*A)*
2 sin. ^ A COS. ^ A.

1 — COS. 2 A

n/

2 tan. ^ A

1 + tan. *i a"
2

cot. ^ A + tan. ^ A *

I
cot. A + tan. ^ A '

2 sin.« (45° + i a) - 1.
1 - 2 sin.» (45° — ^ a).
l-tan.«(45°- j^A)

1 + tan.* (45° -4a)'

tan. (45° + 4 a) - tan. (45*

-4 a)

tan. (45^ + i a) + tan. (45° - 4 a) '
sin. (60° + a) - sin. (60° - a).

VALVES OF COS. A.

,-. sin. A

16. .

tan. A

17. sin. A cot. A.

18. ^(1 - fiin.« a).
1

19.

20.

, or

I

^(1 + tan.* a) sec. a

cot. A

V(l +COt.«A)'

21. COS.* i A — sin.* 4 A.
32. 1-2 ain.« J a.
23. 2 COS.* i A - 1.

24.

25.

\/

26. —

1 + COS. 2 A

2 •

1 - tan.* 4 A
1 + tan.«iA'
cot. 4 A — tan. 4 A

{

27.

28.

29.
30.

cot. i A + tan. 4 A *

1

1 + tan. A tan. J a '

2

tan. (45° + i a) + cot (45° + ^a)'
2 COS. (45° + 4 A) cos. (45° -^ 4 a).
COS. (60° + a) + COS. (60° ^ a)

VALUES OF TAN. A.

31.

32.
33.
34.
35.

sin. A

COS. A

1

cot A

\/(^-0-

sin. A

\/(l — sin.* A) *

^(1 — COS.* a)

36. -

COS. A

2 tan. 4 A

37.

38.

39.
40.

41.

42.

43.

1 — tan.* 4 A *

2 cot. 4 A
cot.* i A - 1 '

2

cot. i A - tan. J A '
cot A -- 2 cot. 2 A.
1 — cox. 2 A

sin. 2 A

sin. 2 A

1 + COS. 2 A

/I — COS. 2 a
V r4-~cosr2A'
tan. (45° + ^ a) - tan. (45°

-iA)

TA.BLE XV.

363

Formula rblativb to two Arcs or Angles.

L siiL (a + b)
2. sin. (a — b)

ft. COS. (a + b)
I. COS. (a -^ b)

I. tan. (a + b) =

8. tan. (a — b) s

sin. A COS. B + COS. a sin. b.
sin. A COS. B ~ COS. a sin. b.
COS. A COS. B - sin. a sin. b.
COS. A COS. B + sin. a sin. b.

tan. A + tan. b
1 — tail. A tan. b

tun. A — tan b
1 + tan. A tan. b

jsin. (45® zb b) =1 cos. b ± sin. b
Icos. (45° ; B) = 3 7^

B. tan. (45° ± b) = -zi- .

'' 1 If tan. B

9. tan.« (45° ± i b^ =

1 d: sin. b
1 ip sin. B

0.

L

2.

sin. f a+b) tan. A+tan. b ^ cot, B+cot. a
siu. (a-bJ

cos. (a+b)

COS. (a-^ b) cot. B + tan. a cot. a 4- tan. b

sin. A + sin. b tan. i^ (a + b)

tan. A — tan. b
cot. B— tan. A

cot. B— cot. A
cot. A— tan. B

14. sin. A COS. B = ^ sin. (a + b) + i sin. (a — b).

15. COS. A sin. B =: ^ sin. (a + b) — j^ sin. (a — b).

16. sin. A sin. b = ^ cos. (a ^ b) — ^ cos. (a + b).

17. COS. ACOS.B =^cos. (a+ b) + J cos. (a «-- b).

18. sin. A + sin. b =: 2 sin. ^ (a+ b) cos. } (a ^ b).

19. COS. A + COS. 8 = 2 COS. i (a + b) cos. iik'^ b).

sin. (a + b)

20. tan. A + Un. b = ^^ .

COS. A COS. B

sin. (a + b)

21. cot. A + cot. B = . ^ . — - .

sin. A sin. B

22. sin. A— sin. b == 2 sin. ^(a— b) cos. } (a + b).

23. COS. B — COS. A = 2 sin. j^ (a» b) sin. } (a + b).

sin. (a — b)

24. tan. a — tan. b = ^ .

COS. A COS. B

sin. (a — b)

2d. cot. B — cot. A == -: : .

sm. A. sm. B

g^ (sin.* A — sin.' b = 1

\C0S.* B — COS.* A = j

sin. A — sin. B

tan. i (a — b) '

cot. j^ (a + b)
COS. B — COS. A tan. J (a — b) *

^ COS. B + COS. A

8. —

sin. (a — b) sin. (a + b).

27. COS.* A — sin.* b = cos. (a •

sin. (a ■
29. tan.« a — tan.« b :r. — ^

29. cot.« B — -ot* A =

b) cos. (a + b).
b) sin, (a + b)

COS.* A COS.* b

sin. (a — b) sin. (a + b)
sin.* A sin.* b

DirrERBNCES OF TRIGONOMETRICAL LINES.

0. A sin. b r= 2 sin. j^ A b com. (b + i^ ^ b).

1. — A COS. B = 2 sin. J A b sin. (b + ^ A b).

^ ^ sin. A R

2. Atan. B = - -- - — : .

COS. B cos (b + A e)

* sin. A B

S. — A cot B = . , --. -: .

sin. B sin. (b + A b)

^ f A(8in.*B)=l . . • /^ I \ ..\

. ^ , , sin. A R sin. (2 b 4- ^ b)

5. A (Un.« b) = ; m\ _^ A ^ '

^ COS. b cos." (b + A B)

, , . , sin. A B sin. (2 B + A b)

6. - A (col.* n) = - . , T-r)~r jr-<- •

sin.* B sin.' (b + A b)

DIFFERENTIALS OF TRIGONOMETRICAL LINKS.

37. d sin. b =: d b cos. b.

38. — d COS. B = d B sin. b.

da

39. d tan. b =

COS.' B

d B
40. — d cot. B = . ,

sin." B

I d(sin..B)=|2d
\ — d (cos.* b) = )

B sin. B cos. B.

- ^ 1 , .V 2 d B tan. b
42. d (tan.* b) =

cos." B

43. - d (cot.« b) =

2 d R cot. B

sin.' B

TABLE ■XVr.
riCAL FoRMUL*, poR SOLVING All the

ANflLE ABC, OF WHICH tHHEt F,

^{■C + ic" - 2 BP X AC col

M Mi. • ± ^;io' - mc' mn*
AOcos.Ai^C.c'-K^.in'

l„.

e«.i + .in.*col.

■c

COS. +iio, OCOI.

AS cm. A + Aa>io.

A col. C.

■c co>. c + sc »a.

col. A.

^C«' + a.'-2b

X A. to). B)

..co..A±V(«:'

- ii« lio.' a).

.Ccoa.o±V(A^

- ^ .in." 0).

v'tK-' + .«»

- 2« ^ *
c*in. B

cco*.c;

V("c'+Afl'

- 2 BC X A. co». »)

x/-(

»»■ + Ar' -

^y

2ai> X A

lin. (ic «>•

C±^AB«

AC>....'C)

IB

jin. > (.B cos

B±V.C«-

A.' .Id.' bJ

- ™. c. " .).

^(,«' + ..•-!» X.« .«..)■

^;k' + .."-s.,xu.....)-

.B" + AC* - IK^

...,..•. T"...,?(.i'-..' .«.'.)

„....„,...*.

±^(...^-.rfA..,-

- u,, (. + c).
t.n,B + tii..c

Un. .laa.O- I'

te >in. *

.B - K CO.. ■

*0.iQ.C^Bol.gVt»'-«'.iB.'<;J
.BO..B±^(.^-..-,i..BB) ,

.III-bTtoH V (AfJ - „^ rill.' -.^ J

TABLE XVI. CONTINUED.

365

VALUBA OF SIN. B.

AC sin. A

BC

55. FOKMULA

.^ AC sin. c

56. .

AB

57. sin. (a + c).

58. sin. A cos. c + c^* a* *'<'• ^*
AC sin. A ^

>^(aB^ + AC* — 2 AB X AC COS. a) '

AC sin. c

60

61

62.

63.

^(BC* + AC* — 2 BC X AC COS. C) '
r /BC« T AB^ — AC*\*

• V ^ " \ 2BC XAB )'

sin. A (ab COS. A i ^Bc'' — AB* sin.* a)

BC

in. c (bo cos, c ± j/as* ^ nc* sin.* c)

sin

AB

64.

65.

66.
67.

68.
69.
70.
71.
72.

▼ALUIS OP cos. B.

73.
74.

BC

±V(AB*-AC*S!n.«0)

AB

— COS. (a + c).
sin. A sin. c — > cos. a cos. o.

AB — AC cos. A

V(a»^ + AC* — 2 AB X AC cos. a) *
BC — AC COS. C

^(BC* + AC* — '2 BC X AC COS. c) *
BC* + AB* — AC*

2 BC X AB
AB sin * A ^ COS. A ^(bC* — AB^ Sin.* a)

BO

BC sin.* c I^I COW, c >^(ab* — bc* tin * c)

AB
VALUES OP TAM. B.

AC sin. A

AC sin. c

± Vu** — ^'^ ***** ^) '
75. — Un. (a 4- c).

tsn. A -|- tAn. c

76.
77.
78.

tsu. A tail, c — 1
AC 4in. A

AB — AC COS. A '

AC sin. o

BC — AC COS. C *

AB COS. A i V("*^ ~ *■' *'"•* *)

80.
81.

AB *iQ. A ip cot. A tj (b<* — AB* sin.* a)

BC cos. c j; ijij^^ " *^* •'"•* c)
BC sin. c ip cot. c ^(ab* — BC* sin.* cV

VALUES OP SIN. C.

82. --_

83.

84.
85.

86.
87.

88.
89»

90.

AB Sin. B
AC

AB sin. A

BC

sin. (a + ■).

sin. A COS. B + COS. a sfn. b.
AB sin. B

^(bC* -f- AB* — 2 BC X AB COB. b) '

AB si;\ A

VCab* + AC* - 2aB X AC CCS. a) *

v/

\ 2bc X AC /

sin. B (BC COS. B + Vac* — bc* »in.* b)

AC

sin. A (ac cos, a ± ^bc* — a<* <in.* a)

BC

VALUES op COS. C.

91 ± V(ac^ — AB^ sio.* B)

AC

d2.

bo

93. — COS. (a + b).

94. sin. A sin. a — cos. a cos. b.

95.
96.
97.
98.
99.

BC — A8 COS. B

100.
101.

102.
103.

104.

105.

106.
107.
108.

i^(BC* + AB* — 2 BC X AB COS. b) '
A C — AB COS. A

V(a8* + AC* - 2 AB X AC COS. a)
BC* + AC^ — AB*

2bc X AC
BO sin.* B If COS. B V(ac* ~ BC* sin.» b)

AC

AC sin.* A y COS. A V(bc* - AC* sin.* a)

BC
VALUES op tan. C.

AB sin. B

± VC^c* — AB* »in.* b) '
AB sin . A

± V(»C* - AB* sio.* a) *

— Un. (a + 8).
tsn. A -|- tsn. B

tan. A tan. b — 1 *

AB sin. R

BC — AB COS. B

AB sin. A

AC — AB COS. A

^ V Ibc* + ac*- ab7 " ^•

BC COS. B ;t V(a*^ "■ ■^* *'"•* ■)

BC sin. B Ifl cot B i^(AC* — BC* sin.* b)'

AC COS. A ± V(*^ "" **^ ""* a)

AC tin. A ip cot A i^(BC* — AC* sin.* a)*

366

TABLE XVII.

Analytical Expressions in reference to a Spherical Triangle ABC.

1. Formula .... sin. a =

sin. EC &in. c

sin. AB

2.

sin.

A

=

sin. Rc sin.

B

sin. AC

8.

sin.

B

=

sin. AC sin.

A

sin. Bc

4.

sin.

B

=

sin. AC sin.

C

sin. AB

5.

sin.

C

• tflB

sin. AB sin.

B

sin. AC

ft

fiin.

n

sin. AR sin.

A

7. cos. A :

8. COS. A :

9. COS. R

10. COS. B

11. COS. C

12. COS. n =

13. tan. A =

14. tan. A =

15. tan. B =

sm. BC

COS. BC ~ COS. AB COS. AC

sin. AB sin. ac
COS. BC sin. B sin. c — cos. b cos. c.

COS. AC — COS. BC COS. AB

sin. BC sin. AB
COS. AC sin. A sin. c -• co.<<. a cos. c.

COS. AB — cos. BC cos. AC

sin. BC sin. ag
cos. AB sin. A sin. b — cos. A cos. b
sin. b

sin. AB cot. BC — cos. AB COS. B '

sin. c
sin. AC cot. BC — cos. ac cos. c *

sin. c

sin. BC cot. AC — cos. bc cos. c

16. tan. B = -7

sin. A

sin. AB cot. AC ^ COS. AB COS. A

17. tan c = -r

sin. A

18. tan. c = -T

Sin. AC cot. AB — COS. AC COS. A

sin. B

sin. BC cot. AB — cos. RC COS. R

19. sin. BC =

20. sin. BC =

21. sin. AC =

22. sin. AC =:

23. sin. AB =

24. sin. AB =r

25. COS. BC ==
26 COS. BC =

27. COS. AC

28. COS. AC

29. COS. AB

30. COS. AB

31. tan. BC =

32. tan. bc :=

33. tan. ac ==
34 tan. ac =

35. tan. ab =

36. tan. ab =

sin AB sin. A

sin. c

sin. AC sin.

A

sin. B

sin. BC sin.

B

sin. A

sin. AB sin.

B

sin. c

sin. AC sin.

C

sin. B

sin. BC sin.

C

sm. A

COS. A + COS. B COS. C

sin. B sin* c
COS.A sin. AB sin. ac +cos. ab (

COS. B + COS. A COS. C

sin. A sin. c
COS. B sin. BC sin. AB + COS. bc <

COS. C + COS. A COS. R

sin. A sin. b
COS c sin. BC sin. ac + cos. bc i
sin. ab

sin. B cot. A -f- COS. B COS. Al

sin. AC

sin. c cot. A -h cos. c cos. At
sin. BC

sin.

c

cot.

B +

sin.

COS.
AB

C

C<iS.

BC

sin.

A

cot.

B +
sin.

COS.
AC

A

COS.

A I

sin. A cot. c -i- cos. a tos. ai
sin. BC

sin. B cot. c -h cos. b cos. bc

In workings by loporitlims it is often necessary to transform tliese expressions by the
duction of a subsidiary arc or angle. Thus, in theorem 26, find a dependent an^le, s, \
expression tan. s = cos. a tan. ab. Subsiitule for cos. a, in theor. 2S. its vahie in this,

(ens. AC cub. s -f- sin. AC i
-

cos. s

= — '-^ ^-^ . The latter expression is evidently logarithmic ; and the transi

COS. s

tion is equivalent to dividing the triangle into two right-angled triangles, by letting fall
I pendicular.

TABLES Xnxi. XIX.

367

s

.V « .

= II II

HM

:3 C

1^

H H

es
S

I ^

.5 5

Z
O

^

^

b CQ I a, c

I II

c

I I

II II

C8 H«

I

O

11 II

^

^

o

»

■
I

II

c

o
o

i2 I

o

c

u

o
o

>

«

I

f

II V .

I -* s

§ i 3

I ^

C4
X

e
eo ^

11 V

+:

fa w

2:

o

o

c
'55

X

(N

<

II

5 H

c a.

••*a

Iw ^>

II II

04

<
a

B

I
II

5 H

I

o

C

I! II

c c

X

<

C

09

H-

a,
+

V.

bo
CO

a*

m

C
O

o

^ i

r a.

O

09

CO

X

■<

O

II II

• •

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c

C

O

*ft.a,x

I 2 0» IN I

4 3 X X S

I
1i*

eo

eo

d

.S fi

'S 'S

I I

II II

9)
X

+

CO

Si*'

.s

a.

I

o

a, ' ca X

<M z^* '^^ -h

o\

II . ^ «

00

.S

li

-2 I-
o

3

'^ •_

Mi M

2: o

B -^

o; a;

•O en

CQ C8

0, «

^ Q>

♦- -C

O o

B >>

.X a.

3 «

cr en

W S

9
en

.S .S I

'S *35 •

II II II

H H H

o o o

o o o

•5 2

a ^

9

a . ^

* "K ^ *<

a

2

•6
%

I

If

-a

>" I «

9

o
z

o

(A

<

I

-Mi

-s II II §

ft,ft, .

^ e e 9

^ *5 i5 " "

•J . • - ■«'

'i's 8 S
II II ^ o

Mini

\ ' * u

° E 5 e
•= •= i 8

o u '5 «o

D

OOOkO^'

^ II C^ ?

"O «f V o

3 ^ j: «

^ ® 3 c •?

/< ^ Si; .^^ ,j

** S o ^ "= =

no S ■£ -o «
« S.r 5 •

o

I.

s

U
CO

§ «

« M

c «» 2 t: S

o > S.'5 5 c-

e« • « .S 01 •* .r

•S *u. t * « .

+t

«» o o ». S

•« ca a.-5 >%#<
c ■£ «j 5 2 c

a c 2 I' -s 'J
11^ a •■5.2

«^ e c ^ cr

= 2

« •

u2

• «

II 11

01 CO

hlTHBEKa OFTEH URKD

) CALCUL*TIOKm WITH THEIB I^Oa*lITH>IB.

Circumference of a circle, to diameter 1 "^

Sufface of a aphere to diameter 1 J- ■= SU15926

Area of a circle to radius 1 J

Area ofa circle to diameter 1 = -TSSSBB^

Capacity of a spliere to diameter I = -5235998

Capacity ofa sphere to radius 1 = 41S87902

3-141S9, &c.. nearly = !/(Sl-0062S). nearly =
V(97-4090B9), nearly = V(306-02), nearly =
V{96l-39). nearly = y(9488b3), arc equal

to radius

Arc equal to radius, expressed in seconds

Len(rt)i of 1 degree

=: 57''2957795

= 206264 "-8

= ■01745329 •

= ■00l)0048&

= 00000970

= •01)001454

= 2-71S2918

= -43429448

= 2-3025851

= 43200

= -00002315

= 86400

= 00001157

= 129C000

= -0033333

= 365-25638

Tropical revolution of ditto = 365 242-26

Number whose Hyper, lof;. is ^ 1

Modulus of ttie common logarithms. ....

Complement lo the same

12 houm, espressed in seconds

Complement to the same

24 houra, expressed in seconds

Complement to the same

360 degrees, expressed in seconds

Compression of the eartli = ^j^

Sidereal revolution of the eaKh, in days .

: 3155815U"
=: 31556929"

Sidereul year, in seconds
Tropical year, in seconds
Passage of a comet, perihelion dbtance 1, from

perihelion loextremity of latus-rectum s= 109*'61545

Log. k, (Gauss. Theor. M. c. c. 1.) k

k in seconds. (Gauss. Theor. M. c. c. 6.) .

rSidereal time into mean solar time

= 00172021
= 3548"1876

P

r}"«-{:

i.=<-

— feet into metres

- toiw into Ensli.h f«l1 „5j..3 /

- feel iiitu English teet j (.

— metre uito English feet

— "^ millimetres inU) English inches

= ;2 I Ceiitcs. degrees of quadrant into sexapsi degrees

^ ~g minules of do. into minutes

^ [_ secpnds of do. into seconds

I The arithmetical complements of these Inst 10 logarithms will serve to cc
j solar lime into sidereal time, metres into toises, &c., English feet into
I and the seugesimal divisions of the quadrant into the centesimal divisi

04971MI

I

d-89309»:

1-75S1226
&-3l44iSI

8 241577S
4-6S53749 '
4-9S66049
&'16!<t»6I
0-434294i

9 6377843
0-3622137
4-6354837
53645163
4-9365137
50634663

6 11)!6050
■■52287S7 1

2-5625979 ,
2-5623910

7 4991116
r-4990947 ,

3-039S71S :

8 2355SI4
3-5JU006J
9-99S9126
O-2S9S2O0

9 5116697
0-&05S372
0<l27G^60
0-51599-29
8'595i;41 :
9-9542425 '
1-7323939 i
3-5105450

/

B't\?/\w isigf^

I

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