TABLES
or
LOGARITHMS OF NUMBERS
AND OF
SUES AND TAIGENTS
FOR EVERT
TEN SECONDS OF THE QUADRANT,
WITH OTHER USEFUL TABLES.
BY ELIAS LOO MIS, LLJX,
PKOFESSOE OF NATURAL PHILOSOPHY AND A8TRONOMV IN TALK COLLEGE, AND ATTTHOK OT
"COTIESE OP MATHEMATICS."
TWENTIETH EDITION.
NEW-YORK:
HARPER & BROTHERS, PUBLISHERS,
329 & 331 PEARL STREET,
FRANKLIN SQUARE.
1862.
Entered, according to Act of Congress, in the year one thousand eight hund ed and forty-eight, bj
HARPER & BROTHERS,
in the Clerk's Office of the District Court of the Southern District of New York.
CONTENTS.
EXPLANATION i)P THE TABLES Y
TABLE OF LOGARITHMS OF NUMBERS 1
LOGARITHMIC SINES AND TANGENTS 21
NATURAL SINES AND TANGENTS . .... 1 16
NATURAL SECANTS 134
LENGTHS OF CIRCULAR ARCS 1 35
TRAVERSE TABLE 136
MERIDIONAL PARTS 142
CORRECTIONS TO MIDDLE LATITUDE 149
LOGARITHMS FOR COMPOUND INTEREST, E^C 1 50
PREFACE.
THE accompanying tables were designed to afford the means of per
forming trigonometrical computations with facility and precision. The
tables chiefly used in this country for purposes of education extend to
six decimal places, like those in the present collection; but the pre-
cision which they are designed to furnish is only attained by a serious
expenditure of labor. In the Table of Logarithms of Numbers they do
not furnish the correction for a fifth figure in the natural number, and
the labor of computing this correction is such that I always prefer the
use of Hutton's Tables, extending to seven places, even in computations
to which six-place logarithms are abundantly competent. In the pres
ent collection, the correction for a fifth figure of the natural number is
introduced at the bottom of each page, and the table is thus rendered
nearly as useful as one of the common kind extending to 100,000. The
whole has been carefully compared with standard authors, and nearly
a dozen errors have thus been detected in the common tables.
The principal table in this collection is that of Logarithmic Sines and
Tangents. The common tables in this country extend only to minutes,
with differences to 100". If, in a trigonometrical computation, angles
are only required to the nearest minute, tables to five places are quite
sufficient ; but if the computation is to be carried to seconds, these can
only be obtained from the common tables by a great expenditure ol
time and labor. In the present collection, the sines and tangents are fur-
nished to every ten seconds of the quadrant, and at the bottom of each
page is given the correction for any number of seconds less than ten, so
that the precision of seconds can be obtained with almost the same fa-
cility as that of minutes with the tables in common use. Moreover,
near the limits of the quadrant, by means of an auxiliary table,<*ines and
tangents are readily obtained, even for a fraction of a second. The
method of arrangement of the sines and tangents was suggested by a
table in Mackay's Longitude ; but the errors of that table, amounting to
several thousand, have been corrected by a careful comparison with the
work of Ursinus. By comparison with the same standard, more than
two hundred errors (chiefly in the final figures) have been detected in
the tables in common use.
The Table of Natural Sines and Tangents is of less use than the loga-
rithmic ; nevertheless, it is often important for reference, particularly in
analytical geometry and the calculus ; and it is useful as a stepping
stone to assist the beginner in comprehending the nature of logarithmic
339660
REFACE.
sines ar.d tangents. The Traverse Table commonly usea in this country
furnishes the latitude and departure to every quarter degree of the quad-
rant, for distances from 1 to 100, and occupies ninety pages. The accom-
panying table occupies but six pages, and yields ten times greater pre-
cision.
The Table of Meridional Parts extends to tenths of a mile, and grea
care has been taken to insure its accuracy. For this purpose, I have
compared all the similar tables within my reach, and among them have
found two which appeared to have been computed independently. Be-
tween them there were detected 674 discrepancies in the final figures.
These cases were all recomputed, and 78 errors were detected in the
jest copy compared. It is probable. that the numbers in this table are
not in every instance true to the nearest tenth of a mile ; but it is be
lieved that the remaining -errors are few in number, as well as minute.
This table is confidently pronounced more accurate than any similar
one with which I have been able to compare it.
The Table of Corrections to Middle Latitude was computed entirely
anew. The corresponding table in common use, which was originally
computed by Workman, contains more than four hundred errors, sev-
eral of them amounting to two minutes.
On the whole, it is believed that the accompanying tables will be
found more convenient to the computer than any tables of six decimal
places hitherto published in this country ; and that they will be pro-
nounced sufficiently extensive for all purposes of academic and collegri-
ite instruction, as well as for practical mechanics and surveyors.
EXPLANATION OF THE TABLES.
TABLE OF LOGARITHMS OF NUMBERS, pp. 1-20.
LOGARITHMS are numbers contrived to diminish the labor of Multiplica-
tion and Division by substituting in their stead Addition ancl Subtrac
tion. All numbers are regarded as powers of some one number, which
is called the base of the system ; and the exponent of that power of the
base which is equal to a given number, is called the logarithm of that
number.
The base of the common system of logarithms (called, from their in-
ventor, Briggs' logarithms) is the number 10. Hence all numbers are
to be regarded as powers of 10. Thus, since
10°= 1, 0 is the logarithm of 1 in Briggs' system ;
10'= 10, 1 " " 10 " "
10a=100, 2 " " 100 " "
103=1000, 3 " " 1000 " "
104= 10,000, 4 " « 10,000
&c., &c., &c. ;
whence it appears that, in Briggs' system, the logarithm of every num-
ber between 1 and 10 is some number between 0 and 1, i. e., is a prop-
er fraction. The logarithm of every number between 10 and 100 is
some number between 1 and 2, i. e., is 1 plus a fraction. The loga-
rithm of every number between 100 and 1000 is some number between
2 and 3, i. e., is 2 plus a fraction, and so on.
The preceding principles may be extended to fractions by means of
negative exponents. Thus, since
10^= 0.1, — 1 is the logarithm of 0.1 in Briggs' system ;
10~2=0.01, —2 " " 0.01 " "
\0~3=0.001, —3 " " 0.001
10~4=0.0001, —4 " " 0.0001
&c., &c., &c.
Hence it appears that the logarithm of every number between 1 and
0.1 is some number between 0 and — 1, or may be represented by — 1
plus a fraction; the logarithm of every number between 0.1 and .01 is
some number between — 1 and — 2, or may be represented by — 2 plus
v'\ EXPLANATION or THE TABLES.
a fraction ; the logarithm of every number between .01 and .001 is some
number between — 2 and — 3, or is equal to — 3 plus a fraction, and so on.
The logarithms of most numbers, therefore, consist of an integer and
a. fraction. The integral part is called the characteristic, and may be
known from the following
RULE.
The characteristic of the logarithm of a number greater than unity, is
cue less than the number of integral figures in the given number.
Thus the logarithm of 297 is 2 plus a fraction ; that is, the character-
istic of the logarithm of 297 is 2, which is one less than the number of
integral figures. The characteristic of the logarithm of 5673.29 is 3 ;
that of 73254.1 is 4, &c.
The characteristic of the logarithm of a decimal fraction is a negative
number, and is equal to the number of places by which its first significant
figure is removed from the place of units.
Thus the logarithm of .0046 is — 3 plus a fraction; that is, the char-
acteristic of the logarithm is — 3, the first significant figure 4 being
removed three places from units.
The accompanying table contains the logarithms of all numbers from
I to 10,000 carried to 6 decimal places.
To find the Logarithm of any Number between 1 and 100.
Look on the first page of the table, along the column of numbers under
N, for the given number, and against it, in the next column, will be found
the logarithm, with its characteristic. Thus,
opposite 13 is 1.113943, which is the logarithm of 13;
" 65 is 1.812913, " " 65.
To find ?//* Logarith?n of any Number consisting of three Figures.
Look on one of the pages from 2 to 20, along the left-hand column
marked N, for the given number, and against it, in the column headed 0,
will be found the decimal part of its logarithm. To this the character-
istic must be prefixed, according to the rule already given. Thus
the logarithm of 347 will be found, from page 8, to be 2.540329 ;
" " 871 " " " 18, " 2.940018.
As the first two figures of the decimal are the same for several suc-
cessive numbers in the table, they are not repeated for each logarithm
separately, but are left to be supplied. Thus the decimal part of the
logarithm of 339 is .530200. The first two figures of the decimal remain
the same up to 347 ; they are therefore omitted in the table, and are to
be supplied.
To find the Logarithm of any Number consisting of four Figures.
Find the three left-hand figures in the column marked N as before
EXPLANATION OP THE TABLES. vii
«jid the fourth figure at the head of one of the other columns. Opposite
to the first three figures, and in the column under the fourth figure, will
be found four figures of the logarithm, to which two figures from the
column headed 0 are to be prefixed, as in the former case. The char-
acteristic, must be supplied by the usual rule. Thus
the logarithm ©f 3456 is 3.538574 ;
" 8765 is 3.042752.
In sever-ai df the columns headed 1, 2, 3, &c., small dots are lound in
the place of figures. This is to show that the two figures which are to
be prefixed from the first column have changed, and they are to be
taken from the horizontal line directly below. The place of the dots is
to be supplied with ciphers. Thus
the logarithm of 2045 is 3.310693 ;
« 9777 is 3.990206.
The two leading figures from the column 0 must also be taken from
the horizontal line below, if any dots have been passed over on the same
horizontal line. Thus
the logarithm of 1628 is 3.211654.
To find the Logarithm of any Number containing more than four
Figures.
By inspecting the table, we shall find that within certain limits the log-
arithms are nearly proportional to their corresponding numbers. Thus
the logarithm of 7250 is 3.860338 ;
" " 7251 is 3.860398 ;
" " 7252 is 3.860458 ;
" " 7253 is 3.860518.
Here the difference between the successive logarithms, called the
tabular difference, is constantly 60, corresponding to a difference of unity
in the natural numbers. If, then, we suppose the logarithms to be pro-
portional to their corresponding numbers (as they are nearly^, a differ-
ence of 0.1 in the numbers should correspond to a difference of 6 in the
logarithms ; a difference of 0.2 in the numbers should correspond to a
difference of 12 in the logarithms, &c. Hence
the logarithm of 7250.1 must be 3.860344 ;
" " 7250.2 " 3.860350;
" " 7250.3 " 3.860356;
&c., &c.
In order to facilitate the computation, the tabular difference is insert-
ed on page 16 in the column headed D, and the proportional part for the
fifth figure of the natural number is given at the bottom of the page.
Thus, when the tabular difference is 60, the corrections for .1, .2, .3
&c., are seen to be 6, 12, 18, &c.
If the given number was 72501, the characteristic of its logarithm
would be 4, but the decimal part would be the same as for
Vlll
EXPLANATION OF THE TABLES.
If it were required to find the correction for a sixth figure in the nat
ural number, it is readily obtained from the Proportional Parts in the
table. Thus, if the correction for .5 is 30, the correction for .05 is ob
viously 3.
As the differences change rapidly in me first part of the table, n
was found inconvenient to give the proportional parts for each tabular
difference ; accordingly, for the first seven pages they are only given
for the even differences, but the proportional parts for the odd differences
will be readily found by inspection.
Required the logarithm of 452789.
The logarithm of 452700 is 5.655810
The tabular difference is 96.
Accordingly, the correction for the fifth figure, 8, is 77, and for the
sixth figure, 9, is 8.6, or 9 nearly. Adding these corrections to the num-
ber before found, we obtain 5.655896.
The preceding logarithms do not pretend to be perfectly exact, bu
only the nearest numbers having but six decimal places. Accordingly
when the fraction which is omitted exceeds half a unit in the sixth deH
mal place, the last figure must be increased by unity.
Required the logarithm of 8765432.
The logarithm of 8765000 is 6.942752
Correction for the fifth figure 4, 20
" " sixth figure 3, 1.5
" " seventh figure 2, 0.1
Therefore the logarithm of 8765432 is 6.942774.
Required the logarithm of 234567.
The logarithm of 234500 is 5.370143
Correction for the fifth figure 6, 111
" sixth figure 7, 13
Therefore the logarithm of 234567 is 5.370267.
To find the Logarithm of a Decimal Fraction.
The decimal part of the logarithm of any number is the same as that
of the number multiplied or divided by 10, 100, 1000, &c. Hence, for
a decimal fraction, we find the logarithm as if the figures were integers
and prefix the characteristic according to the usual rule.
EXAMPLES.
The logarithm of 345.6 is 2.538574 ;
87.65 is 1.942752;
" « 2.345 is 0.370143;
« " .1234 is 1.091315;
« « • 005678 is 3.754195.
EXPLANATION OF THE TABLC 3. .x
The minus sign is placed over the characteristic to show that this
alone is negative, while the decimal part of the logarithm is positive.
To find the Logarithm of a Vulgar Fraction.
We may reduce the vulgar fraction to a decimal, and find its loga-
rithm by the preceding rule ; or, since the value of a fraction is equal to
the quotient of the numerator divided by the denominator, we may sub-
tract the logarithm of the denominator from that of the numerator ; the
difference will be the logarithm of the quotient.
Required the logarithm of T3g-, or 0.1875.
From the logarithm of 3, .0.477121,
Subtract the logarithm of 16, 1.204120.
Leaves logarithm of T\, or .1875, 1.273001.
Tn the same manner we find
the logarithm of ^ is 2.861697 ;
" }ff is 1.147401.
To find the natural Number corresponding to any Logarithm.
Look in the table in the column headed 0 for the first two figures of
the logarithm, neglecting the characteristic ; the other four figures are
to be looked for in the same column, or in one of the nine following col-
umns ; and if they are exactly found, the first three figures of the corre-
sponding number will be found opposite to them in the column headed
N, and the fourth figure will be found at the top of the page. This num-
ber must be made to correspond with the characteristic of the given
logarithm by pointing off decimals or annexing ciphers. Thus
the natural number belonging to the logarithm 4.370143 is 23450 ;
1.538574 is 34.56.
If the decimal part of the logarithm can not be exactly found in the
table, look for the nearest less logarithm, and take out the four figures
of the corresponding natural number as before ; the additional figures
may be obtained by means of the Proportional Parts at the bottom of
the page.
Required the number belonging to the logarithm 4.368399.
On page 6, we find the next less logarithm .368287.
The four corresponding figures of the natural number are 2335.
Their logarithm is less than the one proposed by 112. The tabular
difference is 186 ; and, by referring to the bpttom of page 6, we find
that, with a difference of 186, the figure corresponding to the Propor-
tional Part 112 is 6. Hence the five, figures of the natural number are
23356 ; and, since the characteristic of the proposed logarithm is 4, these
five figures are all integral.
Required the number belonging to logarithm 5.345678.
The next less logarithm in the table is .345570
Their difference 7's 108.
x EXPLANATION OF THE TABLES.
The first four figures of the natural number are 2216.
With the tabular difference 196, the fifth figure corresponding to 108
>a seen to be 5. with a remainder of 10. which furnishes a sixth figure 5
nearly. Hence the required number is 221'
In the same manner we find
the number corresponding to logarithm 3 ~ $ ;
* « T.IV17S17 is .444444.
TABLE OF NATURAL SIN TANGENTS, pp. 116-133.
This is a table of natural sines and tangents for every degree ana
minute of the quadrant, carried to six places of figures. Since the ra-
dius of the circle is supposed to be unity, t:
less than unity. These sines are expressed in decimal parts of the
radius ; and. although the decimal point is not written in the table, it
must always be prefixed. The degrees are arranged in order at the top
of the page, and the minutes in the left hand vertical column. Directly
under the given number of - at the top of the 1 opposite
to the minutes on the left, will be found the sine required. The tw-->
leading figures are repeated at intervals of ten minutes. Thus
the sine of s. 11 2330:
"
The same number in the table is both the sine of an arc and t!
sine of its complement. The degrees for the cosines must be sought at
the bottom of the page, and the minutes on the right. Thus
the cosine oioJ 2:» • .4631
.. „
If a sine is required for an arc consisting of degrees, minuies. and sec
ondsj it may be found by means of the line at the bottom of each page.
which gives the proportional part corresponding to one second of arc
Required the sine of 8° 9' 10".
The sine of 8° 9' is .141:
By referring to the bottom of page 116, in the column mui
find the correction for 1" is 4.80 ; hence the correction for 10" must be
48, which, added to the number above found, gives for the sine of Sc
9' 10", .141813.
In the same manner we find
the cosine of 56° 34' 28" is .550S53.
It will be observed, that since the cosines decrease while the arcs m
crease, the correction for the 2S ' is to be subtracted from the cosine
34.
The arrangement of the table of natural tangents is similar to that of
the table of sines. The tangents for arcs less than 45° are all less than
radius, and, consist wholly of decimals. For arcs above 45C. the tan-
are all greater than radius and contain both integral and decimal
EXPLANATION OF THE T A 111.1:9. xj
ngures. The proportional parts at the bottom of each page enable us
readily to find the correction for seconds. Thus
the natural tangent of 32° 29' 18" is .636784 ;
" 74° 35' 55" is 3.63014.
To find the Number of Degrees, Minutes, and Seconds belonging to «
given Sine or Tangent.
If the given sine or tangent is found exactly in the table, the corre-
sponding degrees will be found afc the top of the page, and the minutes
on the left hand. But when the given number is not found exactly in
the table, look for the sine or tangent which is next less than the pro-
posed one, and take out the corresponding degrees and minutes. Find,
also, the difference between this tabular number and the number pro-
posed, and divide it by the proportional part for 1" found at the bottom
of the page ; the quotient will be the required number of seconds.
Required the arc whose sine is .750000.
The next less sine in the table is .749919, the arc corresponding to
which is 48° 35'. The difference between this sine and that proposed
is 81, which, divided by 3.21, gives 25. Hence the required arc is 48°
35' 25".
In the same manner we find
the arc whose tangent is 2.000000, to be 63° 26' 6".
TABLE OP NATURAL SECANTS, pp. 134-5.
This is a table of natural secants for every ten minutes of the quad-
rant carried to seven places of figures. The degrees are arranged in
order in the first vertical column on the left, and the minutes at the top
of the page. Thus
the secant of 21° 20' is 1.073561 ;
" " 81° 50' is 7.039622.
If a secant is required for a number of minutes not given in the table,
the correction for the odd minutes may be found by means of the last
vertical column on the right, which shows the proportional part for one
minute.
Let it be required to find the secant of 30° 33'.
The secant of 30° 30' is 1.160592.
The correction for 1' is 198.9, which, multiplied by 3, gives 597
Adding this to the number before found, we obtain 1.161189.
For a cosecant, the degrees must be sought in the right-hand vertical
column, and the minutes at the bottom of the page. Thus
the cosecant of 47° 40' is 1.352742.
TABLE OF LOGARITHMIC SINES AND TANGENTS, pp. 21-115.
This is a table of the logarithms of the sines and tangents for every
ten seconds of the quadrant, carried to six places of decimals The de-
in EXPLANATION OF THE TABLES.
grees and seconds are placed at the top of the page, and the minutes .n
the left vertical column. After the first two degrees, the three leading
figures in the table of sines are only given in the column headed 0", and
are to be prefixed to the numbers in the other columns, as in the table
of logarithms of numbers. Also, where the leading figures change, this
change is indicated by dots, as in the former table. The correction foi
any number of seconds less than 10 is given at the bottom of the page.
To find the Logarithmic Sine or Tangent of a given Arc.
Look for the degrees at the top of the page, the minutes on the lelt
hand, and the next less tenth second at the top ; then, under the seconds,
and 'opposite to the minutes, will be found four figures, to which the
three leading figures are to be prefixed from the column headed 0" ; to
this add the proportional part for the odd seconds from the bottom of
the page.
Required the logarithmic she of 24° 27' 34".
The logarithmic sine of 24° 27' 30" is 9.617033.
Proportional part for 4" is 18.
Logarithmic sine of 24° 27' 34" is 9.617051.
This is the logarithm of .414049 found in the table of natural sines on
page 120. The natural sine being less than unity, the characteristic
of its logarithm is negative. Tc obviate this inconvenience, the char-
acteristics in the table nave all been increased by 10 ; or the logarith-
mic sines may be regarded as the logarithms of natural sines computed
for a radius of 10,000,000,000.
Required the logarithmic tangent of 73° 35' 43".
The logarithmic tangent of 73° 35' 40" is 10.531031.
Proportional part for 3" is 23.
Logarithmic tangent of 73° 35' 43" 10.531054.
When a cosine is required, the degrees and seconds must be sought
at the bottom of the page, and the minutes on the right, and the correc
tion for the odd seconds must be subtracted from the number in the table
Required the logarithmic cosine of 59° 33' 47".
The logarithmic cosine of 59° 33' 40" i-s 9.704682.
Proportional part for 7" is 25.
Logarithmic cosine of 59° 33' 47" is 9.704657.
So, also, the logarithmic cotangent of 37° 27' 14" is found to be 10.115744.
The proportional parts given at the bottom of each page correspond
to the degrees at the top oi the page increased by 30', and are not
strictly applicable to any other number of minutes ; nevertheless, the
differences of the sines change so slowly, except near the commence-
ment of the quadrant, that the error resulting from using these numbers'
for every part of the page will sa Jom exceed a unit in the sixth deci-
mal place. For the first two degrees, the differences change so rapidly
EXPLANATION OF THE TABLES. xii
tuat the proportional part for 1" is given for each minute in the right-
hand column of the page. The correction for any number of seconds
less than ten will be found by multiplying the proportional part for i"
by the given number of seconds.
Required the logarithmic sine of 1° 17' 33".
The logarithmic sine of 1° 17' 30" is 8.352991
The correction for 3" is found by multiplying 93.4 by 3, which gives
280. Adding this to the above tabular number, we obtain
the sine of 1° IT 33", 8.353271.
A similar method may be employed for several of the first degrees
of the quadrant, if the proportional parts at the bottom of the page are
not thought sufficiently precise. This correction may, however, be ob-
tained pretty nearly by inspect:on from comparing the proportional
parts for two successive degrees. Thus, on page 26, the correction for
1", corresponding to the sine of 2° 30', is 48 ; the correction for 1", cor-
responding to the sine of 3° 30', is 34. Hence the correction for 1",
corresponding to the sine of 3° 0', must be about 41 ; and in the same
manner we may proceed for any other part of the table.
Near the close of the quadrant, the tangents vary so rapidly, that the
same arrangement of the table is adopted as for the commencement of
the quadrant. For the last as well as the first two degrees of the quad-
rant, the proportional part to 1" is given for each minute separately.
These proportional parts are computed for the minutes placed opposite
to them, increased by 30' , and are not strictly applicable to any other
number of seconds ; nevertheless, the differences for the most part
change so slowly, that the error resulting from. using these numbers for
every part of the same horizontal line is quite small. When great ac-
curacy is required, the table on page 114 may be employed for arcs
near the limits of the quadrant. This table furnishes the differences be-
tween the logarithmic sines and the logarithms of the arcs expressed in
seconds. Thus
the logarithmic sine of 0° 5' is 7.162696 ;
the logarithm of 300" (=5;) is 2.477121 ;
the difference is 4.685575.
This is the number found on page 114, under the heading log. sine
A — log. A", opposite 5 min. ; and in a similar manner the other numbers
in the same column are obtained. These numbers vary quite slowly
for two degrees ; and hence, to find the logarithmic sine of an arc less
than two degrees, we have but to add the logarithm of the arc expressed
iu seconds to the appropriate number found in this table.
Required the logarithmic sine of 0° 7' 22".
Tabular number from page 114, 4.685575.
The logarithm of 442" is 2.645422.
Logarithmic sine of 0° T 22" is 7.330997
xiv EXPLANATION OF THE TABLES.
The logarithmic tangent of an arc less than two degrees is found in
a similar manner.
Required the logarithmic tangent of 0° 27' 36".
Tabular number from page 114, 4.685584.
The logarithm of 1656" is 3.219060.
Logarithmic tangent of 0° 27' 36" is 7.904644.
The column headed log. cot. A+log. A" is found by adding -the log-
arithmic cotangent to the logarithm of the arc expressed in seconds.
Hence, to find the logarithmic cotangent of an arc less than two degrees,
we must subtract from the tabular number the logarithm of the arc in
seconds.
Required the logarithmic cotangent of 0° 27' 36".
Tabular number from page 114, 15.314416.
The logarithm of 1656" is 3.219060.
Logarithmic cotangent of 0° 27' 36" is 12.095356.
The same method will, of course, furnish cosines and cotangents ol
arcs near 90°.
The secants and cosecants are omitted in this table, since they are
easily derived from the cosines and sines.
The logarithmic secant is found by subtracting the logarithmic cosine
from 20 ; and the logarithmic cosecant is found by subtracting the loga-
rithmic sine from 20.
Thus we have found the logarithmic sine of 24° 27' 34" to be 9.617051.
Hence the logarithmic cosecant of 24° 27' 34" is 10.382949.
The logarithmic "cosine of 54° 12' 40" is 9.767008.
Hence the logarithmic secant of 54° 12' 40" is 10.232992.
To find the Arc corresponding to a given Logarithmic Sine or Tangent
If the given number is found exactly in the table the corresponding
degrees and seconds will be found at the top of the page, and the min-
utes on the left. But when the given number is not found exactly in
the table, look for the sine or tangent which is next less than the pro-
posed one, and take out the corresponding degrees, minutes, and sec-
onds. Find, also, the difference between this tabular number and the
number proposed, and, corresponding to this difference, at the bottom of
the page will be found a certain number of seconds, which is to be added
vO the arc before found.
Required the arc corresponding to the logarithmic sine 9.750000.
The next less sine in the table is 9.749987.
The arc corresponding to which is 34° 13' 0".
The difference between its sine and the one proposed is 13, corre-
sponding to which, at the bottom of the page, we find 4" nearly. Hence
the required arc is 34° 19' 4-".
EXPLANATION OF THE TABLES, xv
In the same manner we find the arc corresponding to logarithmic tan
gent 10.250000, to be 60° 38' 57".
When the arc falls within the first two degrees of the quadrant, the
odd seconds may be found by dividing the difference between the tab-
ular number and the one proposed, by the proportional part for 1". We
thus find the arc corresponding to logarithmic sine 8.400000, to be 1°
26' 22" nearly.
We may employ the same method for the last two degrees of the
quadrant when a tangent is given ; but near the limits of the quadrant
it is better to employ the auxiliary table on page 114. If we subtract
the corresponding tabular number on page 114 from the given logarith-
mic sine, the remainder will be the logarithm of the arc expressed in
seconds.
Required the arc corresponding to logarithmic sine 7.000000.
We see, from page 22, that the arc must be nearly 3' ; the correspond
ing tabular number on page 114 is 4.685575.
The difference is 2.314425;
which is the logarithm of 206."265.
Hence the required arc is 3' 26."265.
In the same manner we find the arc corresponding to logarithmic
tangent 8.184008, to be 0° 52' 35/;.
TABLE FOR THE LENGTHS OF CIRCULAR ARCS, p. 135.
This table contains the lengths of every single degree up to 60, and
at intervals often degrees up to 180 ; also for every minute and second
up to 20. The lengths are all expressed in decimal parts of radius.
Required the length of an arc of 57° 17' 44."8.
Take out from their respective columns the lengths answering to each
of these numbers singly, and add them all together thus :
57° 0.9948377
17' 0049451
40" 0001939
4" 0000194
0."8 . .0000039
The sum is 1.0000000.
That is, the length of an arc of 57° 17' 44."8 is equal to the radius of
the circle.
TRAVERSE TABLE, pp. 136-141.
This table shows the difference of latitude and the departure to four
decimal places for distances from 1 to 10, and for bearings from 0° to
90°rat intervals of 15'. If the bearing is less than 45°, the angle will
be found on the left margin of one of the pages of the table, and the dis
*ance at the top or bottom of the page ; the difference of latitude wil
A t i EXPLANATION OF THE TABLES
be found in the column headed lat. at the top -of the page, and the de
parture in the column headed dep. If the bearing is more than 45°, the
angle will be found on the right margin, and the difference of latitude
will be found in the column marked lat. at the bottom of the page, and
the departure in the other column. The latitudes and departures for
different distances with the same bearing, are proportional to the dis-
tances. Therefore the distances may be reckoned as tens, hundreds, or
thousands, if the place of the decimal point in each departure and differ-
ence of latitude be changed accordingly.
Required the latitude and departure for the distance 32.25, and the
bearing 10° 30'.
On page 136, opposite to 10° 30', we find the following latitudes and
departures, proper attention being paid to the position of the decimal
-joints.
Distance. Diff. Lat. Dep.
30 29.498 5.467
2 1.966 .364
.2 .197 .036
.05 .049 .009
32.25 31.710 5.876.
TABLE OF MERIDIONAL PARTS, pp. 142-148.
This table gives the length of the enlarged meridian on Mercators
Chart to every minute of latitude expressed in geographical miles and
tenths of a mile. The degrees of latitude are arranged in order at the
top of the page, and the minutes en both the right and left margins.
Under the degrees and opposite to the minutes are placed the merid-
ional parts corresponding to any latitude less than 80°. Thus
the meridional parts for latitude 12° 23' are 748.9 ;
57° 42' are 4260.5.
TABLE OF CORRECTIONS TO MIDDLE LATITUDE, p. 149.
This table is used in Navigation for correcting the middle latitude
The given middle latitude is to be found either in the first or last verti-
cal column, opposite to which, and under the given difference of latitude,
is inserted the proper correction in minutes, to be added to the middle
latitude to obtain the latitude in which the meridian distance is accu
rately equal to the departure. Thus, if the middle latitude is 41°, and
the difference of latitude 14°, the correction will be found to be 25',
which, added to the middle latitude, gives the corrected middle latitude
41° 25'.
A TABLE
*
OP
LOGARITHMS OF lUMBEHS
FROM 1 TO 10,000.
N.
Log.
K.
Log.
N.
Log.
N.
Log.
i
o.oooooo
26
.4i4973
5i
.707570
76
.880814
52
o.3oio3o
27
.43i364
52
.716003
77
.886491
3
0.477121
28
.447i58
53
.724276
78
.892095
'4
0.602060
29
.462398
54
.732394
79
.897627
5
0.698970
3o
.477121
55
•74o363
80
.903090
6
0.778151
3i
.491362
56
.748188
8 1
.908485
7
0.845098
32
.5o5i5o
57
.755875
82
.913814
8
0.903090
33
.5i85i4
58
.763428
83
.919078
9
0.954243
34
.53i479
59
.770852
84
.924279
10
i .000000
35
.544o68
60
.778151
85
.929419
ii
.041393
36
.5563o3
61
.78533o
86
.934498
12
.079181
37
.568202
62
.792392
87
.939519
i3
.113943
38
.579784
63
.799341
88
. 944483
i4
.146128
39
.591065
64
.806180
89
.949390
i5
.176091
4o
.602060
65
.812913
9°
.954243
16
.204120
4i
.612784
66
.819544
91
.959041
J7
.23o449
4a
.623249
67
.826075
92
.963788
18
.255273
43
.633468
68
.832509
93
.968483
19
.278754
44
.643453
69
.838849
94
.973128
2Q
.3ojo3o
45
.653213
70
.845098
95
.977724
21
.322219
46
.662758
71
.85i258
96
.982271
22
.342423
47
.672098
72
.857332
97
.986772
23
.361728
48
.681241
73
.863323
98
.991226
24
.380211
49
.690196
74
.869232
99
.995635
25
.397940
5o
.698970
75
.875o6i
100
2.OOOOOO
N.B. In the following table, the two leading figures in the first column
of logarithms are to be prefixed to all the numbexs of the same horizontal
line in the next nine columns ; but when a point (.) occurs, its place is to
be suppHfed by a cipher, and the two leading figures are to be taken from
the next lower line.
LOGARITHMS OF NUMBERS.
Nj 0. 1 ,-
2 •
3
.4 5
6
7
8
9
D.
100
oooooo o434
0868
i3oi i 1734
2166
2598
3o29
346i
389i
432
IOI
4321 475i
5x8i
56o9 6o38
6466
6894
7321
7748
8174
428
IO2
8600 9026
945i
9876 .3oo
.724
ii4?
1670
i993
24i5
424
io3
012837 3269
368o
4ioo 452i
49&> 53Co
5779
6i97
6616
419
io4
7o33 745i
•7868
8284 8700
9116
9532
9947
.36i
.775
4x6
io5
021189 i6o3
2016
2428 2841
3252
3664
4o75
4486
4896
419
1 06
53o6 57i5
6i25
6533 6942
735o
7757
8i64
857i
8978
4o8
107
9384 9789
.i95
.600 ioo4
i4o8
1812
2216
26i9
3021
4o4
108
o33424 | 3826
4227
4628 $029
543o
583o
623o
6629
7028
4oo
io9
7426 7825
8223
8620 9017
94i4
9811
.207
.602
.998
396
no
041393 I
i787
2l82
2676 2969
3362
3755
4i48
454o
4932
393
III
5323
57i4
6io5
6495 6885
7275
7664
8o53
8442
883o
389
112
9218
96o6
9993
.38o .766
ii53
i538
1924
23o9
2694
386
n3
053078
3463
3846
423o. 46i3
4996
5378
6760
6142
6524
382
n4
6905
7286
7666
8o46% 8426
88o5
9i85
9563
9942
.320
379
n5
060698
io75
i452
1829 2206
-2582
2958
3333
37o9
4o83
376
116
4458
4832
5206
558o 5953
6326
6699
7071
7443
7815
373
117
8186
8557
8928
9298 9668
..38
• 4o7
.776
ii45
i5i4
369
118
071882
2250
261-7
2986 3352
3718
4o85
445 1
48i6
5i83
366
ii9
5547
59I2
6276
664o 7004
736~8
773i
8094
8457
8819
363
120
9181
9543
9904
.266 ; .625
.987
1 34?
1707
2067
2426
36o
121
082785
3i44
35o3
386i 4219
4576
4934
6291
5647 6o°4
357
N.
0
1
2
3
4 || 5
6
7 8
9
D.
434
43
87
i3o
1 74
217
260
3o4
34?
39i
432
43
86
i3o
I73
216
269
302
346
389
43o
43
86
129
I72
2l5
258
3oi
344
387
428
43
86
128
I7I
2l4
257
3oo
342
385
426
43
85
128
I70
213
256
298
34i
383
424
42
85
127
I70
212
254
297
33o
382
422
42
84
127
169
211
253
295
338
38o
420
42
84
126
168
210
252
294
336
378
4x8
42
84
125
167
209
25l
293
334
376
!
4i6
42
83
125
1 66
208
25o
291
333
3?4
4x4
4i
83
124
166
207
248
290
33i
373
412
4i
82
124
i65
206
247
288
33o
37i
4io
4i
82
123
1 64
2O5
246
287
328
369
4o8
4i
82
122
i63
204
245
286
326
367
4o6
4i
81
122
162
203
. 244
284
325
365
4o4 «
4o
Bi
121
162
2O2
242
283
323
364
402 £a
4o
80
121
161
201
241
281
322
362
(D
4oo ^
4o
80
120
160
200
240
280
320
36o
a
398 1
4o
80
II9
i5o
199
239
279
3i8
358
£ •
J
396 o
4o
79
II9
i58
I98
238
277
3i7
356
ID
5
W !
39
79
118
1 58
I97
236
276
3i5
355
H-i
392 o
39
78
118
i57
I96
235
274
3x4
353
39o CU
39
78
xi7
i56
i95
234
273
3l2
35i
388
39
78
116
i55
194
233
272
3io
349
386
39
77
116
1 54
i93
232
270
3o9
34?
384
38
77
ii5
1 54
192
230
269
307
346
382
38
76
iilS
i53
191
229
267
3o6
344
38o
38
76
n4
152
190
228
266
3o4
342
378
38
76
Ii3
i5i
189
227
265
302
34o
376
38
75
li3
i5o
1 88
226
263
3oi
338
374
37
75
112
i5o
187
224
262
299
337
372
37
74
112
1 49
186
223
260
298
335
37o
368
37
37
74
74
III
no
i48
147
i85
1 84
222
221
258
296
294
333
t3i
366
37
73
IIO
i46
i83
220
256
293
329
364
36
73
109
i46
182
218
255
291
3a8
362
36
72
109
i45
181
217
253
290
326
36o
36
72
108
i44
180
216
•Si
288
324
LOGARITHMS OF NUMBERS.
N.
0
1
2
3
4
5
6
7
8
9
D.
122
o8636o
6716
7071
7426
7781
8i36
8490
8845
9198
9662 355
123
9906
.268
.611
.963
i3i5
1667
2018
2370
272I
3071
35i
124
098422
3772
4l22
447i
4820
6169
55i8
-5866
62l5
6662
349
125
6910
7267
7604
795i
8298
8644
8990
9335
9681
..26
346
126
100371
0716
1069
i4o3
1747
2091
2434
2777
3lI9
3462
343
127
38o4
4i46
4487
4828
6169
55io
585i
6191
653i
6871
34i
128
7210
7649
7888
8227
8565
8903
9241
9679
9916
.253
338
129
110690
0926
1263
1699
1934
2270
2606
2940
3275
3609
335
i3o
3943
4277
46u
4944
6278
56u
5943
6276
6608
6g4o
333
i3i
-7271
7603
7934
8266
8696
8926
9266
9686
9916
.245
33o
132
120674
0903
I23l
1660
1888
2216
2544
2871
3198
3525
328
i33
3852
4178
45o4
483o
5i56
548i
58o6
6i3i
6456
6781
325
1 34
7106
7429
7753
8076-
8399
8722
9o45
9368
9690
. . 12
323
i35
i3o334
o655
0977
1298
1619
I939
2260
2680
2900
3219
321
i36
3539
3858
4177
4496
48i4
5i3§
545i
6769
6086
64o3
3i8
i37
6721
7o37
7354
7671
7987
83o3
8618
8934
9249
9564
3x5
i38
9879
.194
.5o8
.822
n36
i45o
i763
2076
2389
2702
3:4
i39
i43oi5
3327
3639
3961
4263
4574
4885
6196
55o7
58i8
3n
i4o
6128
6438
6748
7068
7367
7676
7986
8294
86o3
8911
309
i4i
9219
9627
9835
.142
.449
.766
io63
1370
i676
1982
3o7
142
162288
2594
2900
3206
35io
38i5
4l20
4424
4728
5o32
3o5
i43
5336
564o
5943
6246
6549
6862
7i54
7457
7769
8061
3o3
i44
8362
8664
8966
9266
9667
9868
.168
• 469
.769
1068
3oi
i45
i6i368
1667
1967
2266
2664
2863
3i6i
346o
3758
4o55
299
i46
4353
465o
4947
5244
554i
5838
6i34
643o
6726
7022
297
147
73i7
76 1 3
7908
8ao3
8497
8792
9086
9380
9674
9968
296
1 48
170262
o555
o848
n4i
i434
1726
2019
23ll
26o3
2896
293
N. 0
1
2 | 3
4 || 5
6
7
8
9
TT"
358
36
72
.107
i43
179
2l5
261
286
322
356
36
71
107
i4a
178
9X4
249
286
320
354
35
71
1 06
142
177
212
248
283
319
352
35
7°
1 06
i4i
176
211
246
282
3i7
35o -
35
70
io5
i4o
176
2IO
245
280
3i5
348
35
70
io4
i3g
1 74
209
244
278
3i3
346
35
69
io4
1 38
i73
208
242
277
3n
344
34
69
io3
i38
172
2O6
241
276
3io
342
34
68
io3
i37
171
206
239
274
3o8
34o
34
68
102
1 36
170
2O4
238
272
3o6
338
34
68
101
1 35
169
203
237
270
3o4
336 '
34
67
101
1 34
168
202
235
269
302
334 .
33
67
IOO
1 34
167
2OO
234
267
3oi
332 g
33
66
IOO
i33
166
I99
232
266
299
•
33o -
33
66
99
132
i65
198
23l
264
297
0
328 ~
33
66
98
i3i
1 64
I97
230
262
296
H
<D
V. *
326 a <
o
33
65
98
i3o
i63
196
228
261
293
|
324 £
32
65
97
i3o
162
194
227
269
292
P
322 a
32
64
97
129
161
193
225
268
290
320 2
32
64
96
128
1 60
I92
224
266
288
3x8 *
32
64
96
127
169
I9I
223
264
286
3i6
32
63
95
126
168
I90
221
253
284
3i4
3i
63
94
126
167
188
22O
261
283
312
3i
62
94
125
1 56
187
218
260
281
3io
3i
62
93
124
i55
186
2I7
248
279
3o8
3i
62
92
123
i54
i85
216
246
277
3o6
3i
61
92
122
i53
i84
214
245
275
3o4
3o
61
91
122
162
182
213
243
274
302
3o
60
91
121
161
181
211
242
272
3oo
3o
60
9°
120
i5o
180
2IO
240
27O
298
3o
60
89
119
149
179
209
238
268
296
3o
69
89
118
i4«
178
2O7
237
266
294
I 29
69
88
118
i47
176
206
235
266
LOGARITHMS OF NUMBERS.
N.
0
1
2
3
4 5
6
7
8
9
D.
i49
178186
3478
3769
4o6o
435i
464i
4982
6222
55i2
58o2
291
i5o
6091
638i
6670
6969
7248
7536
7826
8ii3
84oi
8689
289
161
8977
9264
9662
9839
.126
.4i3
.699
.986
1272
i558
287
162
181844
2129
2416
2700
2985
3270
3555
3839
4l23
4407
286
i53
4691
4976
6269
5542
6826
6io"8
6891
6674
6966
7239
283
1 54
7521
78o3
8o84
8366
8647
8928
9209
9490
9771
..5i
281
i55
190332
0612
0892
1171
i45i
1780
2010
2289
.2667
2846
279
1 56
3i25
34o3
368i
3959
4237
45i4
4792
6069
5346
5623
278
167
6900
6176
6453
6729
7006
7281
7556
7832
8107
8382
276
168
8657
8932
9206
948i
9755
..29
.3o3
.577
.85o
1124
274
169
201897
1670
1943
2216
2488
2761
3o33
33o5
3577
3848
272
1 60
4l20
439i
4663
4934
6204
5475
5746
6016
6286
6556
271
161
6826
7096
7866
7634
79o4
8i73
844i
87io
8979
9247
260.
162
95i5
9783
..5i
.819
.586
.853
I 121
-388
i654
1921
267
i63
212188
2454
2720
2986
3262
35x8
3 7.8 3
4049
43i4
4579
266
1 64
4844
6109
5373
5638
6902
6166
643o
6694
6967
7221
264
i65
7484
7747
8010
8273
8536
8798
9060
9823
9686
9846
262
166
220108
0870
o63i
0892
u53
i4i4
1676
i936
2196
2456
261
167
2716
2976
3236
3496
3755
4oi5
4274
4533
4792
5o5i
269
1 68
5309
5568
6826
6o84
6342
6600
6858
7116
7372
7680
268
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N. 0
1
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4
5
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292
29
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176
204
234
268
290
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LOGARITHMS OF NUMBERS.
N.
0
1
2
3
4 1 5
6
7
8
9
D.
182
260071
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4109
4346
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5o54
5290
5525
576i
5996
6232
6467
6702
6937
235
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7172
7406
764i
7875
8110
8344
8578
8812
9o46
9279
234
186
95i3
9746
9980
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.446
.679
.9I2
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1609
233
187
271842
2074
23o6
2538
2770
3ooi
3233
3464
3696
3927
232
188
4i58
4389
4620
485o
5o8i
53u
5542
5772
6002
6232
230
189
6462
6692
6921
7i5i
738o
76o9
7838
8067
8296
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8754
8982
9211
9439
9667
9895
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1715
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3o75
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3527
3753
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5107
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69o5
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225
194
7802
8026
8249
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8696
892O
9i43
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98l2
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196
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0702
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196
2266
2478
2699
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3i4i
3363
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4o25
4246
221
197
4466
4687
4907
5127
5347
5567
5787
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6446
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6665
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2817
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0
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238
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LOGARITHMS OP .NUMBERS.
N.
0
1
2
3
4
5
6
7
8
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D.
221
344392
4589
4785
498i
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1216
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2i83
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2568
2761
2954
3i47
3339
3532
3724
39i6
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4493
4685
4876
5o68
5260
5452
5643
5834
192
227
6026
621-7
64o8
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6981
7172
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7744
191
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7935
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3o48
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4176
4363
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6610
6796
6983
7l69
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7356
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3464
3647
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4oi5
4i98
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6394
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6577
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7124
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8398
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LOGARITHMS OF NUMBERS.
N.
0
1
2
3
4
5
6
7
8
9
D.
264
421604
1768
1933
2097
2261
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6023
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267
65ii
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6836
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7324
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7811
7973
162
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3290
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1 60
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4888
5o48
5207
5367
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6oo4
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6799
6957
7116
7275
7433
7592
274
775i
7909
8067
8226
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6226
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7i58
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7933
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8706
8861
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9633
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1 54
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LOGARITHMS OF NUMBERS.
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Lo-GARITHMS OF NUMBERS.
N."1" 0
1
2
3
4 ]| 5
6
7
8
9
D
458
66o865
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2758
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3 1 35
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3324
34i8
35i2
3607
94
46 1
3701
3795
3889
3983
4o78
4l72
4266
436o
4454
4548
462
4642
4736
483o
4924
5oi8
5lI2
5206
5299
5393
5487
463
558i
5675
5769
5862
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6o5o
6i43
6237
633i
6424
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65i8
6612
6705
6799
6892
6986
7°79
7i73
7266
736o
465
7453
7546
7640
7733
7826
7920
8oi3
8106
8i99
8293
93
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8386
8479
8572
8665
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8852
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9o38
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3482
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6182
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4837
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5 1 79
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5436
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5693
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0
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2
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9
17
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61
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78
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9
17
26
34
43
52
60
69
77
LOGARITHMS OF NUMBERS.
N.
0
1
2
3
4
5
6
7
8
9
D.
5o8
7o5864
5949
6o35
6120
6206
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7o59
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7655
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7826
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7996
8081
8166
825x
8336
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8421
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8676
8761
8846
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9oi5
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9524
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9694
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2734
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2902
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7837
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8834
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6634
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0
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LOGARITHMS OF J\UMBERS.
13
N.
0
1
2
3
4 5
6
7
8
9
D.
559
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1818
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2816
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3o47
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35o6
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2829
2904
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3i28
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3278
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5828
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6325
6396
6467
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1
2
3
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8
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D.
77 »
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57
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14
LOGARITHMS OF LUMBERS.
N.
0
1
2
3
4
5
6
7
8
9
D.
612
786751
6822
6893 6964
7o35
7io6
7i77
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71
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7673
7744
78i5
7885
7956
802-7
8o98
6i4
8168
8239
83io
838i
845i
8522
8593
8663
8734
88o4
6i5
8875
8946
9016
9o87
9l57
9228
9299
9369
944o
95io
616
958i
965i
9722
9792
9863
9933
...4
..74
• i44
.215
70
6i7
790285
o356
O426
0496
0567
06 3 7
0707
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o9i8
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1059
1129
1199
1269
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i48o
i55o
1620
6i9
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i76i
i83i
1901
1971
2041
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2181
2252
2322
620
2392
2462
2532
2602
2672
2742
•>8l2
2882
2952
3022
621
3o92
3i62
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33oi
337i
344i
35u
358i
365i
372I
622
3790
386o
393o
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4i39
4209
4279
4349
44i8
623
4488
4558
4627
4697
4767
4836
49o6
4976
5o45
5n5
624
5i85
5254
5324
5393
5463
5532
5602
5672
574i
58n
625
588o
5949
6019
6088
6i58
6227
6297
6366
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74o6
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8029
8098
8167
8236
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8-789
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8927
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9o65
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9616
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3o47
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3389
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3798
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637
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4208
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5908
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63i6
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645 1
65i9
6587
6655
6723
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2245
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2646
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33i4
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3448
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378i
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39i4
398i
4o48
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4i8i
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4847
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49i3
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51-79
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66
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5777
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5976
6042
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65o6
6573
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6838
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7o36
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664
2168
2233
2299
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243o
2495
256o
2626
269I
2756
N.
0
1
2
3
4
5
6
7
8
9
D.
71 «
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21
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68 .. .
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20
26
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53
59
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7
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20
26
33
39
46
52
59
LOGARITHMS OF NUMBERS.
N.
0
1
2
3
4 5
6
7
8
9
D.
665
822822
2887
2952
3oi8
3o83
3i48
32i3
3279
3344
3409
65
666
3474
3539
36o5
3670
3735
38oo
3865
393o
3996
4o6i
667
4126
4191
4256
4321
4386
445 1
45i6
458i
4646
4711
668
4776
484i
4go6
4971
5o36
5ioi
5i66
523i
5296
536i
669
5426
5491
5556
562i
5686
575i-
58i5
588o
5945
6010
670
6075
6i4o
6204
6269
6334
6399
6464
6528
6593
6658
671
6723
6787
6852
6917
698i
7046
7111
7i75
•7240
73o5
672
7369
7434
7499
7563
7628
7692
7757
•7821
7886
795i
673
8oi5
8o'8o
8i44
8209
8273
8338
8402
8467
853i
8595
64
674
8660
8724
8789
8853
89i8
8982
9046
9111
9i75
9239
675
93o4
9368
9432
9497
956i
9625
9690
9754
9818
9882
676
9947
. .11
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.189
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.268
.332
.396
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.525
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io37
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1166
678
1230
1294
i358
1422
i486
i55o
1614
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1742
1806
679
1870
1934
1998
2062
2126
2189
2253
23l7
23~8i
2445
680
2509
2573
2637
2700
2764
2828
2892
2956
3020
3o83
68 1
3i47
3211
3275
3338
3402
3466
353o
SSgS
3657
3721
682
3784
3848
3912
3975
4o39
4io3
4i66
4*3o
4294
4357
683
442i
4484
4548
46n
4675
4739
4802
4866
4929
4993
684
5o56
5l20
5i83
5247
53io
5373
5437
55oo
5564
5627
63
685
6691
5754
58i7
588i
5944
6007
6071
6r34
619-7
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686
6324
6387
645 1
65i4
6577
664i
6704
6767
683o
6894
687
6957
7020
7o83
7i46
•7210
7273
7336
7399
7462
7525
688
7588
7652
771.5
7778
784i
7904
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8o3o
8093
8i56
689
8219
8282
8345
84o8
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8534
8597
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87a3
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690
8849
8912
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9o38
9ioi
9164
9227
9289
9352
94i5
691
9478
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96o4
9667
9729
9792
9855
9918
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692
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0232
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1109
1172
1234
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694
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1 547
1610
1672
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1797
1860
I922
695
1985
2047
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2172
2235
2297
236o
2422
2484
2547
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696
2609
2672
2734
2796
2859
2921
2983
3o46
3io8
3170
697
3233
3295
3357
3420
3482
3544
36o6
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373i
3793
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3855
3918
398o
4042
4io4
4i66
4229
4291
4353
44i5
699
4477
4539
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4664
4-726
4788
485o
4912
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5o36
700
5098
5i6o
5222
5284
5346
54o8
5470
5532
5594
5656
701
57i8
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5842
59o4
5966
6028
6090
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6213
6275
702
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6399
646 1
6523
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6708
6770
6832
6894
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7oi7
7079
7141
7202
7264
7326
7388
7449
75n
704
7573
7634
7696
7758
7819
7881
7943
8oo4
8066
8128
705
8189
825i
83i2
8374
8435
8497
8559
8620
8682
8743
706
88o5
8866
8928
8989
9o5i
9112
9i74
9235
9297
^358
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707
9419
948i
9542
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9665
9726
9788
9849
9911
9972
708
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709
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0769
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0891
0952
1014
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1258
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1442
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1625
1686
1747
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711
1870
1931
1992
2o53
2Il4
2175
2236
2297
2358
24l9
712
2480
254i
2602
2663
2724
2785
2846
2907
2968
3o29
718
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3i5o
3211
3272
3333
3394
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3637
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394i
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4o63
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467o
473i
4792
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5o34
5o95
5i56
52i6
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5337
5398
5459
717
55i9
558o
564o
5701
5761
5822
5882
5943
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718
6124
6i85
6245
63o6
6366
6427
6487
6548
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6668
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18
24
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49
55
. 60 £
6
12
18
24
3o
36
42
48
54
LOGARITHMS OF NUMBERS.
N.
0
1
2
3
4
5
6
7
8
9
D.
720
857332
7393
7453
75i3
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8838
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9198
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726
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726
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1116
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1236
1295
i355
i4i5
i475
727
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1594
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1-714
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2191
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LOGARITHMS OF NUMBERS.
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LOGARITHMS OF NUMB
E RS.
N.
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7
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LOGARITHMS OF NUMBERS.
N.
0
1
2
3
4 | 5
6
7
8
9
D.
887
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8217
8266
83i5
8364
49
888
84i3
8462
85u
856o
8609
8657
8706
8755
88o4
8853
889
8902
895i
8999
9048
9°97
9i46
9i95
9244
9292
934i
890
9890
9489
9488
9536
9585
9634
9688
9781
9780
9829
891
9878
9926
9975
..24
..78
.121
. 170
.219
.267
.816
892
95o365
o4i4
0462
o5n
o56o
0608
0657
0706
o754
0808
893
0861
0900
0949
0997
io46
lOgS
u43
1192
1240
1289
894
1888
1886
i435
i483
i532
i58o
1629
1677
1726
i775
895
1828
1872
1920
1969
2017
2066
2Il4
2168
2211
2260
48
896
2808
2356
24o5
2453
2502
255o
2599
2647
2696
2744
897
2792
2841
2889
2988
2986
3o34
3o83
8181
3i8o
8228
898
8276
3325
3373
3421
3470
35i8
3566
36i5
3663
37n
899
8760
8808
3856
8905
3953
4ooi
4o4g
4o98
4i46
4i94
900
4243
4291
4339
4387
4435
4484
4532
458o
4628
4677
901
4726
4??3
4821
4869
4918
4966
5oi4
5o62
5no
5i58
902
6207
5255
53o3
535i
5399
5447
5495
5543
5592
564o
908
5688
5736
5784
5832
588o
5928
5976
6024
6072
6120
904
6168
6216
6265
6818
636i
6409
6457
65o5
6553
6601
906
6649
6697
6745
6793
684o
6888
6986
6984
7082
•7080
906
7128
7176
7224
7272
7820
7368
7416
7464
7512
7559
997
7607
7655
7708
775 1
7799
7847
7894
7942
799°
8088
908
8086
8i34
8181
8229
8277
8325
8878
8421
8468
85i6
909
8564
8612
8659
8707
8755
8808
885o
8898
8946
8994
910
9041
9089
9i37
9i85
9232
928o
9828
9375
9423
9471
911
95i8
9566
9614
9661
-97°9
9757
9804
9852
99°°
9947
912
9995
..42
..90
.188
.i85
.288
.280
.828
.876
.428
9i3
960471
o5i8
o566
o6i3
0661
0709
0756
0804
o85i
0899
914
0946
0994
io4i
1089
n36
n84
1281
1279
1826
i374
47
916
1421
1469
i5i6
i563
1611
i658
1706
i753
1801
1 848
916
i895
1943
1990
2088
2o85
2182
2180
2227
2275
2822
917
2869
2417
2464
25ll
2559
2606
2653
2701
2748
2795
918
2843
2800
2937
2985
'8082
8079
8126
8174
8221
8268
919
33i6
3363
34io
3457
35o4
3552
3599
3646
3693
374i
920
8788
3835
8882
8929
8977
4024
4071
4n8
4i65
4212
921
4a6o
43o7
4354
44oi
4448
4495
4542
4590
4637
4684
922
4?3i
4778
4825
4872
4919
4966
5oi3
5o6i
5io8
5i55
928
6202
5249
5296
5343
5390
5437
5484
553i
5578
5625
924
5672
5719
5766
58i3
586o
59o7
5954
6001
6o48
6oo5
925
6142
6189
6286
6288
6829
6376
64s3
6470
65 1 7
6564
926
66u
6658
6705
6752
6799
6845
6892
6989
6986
7o33
927
7080
7127
7i73
7220
7267
73i4
736i
7408
7454
75oi
928
7548
7595
7642
7688
7735
7782
7820.
7875
7922
7969
929
8016
8062
8109
8i56
8208
8249
8296
8343
8890
8436
980
8483
853o
8576
8628
8670
8716
8768
8810
8856
8908
93!
895o
8996
9o43
9090
9186
9i83
9229
9276
9828
9869
982
9416
9463
95o9
9556
9602
9649
9695
9742
9789
9835
988
9882
9928
9975
. .21
..68
.n4
.161
.207
.254
.800
934
970347
0893
o44o
o486
o533
o579
0626
0672
0719
0765
46
935
0812
o858
0904
ogSi
0997
io44
io9o
1187
1188
1229
986
1276
1822
1869
i4i5
i46i
i5o8
i554
1601
1 647
1698
987
1740
1786
i832
1879
1925
1971
2018
2064
2110
2157
988
2^208
2249
2295
2842
2888
2434
2481
2527
2573
2619
989
21666
2712
2758
2804
285i
2897
2943
2989
3o35
8082
940
8128
3i74
8220
8266
33i3
SSSg
34o5
345 1
3497
3543
94 1
359o
3636
3682
8728
3774
8820
3866
8918
3959
4oo5
942
4o5i
4097
4i43
4i89
4235
4281
4827
4374
4420
4466
943
45i2
4558
46o4
465o
4696
4742
4788
4834
488o
4926
N.
0
1
2
3
4
5
6
7
8
9
D.
u
48 » f 5
10
i4
19 .
24
29
34
38
43
§.
47 M 5
9 i4
*9
24
28
33
38
42
.
46 * I 5
9 r4
18
28
28
32
37
4i
LOGARITHMS OF NUMBERS.
N.
0
1
2
3 4 5
6
7
8
9
D.
944
974972
6018
5o64
5no
5i56
52O2
5248
5294
534o
5386
46
945
5432
5478
5524
557o
56i6
5662
57o7
5753
5799
5845
946
589i
5937
5983
6029
6o75
6121
6i67
6212
6258
63o4
94?
635o
6396
6442
6488
6533
6579
6625
6671
6717
6763
948
6808
6854
6900
6946
6992
7°37
7o83
7I29
7i75
722O
949
7266
7312
7358
74o3
7449
7495
754i
7586
7632
7678
95o
7724
7769
78i5
7861
7906
7952
799s
8o43
8o89
8i35
95i
8181
8226
8272
8317
8363
84o9
8454
85oo
8546
859i
o5'2
8637
8683
8728
8774
8810
8865
89n
8956
9OO2
9o47
953
9o93
9i38
9184
923o
9275
932I
9366
94i2
9457
95o3
954
9548
9^94
9639
9685
973o
9776
982I
9867
99I2
9958
955
98ooo3
oo49
oo94
oi4o
oi85
023l
0276
0322
o367
O4l2
45
966
o458
o5o3
o549
o594
o64o
o685
o73o
o776
0821
o867
967
O9I2
°957
ioo3
1048
io93
n39
n84
I229
I275
1320
968
i366
i4n
i456
i5oi
i547
l592
i637
i683
I728
i773
959
i8i9
1 864
i9o9
i954
20OO
2o45
2090
2i35
2181
2226
960
2271
23i6
2362
2407
2452
2497
2543
2588
2633
2678
961
2723
2769
2814
2859
2904
2949
2994
3o4o
3o85
3i3o
962
3175
3220
3265
33io
3356
34oi
3446
349i
3536
358i
963
3626
367i
37i6
3762
38o7
3852
3897
3942
3987
4o32
964
4077
4l22
4i67
4212
4257
4302
4347
4392
4437
4482
965
4627
4572
46i7
4662
47o7
4752
4797
4842
4887
4932
966
4977
5022
5o67
5lI2
5i57
52O2
5247
5292
5337
5382
967
5426
9*71
55i6
556i
56o6
565i
5696
574i
5786
583o
968
6876
592O
5965
6010
6o55
6100
6:44
6i89
6234
6279
969
6324
6369
64i3
6458
65o3
6548
6593
6637
6682
6727
97°
6772
6817
6861
69o6
695i
6996
7o4o
7o85
7i3o
7i75
971
72I9
7264
73o9
7353
7398
7443
7488
7532
7577
•7622
972
7666
7711
7756
7800
7845
789o
7934
7979
8024
8068
973
8n3
8i57
8202
8247
8291
8336
838i
8425
847o
85i4
974
8559
86o4
8648
8693
8737
878,2
8826
8871
89i6
896o
976
9oo5
9o49
9o94
9i38
9i83
9227
9272
93i6
936i
94o5
976
945o
9494
9539
9583
9628
9672
9717
976i
98o6
985o
44
977
9895
9939
9983
..28
..72
.II7
.161
.206
.250
.294
978
99o339
o383
0428
0472
o5i6
o56i
o6o5
o65o
o694
o738
979
o783
0827
o87i
o9i6
o96o
ioo4
1049
io93
n37
1182
980
1226
1270
i3i5
i359
i4o3
1 448
l492
i536
i58o
i625
981
i669
I7i3
i758
1802
1 846
i89o
i935
i979
2023
2O67
982
2III
2i56
2200
2244
2288
2333
2377
2421
2465
25o9
983
2554
2598
2642
2686
273o
2774
28l9
2863
2907
295i
984
2995
3o39
3o83
3l27
3l72
32i6
3260
33o4
3348
3392
986
3436
348o
3524
3568
36r3
3657
3701
3745
3789
3833
986
3877
392I
3965
4oo9
4o53
4o97
4i4i
4i85
4229
4273
987
43i7
436i
44o5
4449
4493
4537
458i
4625
4669
47i3
988
4757
48oi
4845
4889
4933
4977
5021
5o65
5io8
5i52
989
5i96
524o
5284
5328
5372
54i6
546o
55o4
5547
559i
99°
5635
5679
5723
5767
58n
5854
5898
594a
5986
6o3o
991
6074
6117
6161
62o5
6249
6293
6337
638o
6424
6468
992
65i2
6555
6599
6643
6687
6731
6774
6818
6862
69o6
993
6949
6993
7o37
•7080
•7124
7168
7212
7255
7299
7343
994
7386
743o
7474
75i7
756i
76o5
7648
7692
7736
7779
995
7823
7867
79io
7954
7998
8o4i
8o85
8l29
8l72
8216
996
8259
83o3
8347
839o
8434
8477
852i
8564
8608
8652
997
8695
8739
8782
8826
8869
89i3
8956
9ooo
9043
9o87
998
9i3i
9i74
92l8
9261
93o5
9348
9392
9435
9479
9522
999
9565
9609
9652
9696
9739
9783
9826
9870
99i3
9957
43
N.
0 | 1
2
3
4
5
6
7
8
9
D.
. f 46 * f 5
9
i4
18
23
28
32
37
4i
JS j 45 Si 5
9
i4
18
23
27
32
36
4i
» I 44- «• 1 4
9
i3
18
22
26
3i
35
4o
p I 43 £ { 4
9
i3
i?
22
26
3o
34
39
TABLE
OF
LOGARITHMIC SINES AID TANGENTS
FOR EVERY
TEN SECONDS OF THE QUADRANT.
LOGARITHMIC SINES.
Min.
Sine of 0 Degree.
P. P«rt
0"
10"
20"
30"
40"
50"
to 1".
0
Inf. Neg.
5.685575
5.9866o5
6.162696
6.287635
6.384545
59
1
6.463726
6.53o673
6.588665
639817
685575
726968
58
2
764756
799518
83i7o3
861666
889695
916024
57
3
940847
964328
9866o5
7.007794
7.027997
7-o473o3
56
4
7.065786
7.o835i5
7.ioo548
116939
i32733
i47973
55
5
162696
176936
190725
204089
217054
229643
54
6
241877
253776
265358
276639
287635
298358
53
7
3o8824
319043
329027
338787
348332
357672
52
8
3668r6
37577i
384544
393i45
401578
409850
5i
9
417968
425937
433762
44i449
449002
456426
5o
10
463726
470904
477966
4849i5
491754
498488
49
689.4
ii
5o5n8
5n649
5i8o83
524423
530672
536832
48
629.4
12
542906
548897
5548o6
56o635
566387
572065
47
579. i
i3
577668
583201
588664
594059
599388
6o4652
46
536.2
i4
6o9853
614993
620072
625093
63oo56
634964
45
499.2
i5
6398i6
6446 i 5
649361
654o56
658701
663297
44
467.0
16
667845
672345
676799
681208
685573
689895
43
438.7
J7
694173
698410
702606
706762
710879
714957
te
4i3.6
18
718997
722999
726965
730896
734791
73865i
4i
391.3
J9
742478
746270
75oo3i
753758
757455
761119
4o
371.2
20
764754
768358
771932
775477
778994
782482
39
353.1
21
785943
789376
792782
796162
7995i5
802843
38
336.7
22
806146
809423
812677
815906
819111
822292
37
321.7
23
82545i
828586
831700
834791
83786o
840907
36
3o8.o
24
843934
846939
849924
852889
855833
858757
35
295.4
25
861662
864548
8674i5
870262
873092
875902
34
283.8
26
878695
881470
884228
886968
889690
892396
33
273.1
27
895085
897758
900414
9o3o54
905678
908287
32
263.2
28
910879
9i3457
916019
9i8566
921098
923616
3i
254.0
29
926119
928608
931082
933543
935989
938422
3o
245.4
3o
940842
943248
94564i
948020
950387
952741
29
237.3
3i
955082
957411
959727
962031
964322
966602
28
229.8
32
968870
971126
97337o
9756o3
977824
980034
27
222.7
33
982233
984421
986598
988764 1 990919
993064
26
2:6.1
34
995198
997322
999435
8.ooi538 3.oo363i
8.005714
25
209.8
35
8.007787
8.009850
8.011903
013947 015981
oi8oo5
24
203.9
36
O20O2I
032027
024023
026011 027989
029959
23
198.3
37
03I9I9
o3387i
o358i4
037749 039675
041592
22
193.0
38
o435oi
o454oi
047294
049178 o5io54
052922
21
188.0
39
054781
o56633
o58477
o6o3i4
062142
o63963
20
183.2
4o
065776
067582
069380
071171
072955
074731
'9
178.7
4i
076500
078261
080016
081764 o835o4
o85238
id
174.4
42
086965
088684
090398
092104 093804
095497
J7
170.3
43
097183
o98863
ioo537
102204 io3864
io55i9
16
166.4
44
107167
108809
no444
112074 113697
n53i5
i5
162.6
45
116926
ii8532
I2Ol3l
121725 I233i3
124895
i4
iSg. i
46
126471
128042
129607
i3n66 132720
134268
i3
155.6
47
i358io
i37348
138879
i4o4o6 ] 141927
143443
12
i52.4
48
144953
146458
147959
149453
i 50943
152428
II
149.2
49
153907
155382
156852
~ i 583x6
159776
i6i23i
IO
i46.a
5o
162681
164126
165566
167002
168433
169859
9
i43.3
5i
171280
172697
174109
175517
176920
178319
8
i4o.5
52
179713
i8uo3
182488
183869
185245
186617
7
i37.9
53
187985
189348
190707
192062
I934i3
194760
6
i35.3
54
196102
I9744o
198774
200104
2oi43o
202752
5
i32.8
55
204070
205384
206694
2O8OOO
209302
210601
4
i3o.4
56
211895
2i3i85
214472
2l5755
217034
218309
3
128.1
57
219581
220849
2221 l3
223374
22463i
225884
2
125. 9
58
227134
228380
229622
23o86i
232096
233328
I
123.7
59
234557
235782
237003
238221
239436
240647
O
121. 6
OOP
50"
40"
30" 20"
10"
1
Co-sine of S9 Degrees.
Min.
LOGARITHMIC TANGENTS.
Min.
Tangent of 0 Degree.
P. Part
0"
10"
20"
30" 40" | 50"
to 1 •.
0
Inf. Neg.
5.685575
5.9866o5
6. 162696
6.287635
6.384545
59
I
6.463726
6.53o673
6.588665
639817
685575
•726968
58
2
764756
7995i8
83i7o3
861666
889695
916024
57
3
94o847
964329
9866o5
7.007794
7 O27998
7.o473o3
56
4
7.o65786
7.o835i5
7.ioo548
116939
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147973
55
5
162696
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204089
2i7o54
229643
54
6
24i878
253777
265359
276640
287635
298359
53
7
3o8825
319044
329028
338788
348333
357673
52
8
366817
375772
384546
393146
4oi579
409852
5i
9
4i797o
425939
433764
44i45i
449004
456428
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10
463727
4-70906
477968
484917
49i756
498490
49
689.4
ii
5o5i2o
5n65i
5i8o85
524426
53o675
536835
48
620.. 4
12
5429o9
548900
5548o8
56o638
56639o
5-72068
47
579.i
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577672
583204
588667
5g4o62
699391
6o4655
46
536.2
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609857
614996
620076
625097
63oo6o
634968
45
499.2
i5
639820
644619
649366
654o6i 658706
663302
44
467.o
16
667849
67235o
676804
681213 685578
689900
43
438.7
1-7
6941-79
698416
702612
7o6768 7io885
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42
4i3.6
18
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723oo5
726972
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738658
4i
39i.3
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•742484
746277
750037
753765
757462
•76112-7
4o
371.3
20
76476i
768365
771940
775485
•7-79002
•782490
39
353.1
21
78595i
789384
792790
796i7o
•799524
802852
38
336.7
22
8o6i55
809433
812686
8i59i5
819120
822302
37
321.7
23
825460
828596
831710
8348oi
83787o
840918
36
3o8.o
24
843944
846950
849935
852900
855844
858769
35
295.4
25
861674
86456o
867426
87O274
873io4
8759i5
34
283.9
26
8-78708
88i483
884240
886981
889-704
892410
33
273.2
27
895099
897772
900428
9o3o68
905692
9o83oi
32
263.2
28
910894
913471
9i6o34
9i858i
921113
92363i
3!
254.0
29
926134
928623
931098
933559
986006
938439
3o
245.4
3o
94o858
943265
945658
948o37
95o4o4
952758
29
237.3
3i
gSSioo
957428
959745
962049
964341
966621
28
229.8
32
968889
97ii45
973389
975622
977844
980054
27
222.7
33
982253
984441
986618
988-785
990940
993o85
26
216.2
34
995219
997343
999457
8.ooi56o
8.oo3653
3.oo5736
25
209.8
35
8.007809
8.009872
8.011926
0139-70
016004
oi8o29
24
2o3.9
36
O20044
O22o5l
024048
026o35
028014
029984
23
i98.3
37
031945
o33897
o3584o
o37775
039-701
041618
22
i93.o
38
043527
045428
047321
049205
o5io8i
052949
21
188.0
39
054809
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o585o6
o6o342
0621-71
063992
2O
i83.3
4o
o658o6
067612
069410
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0-72985
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178.7
4i
076531
078293
080047
O8l795
o83536
o8527o
18
i74.4
42
086997
088717
090431
092l37
o93837
095530
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170.3
43
097217
098897
100571
IO2239
108900
io5554
16
166.4
44
107203
io8845
no48i
II2IIO
n3734
n5352
15
162.7
45
116963
n8569
120169
I2i763
i2335i
124933
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i59.i
46
i265io
128081
129646
i3i2o6
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i343o8
i3
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47
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i37389
138921
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' 141969
143485
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48
144996
i465oi
i48ooi
i49497
15098-7
l52472
II
i49.3
49
153952
i55426
156896
i5836i
159821
i6i276
IO
146.2
5o
162727
164172
i656i3
16-7049
168480
i699o6
9
i43.4
5i
171328
172745
I74i58
I75566
1-76969
i78368
8
i4o.6
52
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i8n53
182538
183919
185296
186668
7
137.9
53
i88o36 189400
190760
192115
193466
I948i3
6
135.3
54
196156 197494
198829
200159
2oi485
202808
5
i32.8
55
204126 ao544o
206750
2o8o57
209359
2io658
4
i3o.4
56
211953' 213243
2i453o
2i58i4
21-7093
2i8369
3
128.1
57
219641 220909
222174
223434
224692
225945
2
I25.9
58
227195 228442
229685
230924
232160
233392
I
123.8
59
234621 235846
237068
238286
339502
24o7i3
o
121 .7
60" 50" i 40"
30"
20"
10"
Co-tangent of 89 Degrees.
Min.
LOGARITHMIC SINES.
Mia.
Sine of 1 Degree.
P. Part
0"
10"
20"
30"
40" 50"
to 1".
O
8.24i855
8. 243o6o
8.244261
8.245459
8.246654 8.247845
59
119.6
I
249033
250218
25i4oo
252578
253753 254925
58
117 7
2
256094
257260
258423
259582
26o739 261892
5?
iiS.S
3
263042
264190
265334
266475
267613
268749
56
114.0
4
269881
271010
272137
273260
27438i
275499
55
112. 2
5
276614
277726
278835
27994i
28io45
282145
54
1*0.5
6
283243
284339
28543i
286521
2876o8
288692
53
IOS.8
7
289773
290852
291928
298002
294073 j 295141
52
IO7.2
8
296207
297270
298330
299388
3oo443 | 301496
5i
105.7
9
3o2546
3o3594
3o4639
3o568i
3o672i 307759
5o
104.1
10
8.308794
8.309827
8.3io857
8.3n885
8.312910 8.3i3933
49
IO2.6
ii
3i4954
315972
316987
3i8ooi
319012
320021
48
IOI .2
12
321027
322031
323o33
324o32
325029
326024
47
99.8
i3
327016
328007
328995
329980
330964
33i945
46
98.5
i4
332924
3339oi
334876
335848
3368i9
337787
45
97.1
i5
338753
339717
340679
34i638
342596
34355i
44
95.8
16
3445o4
345456
3464o5
34735£
348297
349240 43
94.6
17
35oi8i
351119
352056
352991
353924
354855
42
93.4
18
355783
3567io
357635
358558
359479
36o398
4i
92.2
X9
36i3i5
36223o
363i43
364o55
364964
36587i
4o
91.0
20
8.366777
8.36768i
8.368582
8.369482
8.370380
8. 37i277
39
89.9
21
372171
373o63
373954
374843
37573o
3766i5
38
88.8
22
377499
37838o
379260
38oi38
38ioi5
381889
3?
87.7
23
382762
383633
384502
38537o
386236
387100
36
86.7
24
387962
388823
389682
3oo539
SgiSgS
392249
35
85.6
25
393ioi
393951
394800
395647
396493
397337
34
84.6
26
398I79
399020
399859
4oo696
4oi532
402366
33
83.7
27
403199
4o4o3o
4o4859
4o5687
4o65i4
4o7338
32
82.7
28
408161
408983
409803
410621
4n438
412254
3i
81.8
29
4i3o68
4i388o
414691
4i55oo
4i63o8
417114
3o
80.8
3o
8.417919
8.418722
8.419524
8.42o325
8.42II23
8.421921
29
80.0
3i
422717
4235ii
4243o4
425o96
425886
426675
28
79..!
32
427462
428248
429032
429815
43o597
43i377
27
78.2
33
432i56
432934
4337io
434484
435257 436029
26
77-4
34
4368oo
437569
438337
439103
439868
44o632
25
76.6
35
44i394
442i56
442915
443674
44443i
445i86
24
75.8
36
44594i 446694
447446
448196
448946
449694
23
75.o
3?
45o44o 45u86
451930
452673
4534i4
454i54
22
74.2
38
454893 45563i
456368
457io3
457837
458570
21
73.5
39
4593oi 46oo32
46o76i
461489
462215
462941
2O
72-7
4o
8.463665 8.464388
8.465no
8.46583o
8.46655o
8.467268
J9
72.O
4i
467985 468701
469416
47oi29
470841
47i553
18
71.3
42
472263 472971
473679
474386
475091
475795
*7
70.6
43
476498 477200
4779oi
478601
479299
479997
16
69.9
44
48o693 ! 48 i 388
482083
482776
483467
484i58
i5
69.2
45
484848 485536
486224
486910
487596
488280
i4
68.6
46
488963 489645
490326
491006
49i685
492363
i3
67.9
4?
498040 493715
494390
495o64
495736
496408
12
67.3
48
497078 497748
498416
499084
49975o
5oo4i6
II
66.7
49
5oio8o
501743
5o24o5
5o3o67
5o3727
5o4386
IO
66.1
5o
8.5o5o45
8.5o57O2
8.5o6358
8. 507014
8.5o7668
8.5o832i
9
65.5
5i
508974
509625
5io275
510925
5ii573
5l222I
8
64. 9
52
512867
5i35i3
5i4i57
5i48oi
5 i5444
5i6o86
7
64.3
53
516726
5i7366
5i8oo5
5i8643
519280
519916
6
63.7
54
52o55i
521186
521819
52245i
523o83
5237i3
5
63.2
55
524343
524972
525599
526226
526852
527477
4
62.6
56
528102
528725
529347
529969 j
53o59o
531209
3
62.1
5?
531828
532446
533o63
533679
534295
534909
2
61.6
58
535523
536i36
536747
537358
537969
538578
I
61.1
59
539186 : 539794
54o4oi
54ioo7
54i6i2
542216
O
6o.5
60" 50"
40"
30"
20"
10"
Co-sine of 88 Degrees.
Min.
LOGARITHMIC TANGENTS.
Min.
Tangent of 1 Degree.
P. Part
0"
10"
20"
30"
40"
50"
to 1".
0
8.241921
8.243126
8.244328
8.245526
8.246721
8.247913
59
II9-7
I
249102
250287
251469
252648
253823
254996
58
117.7
2
256i65
25733i
258494
259654
260811
261965
57
n5,8
3
263n5
264263
2654o8
266549
267688
268824
56
n4.o
4
269956
271086
272213
273337
274458
275576
55
112. 2
5
276691
277804
278913
280020
281124
282225
54
no. 5
6
283323
284419
2855i2
286602
287689
288774
53
io8.9
7
289856
290935
292012
293086
294157
295226
52
107.2
8
296292
297355
298416
299474
3oo53o
3oi583
5i
105.7
9
3o2634
3o3682
304727
305770
3o68u
307849
5o
104.2
10
8.3o8884
8.309917
8.310948
8.311976 8.3i3oo2
8.3i4o25
49
102.7
ii
3i5o46
3i6o65
317081
3i8o95
319106
32on5
48
loi.S
12
32II22
322127
323129
324l29
325i26
326121
47
99-8
i3
327II4
328io5
329093
33oo8o | 33io64
332045
46
98>5
U
333025
334oo2
334977
33595o ! 336921
337890
45
97-2
i5
338856
339821
340783
34i743
342701
343657
44
95.9
16
3446io
345562
3465i2
347459
3484o5
349348
43
94.6
J7
350289
351229
352i66
353ioi
354o35
354966
42
93.4
18
355895
356823
357748
35867i
SSgSgS
36o5i2
4i
92.2
*9
36i43o
362345
363259
364171
365o8i
365988
4o
9I.I
20
8.866895
8.367799
8.368701
8.369601
8.37o5oo
8.371397
39
89.9 ^
21
372292
373i85
374076
374965
375853
376738
38
88.8
22
377622
3785o4
379385
380263
38n4o
382oi5
37
87.8
•23
382889
383760
38463o
385498
386364
387229
36
86.7
24
388092
388953
389813
390670
391526
392381
35
85.7
25
393234
394o85
394934
395782
396628
397472
34
84.7
26
3983i5
399156
399996
4oo834
401670
4o25o5
33
83.7
27
4o3338
404.170
4o5ooo
4o5828
4o6655
407480
32
82.8
28
4o83o4
409126
409946
410765
4n583
412399
3i
81.8
29
4i32i3
414026
4i4837
4i5647
4i6456
417263
3o
80. 9
3o
8.4i8o68
8.418872
8.419674
8.420475
8.421274
8.422072
29
80.0
3i
422869
423664
424458
42525o
426041
42683o
28
79.i
32
427618
428404
4a9i89
429973
43o755
43i536
27
78.3
33
4323i5
433093
433870
434645
4354i9
436191
26
77.5
34
436962
437732
4385oo
439267
44oo33
440797
25
76.6
?5
44i56o
442322
443082
44384i
444599
445355
24
75.8
36
446no
446864
447616
448368
449117
449866
23
75.o
37
45o6i3
45i359
452io4
452847
453589
45433o
22
74,3
38
455070
4558o8
456545
457281
458oi6
458749
21
73.5
39
459481
460212
46o942
461670
462398
463i24
2O
72.8
4o
8.463849
8.464572
8.465295
8. 466016
8.466736
8. 467455
*9
72.1
4i
468172
468889
4696o4
47o3i8
47io3i
471743
18
7i.3
42
472454
473i63
473872
474579
475285
475990
J7
70.7
43
476693
477396
478o97
478798
479497
480195
16
70.0
44
480892
48 i 588
482283
482976
483669
48436o
i5
69.3
45
485o5o
48574o
486428
487115
487801
488486
i4
68.6
46
489170
489852
49o534
491215
491894
492573
i3
68.0
4?
49325o
493927
4946o2
495276
495949
496622
12
67.4
48
497293
497963
498632
499300
499967
5oo633
II
66.8
49
501298
501962
5o2625
503287
5o3948
5o46o8
IO
66.1
5o
8. 505267
8.5o5925
8.5o6582
8. 507238
8.507893
8.5o8547
9
65.5
5i
509200
509852
5io5o3
5m53
5n8o2
5i245i
8
65.o
62
5 i 3098
5i3744
5i4389
5i5o34
5i5677
5i632o
7
64.4
53
516961
517602
518241
5i888o
5i95i8
52oi54
6
63.8
54
520790
52i425
522O59
522692
523324
523956
5
63.3
55
5a4586
5252i5
525844
526472
527098
527724
4
62.7
56
528349
528973
529596
53o2i8
53o84o
53i46o
3
62.2
57
532o8o
532698
5333i6
533933
534549
535i64
2
61.6
58
535779
536392
537oo5
5376i7
538227
538837
I
61.1
59
539447
54oo55
540662
541269
54i875
54248o
O
60.6
fiO» 50" | 40"
30"
20"
10"
Co-tangent of 88 Degrees.
Min.
•26
LOGARITHM c SINES.
i
Sine of 2 Degrees.
d
Sine of 3 Degrees.
8
0"
10"
20"
30'
40"
50"
9
0"
10"
20"
30"
40"
50"
0
8.542819
3422
4023
4624
5224
5823
59
o
8.7i88oo
92O2
96o3
...4
• 4o4
.8o4
59
1
6422
7oi9
7616
8212
8807
94oi
58
I
8. 72I204
i6o3
20O2
2401
2799
3i97
58
2
9995
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1179
I770
236!
295o
57
2
3595
3992
4389
4785
5i8i
5577
57
3
8 553539
4126
4?i3
53oo
5885
647o
56
3
5972
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6543
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53
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1060
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8.711507
1916
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3i39
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57
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9044 9348
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58
3952
4358
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58
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1472
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59
6383
6787
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59
8.841774
2O76
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2680J2982
3283
O
60"
50"
40"
30"
20"
10"
a
60"
50" 40"
30" | 20"
10"
g
Co-sine of 87 Degrees.
s
Co-sine of 86 Degrees.
S
.< 1" 2'' 3" 4" 5" 6" 7" 8" 9"
( I" 2" 3" 4" 5" 6" 7" 8" 9"
irt} 48 96 145 192 241 289 33$ 386 434
Lrt} 34 69 103 138 172 207 241 275 310
LOGARITHMIC TANGENTS.
27
B
Tangent of 2 Degrees. -
a
Tangent of 3 Degrees.
9
0"
10"
20"
30" | 40
50"
&
0"
10"
20"
30"
40" 50"
o
8.543o84
3687
4289
4891
5492
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59
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8.719396
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7289
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9674
58
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8.721806
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2607
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58
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3227
57
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57
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56
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56
4
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9667
248
55
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54
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27
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3276
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32
27
8.780222
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0922
1272
1622
1971
32
28
4256
4746
5235
5723
6211
6698
3i
28
2320
2669
3017
3365
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29
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9I26
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29
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5794
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8.640093
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7177
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7866
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29
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2982
3462
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4420
4898
5376
28
3i
8554
8898
9242
9585
9928
.271
28
32
5853
6329
68o5
728l
7756
823o
27
32
8.790613
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1297
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1980
2321
27
33
87o4
91-78
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. 123
.595
1067
26
33
2662
3oo3
3343
3683
4023
4362
26
34
8.65i537
2008
24-78
2947
34i6
3884
25
34
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5379
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6o56
6394
25
35
4352
4820
5286
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24
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23
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1771
2230
22
37
8.800763
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1432
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2432
22
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8.662689
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21
38
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343 1
3763
4095
4427
21
39
5433
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6412
20
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1320
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18
42
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17
42
8.8io683
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1989
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17
43
6239
6684
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7572
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8457
16
43
2641
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2860
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46
4172
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5480
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46
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910:
9744
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47
6784
-7218
7652
8o85
85i7
895o
12
47
8.820382
0703
102:
1 342
1661
1980
12
48
9381
98i3
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1104
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II
48
229^
2617
2935
3253
357o
3888
II
49
8.691963
2392
2820
3248
3675
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10
49
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4522
4838
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547i
5787
10
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7049
7363
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9
Si
7081
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7928
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8773
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8
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52
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7
52
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1 1 22
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7
53
8.702139
2558
29-76
33g5
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4230
6
53
8.83i748
2059
237I
2682
2992
33o3
6
54
4646
5o63
5479
5895
63io
6725
5
54
36i3
3924
4234
4543
4853
5i62
5
55
7i4o
7554
7967
838i
8794
9206
4
55
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578o
6089
6397
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4
56
9618
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1263
1672
3
56
732I
7629
7936
8243
855o
8857
3
57
8.7i2o83
2493
2902
33xi
37i9
4127
2
57
9i63
9470
9776
..81
.387
.692
2
58
4534
4942
5348
5755
6161
6567
I
58
8.840998
i3o3
160-7
1912
2216
2521
I
59
69-72
7377
7781
8186
8589
8993
O
59
2825
3i28
3432
3735
4o38
434i
O
60"
50"
40"
30"
20"
10"
rt
60"
50"
40"
30"
20"
10"
d
Co-tangent of 87 Degrees.
1
Co-tangent of 86 Degrees.
9
, .5 I" 2" 3" 4" 5" 6" 7" 8" 9"
C 1" 2" 3" 4" 5" 6" 7" 8" 9"
lrl} 48 97 145 193 242 290 338 387 435
drt { 35 69 104 138 173 207 242 276 311
LOGARITHMIC SINES.
1
Sine of 4 Degrees.
Sine of 5 Degrees.
H
0"
10"
20"
30"
40"
50"
0"
10" 20"
30"
40"
50"
o
8.843585
3886
4i86
4487
4?«7
6087
59
o
8.940296
o537
0777
IOI7
1258
1498
59
i
5387
5687
5987
6286
6585
6884
58
I
173?
1977
2217
2457
2696
2935
58
2
7i83
748 1
7780
80-78
8376
8673
57
2
8174
34x3
3652
3891
4129
4368
57
3
8971
9268
9565
9862
.i59
.455
56
3
46o6
4844
5o83
532i
5558
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60"
50"
40"
30"
20"
10"
^
60"
50"
40"
30"
20"
10"
d
Co-sine of 85 Degrees.
3
Co-sine of 84 Degrees.
fl
s,
/ 1 // nil o// 411 K.II ell fll oil nil
P PortJ l<J-*45b789
ITI\ 27 53 80 107 134 160 187 214 241
p p. < 1" 2" 3" 4" 5" 6" 7" 8" 9"
1 n\ 22 44 66 87 109 131 153 175 197
LOGARITHMIC TANGENTS.
1
Tangent of 4 Degrees.
d
Tangent of 5 Degrees.
2
0"
10"
20"
30"
40"
50"
S
0"
10"
20"
30" 40" ) 50"
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3
57
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60"
50"
40"
30"
20"
10"
£3
60"
50"
40"
30*
20"
10"
a
Co-tangent of 85 Degrees.
1
Co-tangent of 84 Degrees.
i
p p t< 1"2" 3" 4" 5" 6" 7" 8" 9"
p p , ( 1" 2" 3" 4" 5" 6" 7" 9" 9"
irl\ 27 54 81 108 135 162 188 215 242
' art£22 44 66 88 110 132 154 177 199
LOGARITHMIC SINES.
A
Sine of 6 Degrees.
J
Sine of 7 Degrees.
s
0"
10"
20"
30"
40" | W
8
0"
10" 20"
30"
40"
50"
o
9.019235
9435
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59
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58
2
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2229
2428
2627
57
2
7947
8118
8288
8459
8629
8800
57
3
2826
3024
3223
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38i8
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60"
50"
40"
30"
20"
10"
E
60" 50" 40" | 30" 20" i 10" .
Co-sine of 83
Degrees.
§
Co-sine of 82 Degrees. a
_ < 1" 2" 3" 4" 5" 6" 7" 8' 9"
p p .< 1" 2" 3" 4" 5" 6" 7" S" 9''
irt{ 18 37 55 74 92 111 129 148 166
"{ 16 32 48 64 80 96 112 128 144
LOGARITHMIC TANGENTS.
.5
Tangent of 6 Degrees.
.a
Tangent of 7 Degrees.
m
0"
10" | 20" j 30"
40"
50"
s
0"
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20"
30"
40"
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O
60"
50"
40"
30"
20"
10"
rj
60"
50" 40"
30" j 20"
10"
A
Co-tangent of 83 Degrees.
.y
§
Co-tangent of 82 Degrees.
i
P P«rt5 l" 2" 3// 4" 5" 6// 7" 8" 9"
p p .<!" 2" 3" 4" 5" 6" 7" 8" 9"
irc* 19 37 56 75 94 112 131 150 168
trt{ 16 33 49 65 81 98 114 130 146
LOGARITHMIC
i
Sine of 8 Degrees.
A
Sine of 9 Degrees.
i
0- | 10" 20"
30"
40" | 50*
s
0" | 10"
20"
30"
40"
50"
o
9. M3555 37o5J3855
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60"
50"
40"
30"
20"
10"
d
60"
50" 40"
30" | 20"
10"
^
Co-sine of 81
Degrees.
9
Co-sine of 80 Degrees.
8
( \" 2" 3" 4" 5" 6" 7" 8" 9"
P P f fl" 2// 3// 4// 5" 6" 7" 8" 9"
P. Part J H 2g 42 5fi 7Q 85 9g H3 12?
irt\ 13 25 38 50 63 75 88 101 113
LOGARITHMIC TANGENTS.
33
d
Tangont of 8 Degrees.
.s
Tangent of 9 Degrees.
ii
0"
10"
20"
30"
40"
50"
2
0"
10"
20"
30"
40"
50"
0
9.147803
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53
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54
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54
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2114
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55
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6018
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6293
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55
26^0
2734
2858
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4
56
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6567
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3
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3974
3
57
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75.27
7664
7801
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2
57
4097
4221
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4468
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a
58
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8211
8348
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58
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o
60"
50"
40"
30"
20"
10"
a
60"
50"
40"
30"
20"
10"
d
Co-tangent of 81 Degrees.
§
Co-tangent of 80 Degrees.
1
P P f<l" 2" 3" 4" 5" 6" 7" 8" 9"
.5 1" 2" 3" 4" 5" 6" 7" 8" 9"
1 14 29 43 58 72 86 101 115 130
in\ 13 26 39 52 65 7$ 91 103 116
LOGARITHMIC SINES.
.5
Sine of 10 Degrees.
O
Sine of 1 1 Degrees.
m
0" | 10" | 207
30"
40" 5(X
2
0" 10" | 20"
30"
40"
50"
0
9.23967o!979o|99o9
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59
0
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3
1814 I933'2o52
2170
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2408
56
3
2544 2652
2760
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56
4
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55
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55
5
3237
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54
5
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4i58
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54
6
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53
6
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5oi7
53
7
4656
4774
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5i28
5245
52
7
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59
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7383
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7582 7681 7780
O
60"
50"
40"
30"
20"
10"
B
60" 50" | 40"
30" 20" I 10"
.
Co-sine of 79
Degrees.
.££
~.
Co-sine of 78 Degrees
1
A I" .2" 3" 4"
5" 6" 7" 8" 9"
P P tf 1" 2" 3" 4" 5" 6" 7" 8" 9"
r'PartJ 11 23 34 45
57 68 80 91 102
m\ 10 21 31 41 32 62 72 83 93
LOGARITHMIC TANGENTS.
fl.
Tangent of 10 Degrees.
a
Tangent of 1 1 Degrees.
9
0"
10"
20"
30"
40"
50"
••
0"
10"
20"
30"
40"
50"
o
9.2463i9
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28
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9324
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28
32
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27
32
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27
33
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3
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6624
6737
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6963
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2
57
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58i5
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58
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7527
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58
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0
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7060
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O
60"
50"
40"
30"
20"
10"
.
60"
50"
40"
30"
20"
10"
d
Co-tangent of 79 Degrees.
%
Co-tangent of 78 Degrees.
i
P Port 5 l" %" 3" 4" 5" 6" 7" 8" 9"
( 1" 2" 3" 4" 5" 6" 7" S" 9"
irl\ 12 23 35 47 59 70 82 94 106
P.PartJn 22 32 43 54 65 75 86 97
36
LOGARITHMIC SINES.
Jj
Sine of 12 Degrees.
«•
Sine of 13 Degrees.
53
0"
10"
20" 30" 40"
50"
*
0"
10"
20"
30"
40"
50"
o
9-3i7879
797«
8077:81768275
8374
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09.352088
2179
2270
2362 2453
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59
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8868
8967
58
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2908
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58
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53
6
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5720
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53
7
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2II7
2215
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52
7
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52
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10
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7794
7884
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49
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4366
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48
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8064
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48
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5437
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12
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5826
5923
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46
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45
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9678
9768
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45
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67oo
6797 6894
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44
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9.36o2i5
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44
16
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7378 7475
7572
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43
16
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1109
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43
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8248
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42
17
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18
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1822
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20
9.329599
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39
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3244
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39
21
9.33oi76
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38
21
3422
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3688
3777
3865
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22
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37
22
3954
4042
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4220
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37
23
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36
23
4485
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4839
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36
24
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2286
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35
24
5oi6
5io4
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5281
5369
5457
35
25
2478
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2-764
2860
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34
25
5546
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5722
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5899
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34
26
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3i47
3242
3337
3433
3528
33
26
6o75
6i63
625i
6339
642-7
65i6
33
27
3624
37i9
38i4
39io
4oo5
4ioo
32
27
66o4
6692
678o
6868
6956
7o44
32
28
4i95
4291
4386
448 1
4576
467i
3i
28
7i3i
72I9
73o7
7395
7483
757i
3i
29
4767
4862
4957
5o52
5i47
5242
3o
29
7659
7747
7834
7922
8010
8098
3o
3o
9.335337
5432
5527
5622
57i6
58ii
29
3o
9.368i85
8273
836i
8448
8536
8624
29
3i
59o6
6001
6o96
6i9i
6285
638o
28
3i
8711
8799
8886
8974
9o6i
9i49
28
32
6475
657o
6664
6759
6854
6948
27
32
9236
94n
9499
9586
9673
27
33
?o43
7l37 7232
7326
7421
75i5
26
33
9761
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. no
.i97
26
34
76io
77o4 7799
7893
7988
8082
25
34
9.370285
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25
35
81-76
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8459
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24
35
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36
8742
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23
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37
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37
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21
38
2373
2460
254-7
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272I 28o7
21
39
9. 34o434
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0903
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298i
3o67
3i54
324i 3327
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9.340996
1090 1184
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i37i
1 464
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9.3734i4
35oo
3587
3674
376o
3847
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4i
i558
1 652 i745
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I932
2026
18
4i
3933
4O20
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4l92
4279
4365
18
42
2119
2212 23o6
2399
2493
2586
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42
4452
4538
4624
47n
4797
4883
17
43
2679
2772 2866
2959
3o52
3i45
16
43
497o
5o56
5i42
5228
53i4
54oi
16
44
3239
3332 3425
35i8
36ii
3704
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5487
5573
5659
5745
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59i7
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45
3797
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4i69
4262
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45
6oo3
6o89
6i75
6261
6347
6433
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46
4355
4448454i
4634
4727|4820
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46
65i9
66o5
6691
6777
6863
6949
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47
4912
5oo5
5o98
5i9i
5283l5376
12
47
7o35
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-7206
7292
7378
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12
48
5469
6024
556i 5654
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5747
63o2
5839|5932
63956487
II
IO
48
49
7549
8o63
7635
8i49
8235
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8320
7892
84o6
7978
849i
II
10
5o
9.346579
66-72 6764
6857
6949 7o4i
9
5o
9.378577
8662
8748
8833
8919
9oo4
9
5i
7i34
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74io
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8
5i
9o89
9i75
9260
9346
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95i6
8
52
7687
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7963
8o568i48
7
52
96oi
9687
9772
9857
9942
..28
7
53
8240
8332 8424
85i6
8608 87oo
6
53
9.38oii3
oi98
0283
o368
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6
54
8792
8884189-76
9o67
9i59 925i
5
54
0624
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0-794
0879
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5
55
9343
9435
9526
96i8
97io 98o2
4
55
1 1 34
I2I9
i3o4
i389
1474
i559
4
56
9893
9985
••77
.168
.260
.352
3
56
i643
1-728
i8i3
i898
i983
2068
3
57
9.35o443
o535
0626
0-718
o8o9
0901
2
57
2l52
2237
2322
2406
249I
2576
2
58
0992
1084
n75
1266
i358i449
I
58
266l
2745
283o
29i4
2999
3o84
I
59
i54o
i632 i723
1814
I9o6|i997
O
59
3i68
3253
3337
3422
35o6
359i
0
60"
50" ! 40"
30"
20" 10"
a
60"
50"
40" 30"
20" 10"
d
Co-sine of 77 Degrees.
1
Co-sine of 76 Degrees.
1
P Part 5 l" 2" 3" 4" 5" 6// 7" 8// 9"
p p (1" 2" 3" 4" 5" 6" 7" 8" 9"
I 9 19 28 38 47 57 66 76 85
{9 18 26 35 44 53 61 70 79
LOGARITHMIC TANGENTS.
ri
°
Tangent of 12 Degrees.
I
Tangent of 13 Degrees.
0"
10"
20"
30"
40"
50"
m
0"
10"
20"
30"
40"
50"
o
9.327475
7578
7682
7785
7888
7992
59
o
9. 363364
346o
3556
3652
3748
3844
59
I
8o95
8i99
8302
84o5
85o9
8612
58'
i
394o
4o36
4i32
4228
4324
4420
58
2
87i5
8819
8922
9025
9I28
923l
57
2
45i5
46u
4707
48o3
4899
4994
57
3
9334
9438
9541
9644
9747
985o
56
3
5o9o
5i86
5282
5377
5473
5568
56
4
9953
..56
.i59
.262
.365
.468
55
4
5664
576o
5855
595i
6o46
6142
55
5
9.330570
o673
0776
o879
0982
1084
54
5
6237
6333
6428
6524
66I9
67i5
54
6
1187
1290
i393
i495
i598
1701
53
6
6810
69o5
7001
7096
7i9i
7287
53
7
i8o3
1906
2008
2III
22l3
23i6
52
7
738a
7477
7572
7668
7763
7858
52
8
2418
2521
2623
2726
2828
293o
5i
8
7953
8o48
8i43
8239
8334
8429
5i
9
3o33
3i35
3237
334o
3442
3544
5o
9
8524
8619
8714
88o9
89o4
8999
5o
10
9.333646
3 748
385i
3953
4o55
4i57
49
10
9.369o94
9i89
9284
9378
9473
9568
49
ii
4259
436i
4463
4565
4667
4769
48
ii
9663
9758
9853
9947
..42
.i37
48
12
487i
4973
5o75
5i77
5279
538o
47
12
9.370232
o326
O42I
o5i6
0610
o7o5
47
i3
5482
5584
5686
5788
5889
599i
46
i3
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o894
o989
io83
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I272
46
i4
6093
6194
6296
6398
6499
6601
45
i4
i367
i46i
i556
i65o
1744
i839
45
i5
6702
6804
6905
7oo7
7io8
7210
44
T5
i933
2028
2122
2216
23ll
24o5
44
16
73n
74i3
?5i4
76i5
77I7
7818
43
16
2499
2593
2688
2782
2876
297°
43
*7
79 * 9
8021
8122
8223
8324
8426
42
17
3o64
3i59
3253
3347
344i
3535
42
18
8527
8628
8729
883o
893i
9o32
4i
18
3629
3?23
38i7
39n
4oo5
4o99
4i
»9
91 33
9234
933$
9436
9537
9638
4o
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4i93
4287
438i
4475
4569
4662
4o
20
9.339739
9840
9941
..42
.i43
.243
39
20
9.374756
485o
4944
5o38
5i3i
5225
39
21
9.34o344
o445
o546
o646
0747
o848
38
21
53i9
54i3
55o6
56oo
5694
5787
38
22
b948
1049
n5o
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i35i
i45i
37
22
588i
5975
6068
6162
6255
6349
37
23
i552
i652
1753
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i954
2o54
36
23
6442
6536
6629
6723
6816
69io
36
24
2i55
2255
2355
2456
2556
2656
35
24
7oo3
7096
7I9°
7283
7376
747o
35
25
2757
2857
2957
3o57
3i58
3258
34
25
7563
7656
775o
7843
7936
8o29
34
26
3358
3458
3558
3658
3758
3858
33
26
8122
8216
83o9
8402
8495
8588
33
27
3958
4o58
4i58
4258
4358
4458
32
27
8681
8774
8867
896o
9o53
9i46
32
28
4558
4658
4758
4858
4957
5o57
3i
28
9239
9332
9425
95i8
96n
97o4
3i
29
5i57
5257
5357
5456
5556
5656
3o
29
9797
989o
9983
..75
.168
.261
3o
3o
9.345755
5855
5954
6o54
6i54
6253
29
3o
9.38o354
o446
o539
o632
O725
0817
29
3i
6353
6452
6552
665i
6751
685o
28
3i
0910
ioo3
io95
1188
1280
1373
28
32
6949
7049
7i48
7248
?347
7446
27
32
i466
i558
i65i
1743
i836
I928
27
33
7545
7645
7744
7843
7942
8042
26
33
2020
2Il3
22O5
2298
239o
2482
26
34
8i4i
8240
8339
8438
8537
8636
25
34
2575
2667
2759
2852
2944
3o36
25
35
8735
8834
8933
9o32
9i3i
923o
24
35
3l29
3221
33i3
34o5
3497
3589
24
36
9329
9428
9527
9626
9724
9823
23
36
3682
3774
3866
3958
4o5o
4i42
23
37
9922
. .21
. I2O
.218
.817
.4i6
22
37
4234
4326
44i8
45io
4602
4694
22
38
9.35o5i4
o6i3
0712
0810
o9o9
1007
21
38
4786
4878
497o
5o62
5i53
5245
21
39
1106
I2O4
i3o3
i4oi
i5oo
i598
2O
39
5337
5429
552i
56i2
5704
5796
2O
4o
9.35i697
I795
i894
I992
2O9O
2i89
J9
4o
9 385888
5979
6o7i
6i63
6254
6346
J9
4i
2287
2385
2483
2582
2680
2778
18
4i
6438
6529
6621
6712
68o4
6895
18
42
2876
2974
3o73
3i7i
3269
3367
17
42
6987
7o78
7i7o
7261
7353
7444
i?
43
3465
3563
36Gi
3759
3857
3955
16
43
7536
7627
77i8
7810
79oi
7992
16
44
4o53
4i5i
4249
4347
4445
4542
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44
8o84
8i75
8266
8358
8449
854o
i5
45
464o
4738
4836
4934
5o3i
5l29
i4
45
863i
8722
88i4
89o5
8996
9o87
i4
46
5227
5324
5422
5520
56i7
57i5
i3
46
9178
9269
936o
945i
9542
9633
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47
58i3
5910
6008
6io5
6203
63oo
12
47
9724
98i5
99o6
9997
..88
.179
12
48
6398
6495
6593
669o
6787
6885
II
48
9.390270
o36i
o452
o543
o633
0724
II
49
6982
7°79
7177
7274
737i
7469
10
49
o8i5
o9o6
°997
1087
1178
I269
IO
5o
9.357566
7663
7760
7857
7954
8o52
9
5o
9.391360
i45o
i54i
i632
1722
i8i3
9
5i
8i49
8246
8343
844o
8537
8634
8
5i
1903
i994
2080
2175
2266
2356
8
52
873i
8828
8925
9O22
9119
92l6
7
52
2447
2537
2628
2718
2808
2899
7
53
93i3
94o9
95o6
96o3
9700
9797
6
53
2989
3o8o
3i7o
3260
335i
344i
6
54
9893
999°
..87
.184
.280
.377
5
54
353!
3622
37I2
38o2
3892
3983
5
55
9.36o474
o57o
0667
o763
0860
o957
4
55
4o73
4i63
4253
4343
4433
4523
4
56
io53
n5o
1246
1 343
i439
i535
3
56
46i4
4704
4794
4884
4974
5o64
3
57
i632
I728
1825
I92I
2017
2Il4
2
57
5i54
5244
5334
5424
55i4
56o4
2
58
22IO
23o6
24o3
2499
2595
269I
I
58
5694
5783
5873
5963
6o53
6i43
I
59
2787
2884
298o
3o76
3172
3268
0
59
6233
6322
64i2
65o2
6592
6681
0
60"
50" 40"
30''
20"
10"
^
60" 50"
40"
30"
20"
10"
•
Co-tangent of 77 Degrees.
§
Co-tangent of 76 Degrees.
s
p p C 1" 2" 3" 4" 5" 6" 7" 8" 9"
. C 1" 2" 3" 4" 5" 6" 7" 8" 9"
I 10 20 30 40 50 60 70 80 90
r.rari^ 9 ig 2g 3? 46 f>6 65 74 gg
LOGARITHMIC SINES.
.3
Sine of 14 Degrees.
d
Sine of 15 Degrees.
1
0"
10"
20" 30" j 40"
50"
9
0"
10"
20"
"30"
40"
50"
0
9.383675
376o
38443928i4oi3
4o97
59
o
9.4i2996
3o75
3i53
3232
33io
3389
59
I
4182
4266
435o443545i9
46o3
58
I
3467
3546
3624
37o3
378i
386o
58
2
4687
4772
4856494o5o24
5io8
57
2
3938
4oi6
4o95
4i73
4252
433o
57
3
4
5l92
5697
5277
578i
536i 54455520.
5865 5949'6o33
56i3
6n7
56
55
3
4
44o8
4878
4486
4956
4565
5o34
4643
5lI2
472I
5i9o
48oo
5269
56
55
5
6201
6285
63696452
6536
6620
54
5
5347
5425
55o3
558i
5659
5737
54
6
6704
6788
6872 6955
7o39
7I23
53
6
58i5
5893
597i
6o49
6l27
6205
53
7
7207
729o
7374 7458
754i
7625
52
7
6283
636i
6439
65i7
6595
6673
52
8
7709
7792
7876 7959 8o43
8l27
5i
8
675i
6828
69o6
6984
7o62
7i4o
5i
9
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6747
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9.3986oo
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8762
8844
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29
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9.4268q9
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7127
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29
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9o88
9i69 925o
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94i3
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28
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7354
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75o6
7582
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28
32
9575
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98i9
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27
32
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7885
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27
33
9. 400062
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26
33
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26
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25
34
87i7
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24
35
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9397
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1682
1762
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9623
9698
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23
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2005
2085
2166
2247
2328
2408
22
37
9.43oo75
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2489
257o 265o
2731
2811
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3536 36i6
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3938
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4259
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2104
2I79
2254
18
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4420
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466o
474i
4821
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42
2329
24o3
2478
2553
2628
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4981
5o6i
5i4i
5221
5302
16
43
2778
2853
2927
3002
3o77
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5382
5462
5542
5622
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5782
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3226
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3376
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3824
3898
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7378 7458
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7538
7i39
76i7
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II
47
48
4569
5oi6
4644
5o9i
47i8
5i65
4793
5239
4867
53x4
4942
5388
12
II
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7777
7856
79368oi5
8o95
8i74
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5462
5537
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5685
576o
5834
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9. 4o8254
8333
84i3
8492
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9.4359o8
5982
6o56
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62o5
6279
9
5i
8731
8810 8889
8969
9o48 9i27
8
5i
6353
6427
65o2
6576
665o
6724
8
52
0,207
0.286 9365
9445
952496o3
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52
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6872
6946
7020
7o94
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53
0,682
9762.9841
9920
9999
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6
53
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73i6
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7464
7538
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6
54
9.4ioi57
O237 o3i6
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5
54
7686
776o
7834
79o8
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8o55
5
55
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o869
O948JIO27
4
55
8i29
82o3
8277
835i
8424
8498
4
56
1 1 06
n85
1264
i343
1422
i5oo
3
56
8572
8646
87i9
8793
8867
894i
3
57
i579
i658
i737
1816
i895
i973
2
57
9oi4
9o88
9l62
9235
93o9
9382
2
58
2052
2l3l
2210
2288
2367
2446
I
58
9456
953o
96o3
9677
975o
9824
I
59
2524
26o3
2682
276o
2839
29l8
O
59
9897
997i
..44
.118
.101
.265
0
GO"
50"
40"
30"
20"
10"
e
60"
50"
40"
30"
20"
10"
c
Co-sine of 75 Degrees.
i
Co-sine of 74 Degrees.
5
(I// o" Q'
P Pni-t) J
' 4" 5" Q" 7" 8" 9"
, ( 1" 2" 3" 4" 5" 6" 7" 8" 9"
Ul} 8 16 24 33 41 49 57 65 73
irt} 8 15 23 30 38 46 53 61 68
LOGARITHMIC TANGENTS.
a
Tangent of 14 Degrees.
a
Tangent of 15 Degrees.
.
0"
10"
20"
30"
40"
50"
m
0"
10"
20"
30"
40"
50"
o
9,396771
6861
695o
7040
7i3o
72I9
59
o
9. 428052
8137
8221
83o5
8389
8473
69
i
73o9
7399
7488
7578
7667
7757
58
i
8558
8642
8726
8810
8894
8978
58
2
7846
7936
8025
8n5
8204
8294
57
2
9062
9i46
923o
93i4
9398
9482
57
3
8383
8472
8562
865i
874o
883o
56
3
9566
965o
9734
98i8
9902
9986
56
4
8919
9008
9o98
9l87
9276
9365
55
4
9.430070
oi54
0237
0321
o4o5
o489
55
5
9455
9544
9633
9722
9811
9900
54
5
o573
0657
o74o
0824
0908
0992
54
6
999°
••79
.168
.257
.346
.435
53
6
1075
iiSg
1243
i326
i4io
i494
53
7
9 ,4oo524
o6i3
O7O2
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0880
0969
52
7
i577
1661
1745
1828
1912
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52
8
io58
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1236
i325
i4i3
1502
5i
8
2079
2162
2246
2329
24l3
2496
5i
9
1591
1680
i769
i857
1946
2035
5o
9
258o
2663
2747
283o
2914
2997
5o
10
9.402124
2212
2301
2390
24-78
2567
49
IO
9.433o8o
3i64
3247
333i
34i4
3497
49
ii
2656
2744
2833
2922
3oio
3o99
48
ii
358o
3664
3747
383o
3914
3997
48
12
3187
3276
3364
3453
354i
363o
47
12
4o8o
4i63
4246
433o
44i3
4496
47
i3
37i8
38o7
3895
3983
4072
4i6o
46
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4579
4662
4745
4828
4912
4995
46
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4249
4337
4425
45i4
4602
4690
45
U
5o78
5i6i
5244
5327
54io
5493
45
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4778
4867
4955
5o43
5i3i
5219
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5^76
5659
5742
5825
5907
599o
44
16
53o8
5396
5484
5572
566o
5748
43
16
6o73
6i56
6239
6322
64o5
6488
43
17
5836
5924
6012
6100
6!88
6276
42
17
657o
6653
6736
68i9
6901
6984
42
18
6364
6452
654o
6628
67i6
68o4
4i
18
7o67
7i5o
7232
73!5
7398
748o
4i
19
6892
6980
7o68
7i55
7243
733i
4o
J9
7563
7646
7728
7811
7894
7976
4o
20
9.407419
75°7
7594
7682
777°
7858
39
20
9.438059
8i4i
8224
83o6
8389
847i
39
21
7945
8o33
8121
8208
8296
8384
38
21
8554
8636
8719
8801
8884
8966
38
22
8471
8559
8646
8734
8821
8909
37
22
9048
9i3i
92l3
9296
9378
946o
37
23
8996
9084
9171
9259
9346
9434
36
23
9543
9625
97°7
979°
9872
9954
36
24
9521
9609
9696
9783
9871
9958
35
24
9.44oo36
0119
0201
0283
o365
o447
35
25
9 .4ioo45
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O22O
o3o7
o395
0482
34
25
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0612
o694
o776
o858
0940
34
26
0569
o656
0743
o83i
0918
ioo5
33
26
IO22
no4
1186
1268
i35o
i432
33
27
1092
1179
1266
i353
i44i
i528
32
27
i5i4
i596
i678
i76o
1842
1924
32
28
i6i5
1702
1789
i876
i963
2o5o
3i
28
2006
2088
2I70
2252
2334
2416
3i
29
2 1 37
2224
23lO
2397
2484
257I
3o
29
249-7
2579
266l
2743
2825
2907
3o
3o
Q, 4i2658
2745
2832
29I9
3oo5
3092
29
3o
9.442988
3070
3i52
3234
33i5
3397
29
3i
3i79
3266
3352
3439
3526
36i3
28
3i
34-79
356o
3642
3724
38o5
3887
28
32
3699
3786
3873
3959
4o46
4i32
27
32
3968
4o5o
4l32
4213
4295
4376
27
33
4219
43o6
4392
4479
4565
4652
26
33
4458
4539
4621
4702
4784
4865
26
34
4?38
4825
4911
4998
5o84
5i7i
25
34
4947
5o28
5no
5i9i
5272
5354
25
35
5257
5343
543o
55!6
56o3
5689
24
35
5435
55i7
5598
5679
5761
5842
24
36
5775
5862
5948
6o34
6120
620-7
23
36
5923
6oo5
6086
6167
6248
633o
23
37
6293
6379
6465
655i
6638
6724
22
37
64n
6492
6573
6654
6735
681-7
22
38
6810
6896
6982
7o68
7i54
7240
21
38
6898
6979
-7060
7141
7222
73o3
21
39
7326
74i3
7499
7585
767i
7757
2O
39
7384
7465
7546
7627
7708
7789
20
4o
9.417842
7928
8014
8100
8186
A
8272
J9
4o
9.44787°
795i
8o32
8n3
8i94
8275
19
4i
8358
8444
853o
8616
87oi
8787
18
4i
8356
8437
85i8
8599
8680
8-760
18
42
8873
8959
9044
9i3o
9216
9302
ll
42
884i
8922
9oo3
9o84
9i64
9245
J7
43
9387
9473
9559
9644
973o
9816
16
43
9326
94o7
9487
9<<S
9649
973o
16
44
99oi
9987
..72
.1.58
.244
.329
i5
44
9810
989i
9972
. .^2
.i33
.213
i5
45
9.42o4i5
o5oo
o586
o67i
o757
0842
i4
45
9.450294
o375
o455
o536
0616
o697
i4
46
°927
ioi3
1098
1184
1269
i354
i3
46
0777
o858
o938
ioi9
io99
1180
i3
47
i44o
i525
1610
i696
i78i
1866
12
47
1260
i34i
1421
i5o2
i582
1662
12
48
I952
2037
2122
22O7
2292
2378
II
48
1743
1823
I9o3
i984
2084
2i44
II
49
2463
2548
2633
27l8
28o3
2888
IO
49
2225
23o5
2385
2465
2546
2626
IO
5o
9.422974
3o59
3i44
3229
33i4
3399
9
5o
9.452706
2-786
286-7
20.47
3027
3io7
9
5i
3484
3569
3654
3739
3824
39o9
8
5i
3i87
3267
3347
3428
35o8
3588
8
52
3993
4o78
4i63
4248
4333
44i8
7
52
3668
3748
3828
39o8
3988
4o68
7
53
45o3
4587
4672
4757
4842
492-7
6
53
4i48
4228
43o8
4388
4468
4548
6
54
Son
5o96
5i8i
5265
535o
5435
5
54
4628
47o8
4787
4867
4947
5027
5
55
55i9
56o4
5689
5773
5858
5942
4
55
6107
5i87
5267
5346
5426
55o6
4
56
602-7
6112
6196
6281
6365
645o
3
56
5586
5655
5745
5825
59o5
5984
3
57
6534
66i9
670^
6788
6872
6g56
2
5?
6064
6i44
6223
63o3
6383
6462
2
58
7o4i
7I25
7210
7294
7378
7463
I
58
6542
6622
6-701
6781
6860
694o
I
59
7547
763i
77i5
78oo
7884
7968
O
59
7019
7°99
7178
7258
7337
74i7
O
60"
50"
40"
30" 20"
10"
a
60" | 50" 40" 30"
20" 10" | d
Co-tangent of 75 Degrees.
i
Co-tangent of 74 Degrees. | §
„ T, * $ 1" 2" 3" 4" 5" 6" 7" 8" 9"
.C 1" 2" 3" 4" 5" 6" 7" 8" 9"
r* ravf1 /
"} 9 17 26 35 43 52 61 69 78
r. rartj g J6 25 33 41 49 5? 65 74
40
LOGARITHMIC SINES.
A
Sine of 16 Degrees.
d
Sine of 17 Decrees.
s
0"
10"
20"
30"
40"
50"
"S
0"
10" 20" 30" 1 40"
50"
0
9.44o338
o4n
o485
o558
o632
o7o5
59
O
9.465935 6oo4 6o-3 6i4s 621 1
6280
59
I
0778
o852
0925
0998
1072
n45
58
I
6348
64i7 6486 6555 6623
6692
58
2
1218
1292
i365
i438
i5u
1 584
57
2
676i
683o6898
6967
7o36
7io4
57
3
i658
i73i
1804
1877
igSo
2023
56
3
7i73
7242
73io
7379
7448
75i6
56
4
2096
2170
2243
23i6
2389
2462
55
4
7585
7653
7722
779°
7859
7928
55
5
2535
2608
2681
2754
2827
2900
54
5
7996
8o65
8i33
8202
8270
8338
54
6
2973
3o46
3119
3192
3265
3337
53
6
8407
8475
85448612
8681
8749
53
7
34io
3483
3556
3629
3702
3774
52
7
8817
8886
895419022
9091
9l59
52
8
3847
3920
3993
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60"
50"
40"
30" 20''
10"
c ,
60"
50"
40"
30"
20"
10"
J
Co-sine of 73
Degrees.
S
Co-sine of 72 Degrees.
1
5 1" 2" 3" 4"
5" 6" 7" 8" 9"
p p ,51" 2" 3" 4" 5" 6" 7" 8" 9"
' art} 7 14 21 28
36 43 50 57 64
'{ 7 13 20 27 33 40 47 53 60
LOGARITHMIC TANGENTS.
41
1
Tangent of 1 6 Degrees.
d
Tangent of 17 Degrees.
s
0" 10"
20"
30"
40"
50"
*
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60"
50" 40"
30"
20"
10"
a'
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50"
40"
30"
20"
10"
.
Co-tangent of 73 Degrees.
ii
Co -tangent of 72 Degrees.
§
.( \" 2" 3" 4" 5" 6" 7" 8" 9"
P. Part J g 15 23 31 39 46 54 62 7Q
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LOGARITHMIC SINES.
.9
Sine of 18 Degrees.
.5
Sine of 19 Degrees.
i
0"
10"
20"
30" 40"
50"
a
0"
10"
20"
30"
40"
50"
o
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3704
3762
3820
3878
3936
3994
O
60"
50"
40"
30"
20"
10"
.
60"
50"
40"
30"
20"
10"
Co-sine of 71 Degrees.
a
Co-sine of 70 Degrees.
.5
Si
f -til nil q/
P Part) "
' 4»
5'' 6" 7" 8" 9"
P P»rt5 !" 2" 3" 4" 5" 6" 7" 8" 9"
ml 6 13 19 25
31 38 44 50 57
irt} 6 12 18 24 30 36 42 48 54
LOGARITHM j TANGENTS.
43
A
Tangent of 18 Degrees.
a
Tangent of 19 Degrees.
-
8
ov
10"
20"
30"
40"
50"
3
0"
10"
20"
30"
40"
50"
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O
60" | 50" 40"
30"
20"
10"
a
60"
50"
40"
30"
20"
10"
d
Co-tangent of 7 1 Degrees.
•9
s
Co-tangent of 70 Degrees.
1
p Part$ 1" 2" 3" 4" 5" 6" 7" 8" 9"
I 7 14 21 28 35 42 49 56 63
P. Part J 7 13 2Q -7 33 4Q 47 54 6Q
44
LOGARITHMIC SINES.
c
Sine of 20 Degrees.
.3
Sine of 21 Degrees.
S
0"
10"
20"
30"
40"
50"
™
0"
10"
20"
30"
40"
50"
0
9.534o52
4i 10
4i67
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4283
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59
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58
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58
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3
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56
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5
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54
6
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6
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6735
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6844
6898
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7392
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9
7280
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7552
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2323
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3263 33i5
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60" 50"
40"
30" 20" 10"
fl
60" 50"
40"
30" 20"
10"
c-
Co-sine of 69 Degrees.
i
Co-sine of 68 Degrees.
.5
S
< 1" 2" 3" 4"
5" 6" 7" 8" 9"
.( I" 2" 3" 4" 5" 6" 7" 8" 9"
art{ 6 11 17 23
28 34 39 45 51
i
r.rart^ 5 n lg 21 ^ ^ ^ ^ 4g
LOGARITHMIC TANGENTS.
1
Tangent of 20 Degrees.
A
Tangent of 21 Degrees.
8
0"
10"
20"
30"
40"
50"
2
0"
10"
20"
30"
40"
50"
o
9.56io66
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1197
1262
1328
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59
0
9- 584i77
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4366
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1721
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5i83
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25o5
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2636
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2832
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55
5
3028
3o93
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5
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4532
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32
28
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2031
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2160
2224
2288
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28
4656
4718
4780
4842
4903
4965
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29
2352
2417
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2609
2673
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29
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5o89
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5274
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9.572738
2802
2866
2930
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29
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9.595398
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5583
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29
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3i23
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33i5
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28
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28
32
35o7
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27
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27
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26
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36i5
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3736
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7
53
i528
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1718
1781
1 844
6
53
3858
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398o
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4lO2
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54
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1971
2034
2097
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2223
5
54
4223
4284
4345
44o6
4467
4527
5
55
2286
235o
24i3
2476
2539
2602
4
55
4588
4649
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4771
483i
4892
4
56
2665
2728
279i
2854
29I7
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3
56
4953
5oi4
5o74
5i35
5i96
5257
3
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3o44
3107
3i7o
3233
3296
3359
2
57
53i7
5378
5439
55oo
556o
562i
2
58
3422
3485
3548
36n
3674
3737
I
58
5682
5742
58o3
5864
5924
5985
I
59
38oo
3863
3926
3989
4o52
4n4
0
59
6o46
6106
6167
6228
6288
6349
O
60"
50"
40"
30"
20"
10"
a
60"
50" | 40"
30"
20"
10"
.
a
Co-tangent of 69 Degrees.
S
Co-tangent of 68 Degrees.
i
p p. ( 1" 2" 3" 4" 5" 6" 7" 8" 9"
p p < 1" 2" 3" 4" 5" 6" 7" 8" 9"
$ 6 13 19 26 32 39 45 51 58
irlj 6 12 19 25 31 37 43 49 56
46
LOGARITHMIC SINES.
.a
Sine of 22 Degrees.
d
Sine of 23 Degrees.
B
0"
10"
20" 30" 40"
50"
jjj
0"
10"
20"
30"
40"
50"
o
9.573575
3628
368o37323784
3836 59
0
9.59i878
I928
I977
2027
20-76
2126
59
I
3888
394o
3992 4o44 4o96
4i4858
I
2176
2225
2275
2324
2374
2423
58
2
4200
4262
43o44356,44o8
446o
57
2
2473
2522
2572
2621
26-71
2720
57
3
45ia
4564
46i64668472o
4772
56
3
2770
28l9
2869
29i8
2968
3017
56
4
4824
4876
4928 498o 5o32
5o84
55
4
3067
3n6
3i65
32i5
3264
33i4
55
5
5i36
5187152395291 5343
5395
54
5
3363
34i2
3462
35n
356i
36io
54
6
5447
5499 555o56o2 5654
57o6
53
6
3659
37o9
3758
38o7
3857
39o6
53
7
5758
58io|586i 6913 5965
6oi7
52
7
3955
4oo5
4o54
4io3
4i53
4202
52
8
6o69
6120 6172 6224
6276
6327
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8
4261
43oi
435o
4399
4448
4498
5i
9
643i
6482 6534
6586
6638
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9
4547
4596
4645
4695
4744
4793
5o
10
9.576689
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6793 6844
6896
6948
49
IO
9.594842
489i
494i
499o
5o39
5o88
49
ii
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58
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8887
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1680
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1729
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59
9029
9°77
9I24
9171
92I9
9266
0
60"
50"
40"
30" 20" 10"
.
60"
50"
40"
30"
20"
10"
c
Co-sine of 67 Degrees.
a
Co-sine of 66 Degrees. a"
PPartJ1" 2" 3/
' 4" 5" 6" 7" 8" 9"
p p ( 1" 2" 3" 4" 5" 6" 7" 8" 9"
\ 5 10 15 20 25 31 36 41 46
ff I 5 10 15 19 24 29 34 39 44
LOGARITHMIC TANGENTS.
4-7
1
Tangent of 22 Degrees.
J
Tangent of 23 Degrees.
s
0"
10"
20" | 30" 40" 50"
2
0"
10"
20"
30" 1 40"
50"
o
9.606410
6470
653l
6691
6652
6713
59
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9.627852
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59
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3
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7621 76811
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56
55
2
3
4
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57
56
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28
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6628
6688
6748
6807
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28
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7668
7726
7783
7841
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29
6867
6926
6986
7o46
7io5
7i65
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29
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8oi4
8o72
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8187
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7343
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29
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29
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28
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8762
8820
8877
8935
28
32
7939
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8o57
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27
32
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9io7
9i65
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27
33
8295
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26
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9337
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26
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25
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2797
2856
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3463
3520
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3328
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48
4490
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4718
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49
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4271
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4388
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8
62
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5i53
5212
5271
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7
52
5857
5gi4
597'
6028
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7
53
5388
5447
55o6
5565
5623
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6
53
6199
6256
63i3
6369
64266483
6
54
574i
58oo
5858
59I7
5976
6o35
5
54
654o
6597
6654
6710
6767;6824
5
55
6o93
6i52
6211
6269
6328
6387
4
55
6881
6938
6995
7o5i
7io8;7i65
4
56
6445
65o4
6563
6621
6680
6739
3
56
7222
7279
7335
7392
7449 75°6
3
57
6797
6856
69i5
6973
7032
7090
2
57
7562
7619
7676
7733
7789*7846
2
58
7149
7208
•7266
7325
7383
7442
I
58
79o3
7960 8016:807!:
8i3o8i86
I
59
75oi
7559
76i8
7676
7735
7793
0
59
8243
83oo835684i3
8470:8626
0
60"
50"
40"
30"
20"
10"
.
60" | 50" | 40" | 30"
20" 1 10"
.
Co-tangent of 67 Degrees.
S3
Co-tangent of 66 Degrees.
a
P P A I" 2" 3" 4" 5" 6" 7" 8" 9"
.( 1" 2" 3" 4" 5" 6" 7" 8" 9"
trc£ 6 12, 18 24 30 36 42 48 54
in\ 6 12 17 23 29 35 40 46 52
LOGARITHMIC SINES.
FT
Sine of 24 Degrees.
a
Sine of 25 Degrees.
•
0"
10"
20"
| 30"
40"
50"
9
0" 10" 20" 30"
40V
50"
0
I
9 6o93i3
9597
936i
9644
9691
9455
9739
9502
9786
955o
9833
59
58
o
I
9.625948
6219
5993
62^4
6039 6o84 6129
63o9 6354i64oo
6i74
6445
59
58
2
988o
9928
9975 ..22
..69
.116
57
2
6490
6535
658o 6625 6670
67i5
57
3
9.610164
O2II
0258
o3o5
o352
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56
3
6760
68o5
685o 6895 6940
6985
56
4
o44?
o494
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0682
55
4
7o3o
7o75
7120 7165 7210
7255
55
5
6
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0823 o87i
1106 u53
0918
1 200
0965
1247
54
53
5
6
73oo
757o
7345
76i5
739o
7660
7435
77°5
748o
775o
7525
7795
54
53
8
1294
i576
i34i
i623
i388
i67o
i435
1717
1482
1764
1529
1811
52
5i
7
8
784o
8109
7885
8i54
792979748019
8i99]8a448a89
8o64
8333
52
5i
9
i858
I9o5
1952
1999
2046
2093
5o
9
8378
8423
8468 85 1 3
8558
8602
5o
10
9.612140
2l87
2234
2280
2327
2874
49
10
9.628647
8692
8737
8782
8826
887i
49
n
2421
2468
25i5
2562
2609 2655
48
n
8916
8961
9oo6
9o5o
9o95
9i4o
48
12
2702
2749
2796
2843
2890 2936
47
12
9 1 85
9229
9274
93i9
9363
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60"
50"
40" J
30" 20"
10"
B
60" 50" 40" 30" 20" i 10" 1 ^
Co-sine of 65
Degrees.
Co-sine of 64 Degrees. ^
P T> tf 1" 2" 3" 4"
5" 6" 7" 8" 9"
p p ( 1" 2" 3" 4" 5" 6" 7" S" 9" 1
P'Part{ 5 9 14 18
23 28 32 37 42
ij
^4 9 13 18 22 26 31 35 40
LOGARITHMIC TANGENTS.
49
A
Tangent of 24 Degrees.
A
Tangent of 25 Degrees.
m
0"
10"
20"
30"
40"
50"
m
0"
10"
20"
30"
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50"
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60"
50"
40"
30" 1 20"
10"
.
60"
50"
40"
30"
20"
10"
j
Co-tangent of 65 Degrees.
a
Co-tangent of 64 Degrees.
s
r !// 2// 3// 4// 5// 6// 7// 8" 9"
( 1" 2" 3" 4" 5" 6" 7" 8" 9"
in{ 6 11 17 22 28 33 39 45 50
art{ 5 11 16 22 27 33 38 43 49
50
LOGAIIIHMIC SINES.
.9
Sine of 26 D -grees.
d
Sine of 27 Degrees.
I
0"
10"p 20"p 1 0" ' 40" J NV'
3
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10' H
20"
30" | 40"
50"
o
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7027 7069
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2092
2i33
2174
39
21
7240
7282 7325
7367
7409
7452
38
21
2214
2255
2296
2337
2377
2418
38
22
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75377579
7622
7664
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37
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258i
2621
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7749
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8893
8936
8978
32
27
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37i7
3758
3798
3839
3879
32
28
9020
9063 9105
9147
9189
9232
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28
3920
3960
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4o4i
4082
4l22
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29
9274
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94oi
9443
9485
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29
4i63
4203
4244
4284
4325
4365
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9.649527
9781
9570 9612
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9654
9907
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29
28
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3i
9.6644o6
4648
4446
4689
4486
4729
4527
4769
4567
48io
46o8
485o
29
28
32
9.65oo34
0076 01 18
0160
0202 O245.
27
32
4891
493i
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5012
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27
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26
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1716 1758
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6342
6382
6422
6462
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1800
1842 1884
1926
1968 20IO
20
39
6583
6623
6663
67o3
6743
6784
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9.652o52
2094 2 1 36
2178
2220 2262
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4o
9.666824
6864
6904
6944
6984
7025
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4i
a3o4
2345 2387
2429
2471 25i3
18
4i
7o65
7io5
7i45
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7225
7265
18
42
2555
25972638
2680
2722 2764
17
42
73o5
7346
7386
7426
7466
75o6
17
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2806
2848 2890
2931
2973 3oi5
16
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7546
7586
7626
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7946
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3683
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8347
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8426
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8546
8586
8626
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4059
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4i84
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8746
8786
8826
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8906
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49
43o9
435o;4392
4434
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9026
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9io5
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4683
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9.669225
9265
93o5
9345
9384
9424
9
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48o8
48504891
4933
4974 5oi6
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9464
95o4
9544
9584
9624
9663
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52
5o58
6099 5i4i
5i82
52245265
7
52
97o3
9743
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9823
9862
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7
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54
9. 670181
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0260
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o379
5
55
58o5
58465888
5929
5971 6012
4
55
o4i9
o459
0499
o538
o578
0618
4
56
6o54
6096 6i36
6178
6219 6261
3
56
o658
0697
o737
0777
0816
o856
3
57
63o2
63446385
6426
6468 65o9
2
57
o896
o935
o975
ioi5
io54
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2
58
655i
65926633
6675
67166757
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58
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I2l3
1253
1292 i332
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59
6799
684o!688i
6923
6964 7005
O
59
1372
i4 1 1
i45i
1490
i53o 1670
0
60"
40" | 30"
20" j 10"
a
60"
50"
40"
30"
20" 10"
a
Co-sine of 63 Degrees.
i
Co-sine of 62 Degrees.
1
P Part 5 !" 2// 3// 4// 5" 6" 7" 8' 9"
p p .(!" 2" 3" 4" 5" 6" 7" 8" 9"
I 4 8 13 17 21 25 30 34 38
{T I 4 8 12 16 20 24 28 32 36
LJGARITHMIC TANGENTS.
.3
Tangent of 26 Degrees.
0
Tangent of 27 Degrees.
SI
0"
10"
20"
30"
40" 50"
S
0"
10"
20"
30"
40" 50"
o
9.688182
8235
8289
8342
8395
8449
59
o
9.707166
-7218
7270
7322
7374 7426
69
i
85o2
8556
86o9
8663
87i6
8769
58
I
7478
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7582
7634
7686
7738
58
2
8823
8876
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8983
9o36
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57
2
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7842
7894
79-46
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57
3
9i43
9196
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93o3
9356
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56
3
8102
8i54
8206
8258
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8362
56
4
9463
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9623
9676
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55
4
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8466
85i8
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8622
8674
55
5
9783
9836
9890
9943
9996
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54
5
8726
8778
883o
8882
8934
8985
54
6
9.690103
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0263
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53
6
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9!93
9245
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53
7
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52
7
9349
9401
9453
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9608
52
8
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1008
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8
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9712
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9
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1221
1274
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2019
2072
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2338
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2444
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26o3
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2656
2710
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2816
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2922
45
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1732
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2975
3028
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3i34
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1991
2043
2094
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3293
3346
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3453
35o6
3559
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16
2 1 46
2198
2249
2301
2353
24o5
43
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36i2
3665
37i8
377i
3824
3877
42
17
2456
2608
256o
2611
2663
27l5
42
18
393o
3983
4o36
4o89
4i42
4i95
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18
2-766
2818
2870
2921
2973
3o25
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4248
43oi
4354
4407
446o
45i3
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3o76
3i28
3i79
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3283
3334
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20
9.694566
46i9
4672
4724
4777
483o
39
20
9.7i3386
3438
3489
354i
3592
3644
39
21
4883
4936
4989
5o42
5o95
5i48
38
21
3696
3747
3799
385o
3902
3954
38
22
5201
5254
536o
54i2
5465
37
22
4oo5
4o57
4io8
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4211
4263
37
23
55i8
557i
5624
5677
573o
5783
36
23
43i4
4366
44i8
4469
452i
4572
36
24
5836
5888
5g4i
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6o47
6100
35
24
4624
4675
4727
4778
483o
488 1
35
25
6i53
6206
6258
63n
6364
6417
34
25
4933
4984
5o36
5o87
5i39
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34
26
647o
6522
6575
6628
6681
6734
33
26
5242
5293
5345
5396
5448
5499
33
27
6787
6839
6892
6945
6998
7o5o
32
27
555i
56o2
5654
57o5
5757
58o8
32
28
7io3
7i56
7209
7262
73i4
7367
3i
28
586o
5911
5962
6oi4
6o65
6117
3i
29
7420
7473
7525
7578
763i
7684
3o
29
6168
6220
62-71
6322
6374
6425
3o
3o
9.697736
7789
7842
7894
7947
8000
29
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9.7i6477
6528
6579
663i
6682
6734
29
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8o53
8io5
8i58
8211
8263
83i6
28
3i
6785
6836
6888
6939
6991
7o42
28
32
8369
8421
8474
8627
8579
8632
27
32
. 7093
7i45
7i96
7247
7299
735o
27
33
8685
8737
879o
8843
8895
8948
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33
74oi
7453
75o4
7555
76o7
7658
26
34
9ooi
9o53
9io6
9l59
9211
9264
25
34
77°9
776i
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7863
79i5
7966
25
35
93i6
9369
9422
9474
9527
95-79
24
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80 1 7
8069
8120
8171
8223
8274
24
36
9632
9685
9737
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9842
9895
23
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8376
8428
8479
853o
858i
23
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53
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22
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8684
8735
8786
8838
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38
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21
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38
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8991
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9094
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9196
21
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20
39
02.4.0
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9452
95o4
20
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9.7oo893
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9.719555
96o6
9657
97o8
976o
9811
19
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1208
1260
i3i3
i365
i4i8
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18
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9862
99i3
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.118
18
42
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1628
1680
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42
9. 720160,
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17
43
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1942
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2047
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16
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0476
0527
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0629
0680
0732
16
44
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2257
23o9
2362
24i4
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0936
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45
2466
25l9
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2623
26-76
2-728
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45
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1191
1243
1294
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278l
2833
2885
2938
2990
3o42
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1498
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1600
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3o95
3i47
3i99
3252
33o4
3356
12
47
i -702
I753
i8o4
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1906
i957
12
48
34o9
346i
35i3
3566
36i8
367o
I I
48
2009
2060
2III
2162
22l3
2264
II
49
3722
3775
3827
3879
3932
3984
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49
23 1 5
2366
24l7
2468
2519
2570
10
5o
9.7o4o36
4o88
4i4i
4i93
4245
4297
9
5o
9. -722621
26-72
2723
2774
2825
2876
9
5i
435o
4402
4454
45o6
4559
46n
8
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2927
2978
3o29
3o8o
3i3o
3i8i
8
52
4663
47i5
4768
4820
4872
4924
7
52
3232
3283
3334
3385
3436
3487
7
53
4976
5o29
5o8i
5i33
5i85
5237
6
53
3538
3589
364o
3691
3742
3793
6
54
529o
5342
5394
5446
5498
555i
5
54
3844
3895
3945
3996
4o47
4o98
5
55
56o3
5655
5707
5759
58n
5863
4
55
4i49
4200
425i
4302
4353
44o3
4
56
59i6
5968
6020
6o72
6124
6176
3
56
4454
45o5
4556
46o7
4658
47Q9
3
57
6228
6280
6333
6385
6437
6489
2
57
476o
48io
486i
49I2
4963
5oi4
2
58
654i
6593
6645
6697
6749
6801
I
58
5o65
5u5
5i66
52i7
5268
53i9
I
59
6854
69o6
6958
-7010
-7062
7114
O
59
537o
5420
547i
5522
5573J5624
O
60"
50"
40"
30"
20"
10"
.
60"
50"
40"
30"
20" 10"
^
Co-tangent of 63 Degrees.
S
Co-tangent of 62 Degrees.
s
p p A I" 2" 3" 4" 5" 6" 7" 8" 9"
( V 2" 3" 4" 5" 6" 7" 8" 9"
I 5 11 16 21 26 32 37 42 47
ar > 5 10 15 21 26 31 36 41 46
52
LOGARITHMIC SINES.
d
Sine of 28 Degrees.
g
Sine of 29 Degrees.
s
0"
10"
20"
30"
40"
50"
9
0"
10" 20" 30" l 40"
50"
0
9.671609
1649
1688
I728
i768
i8o7
59
o
9.68557i
56o9 5647
5685
5723
576i
59
I
i847
1886
1926
i965
2005
2o45
58
I
5799
5837
5875
59i3
595i
5989
58
2
2084
2124
2i63
2203
2242
2282
57
2
6o27
6o65
6io36i4i
6i78
6216
57
3
2321
236i
2400
2440
2479
2519
56
3
6254
6292
633o!6368
64o6
6444
56
4
2558
2598
2637
2677
27l6
2756
55
4
6482
6519
6557
6595
6633
667i
55:
5
2795
2835
2874
2914
2953
2992 54
5
67o9
6747
6785
6822
6860
6898
54;
6
3o32
3071
3m
3i5o
3190
322953
6
6936
6974
7OI2
7o49
7o87
7I25
53
7
3268
33o8
334? 3387
3426
3465 52
7
7i63
7201
7238
7276
73i4
7352
52
8
35o5
3544
3583 3623
3662 3702 5i
8
7389
7427
7465
75o3
754i
7578
5ii
9
374i
3780
38203859
38983938
5o
9
7616
7654
7692
7729
7767
78o5
5o
10
9.673977
4oi6
4o56 4095
4i34'4i73
49
10
9. 687843
7880
79i8
7956
7993
8o3i
49
ii
42l3
4252
4291
433i
437o'44o9
48
ii
8o69
8106
8i44
8182
8220
8257
48
12
4448
4488
45274566
46o64645
47
12
8295
8333
837o
84o8
8446
8483
47
i3
4684
4723
4762:4802
484i 488o
46
i3
852i
8559
8596
8634
867i
87o9
46
i4
4919
4959
4998:5037
5o76 5n5
45
i4
8747
8784
8822
8860
8897
8935
45
i5
5i55
5i94
52335272
53n
535o
44
i5
8972
9010
9o48
9o85
9I23
9i6o
44
16
5390
5429
5468 55o7
5546 5585
43
16
9i98
9235
9273
93n
9348
9386
43
J7
5624
5664
57o35742
578i 5820
42
*7
9423
9461
9498
9536
9573
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28
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2902
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3858 3896
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57 4887
4925
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83i3
8349
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2
58
5n5
5i53
5191
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53o5
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58
8532
8569
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8642 8678
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59
5343
538i
54i9
5457 5495
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59
875i
8788
8824
886i|8897
8934
0
60"
50"
40"
30" 20"
10"
c
60"
50"
40"
30" 20"
10"
a
Co-sine of 6 1 Degrees.
§
Co-sine of 60 Degrees.
i
t< \" 2" 3" 4" 5" 6" 7" 8" 9"
in\ 4 8 12 16 19 23 27 31 35
p p . < 1" 2" 3" 4" 5" 6" 7" 8" 9"
irt} 4 7 11 15 19 22 26 30 33
LOGARITHMIC TANGENTS.
53
1
Tangent of 28 Degrees.
c
Tangent of 29 Degrees.
s
0"
10"
20"
30"
40"
50"
9
0"
10"
20"
30"
40"
50"
o
9.725674
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29
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9.734764
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29
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2839
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29
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28
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2937
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3i33
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28
32
5367
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55i7
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27
32
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3280
333o
3379
3428
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27
33
5668
57i8
5768
58i8
5868
59i8
26
33
3526
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3722
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26
34
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7
53
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763
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6
53
9395
9443
9492
954i
959o
9638
6
54
1962
2OI2
2062
2112
2161
2211
5
54
9687
9736
9785
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9882
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5
55
2261
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4
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4
56
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2758
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3
56
9.76o272
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3
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2858
2007
957
3007
3o56
3io6
2
57
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0661
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2
58
3i56
3206
3255
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1245
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1 342
1391
O
60"
50"
40"
30"
20"
10"
d
60" 50" | 40"
30"
20"
10"
.
Co-tangent of 61 Degrees.
•9
g
Co-tangent of 60 Degrees.
i
P Part* l" 2" 3// 4// 5" 6" 7// 8" 9"
. ( 1" 2" 3" 4" 5" 6" 7" 8" 9"
irl$ 5 10 15 20 25 30 35 40 45 IIL} 5 10 15 20 25 29 34 39 44
54
LOGARITHMIC SINES.
1
Sine of 30 Degrees.
*
Sine of 3 1 Degrees.
s
0"
10"
20" 1 30" | 40"
50"
§
0" | 10"
20"
30"
40"
50"
0
9.69897o
9oo6
9043 9079 9116
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59
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9.7n839
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1944
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59
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9262 9298:9334
937I 58
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2o5o
2o85
2120
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2225
58
2
9407
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94809517:9553
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2
2260
2295
2330
2365
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2434
57
r
9626
9662
969997359771
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56
3
2469
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56
4
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55
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55
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9.700062
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54
5
2889
2924
2959
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3o63
54
6
0280
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0425
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53
6
3o98
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3238
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53
7
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33o8
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16
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16
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5255
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43
17
2669
27o5 2741^777
28i3
2849
42
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5394
5428
5463
5498
5532
5567
42
18
2885
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2957 2993
3029
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18
56o2
5636
567i
57o5
574o
5775
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3ioi
3i37
3173 3209
3245
3281
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58o9
5844
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59i3
5948
5982
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9.7o33I7
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39
20
9. 716017
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6086
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21
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3677
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38
21
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6328
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38
22
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37
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6432
6466
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26
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33
27
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4968
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32
27
7466
7535
7569
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7638
32
28
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5075
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28
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77°7
774i
7776
7810
7844
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29
5254
5290
5326
5362
5397
5433
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29
7879
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7948
7982
8016
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9.7o5469
55o5
554o
5576
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29
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9. 718085
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8188
8223
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5826
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28
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32
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7429
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2O
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9. 707606
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8
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4
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56
34oo 3434 3468;35oi 3535 3569
3
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1208
1243
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2
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36o33636367o37o43738377i 2
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58
38o5:38393873 39o6 394o3974 i
59
i629
1664
1699
1734
1769 1 8o4
O
59
4oo7 4o4i 4075 4io9 4i42 4176 o
60"
50"
40" | 30" | 20" i 10"
a
60" 50" . 40" 30" 20" 10" 1 .
Co-sine of 59 Degrees.
•fl
Co-sine of 58 Degrees. '£
. ( 1" 2" 3" 4" 5" 6" 7" 8" 9" „ „ J 1" 2" 3" 4" 5" 6" 7" 8" 9"
"{ 4 7 11
14 18 21 25 29 32 \ 3 7 10 14 17 21 24 27 31
LOGARITHMIC TANGENTS.
.5
Tangent of 30 Degrees.
Jj
Tangent of 3 1 Degrees.
0"
10"
20"
30"
40"
50"
0"
10"
20"
30"
40"
50"
0
9. -761439
i486
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9. 778774
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2
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2168
2217
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57
2
9346
9394
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9489
9537
9584
57
3
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2363
2411
2460
25o8
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56
3
9632
9679
9727
9775
9822
987o
56
4
2606
2654
27o3
2751
2800
2848
55
4
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55
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2249
2296
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2439
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5224
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532i
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55i4
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28l9
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29i4
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3246
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16
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6192
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6288
6337
43
16
334i
3388
3436
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353i
3578
43
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6385
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653o
6578
6627
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3768
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18
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6723
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6820
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4242
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39
20
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4527
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7738
7786
38
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38
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80-76
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32
27
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32
28
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9763
9811
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28
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6799
6847
6894
6941
6988
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29
9860
99o8
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. 100
3o
29
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7o83
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7178
7225
7272
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29
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9.7873I9
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7556
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06-78
28
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765o
7697
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7792
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28
32
0-726
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0822
0870
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27
32
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8028
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27
33
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1 1 1 1
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1207
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26
33
81-70
821-7
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8359
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26
34
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22
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21
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5i42
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5238
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12
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2128
2I75
2222
2269
23i6
2363
12
48
5333
538i
5429
5477
5525
5573
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48
2410
2457
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255i
2598
2645
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49
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5668
5716
5764
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2692
2739
2786
2833
2880
2927
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5956
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9
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3o68
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3i62
3209
9
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6195
6243
6290
6338
6386
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3256
33o3
335o
3397
3444
349i
8
52
6482
6529
6577
6625
6673
672I
7
52
3538
3585
3632
3679
3726:3773
7
53
6768
6816
6864
69I2
6960
7°°7
6
53
38i9
3866
39i3
396o
4oo7 4o54
6
54
7o55
7io3
7i5i
7i99
7246
7294
5
54
4ioi
4i48
4i95
4242
42894336
5
55
7342
739o
7437
7485
7533
758i
4
55
4383
443o
4
56
-7628
7676
7724
7772
78i9
7867
3
56
4664
47n
4758
48o5 4852 4899
3
57
79i5
7963
8010
8o58
8106
8i54
2
57
4946
4992 5o39
5o865i335i8o
2
58
8201
8249
8297
8344
8392
844o
I
58
5227
5274532i 5367!54i4546i
I
59
8488
85358583
863i
8678
8726
O
59
55o8 5555 56o2 5649
5696 5742
O
W 50" 40"
30" 20"
10"
~T~
60" 50" ) 40" i 30"
20" , 10"
G
Co-tangent of 59 Degrees.
S3
Co-tangent of 58 Degrees.
1
P Part* l" ~" 3" 4" 5" 6" 7" 8" 9"
C l" 2" 3" 4" 5" 6" 7" 8" 9"
\ 5 10 14 19 24 29 34 39 43
irt\ 5 9 14 19 24 28 33 38 43
bfl
LOGARITHMIC SINES.
_g
Sine of 32 Degrees.
.s
Sine of 33 Degrees
9
0
10"
20"
30"
40"
50"
2
0" 10" 20" | 30". 40"
50"
o
9.724210
4243
4277:4311
4344
4378
59
0
9.736io9 6i4i 6i74 6206
6238
627I
59
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44i2
4445
447945i3
4546
458o
58
I
63o3 6336 636864oo
6433
6465
58
2
46i4
4647
468i 47i5
4748
4782
57
2
6498653066626696
6627
6659
57
3
48i6
4849
4883 49i7
495o
4984
56
3
6692,6-724 6757|6789
6821
6854
56
4
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5o5i
5o85'
5n8
5i52
5i85
55
4
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7oi5
7o48
55
5
5219
5253
5286
5320
5353
5387
54
5
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7209
7241
54
6
5420
5454
5488
552i
5555
5588
53
6
7274
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33
7
5622
5655
5689
5722
5756
5789
52
7
7467
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76327664
7597
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8
9
10
5823
6024
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589o5923
6091 6124
6292 6325
5957
6i58
6359
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6i9i
6392
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49
8
9
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7693772617768
788779197961
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5o
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6426
6459
6493 6526
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6593
48
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7061
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9943
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20
9.728227
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39
20
9.739975
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39
21
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84938526
856o8593
38
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38
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37
22
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23
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8858
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36
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36
24
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9223
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9290
9I24
9323
915719190
93569389
35
34
24
25
0742
o934
0774
o966
0806
°997
o838
I029
o87o
1061
O902
io93
35
34
26
9422
9455
9489 9522
95559588
33
26
1125
1 157
n89
1221
1253
1284
33
27
9621
9654
96879720
9753
9787
32
27
i3i6
1 348
i38o
1412
1 444
i476
32
28
9820
9853
9886 9919
9952
9985
3i
28
i5o8
i539
1671
i6o3
i635
i667
3i
29 9.730018
oo5i
oo84
0117
oi5o
oi83
3o
29
i699
1730
1762
i794
1826
i858 3o
*3o 9.730217
025o
0283 o3i6
0349 o382
29
3o
9.74i889
I92I
i953
i985
20I7
2049
29
3i
o4i5
o448
0481
o5i4
o547 °58o
28
3i
2080
2112
2i44
2I76
22O7
2239 28
32
o6i3
0646
06790712
o745
0778
27
32
2271
23o3
2335
2366
2398
243o
27
33
0811
o844
0877
o9io
o943
o976
26
33
2462
2493
2525
2557
2589
2620
26
34
1009
1042
1075
1 1 08
n4i
n73
25
34
2652
2684
27l5
2747
2779
28 1 i
25
35
1206
1239
1272
i3o5
i338
i37i
24
35
2842
28-74
29o6
2937
2969
3ooi
24
36
i4o4
i437
1470
i5o3
i536
i569
23
36
3o33
3o64
3o96
3128
3i59
3i9i
23
37
1602
1 634
1667
1700
i733
1766
22
37
3223
3254
3286
33i83349
338i
22
38
1799
i832
i865
i897
I93o
i963
21
38
34i3
3444
3476
35o8 3539
357i
21
39 1996
2029
2062
2095
2127
2160
20
39
36o2
3634
3666
3697
3729
376i
20
409.732193
2226
2259 2292
2325
2357
I9
4o
9.743792
3824
3855
3887
39i9
395o
J9
4i
2390
2423
2456 2489
2521
2554
18
4i
3982
4oi3
4o45
4o77
4io8
4i4o
18
42
2587
2620
2653 2685
2718
2?5l
17
42
4i7i
4203
4234
4266
429-7
4329
17
43
2784
2816
2849 2882
29l5
2948
16
43
436i
4392
4424
4455
4487
45i8
16
44
2980
3oi3
3o46 3o79
3in
3i44
i5
44
455o
458i
46i3
4644
4676
47o7
i5
45
3i77
3210
8242
3275
33o8
334o
i4
45
4739
477o
4802
4833
4865
4896
i4
46
3373
34o6
34393471
35o4
3537
i3
46
4928
4959
499i
5022
5o54
5o85
i3
47
48
49
3569
3765
396i
36o2
3798
3994
3635 36673700
383i 3863|3896
4027 4o59 4092
3733
3929
4i25
12
II
IO
47
48
49
5n7
53o6
5494
5i48
5337
5526
5i8o
5369
5557
5211
5400
5589
5243
543i
5620
5274
5463
565i
12
II
IO
5o
9.734157
4i9o
4222
4255
4288
4320
9
5o
9.745683
57i4|5746
5777
58o8
584o
9
5i
4353
4386
44i8
445 1
4483
45i6
8
5i
587i
69036934
5965
5997
6028
8
52
4549
458i
46i4
4646
4679
47n
7
52
6060
6091 6122
6 1 54 6 1 85
6216
7
53
4744
4?77
4809
4842
4874
49o7
6
53
6248!6279!63io
63426373
64o4
6
54
4939
4972
5oo4
5o37 5069
5l02
5
54
6436 6467 6498
653o656i
6592
5
55
5i35
5i67
52OO
52325265
5297
4
55
6624 6655 6686
67i86749
678o
4
56
533o
5362
5395
5427
546o
5492
3
56
68i2'6843
6874
69o5
6937
6968 3
57
5525
5557
559o
5622
5655
5687
2
57
6999!7o3i
-7062
7o93
•7124
7i56
2
58
57i9
5752
5784
58i7
5849
5882
I
58
71877218
7249
728lJ73l2
7343
I
59
5gi4
5947
5979
601 1 6o44
6o76
O
59
7374|74o6
7437 7468)7499 753o
O
60"
50"
40'
30" 20"
10"
B
60" 50" 40" 30" 20" 10"
a
Co-sine of 57
Degrees.
i
Co-sine of 56 Degrees.
i
.< 1" 2" 3" 4"
5" 6" 7" 8" 9"
p p C 1" 2" 3" 4" 5" 6" 7" 8" 9"
P.PMtj 3 7 10 13
17 20 23 26 30
1 n\ 3 6 10 13 16 19 22 25 29
LOGARITHMIC TANGENTS.
rl
Tangent of 32 Degrees.
d
Tangent of 33 Degrees.
*
0"
10"
20" 30"
40"
50"
a
0"
10"
20"
30" 40"
00"
o
9-795789
5836
5883593o
5977
6023
59
o
9.8i25i7
2563
2610
2656
27O2
2748
59
I
6070
6n7
616416211
6258
63o4
58
i
2794
2840
2886
2932
2978
3o24
58
6
635i
6398
6445
6492
6539
6585
57
2
3070
3n6
3i63
3209
3255
33oi
57
3
6632
6679
6726
6773
68i9
6866
56
3
3347
3393
3439
3485
353i
3577
56
4
69i3
696o
7oo7
7o53
7100
7i47
55
4
3623
3669
37i5
376i
38o7
3853
55
5
7i94
724l
7287
7334
738i
7428
54
5
3899
3945
399i
4o37
4o83
4i29
54
6
7474
752I
7568
76i5
7662
77o8
53
6
4176
4222
4268
43i4
436o
44o6
53
7
7755
7802
7849
7895
7942
7989
52
7
4452
4498
4544
4590
4636
4682
52
8
8o36
8082
8i29
8176
8223
8269
5i
8
4728
4774
4820
4866
49I2
4958
5i
9
83i6
8363
84o9
8456
85o3
855o
5o
9
5oo4
5o5o
5o96
5i42
5i88
5 2 34
5o
10
9.798596
8643
8690
8737
8783
883o
49
10
9.8i528o
5326
5371
5417
5463
55o9
49
ii
8877
8923
897o
9017
9o63
9no
48
ii
5555
56oi
5647
5693
5739
5785
48
12
9i57
9204
925o
9297
9344
939o
47
12
583i
5877
5923
5969
6oi5
6061
47
i3
9437
9484
953o
9577
9624
967o
46
i3
6107
6i53
6i99
6245
629I
6336
46
i4
97i7
9764
9810
9857
99o4
995o
45
i4
6382
6428
6474
6520
6566
6612
45
i5
9997
..44
..90
.i37
.184
.230
44
i5
6658
6704
6750
6796
6842
6888
44
16
9.8oo277
0324
o37o
o463
o5io
43
16
6933
6979
7025
7071
7117
7i63
43
I7
o557
o6o3
o65o
o697
o743
°79°
42
17
7209
7255
73oi
7347
7392
7438
42
18
o836
o883
ogSo
o976
1023
I07O
4i
18
7484
753o
7576
7622
7668
7714
4i
19
1116
n63
1209
1256
i3o3
1 349
4o
i9
7759
7805
785i
7897
7943
7989
4o
20
9.8oi396
1442
1489
i535
i582
1629
39
20
9.8i8o35
8081
8126
8172
8218
8264
39
21
1675
1722
1768
i8i5
1862
1908
38
21
83io
8356
8402
8447
8493
8539
38
22
i955
2OOI
2048
so94
2l4l
2l87
37
22
8585
863i
8677
8722
8768
8814
37
23
2234
228l
2327
2374
2420
2467
36
23
8860
89o6
8952
8997
9o43
9o89
36
24
25i3
256o
2606
2653
2699
2746
35
24
9i35
9i8i
9226
9272
93i8
9364
35
25
2792
2839
2886
2932
2979
3o25
34
25
94io
9455
95oi
9547
9593
9639
34
26
3072
3n8
3i65
3211
3258
33o4
33
26
9684
973o
9776
9822
9868
99i3
33
27
335i
3397
3444
349o
3537
3583
32
27
9959
..96
.142
.188
32
28
363o
3676
3723
3769
38i6
3862
3i
28
9.820234
0280
o325
o37i
o4i7
o463
3i
29
39o9
3955
4ooi
4o48
4o94
4i4i
3o
29
o5o8
o554
0600
o646
o69i
o737
3o
3o
9.8o4i87
4234
4280
4327
4373
4420
29
3o
9:820783
o829
o874
0920
0966
1012
29
• 3i
4466
45i3
4559
46o5
4652
4698
28
3i
1057
no3
n49
iigS
1240
1286
28
32
4745
479i
4838
4884
493o
4977
27
32
i332
i377
1423
1469
i5i5
i56o
27
33
5o23
5070
5n6
5i63
5209
5255
26
33
1606
i652
i697
1743
1789
i835
26
34
5302
5348
5395
544i
5487
5534
25
34
1880
I926
I972
2017
ao63
2I09
25
35
558o
5627
5673
57i9
5766
58i2
24
35
2i54
22OO
2246
2292
•-337
2383
24
36
5859
59o5
595i
5998
6o44
6091
23
36
2429
2474
2520
2566
2611
2657
23
37
6i37
6i83
623o
6276
6322
6369
22
37
2703
2748
2794
2840
2885
293i
22
38
64i5
6462
65o8
6554
6601
6647
21
38
2977
3022
3o68
3n4
3i59
32o5
21
39
6693
6740
6786
6832
6879
6925
20
39
325i
3296
3342
3387
3433
3479
20
4o
9 806971
7018
7064
7IIO
7i57
7203
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4o
9. 823524
357o
36i6
366i
37o7
3753
19
4i
7249
7296
7342
7388
7435
748i
18
4i
3798
3844
3889
3935
398i
4026
18
42
7527
7574
7620
7666
77i3
7759
17
42
4072
4u7
4i63
4209
4254
43oo
17
43
78o5
785i
7898
7944
799°
8o37
16
43
4345
439i
44?7
4482
4528
4573
16
44
8o83
8129
8176
8222
8268
83i4
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44
46i9
4665
4710
4756
48oi
4847
i5
45
836i
84o7
8453
8499
8546
8592
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45
4893
4938
4984
5029
5o75
5l2O
i4
46
8638
8685
873i
8777
88a3
887o
i3
46
5i66
5212
5257
53o3
5348
5394
i3
47
89i6
8962
9008
9o55
9ioi
9147
12
47
54>9
5485
553i
5576
5622
5667
12
48
• 9i93
9240
9286
9332
9378
9424
II
48
57i3
5758
58o4
5849
5895
594o
II
49
947i
95i7
9563
96o9
9656
9702
IO
49
5986
6o32
6077
6i23
6168
6214
IO
5o
9.8o9748
9794
9840
9887
9933
9979
9
5o
9.826259
63o5
635o
6396
644i
648 7
9
5i
9. 810025
0071
0118
0164
0210
0256
8
5i
6532
6578
6623
6669
67i4
6760
8
52
o3o2
o349
o395
o44i
o487
o533
7
52
68o5
685i
6896
6942
6987
7o33
7
53
o58o
0626
0672
0718
o764
0810
6
53
7078
7I24
7i69
72l5
7260
73o6
6
54
o857
o9o3
0949
o995
io4i
io87
5
54
735i
7397
7442
7488
7533
7579
5
. 55
1 1 34
1180
1226
I272
i3i8
1 364
4
55
7624
767o
77i5
776i
7806
785i
4
56
i4io
i457
i5o3
I 549
i595
i64i
3
56
7897
7942
7988
8o33
8o79
8124
3
57
1687
i733
1780
:826
l872
1918
2
57
8170
82i5
8261
83o6
835i
8397
2
58
i964
2010
2o56
2IO2
2l49
2195
I
58
8442
8488
8533
8579
8624
8669
1
59
224l
2287
2333
2379
2425
2471
O
59
87i5
8760
8806
885i
8897
8942
O
60"
50"
40"
30"
20"
10"
a
60"
50" | 40"
?0"
20"
10"
.
Co-tangent of 57 Degrees.
a
Co-tangent of 56 Degrees.
a
f 1 // a// o// AH c// en 7/7 Q// a/i
P T*nrt I •*•*•** ^* ** "D ' o I/
. ( 1" 2" 3" 4" 5" 6" 7" 8" 9"
ir I 5 9 14 18 23 27 32 37 41
58
LOGARITHMIC SINES
.3
Sine of 34 Degrees.
rf
Sine of 35 Degrees.
1
s
0"
10"
20" 30"
40"
50"
s
0" | 10" | 20"
30''
40"
50"
o
9.747562
7593
7624 7655
7686
7718
59
o 9.75859i 8621
865i
8681 8712
8742
59
I
7749
778o
7811 7842
7874
79°5
58
i
87728802
8832 8862i8892
8922
58
2
7936
7967
7998 8o3o
8061
8o92
57
2
8952 8982
9OI2|9042 9072
9IO2
57
L
8i23
83io
8i54
834i
8i8582i6
8372 84o3
8248
8434
8466
56
55
L
9l32 9l62
93l2 9342
9192 9222 9262
9372 94o2 9432
9282
9462
56
55
5
8497
8528 85598590
8621
8652
54
5
9492 9522
95529582
9612
9642
54
6
8683
87i4
8745,8777
8808
8839
53
6
9672
9702
9732
9762
9792
9822
53
7
8870
8901
89328963
8994
9025
52
7
9852
988i
99"
994i
99-71
... I
52
8
9o56
9o87
9118 9149
9180
92I2
5i
8
9. 76003 1
0061
0091
OI2I
oi5i
0181
5i
9
9243
9274'93o59336
9367
9398
5o
9
O2I I
0240
0270
o3oo
o33o
o36o
5o
10
9.749429
9460 9491 9522
9553
9584
49
IO
9. 760390
0420
o45o
o48o
0509
o539
49
n
96i5
9646 967-7 9-708
9739
9770
48
n
o569
o599
0629
o659
0689
0718
48
12
98oi
9832
9863 9894
9925
9956
47
12
o748
o778
0808
o838
0868
0898
47
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9987
..18
..48.. 79
. no
46
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0927
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o987
IOI7
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1076
46
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9. 750172
0203
0234 0265
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0327
45
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I I 06
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1166
1196
1225
1255
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44
16
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43
16
1 464
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43
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0760
0791
0821
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o883
42
17
1642
16-72
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1791
42
18
o9M
0945 O976 ioo7
io37
1068
4i
18
1821
i85i
1880
1910
1940
1969
4i
19
io99
ii3o
i i6i|i 192
1222
1253
4o
'9
1999
2O29
2059
2088
21 18
2148
4o
20
9.75i284
i3i5
i346 1377
i4o7
i438
39
20
9.762i77
22O7
2237
2267
2296
2326
39
21
i469
i5oo
i53i
i56i
l592
1623
38
21
2356
2385
24i5
2445
2474
25o4
38
22
i654
1 685
1715 1746
I777
1808
37
22
2534
2563
2593
2623
2652
2682
37
23
i839
1869
1900 1931
I962
I992
36
23
27I2
274i
277I
2801
283o
2860
36
24
2O23
2o54 2o85 2ii5
2146
2I77
35
24
2889
29I9
2949
2978
3oo8
3o38
35
25
22O8
2238
2269 23oo
233o
236i
34
25
3o67
3o97
3i26
3i56
3i86
32i5
34
26
2392
3423,2453 2484
25i5
2545
33
26
3245
3274
33o4
3333
3363
3393
33
27
2576
26o7 2637
2668
2699
2729
32
27
3422
3452
348i
35ii
354o
357o
32
28
2760
279I
2822 2852
2883
29i4
3i
28
36oo
3629
3659
3688
37i8
3747
3i
29
2944
2975
3oo5 3o36
3o67
3o97
3o
29
3777
38o6
3836
3865
3895
3925
3o
3o
9.753i28
3i59
3l8g 3220
325i
3281
29
3o
9.763954
3984
4oi3
4o43
4o72
4102
29
3i
33i2
3342
3373 34o4
3434
3465
28
3i
4i3i
4i6i
4i9o
4249
4279
28
32
. 3495
3526 3557
3587
36i8
3648
27
32
43o8
4338
4367
4396
4426
4455
27
33
3679
37io 374o
377i
38oi
3832
26
33
4485
45i4
4544
4573
46o3
4632
26
34
3862
3893
3923
3954
3985
4oi5
25
34
4662
469i
4720
475o
4779
48o9
25
35
36
4o46
4229
4o76 4io7
42594290
4i37
4320
4i684i98
435i 438i
24
23
35
36
4838
5oi5
4868
5o44
4897
5o74
5io3
4g56
4985
5i62
24
23
37
44 1 2
4442
4473
45o3
4534 4564
22
37
5i9i
5221
525o
5279
53o9
5338
22
38
4595
46254656
4686
47i74747
21
38
5367
5397
5426
5456
5485
55i4
21
39
4778
48o8 4839
4869
49oo 493o
20
39
5544
5573
56o2
5632
566i
5690
20
4o
9. 754960
4991 5o2t
5o52
5o82:5n3
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4o
9. 765720
5749
5778
58o8
5837
5866
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4i
5i43
5i73
52o4
5234
5265 5295
18
4i
5896
5925
5954
5984
6oi3
6042
18
42
5326
53565386
54i7
54475478
17
42
6072
6101
6i3o
6i59
6189
6218
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43
55o8
5538
5569
5599
5629566o
16
43
6247
6277
63o6
6335
6364
6394
16
44
5690
572I
575i
578i
58i2;5842
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44
6423
6452
648 1
65n
654«
6569
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45
5872
59o3
5933
5963
5994 6024
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45
6598
6628
6657
6686
67i5
6745
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46
6o54
6o856n5
6i45
61766206
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46
6774
68o3
6832
6862
6891
6920
i3
47
6236
6267 6297
6327
63586388
12
47
6949
6978
7oo8
7°37
7o66
7o95
12
00 O O
xjxjvo
64i8
6600
9.756782
6448 6479
663o 6660
6812 6842
65o96539|657o
669ii672i:675i
6872 69o3 6933
IO
9
48
49
5o
7124
73oo
9. 767475
7i54
7329
75o4
7i83
7358
7533
7212
7387
7562
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74i6
759i
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7445
7620
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IO
9
5i
6963
6993 7O23
7o54
708417114
8
5i
7679
77o8
7737
7766
7795
8
52
7i44
7i75 72o5
7235
7265 7295
7
52
7824
7853
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-7912
794i
797°
7
53
7326
7356 7386
74i6
7446 7477
6
53
7999
8028
8o57
8086
3ii5
8i44
6
54
7507
7537 7567
7597
7627 7658
5
54
8i73
82o3
8232
8261
^290
83i9
5
55
7688
77187748
7778
7808 7839
4
55
83488377
84o6 8435
8464
8493 4
56
7869
7899 7929 7959
7989 8oi9
3
56
85228551
8580860986388668
3
57
58
8o5o
823o
8080 8110 8i4o
826082908321
8170 8200
835i 838i
2
57
58
8697 8726
8871 89oo
87558784
8929!8958
88 1 3 8842
8987 9016
2
59
84ii
844i 8471 85oi
853i 856i
O
59
9o45 9o74 9io3 9i32 9i6i
9i9o
O
60"
50" :
40" 30" 20" 10"
.
60" 50" 40" | 30" 20"
10" 1
Co-sine of 55 Degrees.
s
Co-sine of 54 Degrees.
§
P'*H13 2e' 39"
4" 5" 6" 7" 8" 9"
12 15 18 21 25 28
p p .< 1" 2" 3" 4" 5" 6" 7" B" 9"
} 3 6 9 12 15 18 21 24 27
LOGARITHMIC TANGENTS.
1 —
-S
Tangent of 34 Degrees.
.3
Tangent of 35 Degrees.
9
0"
10" | 20"
30"
40" 50"
9
0"
10"
20"
30"
40"
50"
0
9.828987
9o339o78
9124
9i6g!92i5
59
o
9. 845227
5272
53i6
536i
54o6
545 1
59
I
9260
93o5935i
9396
9442
9487 58
I
5496
554o
5585
563o
5675
572O
58
2
9532
9578
9623
9669
97i4
9759
57
2
5764
58o9
5854
5899
5944
5988
57
0
9805
985o
9895 gg4i
9986
..32
56
3
6o33
6o78
6i23
6168
6212
6257
56
4
9.830077
0122
0!68
02l3
0258
o3o4
55
4
63o2
6347
639i
6436
648i
6526
55
c
o349
o395
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54
5
6570
66i5
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67o5
675o
6794
54
6
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53
6
6839
6884
6929
6973
7oi8
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53
7
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1029
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1120
52
7
7108
7i52
7i97
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52
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5!
8
7376
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9
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1 664
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9
7644
7689
7734
7779
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10
9.831709
i755
1800
i845
i89i
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49
IO
9.8479i3
7957
8002
8047
8092
8i36
49
ii
1981
2026
2O72
2117
2162
2208
48
ii
8181
8226
8270
83i5
836o
84o5
48
12
2253
2298
2343
2389
2434
2479
4?
12
8449
8494
8539
8583
8628
8673
47
i3
2525
257O
26i5
2660
2-706
2751
46
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87i7
8762
8807
885i
8896
894i
46
i4
2796
2842
2887
2932
2977
3o23
45
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8986
9o3o
9o75
9I20
9164
9209
45
i5
3o68 3n3
3i58
3204
3249
3294
44
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9254
9298
9343
9388
9432
9477
44
16
3339
3385
343o
3475
3520
3566
43
16
9522
9566
96n
9656
97oo
9745
43
!7
36ii
3656
37oi
3747
3792
3837
42
17
979°
9834
9879
9924
9968
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42
' 18
3882
3927
3973
4oi8
4o63
4io8
4i
18
9.85oo57
OIO2
0147
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0236
0281
4i
19
4i54
4199
4244
428g
4334
438o
4o
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o325
0370
o4i5
o459
o5o4
o548
4o
20
9.834425
447o
45:5
456i
46o6
465i
39
20
9.85o593
o638
0682
0727
°772
0816
39
21
4696
474i
4787
4832
4877
4922
38
21
0861
o9o5
o95o
o995
1039
1084
38
22
4967
5012
5o58
5io3
5i48
5i93
37
22
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1218
1262
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i352
37
23
5238
5284
5329
5374
54i9
5464
36
23
i396
i44i
i485
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36
24
55o9
5555
56oo
5645
569o
5735
35
24
1 664
1708
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i797
1842
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35
25
5780
5826
587i
59i6
596i
5oo6
34
25
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2O2O
2o65
2110
2i54
34
26
6o5i
6o96
6 1 42
6i87
6232
6277
33
26
2199
2243
2288
2332
2377
2422
33
27
6322
6367
6412
6458
65o3
6548
32
27
2466
25ll
2555
2600
2644
2689
32
28
6593
6638
6683
6728
6773
68i9
3i
28
2733
2778
2823
286-7
2912
2956
3i
29
6864
69o9
6954
6999
7o44
7o89
3o
29
3ooi
3o45
3ogo
3i34
3i79
3223
3o
3o
9.837i34
7J79
7225
7270
73i5
736o
29
3o
9. 353268
33i3
3357
3402
3446
349i
29
3i
74o5
745o
7495
754o
7585
763o
28
3i
3535
358o
3624
3669
37i3
3758
28
32
7675
7721
7766
78n
7856
79oi
27
32
38o2
3847
38gi
3936
398o
4o25
27
33
7946
7991
8o36
8081
8126
8171
26
33
4o69
4n4
4i58
4203
4247
4292
26
34
8216
8261
83o7
8352
8397
8442
25
34
4336
438i
4425
447o
45i4
4559
25
35
8487
8532
86778622
8667
8712
24
35
46o3
4648
4692
4737
4781
4826
24
36
8757
8802
8847
8892
8937
898a
23
36
487o
49i5
4959
5oo4
5o48
5o93
23
37
9027
9072
9n7
9l62
9207
9252
22
37
5i37
5i82
5226
527I
53i5
536o
22
38
9297
9343
9388
9433
9478
9523
21
38
54o4
5449
5493
5537
5582
5626
21
39
9568
96i3
9658
97o3
9748
9793
2O
39
567i
57i5
5760
58o4
5849
5893
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9.839838
9883
9928
9973
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9.855938
5982
6026
6071
6n5
6160
19
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9.84oio8
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0243
0288
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18
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6204
6249
6293
6338
6382
6426
1 8
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65i5
656o
66o4
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17
43
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0-782
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16
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6737
6782
6826
6871
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6959
16
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100-7
1052
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44
7oo4
7o48
7o93
7i37
-7182
7226
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45
n87
1232
I277
1322
i367
l4l2
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45
7270
73i5
7359
7404
7448
7492
i4
46
i457
1502
1 54?
l592
i637
1682
i3
46
7537
758i
7626
7670
77i4
775g
i3
47
I727
1771
1816
1861
1906
i95i
12
47
78o3
7848
7892
7936
7981
8c25
12
48
I996
2o4l
2086
2l3l
2176
2221
I I
48
8o69
8n4
8i58
8203
8247
829i
II
49
2266
23ll
2355
2400
2445
2490
IO
49
8336
838o
8424
8469
85i3
8558
10
5o
9 842535
2 5 80
2625
26-70
2715
2760
9
5o
9. 858602
8646
869i
8735
8779
8824
9
5i
28o5
2849
2894
2939
2984
3o29
8
5i
8868
89I2
8957
9ooi
9045
9090
8
52
3o74
3ii9
3i64
3209
3253
3298
7
52
9i34
9i78
9223
9267
93n
9356
7
53
3343
3388
3433
3478
3523
3568
6
53
94oo
9444
9489
9533
9577
9622
6
54
36i2
3657
3702
3747
3792
3837
5
54
9666
97io
9755
9799
9843 9888
5
55
3882
3927
397i
4oi6
4o6i
4io6
4
55
9932
9976
. .21
..65
.109). i54
4
56
4i5i
4i96
4241
4285
433o
4375
3
56
9.86oi98
0242
0287
o33i
o375io42o
3
57
4420
4465
45io
4554
45gg
4644
2
57
o464
o5o8
o552
o597 o64i o685
2
58
59
4689
4958
4734
5oo3
4779
5o48
4823
5o92
4868
5i37
5?82
I
0
58
59
o73o
o995
0774
io4o
0818
io84
0862 090-7,0951
II28JII72 1217
I
O
60"
50" 40"
30"
20"
10"
.
60" [ 50" 40" 30" 20" j 10"
a
Co-tangent of 55 Degrees.
&
Co-tangent of 54 Degrees.
.< \" 2" 3" 4" 5" 6" 7" 8" 9"
.( 1" 2" 3" 4" 5" 6" 7" S" 9"
in\ 5 9 14 18 23 27 32 36 41
irtl 4 9 13 18 22 27 31 36 40
LOGARITHMIC SINES.
d
D
Sine of 36 Degrees.
_s-
Sine of 37 Degrees.
H
0"
10" 20"
30'
40" 50"
s
0"
10"
20" | 30" 1 40"
50"
o
9.769219
92489277
93o6
93359364i59
o
9-779463
949i
95i9|9547 9575
9603
59
i
9393
9421
945o 9479
95o8 953-7
58
i
963i
9659
9686 97i4 9742
977°
58
2
9566
9595
96249653
9682 9711
5?
2
9798
9826
9854
9882
9910
9938
57
3
974o
9769
97989827
9856 9884
56
3
9966
9993
. .21
. .49
••77
.io5
56
4
99i3
9942
997i
. . . .
..29
..58
55
4
9. 78oi33
0161
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0216
0244
0272
55
5
9.770087
0116
oi45 0173
O202 O23l
54
5
o3oo
o328
o356
o384
o4n
o439
54
6
0260
0289
o3i8o347
0376 o4o4
53
6
0467
o495
o523
o55i
o578
0606
53
7
o433
0462
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O520
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52
7
o634
0662
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0718
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077$
52
8
0606
o635
o664 o693
072210750
5i
8
0801
o829
o857
0884
0912
0940
5i
9
0779
0808
08370866
0895 0923
5o
9
o968
o996
1023
io5i
1079
1107
5o
10
9.7709520981
IOIO
io39
1067 1096
49
IO
9.781134
1162
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1218
1246
1273
49
ii
ii25ii54
n83
121 I
1240)1269
48
ii
i3oi
i329
i357
1 384
l4l2
i44o
48
12
1298 i326
i355
1 384
i4i3 i44i
47
12
i468
i495
i523
i55i
1578
1606
47
i3
1470
1499
i528
i556
i585 1614
46
i3
i634
1662
i689
1717
1745
1772
46
i4
1 643
1671
1700
I729
1758 1786
45
i4
1800
1828
i856
i883
1911
1939
45
i5
i8i5
1 844
1872
I9OI
i93oi959
44
i5
i966
i994
2O22
2049
2077
2105
44
16
1987
2016
2o45
2073
2102 2l3l
43
16
' 2l32
2160
2188
22l5
2243
2271
43
17
2159
2188
2217
2245
2274 23o3
42
17
2298
2326
2354
238i
2409
2437
42
18
233i
236o
2389
2417
2446 2475
4i
18
2464
2492
252O
2547
2575
2602
4i
I9
25o3
2532
256i
2589
2618 2646
4o
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263o
2658
2685
2713
2741
2768
4o
20 9. 772675
2704
2732
2761
2790
2818
39
20
9.782796
2823
285i
2879
2906
2934
39
21
2847
2875
2904
2933
2961
2990
38
21
296i
2989
3017
3o44
3072
3o99
38
22
3oi8
3o47
8076
3io4
3i33
3i6i
37
22
3127
3i54
3i82
3210
3237
3265
37
23
3190
3219
3247
3276
33o4
3333
36
23
3292
3320
3347
3375
34o2
343o
36
24
336i
3390
34i8
3447
3476
35o4
35
24
3458
3485
35i3
354o
3568
3595
35
25
3533
356i
359o
36i8
3647
3675
34
25
3623
365o
3678
37o5
3733
376o
34
26
3704
3732
376i
3789
38i8
3846
33
26
3788
38i5
3843
3870
3898
3925
33
27
3875
3903
396o
3989
4017
32
27
3953
39«o 4oo8
4o35
4o63
4o9o
32
28
4o46
4074
4io34i3i
4i6o
4i88
3i
28
4n8
4i45
4i73
4200
4228
4255
3i
29
4217
4245
4274
4302
433i
4359
3o
29
4282
43io
4337
4365
4392
4420
3o
309.774388
44x6
4445 4473
45oi
453o
29
3o
9 . 784447
4475
45o2
4529
4557
4584
29
3i
4558
4587
46i546444672
4700
28
3i
4612
4639
4667
4594
4721
4749
28
32
4729
4757
4786 48i4'4842
487i
27
32
4776
48o4
483i
4858
4886
49i3
27
33
34
4899
5070
4928
5098
495649855oi3|5o4i
5i265i55|5i8352i2
26
25
33
34
494i
5io5
4968
5i32
4995
5 1 60
5o23
5187
5o5o
52i4
5o78
5242
26
25
35
524o
5268
5297
53255353
5382
24
35
5269
5296
5324
535i
5378
54o6
24
36
54io
5438
5467 5495
5523
5552
23
36
5433
546i
5488
55i5
5543
557o
23
37
558o
56o8
56375665
5693
5722
22
37
5597
5624
5652
5679
57o6
5734
22
38
575o
5778
58o7
5835 5863
5892
21
38
576i
5788
58i6
5843
587o
5898
21
39
5920
5948
5977
6oo5
6o33
6061
2O
39
5925
5952
5979
6007
6o34
6061
2O
4o'9« 776090
61186146
61756203
623i
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4o
9.786o89
6116
6i43
6170
6198
6225
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6259
6288 63i6
63446372
64oi
18
41
6252
6279
63o7
6334
636i
6388
18
42
6429
6457
6485
65i46542
657o
17
42
64i6
6443
647o
6497
6525
6552
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43
44
6598
6768
6627
6796
6655
6824
6683
6852
6711
6880
6739
69o9
16
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43
44
6579
6742
6606 6634
6770 6707
6661
6824
6688
685i
67i5
6878
16
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45
6937
6965
6993
7021
7o5o
7078
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69o6
6933
696o
6987
7014
7042
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7106
7i34
7162
7191
7219
7247
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7o69
7096
7123
7i5o
7177
72o5
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7275
73o3
733i
7359
7388
74i6
12
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7232
7259
7286
73i3
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7367
12
48
7444
7472
75oo
7528
7556
7585
II
48
7395
7422
7449
7476 75o3
753o
II
49
7613
764i
7669
7697
7725
7753
IO
49
7557
7585
7612
7639 7666
7693
10
5o
5i
9.777781
795o
7810
7978
7838
8006
7866 7894
80348062
7922
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|
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7883
7747
79io
7774
7937
7801
7964
7829
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7856
8018
1
52
8119
8i4?
8175
8203
823i
8259
7
52
8o45
8072
8o99
8127
8i54
8181
7
53
8287
83i5
8343
837i
8399
8427
6
53
8208
8235
8262
8289
83i6
8343
6
54
8455
8483
85n
85398567
8595
5
54
837o
8397
8424
845 1
8478
85o5
5
55
8624
8652
8680
870818736
8764
4
55
8532
8559
8586
86i3
864o
8667
4
56
8792
8820
8848
8876180.04
8932
3
56
86^8721 8748
8775
8802
8829
3
57
8960
8988
9oi6
9o44
9072
9ioo
2
57
8856 8883 89io
89378964899i
2
58
9128
9i56
9i83
92II
9239
9267
I
58
9oi8 9o45 9072
9099 9126 91 53
I
59
9295
9323
935i
93799407
9435
0
59
9i8o 92O7'9234!926i 9288 93i5 o
60"
50"
40"
30" 20"
10"
d
60" 50" 40" i 30" 20" 10"
Co-sinb of 53
Degrees.
§
Co-sine of 52 Degrees. %
P Parti l" 2// 3" 4"
5" 6" 7" 8" 9"
p p A \" 2" 3" 4" 5" 6" 7" 8" 9"
l.rartj 3 6 9 n
14 17 20 23 26
m\ * 5 8 11 14 16 19 22 25
LOGARITHMIC TANGENTS.
.s
Tangent of 36 Degrees.
£
Tangent of 37 Degrees.
m
0"
10"
20"
30"
40"
50"
s
0"
10"
20"
30"
40"
50"
0
9.861261
i3o5
i35o
i394
i438
1482
59
O
9-877114
7i58
7202
7246
7290
7333
59
1
1527
1571
1616
:659
1704
1748
58
I
7377
742I
7465
75o9
7552
7596
58
2
1792
1837
1881
I925
i969
2Ol4
57
2
7640
7684
7?28
777i
78i5
7859
57
3
2o58
2102
2!46
2 I 01
2235
2279
56
3
79°3
7947
799°
8o34
8078
8122
56
4
2323
2368
2412
s456
25oo
2545
55
4
8i65
8209
8253
8297
834i
8384
55
5
2689
2633
2677
2721
2766
2810
54
5
8428
8472
85i6
8559
86o3
8647
54
6
2854
2898
2943
2987
3o3i
3075
53
6
869i
8734
8778
8822
8866
89o9
53
7
3119
3i64
3208
3252
3296
334i
52
7
8953
8997
9041
9o85
9128
9I72
52
8
3385
3429
3473
35i7
3562
36o6
5i
8
9216
9260
93o3
9347
939i
9435
5i
9
365o
3694
3738
3783
3827
3871
5o
9
9478
9522
9566
96o9
9653
9697
5o
10
9.8639i5
3959
4oo4
4o48
4092
4i36
49
10
9-879741
9784
9828
9872
99i6
9959
49
ii
4i8o
4225
4269
43i3
4357
44oi
48
ii
9.88ooo3
0047
0091
oi34
0178
O222
48
12
4445
449o
4534
4578
4622
4666
47
12
0265
oSog
o353
o397
o44o
o484
47
i3
4710
4755
4799
4843
4887
493i
46
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0703
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46
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5io8
5i52
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45
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079o
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092I
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1008
45
i5
5240
5285
5329
5373
54i7
546i
44
i5
IO52
1096
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1227
1271
44
16
55o5
5549
5594
5638
5682
5726
43
16
i3i4
i358
1402
i445
i489
i533
43
|7
5770
58i4
5858
5'9o3
5947
599i
42
17
i577
1620
1 664
I7o8
1751
i795
42
18
6o35
6o79
6i23
6167
6211
6256
4i
18
i839
1882
1926
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20l3
2067
4i
J9
63oo
6344
6388
6432
6476
6520
4o
J9
aioi
2i44
2188
2232
2275
23i9
4o
20
9.866564
66o9
6653
6697
6741
6785
39
20
9. 882363
2406
245o
2494
2537
258i
39
21
6829
6873
6917
696i
7006
7o5o
38
21
2625
2668
27I2
2756
2799
2843
38
22
7094
7i38
7182
7226
7270
73i4
37
22
2887
2930
2974
3oi8
3o6i
3io5
37
23
7358
7402
7446
749i
7535
7579
36
23
3i48
3192
3236
32-79
3323
3367
36
24
7623
7667
7711
7755
7799
7843
35
24
34io
3454
3498
354i
3585
3628
35
25
7887
793i
7975
8oi9
8o64
8108
34
25
3672
37i6
3759
38o3
3847
389o
34
26
8i52
8i96
8240
8284
8328
8372
33
26
3934
3977
4O2I
4o65
4io8
4i52
33
27
84i6
846o
85o4
8548
8592
8636
32
27
4i96
4239
4283
4326
437o
44i4
32
28
8680
8724
8768
88i3
8857
89oi
3i
28
4457
45oi
4544
4588
4632
4675
3i
29
8945
8989
9o33
9°77
9I2I
9i65
3o
29
4719
4-762
48o6
485o
4893
4937
3o
3o
0.860209
9253
9297
934i
9385
9429
29
3o
9.88498o
5o24
5o68
5m
5i55
5i98
29
3i
9473
95l7
956i
96o5
9649
9693
28
3i
5242
5286
5329
5373
54i6
546o
28
32
9?3?
9781
9825
9869
99i3
9957
27
32
55o4
5547
559i
5634
5678
5721
27
33
9.870001
oo45
oo89
oi33
0177
O22I
26
33
5765
58o9
5852
5896
5939
5983
26
34
O265
oSog
o353
o397
o44i
o485
25
34
6026
6o7o
6n4
6i57
6201
6244
25
35
0529
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0617
0661
0705
0749
24
35
6288
633i
6375
64i9
6462
65o6
24
36
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6837
0881
6925
o969
ioi3
23
36
6549
6593
6636
6680
6723
6767
23
3?
1057
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n45
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1233
1277
22
37
• 6811
6854
6898
694i
6985
7028
22
38
1321
i365
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21
38
7072
7116
7i59
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7246
7289
21
39
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1629
i673
1717
1761
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2O
39
7333
7377
7420
7464
75°7
755i
2O
4o
9.871849
1893
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2024
2068
1 9
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9.887594
7638
768i
7725
7768
7812
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4i
2112
2i56
230O
2244
2288
2332
18
4i
7855
7899
7942
7986
8o29
8o73
18
42
2376
2420
2464
25o8
2552
2596
17
42
8116
8160
8203
8247
829I
8334
17
43
264o
2684
2727
2771
2815
2859
16
43
8378
8421
8465
85o8
8552
8595
16
44
29O3
2947
299I
3o35
3079
3i23
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44
8639
8682
8-726
8769
88i3
8856
16
45
3i67
3211
3255
3299
3342
3386
i4
45
89oo
8943
8987
9o3o
9Q74
9117
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46
343o
3474
35i8
3562
36o6
365o
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46
9161
9204
9248
9291
9334
9378
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4?
3694
3738
3781
3825
3869
39i3
12
47
9421
9465
95o8
9552
9595
9639
12
48
3957
4ooi
4o45
4o89
4i33
4177
II
48
9682
9726
9769
9813
9856
9900
II
49
4220
4264
43o8
4352
4396
444o
10
49
9943
9987
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..74
.117
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10
5o
9,874484
4528
4572
46i5
4659
47o3
9
5o
9.890204
0247
029I
o334
0378
O42I
9
5i
4747
4791
4835
4879
4923
4966
8
5i
o465
o5o8
o552
o595
o639
0682
8
52
5oio
5o54
5o98
5i42
5i86
523o
7
52
O725
o769
0812
0856)0899
o943
7
53
5273
53i7
536i
54o5
5449
5493
6
53
0986
io3o
io73
1116
1160
1203
6
54
5537
558o
5624
5668
5712
5756
5
54
1247
1290
i334
i377
1421
1 464
5
55
58oo
5843
5887
593i
5975
6oi9
4
55
1507
i55i
i594
i638
1681
1725
4
56
6o63
6107
6i5o
6i94
6238
6282
3
56
1768
1811
i855
1898
I942
i985
3
57
6326
6370
64i3
6457
65OI
6545
2
57
2028
2O72
2Il5
2i59
22O2
2246
a
58
6589
6632
6676
6720
6764
6808
I
58
2289
2332
2376
2419
2463
25o6
i
59
6852
6895
6939
6983
7027
7071
O
59
2549
25g3
2636
2680
2723
2766
o
60"
50"
40"
30"
20"
10"
,
60" 50"
40"
30" 20" | 10"
.
Co-tangent of 53 Degrees.
1
Co-tangent of 52 Degrees.
S
p p .< 1" 2" 3" 4" 5" 6" 7" 8" 9"
, I" 2" 3" 4" 5" 6" 7" 8" 9"
lrt{ 4 9 13 18 22 26 31 35 40
J.-fartj 4 9 13 17 22 26 31 35 39
LOGARITHMIC SINES.
.a
Sine of 38 Degrees.
_g
Sine of 39 Degrees.
m
0
10"
20" 30" 40" 50"
%
0"
10"
20"
30" | 40"
50"
0
9. 789342
9369
9396;9423 945o'9477
59
O
9.798872
8898
8924
895o8976
9002
59
I
9604
953i
9557 9584 96i i
9638
58
I
9028
9064
9o8o
9io6 9i32
9168
58
2
9666
9692
97x0074607739800
67
2
9184 9210
9236
9262 92&7
93i3
57
3
9827
9854!988o 9907 9934 9961
56
3
93399365
939i
94i7
9443
9469
56
4
9988
,.x5..4a .,69 ..96
. 122
55
4
949519621
9547
9573
9599
9626
55
5
9-79oi49
0176:0203 O23o 0267
0284
54
5
9661
9677
97o3
9728
9754
9-780
54
6
o3io
o337o364o39i o4i8
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53
6
9806
9832
9858
9884
9910
9936
53
8
0471
o632
o498
o659
0626
0686
0662 0679
071310740
0606
0767
52
5i
8
9962
9.8001 17
9987
oi43
oi69
..39
oi95
..65
O220
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0246
52
5!
9
0793
08200847
0874 0901
0927
5o
9
0272
0298
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o35o
o376
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5o
10
9.790954
0981
1008
io34 1061
1088
49
IO
9.800427
o453
o479
0606
o53i
o556
49
ii
xxx5
1142
1168
1 196
1222
1249
48
ii
0682
0608
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0660
0686
07I I
48
12
1276
1302
1329
i356
1382
1409
47
12
o737
o763
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0816
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0866
47
i3
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i463
1489
1616 i543
1670
46
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0892
0918
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0996
1021
46
i4
i596
1623
i65o
1676 1703
1730
45
U
1047
1073
io98
1124
1 160
n76
45
i5
1767
i783
1810
i837
i863
1890
44
16
1201
1227
1263
I279
i3o5
i33o
44
16
I9i7
i943
1970
1997
2024
2060
43
16
i356
1 382
i4o8
1433
i459
i486
43
17
2077
2104
2i3o
2167
2184
22IO
42
17
i5n
1 536
1662
1 588
i6i3
i639
42
18
2237
2264
2290 2317
2344
2370
4i
18
1666
1691
1716
1742
i768
i794
4i
19
2397
2423
2460 2477
25o3
253o
4o
19
1819
1846
1871
i896
1922
1948
4o
20
21
9.792557
2716
2583
2743
2610 2636
2770 2796
2663
2823
2690
2849
39
38
20
21
9.8oi973
2128
1999
2i53
2026
2I79
2061
2206
2O76
223O
2102
2256
39
38
22
2876
29o3
2929
2966
2982
3009
37
22
2282
2307
2333
2359
2384
24lO
37
23
3o35
3o62
3o89
3n5
3 1 42
3i68
36
23
2436
2461
2487
2612
2538
2564
36
24
3i95
3222
3248
3275
33oi
3328
35
24
2589
2616
2641
2666
2692
27l8
35
25
3354
338i
3407
3434
346o
3487
34
25
2743
2769
2794
2820
2846
287I
34
26
35i4
3540
3667
3593
3620
3646
33
26
2897
2922
2948
2974
2999
3o25
33
27
3673
3699
3726
3752
3779
38o5
32
27
3o5o
3076
3lO2
3l27
3i53
3i78
32
28
3832
3858
3885
3911
3938
3964
3i
28
32o4
3229
3255
3281
33o6
3332
3i
29
399i
4oi7 4o44
4070
4097
4123
3o
29
3357
3383
34o8
3434
3459
3485
3o
3o
3i
9.794i5o
43o8
4i7642o3
4335436i
4229
4388
4255
44i4
4282
444 1
29
28
3o
3i
9.8o35n
3664
3536
3689
3562
37i5
3687
3?4o
36i3
3766
3638
379i
29
28
32
4467
4493 4620
4546
4573
4599
27
32
38i7
3842
3868
3893
39i9
3944
27
33
4626
4652 4678
4706
473i
47*8
26
33
397o
3995
4021
4o46
4o72
409-7
26
34
4784
48io4837
4863
4890
49i6
25
34
4123
4i48
4i?4
4199
4226
4260
26
35
4942
4969 4996
5022
5o48
5o74
24
35
4276
43oi
4327
4352
4377
44o3
24
36
5ioi
5i27 5i54
5i8o
6206
5233
23
36
4428
4454
4479
45o5
453o
4556
23
37
5259
6286
53i2
5338
5364
539i
22
3-7
458i
4607
4632
4657
4683
47o8
22
38
54i7
5443 547o
5496
5522
5549
21
38
4734
4769
4784
48io
4835
486i
21
39
5575
56oi
6628
5654
568o
6707
2O
39
4886
49I2
4937
4962
4988
5oi3
2O
4o
9.796733
5759 5786
6812
5838
5865
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4o
9.806039
5o64
5o89
5n5
5i4o
5i65
J9
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6891
59i7
5943
6970
5996
6022
18
4i
6191
6216
6242
6267
6292
53i8
18
42
6049
6o75
6101
6127
6i54
6180
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42
5343
5368
5394
5419
5444
547o
17
43
6206
6233
6269
6286
63n
6338
16
43
5495
6620
5546
557i
5597
6622
16
44
6364
639o64i66443
6469
6495
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44
6647
5673
5698
5723
5748
5774
16
45
6621
6547 6574 6600
6626
6662
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45
6799
6824
585o
5875
6900
6926
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46
6679
67o5
673i
6767
6783
6810
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46
595i
5976
6002
602-7
6062
6o77
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47
6836
6862
6888
69i4
6941
6967
12
47
6io3
6128
6i53
6179
6204
6229
12
48
6993
7oi9
7045
7072
7098
7124
II
48
6264
6280
63o5
633o
6355
638i
II
49
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7I76 7202
7229
7255
7281
IO
49
64o6
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6456
6482
65o7
6532
10
5o
9.797307
7333
7359
7386
7412
7438
9
5o
9. 806667
6583
6608
6633
6658
6684
9
5i
7464
749o 75i6
7642
7669 7595
8
5i
67°9
6734
6759
6785
6810
6835
8
52
7621
7647
76737699
7725 7761
7
62
6860
6885
69n
6936
6961
6986
7
53
7777
78o4
783oJ7856 7882 7908
6
53
7011
7o37
7062
7o87
7II2
7i37
6
54
7934
796o 7986 8012 8o38 8o65
5
54
7i63
-7188
7213
7238
7263
•7288
5
55
56
57
8091
8247
84o3
8n7 8i43 8i698i95'822i
82738299!8325835i 8377
8429 8455 848il85o8 8534
4
3
2
55
56
57
73i4
7465
7616
7339
7490
764i
?364
7616
7666
7389
754o
769i
74i4
7565
77i6
7439
-7690
774i
4
3
2
58
856o
858686128638
86648690
I
58
7766 779i 78167842
7867 7892
I
59
8716
8-742
87688794
8820 8846
O
59
7917 7942 7967 7992 8017 8042 o
60"
50" I
40" | 30" 20" 10"
S"
60" 50" j 40" 30" 20" i 10" e-
Co-sine of 51 Degrees.
S,
Co'Sine of 50 Degrees.
S
f i// nil o/
P Part)
4" 5" 6" 7" 8" 9"
.$ 1" 2" 3" 4" 5" 6" 7" 8" 9"
™l\ 3 5 8
11 13 16 19 21 24
irij 3 5 8 10 13 15 18 20 23
LOGARITHMIC TANGENTS.
J
Tangent of 38 Degrees.
.s
Tangent of 39 Degrees.
s
0"
10"
20" ] 30"
40"
50"
si
0"
10"
20"
30"
40"
50"
0
9.892810
2853
2897
2940
2983
3O27
r
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9.9o8369
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8455
8498
854i
8584
59
I
3070
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3i57
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3244
3a87
58
I
8628
8671
8714
8757
8800
8843
58
2
333i
3374
34i7
346i
35o4
3547
57
2
8886
8929
8972
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9o58
9101
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3
359i
3634
3678
3721
3764
38o8
56
3
9i44
9187
9230
9273
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9359
56
4
385i
3894
3938
398i
4o25
4o68
55
4
9402
9445
9488
953i
9574
96l7
55
5
4i 1 1
4i55
4198
4241
4285
4328
54
5
9660
97°3
9746
9789
9832
9875
54
6
4372
44i5
4458
45o2
4545
4588
53
6
9918
9961
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53
7
4632
4675
47i8
4762
48o5
4848
52
7
9.910177
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8
4892
4935
4979
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5o65
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9
5i52
5i95
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5282
5325
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9.895412
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5585
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10
9.910951
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1080
1123
1 166
4y
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5672
57i5
5759
58o2
5845
5889
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1209
1252
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12
5932
5975
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6io5
6149
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12
1467
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1682
47
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6192
6235
6278
6322
6365
64o8
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1725
1768
1810
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6452
6495
6538
6582
6625
6668
45
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2025
2068
21 II
2i54
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45
15
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44
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2283
2326
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44
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7o58
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7i45
7188
43
16
2498
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2713
43
17
7231
7275
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7448
42
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2799
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26862928
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42
18
7491
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7621
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7707
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18
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3o57
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3i43
3i85
3228
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7837
7881
7924
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3271
33i4
3357
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3443
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20
9.898010
8o54
8o97
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8i83
8227
39
20
9.913529
3572
36i5
3658
3701
3744
39
21
8270
83i3
8357
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8443
8486
38
21
3787
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3873
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38
22
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22
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24
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24
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25
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27
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32
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28
559o
5633
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5761
vs^x 44. i
58o4
3i
20
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0432
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29
5847
5890
5933
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6019
6062
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3o
9.900605
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29
3o
9.916104
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6233
6276
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29
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0864
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0994
1037
1081
28
3i
6362
64o5
6448
649i
6533
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28
32
1124
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27
32
6619
6662
6705
6748
6791
6834
27
33
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26
33
6877
6919
6962
7005
7o48
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26
34
1642
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25
34
7i34
7177
7220
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25
35
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2031
2074
2117
24
35
739i
7434
7477
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24
36
2160
2204
2247
2290
2333
2376
23
36
7648
7691
7734
7777
7820
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23
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2420
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2592
2635
22
37
7906
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22
38
2679
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2808
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2894
21
38
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21
39
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39
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9.903197
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9.918677
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3456
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3585
3628
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18
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11
43
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16
43
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16
44
4232
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9705
9748
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4534
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45
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4793
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9.920219
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12
47
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12
48
5267
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5397
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5526
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52
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52
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7
53
656o
66o3
6646
6690
6733
6776
6
53
2017
2060
2103
2i45
2188
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6
54
6819
6862
6905
6948
6991
7034
5
54
2274
23i6
2359
2402
2445
2488
5
55
7077
7120
7i63
7207
725o
7293
4
55
253o
2573
2616
2659
2702
2744
4
56
7336
7379
7422
7465
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755i
3
56
2787
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2873
29l5
2958
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3
5?
7594
7637
7680
7723
7766
78o9
2
57
3o44
3087
3i29
3172
32i5
3258
2
58
7853
7896
7939
7982
8025
8068
I
58
33oo
3343
3386
3429
347i
35i4
I
59
Bin
8i54
8i97
8240
8283
8326
0
59
3557
36oo
3642
3685
3728
377i
O
60"
50"
40"
30"
20"
10"
CJ
60" 50"
40"
30"
20"
10"
j
Co-tangent of 5 1 Degrees.
s
Co-tangent of 50 Degrees.
s
p pa%t 5 *" 2" 3" 4" 5" 6// 7" 8// 9"
. < I" 2" 3" 4" 5" 6" 7" 8" 9"
1 lrl{ 4 9 13 17 22 26 30 35 39
irt\ 4 9 13 17 21 26 30 34 39
64
LOGARITHMIC SINES.
g-
Sine of 40 Degrees.
J
Sine of 41 Degrees.
5
0"
10" 20"
! 30" 40"
50"
S
0"
10"
20"
30" | 40"
50"
0
9. 808067
8o93 8u88i43 8168
8i93
59
O
9.8i6943
6967
6991
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59
I
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824382688293:83188343
58
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7i37
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58
2
8368
8393 8419 8444 8469 8494
57
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7233
7258
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57
3
85i9
8544 8569859^ 8619 8644
56
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7379
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4
8669
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8794
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5
8819
8844886988948919
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54
5
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7693
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6
8969
8994 9019 9044 9069 9o94
53
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7862
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9144 9169 9194 9219 9244
52-
7
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8o55
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52
8
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9294 9319 9344 9369 9394
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9
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9.809569
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20
9.819832
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1 309
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38
21
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. . . .
..24
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38
22
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19-7-7 200112026
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34
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2569 2594 2618
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27I7 2742
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28
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28
32
2840
2865 2889 2914
2939 2963
27
32
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27
33
2988
3oi2 3o37
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26
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26
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3234
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25
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1906
1930
1954
25
35
3283
33o733323357
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24
35
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2001
2025
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20-72
2096
24
36
343o
3455 3479 35o4
3529!3553
23
36
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216-7
2191
22l5
2238
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3578
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22
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2262
2286
2309
2333
2357
2 38 1
22
38
3725
3749 3774
3799
3823
3848
21
38
2404
2428
2452
2475
2499
2523
21
39
3872
389-73921
3946
3970 3995
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2546
257O
2594
261-7
2641
2665
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2736
2759
2783
280-7
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4191 42i5
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6240 6264 6288:6312 6337
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6385 64o9'6434 6458 6482
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4949
4972
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57
58
59
65o7
6652
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653i.6555j6579 66o4 6628
6676 67oi 6725i6749 6773
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57
58
59
5090
523o
537i
5n3
5254
5394
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5277
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5324
5464
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2
I
O
60"
50" ; 40"
30" | 20" ,
10"
c
60"
50" j 40"
30"
20"
10"
fl
Co-sine of 49
Degrees.
1
Co-sine of 48 Degrees.
P. Part J 2 5 7 10
5" 6" 7"
12 15 17
8" 9"
20 22
p p . $ 1" 2" 3" 4" 5" 6" 7" A" 9"
r*\ 25 7 10 12 14 17 19 21
LOGARITHMIC TANGENTS.
.5
Tangent of 40 Degrees.
.S
Tangent of 41 Degrees.
i
0"
10"
20"
30"
40" 50"
i
0"
10"
20"
30"
40"
50"
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2223
2266
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2521
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2606
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18
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1925
1968
28
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7233
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32
2010
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32
73i8
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27
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2266
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26
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7572
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2522
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2607
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3289
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22
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60"
50"
40"
30" 20"
10"
.
60" 50"
40" 30" 20" 10"
a
Co-tangent of 49 Degrees.
a
Co-tangent of 48 Degrees.
i
.< 1" 2" 3" 4" 5" 6" 7" 8" 9"
.< 1" 2" 3" 4" 5" 6" 7" 8" 9"
in\ 4 9 13 17 21 26 30 34 38
in\ 4 8 13 17 21 25 30 34 38
E
66
LOGARITHMIC SINES.
c
Sine of 42 Degrees.
S
Sine of 43 Degrees.
i
0"
10"
20"
30"
40" ! 50"
S
0" I 10"
20"
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925o
19
4i
1195
1218
1241
1263
1286
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18
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9272
9294
9316
9338
936o
9382
18
42
1332
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17
42
9404
9426
9448
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9492
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43
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l492
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16
43
9536
9558
958o
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44
1606
1628
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i674
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1720
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44
9668
9690
9712
9734
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9778
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45
1742
1765
1788
1811
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45
9800
9822
9844
9866
9888 9910
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46
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1902
1924
194-7
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46
9932
9954
9976
9998
. .20 . .42
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47
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2061
2084
2106
2129
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9.84oo6/!
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0108
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12
48
2l52
2I75
2197
222O
2243
2266
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48
0196
0218
0240
0262
0284
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49
2288
23ll
23342356
2379
2402
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0372
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2447
2470
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9.840459
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256i
2584
2606
2629
2652
2674
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2720
2742
2765
2788
2810
7
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7
53
2833
2856
2878
2901
2924
2946
6
53
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0919 0941
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6
54
2969
2992
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3082
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54
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1029
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1072
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5
55
3io5
3i28
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3i73
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4
55
1116
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1182 \izoi
1226
4
56
3s4 i
3263
3286
3309
333i
3354
3
56
1247
1269
1291
i3i3 i335
i357
3 ,
57
3377
3399
3422
3444
3467
349o
2
57
i378
i4oo
1422
i444i466
i486
58
35i2
3535
3557
358o
36o3
3625
I
58
i5og
i53
i553
i575 i597
1619
59
3648
367o
3693
37i6
3738
376i
O
59
1640
1662
1 684
I706;I728
i749 o
60"
50"
40"
30"
20"
10"
d
60"
50"
40"
30" 20" 10"
d
Co-sine of 47
Degrees.
g
Co-sine of 46 Degrees.
1
PPartJ1" 2" 3" 4//
5" 6" 7" 8" 9"
. f 1" 2" 3" 4" 5" 6" 7" 9" 9"
F>lart{ 2579
11 14 16 18 21
in\ 2 4 7 9 11 13 16 18 20
LOGARITHMIC TANGENTS.
1
Tangent of 42 Degrees.
a
Tangent of 43 Degrees.
s
0"
10"
20" 1 30"
40"
50"
§
0" 10" 20"
30"
40"
50"
o
9.954437
448o
4522
4564
4607
4649
59
0
9.969656
9698
974o
9783
9825
9867
59
I
469i
4734
4776
4819
486 1
49o3
58
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99°9
995i
9994
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. 120
58
2
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4988
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5o73
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57
2
9.97oi62
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57
3
5200
5242
5284
5327
5369
54n
56
3
o4i6
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56
4
5454
5496
5538
558i
5623
5665
55
4
o669
0711
o753
0796
o838
0880
55
5
57o8
575o
5792
5835
5877
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54
5
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1049
1091
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54
6
596i
6oo4
6o46
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6i3i
6i73
53
6
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1218
1260
1302
1 344
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53
7
62i5
6258
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6342
6385
6427
52
7
1429
1471
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i555
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52
8
6469
65i2
6554
6596
6639
6681
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8
1682
1724
1766
1808
i85i
i893
5i
9
6723
6766
6808
685o
6893
6935
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9
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2062
2104
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10
9.956977
7020
7062
7104
7i46
7:89
49
10
9.972188
2230
2273
23i5
2357
2399
49
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7231
7273
73i6
7358
7400
7443
48
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244i
2484
2526
2568
2610
2652
48
12
7485
7527
757o
7612
7654
7697
47
12
2695
2737
2779
2821
2863
29o5
47
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7739
7781
7823
7866
79o8
795o
46
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2948
2990
3o32
3o74
3n6
3i59
46
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7993
8o35
8077
8120
8x62
8204
45
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3201
3243
3285
3327
337o
34l2
45
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8247
8289
833i
8373
84i6
8458
44
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3454
3496
3538
358i
3623
3665
44
16
85oo
8543
8585
8627
8670
8712
43
16
37o7
3749
379i
3834
3876
39i8
43
i?
8754
8796
8839
8881
8923
8966
42
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3960
4O02
4o45
4o87
4129
4171
42
18
9008
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9093
9i35
9i77
92I9
4i
18
42 I 3
4255
4298
434o
4382
4424
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9262
93o4
9346
9389
943i
9473
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4466
45o9
455i
4593
4635
4677
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20
9.959516
9558
96oo
9642
9685
9727
39
20
9.974720
4762
48o4
4846
4888
493o
39
21
9769
9812
9854
9896
9938
998!
38
21
4973
5oi5
5o57
5099
5i4i
5i83
38
22
9.960023
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0108
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37
22
5226
5268
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5352
5394
5437
37
23
0277
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36
23
5479
552i
5563
56o5
5647
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36
24
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0573
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0667
0700
0742
35
24
5732
5774
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5943
35
25
0784
0826
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34
25
5985
6027
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34
26
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1080
1122
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1207
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33
26
6238
6280
6322
6364
64o7
6449
33
27
1292
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32
27
6491
6533
6575
6617
6660
6702
32
28
1 545
i587
i63o
1672
1714
i757
3i
28
6744
6786
6828
6870
69i3
6955
3i
29
1799
i84i
i883
I926
I968
2010
3o
29
6997
7°39
7081
7123
7i66
7208
3o
3o
9.962062
2095
2137
2I79
2222
2264
29
3o
9>97725o
7292
7334
7377
74i9
746 1
29
3i
23o6
2348
239I
2433
2475
2517
28
3i
75o3
7545
7587
763o
7672
7714
28
32
256o
2602
2644
2686
2729
2771
27
32
7756
7798
7840
7882
7925
7967
27
33
28i3
2856
2898
2940
2982
3o25
26
33
8oo9
8o5i
8o93
8i35
8178
8220
26
34
3o67
3109
3i5i
3i94
3236
327a
25
34
8262
83o4
8346
8388
843 1
8473
25 •
35
3320
3363
34o5
3447
3489
3532
24
35
85i5
8557
8599
864i
8684
8726
24
36
3574
36i6
3659
3701
3743
3785
23
36
8768
8810
8852
8894
8937
8979
23
37
3828
3870
39I2
3954
3997
4o39
22
37
9O2I
9063
9io5
9i47
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9232
22
38
39
4o8i
4335
4l23
4377
4i66
44i9
4208
446 1
4260
45o4
4292
4546
21
20
38
39
0274
9527
93i6
9569
9358
9611
94oo
9653
9442
9695
9485
9738
21
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9.964588
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46?3
47i5
4757
4799
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9.97978o
9822
9864
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19
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4842
4884
4926
4968
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5o53
18
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9.980033
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18
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17
42
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43
5349
539i
5433
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16
43
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16
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5855
5898
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5982
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45
1044
1086
1129
1171
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1255
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46
6109
6i5i
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6236
6278
6320
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46
1297
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6362
64o5
6447
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12
47
i55o
l592
1634
1677
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12
48
6616
6658
6700
6742
6785
6827
II
48
i8o3
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49
6869
6911
6954
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7o38
7080
10
49
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2224
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10
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9.967123
7i65
7207
7249
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7334
9
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9.982309
235i
2393
2435
2477
25l9
9
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7376
74i8
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75o3
7545
7587
8
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2562
2604
2646
2688
2730
2772
8
52
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7672
77i4
7756
7798
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7
52
2814
2857
2899
294i
2983
3o25
7
53
7883
7925
7967
8oo9
8o52
8o94
6
53
3067
3io9
3i52
3i94
3236
3278
6
54
8i36
8178
8220
8263
83o5
8347
5
54
3320
3362
34o4
3447
3489
353i
5
55
• 8389
8432
84?4
85i6
8558
8600
4
55
3573
36i5
3657
3699
374z
3784
4
56
8643
8685
8727
8769
8812
8854
3
56
3826
3868
3910
3952
3994
4o37
3
57
8896
8938
8980
9023
9o65
9io7
2
57
4079
4l2I
4x63
42o5
4247
4289
a
58
9149
9192
9234
9276
93i8
936o
I
58
4332
4374
44i6
4458
45oo
4542
i
59
94o3
9445
9487
9529
957i
96i4
O
59
4584
4627
4669
4711
4753
4795
o
60"
50"
40"
30"
20"
10"
a
60"
50"
40"
30"
20"
10"
.
Co-tangent of 47 Degrees.
1
Co-tangent of 46 Degrees.
1
P Part 5 l" 2" 3// 4" 5" 6" 7" 8" 9"
PPoff1" 2" 3" 4" 5" 6" 7" 8" 9"
£ 4 8 13 17 21 25 30 34 38
m\ 4 8 13 17 21 25 30 34 38
68
LOGARITHMIC SINES.
jj
Sine of 44 Degrees.
.3
Sine of 45 Degrees.
i
0"
10"
20" 30" 40"
50"
Si
0"
10"
20"
30"
40"
50"
0
9. 841771
i793
i8i5ii837 i858
1880
59
09.849485
95o6
9527
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9569
959o
59
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i946 i967 i989
2OII
58
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96n
9632
9653
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58
2
2o33
2o55
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2
9738
9759
978o
98oi
9822
9843
57
r.
2i63
2i85
2207
2229 225o
2272 56
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9864
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9927
9948
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56
4
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4
999°
. .11
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55
i
242^
2446
2468
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253354
e
9.85oi 16
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2555
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53
6
0242
0263
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53
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2685
2707
2729 275o 2772
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52
7
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8
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3206
3227 3249 3271
3292
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45
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44
16
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16
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1601
43
17
3984
4oo6 4o27
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42
17
1622
1 643
1 664
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42
18
4n4
4i354i57
4178
4200
4222
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18
1747
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20
4243
9. 844372
4265428643o8
4394 44i64437
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39
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20
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9.85i997
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2018
2o39
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39
21
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38
21
2122
2i43
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22
463i
4652 4674!4696
4717
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37
22
2247
2267
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235o
37
23
4760
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36
23
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24
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5211
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33
26
2745
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33
27
5276
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5362
5383
32
27
2869
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2952
2973
32
28
54o5
5426 5447 5469
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55i2
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28
2994
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29
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9. 853242
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29
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3366
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28
32
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27
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3532
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4542
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18
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4686
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18
42
7i99
7220 7242
7263
7284^305
17
42
4727
4747
4768
4788
48r>9
4829
17
43
7348 7369
739i
74i27433
16
43
485o
4870
489i
49n
4932
4953
16
44
7454
7476 7497
75i8
7539 7561
i5
44
4973
4994
5oi4
5o35
5o55
5o76
i5
45
7582
7603 7624
7645
7667 7688
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45
5o96
5n7
5i37
5i58
5i78
5i99
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46
77°9
77307752
7773
779478i5
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46
52I9
524o
5260
5281
53oi
5322
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47
7836
7858 7879
79oo
792ij7943
12
47
.5342
5363
5383
54o4
5424
5445
12
48
7964
7985]8oo6
8027
8o49 8070
II
48
5465
5485
55o6
5526
5547
5567
II
49
8o9i
8112
8i33
8i54
81768^7
10
49
5588
56o8
5629
5649
567o
569o
IO
5o
9. 848218
8239 8260
8282
83o38324
9
5o
9.8557n
573i
575i
5772
5792
58i3
9
5i
8345
8366 8387
84o9
843o845i
8
5i
5833
5854
5874
5895
59i5
5935
8
52
8472
8493
85i4
8535
85578578
7
52
5956
5976
5997
6017
6o38
6o58
7
53
8599
86208641
8662
8683 87o5
6
53
6o78
6o99
6n9
6i4o
6160
6180
6
54
8726
8747'8768
8789
8810 883i
5
54
6201
6221
6242 6262
6282 63o3
5
55
8852
8874
8895
89i6
89378958
4
55
6323634463646384
64o5 6425
4
56
8979
9000 9O2I
9o42
9o63 9o85
3
56
6446
6466 6486 6507 6527 6547
3
57
9io6
9I27
9i48 9i69
9I90 92II
2
57
6568
6588
66o9 66s9 6649 6670
2
58
9232
9253
92749295
93i6'9338
I
58
669o 67io
673i675i:677i 6792 i
59
9359
938o
94oi
9422
94439464
O
59
6812 6832 6853 6873|689369i4 o
60"
50" |
40" 30"
20" 10"
j
60" | 50" 40" i 30" i 20" 10" _.
Co-sine of 45 Degrees.
1
Co-sine of 44 Degrees. s
t •tn o" *V'
P Part I
4" 5" 6" 7" 8" 9"
p P ,51" 2" 3" 4" 5" 6" 7" 8" 9" :
•"{ 2 4 6
9 11 13 15 17 19
m\ 2 4 6 8 10 12 14 17 19
LOGARITHMIC TANGENTS.
1
Tangent of 44 Degrees.
a
Tangent of 45 Degrees.
jg
0"
10"
20"
30"
40" j 50"
*
0"
10"
20"
30"
40"
50"
o
9.98483-7
4879
492I
4964
5oo6
5o48
59
o
IO.OOOOOO
OO42
oo84
0126
0168
O2II
59
i
5090
5i32
5i74
52i6
5259
53oi
58
I
0253
0295
o337
o379
O42I
o463
58
2
5343
5385
542-7
5469
55n
5553
57
2
o5o5
o547
o59o
o632
o674
o7i6
57
3
5596
5638
568o
5722
5764
58o6
56
3
o758
0800
0842
0884
0926
o969
56
4
5848
5891
5933
5975
6oi7
6o59
55
4
IOII
io53
io95
n37
"79
1221
55
5
6101
6i43
6i85
6228
6270
63i2
34
5
1263
i3o5
1 348
1390
1432
i474
54
6
6354
6396
6438
648o
6523
6565
53
6
i5i6
i558
1600
1642
1 684
1727
53
7
66o7
6649
669i
6733
6775
68i7
52
7
i769
1811
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i937
i979
52
8
6860
6902
6944
6986
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7o7o
5i
8
2O2I
2o63
2106
2148
2190
2232
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9
7II2
7i54
7i97
7s39
-7281
7323
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9
2274
23i6
2358
2400
2442
2485
5o
10
9.987365
74o7
7449
749 1
7534
7576
49
10
IO.OO2527
2569
2611
2653
2695
2737
49
ii
-7618
766o
7702
7744
7786
7829
48
ii
2779
2821
2864
2906
2948
299°
48
12
7871
79i3
7955
7997
8o39
8081
47
12
3o32
3o74
3n6
3i58
3200
3243
47
i3
8i23
8166
8208
825o
8292
8334
46
i3
3285
3327
3369
34n
3453
3495
46
i4
8376
84i8
846o
85o3
8545
8587
45
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3537
3579
3622
3664
37o6
3748
45
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8629
867i
87i3
8755
8797
884o
44
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379°
3832
3874
3916
3958
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44
16
8882
8924
8966
9008
9o5o
9092
43
16
4o43
4o85
4l27
4i69
4211
4253
43
ll
9i34
9i77
9219
9261
93o3
9345
42
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4295
4337
438o
4422
4464
45o6
42
18
9387
9429
9471
95i3
9556
9598
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18
4548
459o
4632
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47i6
4759
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19
964o
9682
9724
9766
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19
48oi
4843
4885
4927
4969
Son
4o
20
9.989893
9935
9977
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.io3
39
20
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21
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5432
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22
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23
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23
58! i
5854
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5938
5980
6022
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34
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1-577
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33
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6612
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678o
33
27
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l872
32
27
6822
6864
6906
6949
6991
7o33
32-
28
i9i4
1956
1999
2o4l
2o83
2125
3i
28
7o75
7117
7l59
720I
7243
7285
3i
29
2l67
2209
r
225l
2293
2336
2378
3o
29
7328
737o
74i2
7454
7496
7538
3o
3o
9.992420
2462
2504
2546
2588
263o
29
3o
io.oo758o
-7622
7664
77°7
7749
7791
29
3i
2672
27l5
2757
2799
2841
2883
28
3i
7833
7875
79i7
7959
8001
8o44
28
32
2925
296?
3009
3o5i
3o94
3i36
27
32
8086
8128
81-70
8212
8254
8296
27
33
3i78
3220
3262
33o4
3346
3388
26
33
8338
838o
8423
8465
85o7
8549
26
34
343i
3473
35i5
3557
3599
364i
25
34
859i
8633
8675
87i7
876o
8802
25
35
3683
3725
3767
38io
3852
3894
24
35
8844
8886
8928
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9012
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24
36
3936
3978
4020
4062
4io4
4i46
23
36
9°97
9i39
9181
9223
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23
37
4189
423i
4273
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4357
4399
22
37
9349
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9433
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22
38
444i
4483
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4652
21
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21
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1 1 60
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6252
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6463
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6547
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1624
1666
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18
47
67i5
6757
6800
6842
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6926
12
47
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1919
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2O03
2045
208-7
12
48
6968
7010
7o52
7o94
7i36
7i79
II
48
2I29
2I7I
22l4
2256
2298J234o
II
49
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7263
73o5
7347
7389
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10
49
2382
2424
2466
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255i 2593
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9.997473
75!5
7558
76oo
7642
7684
9
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10.012635
2677
2719
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28o3 2846
9
5i
7726
7768
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7852
789417937
8
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2888
2930
2972
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3o56
3o98
8
52
7979
8021
8o63
8io5
8i47|8i89
7
52
3i4o
3i83
3225
3267
33o9
335i
7
53
823i
8273
83i6
8358
84oo
8442
6
53
3393
3435
3477
3520
3562 36o4
6
54
8484
8526
8568
8610
8652
8695
5
54
3646
3688
373o
3772
38i5
3857
5
55
8737
8779
8821
8863
89o5
8947
4
55
3899
3g4i
3983
4o25
4o67
4109
4
56
57
8989 9031
9242 928^
90-74
9326
9n6
9368
9i58
94io
9200
9453
3
2
56
4i52
44o4
4i94
4447
4236
4489
4278
453i
4320
4573
4362
46i5
3
2
58
9495
95379579
962I
9663
97o5
I
58
4657
4699
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4?84
4826
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59
9747
97899832
9874
99i6
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0
59
49io
4952
4994
5o36
5o79j5i2i
0
60" 50" 40"
30"
20" 10"
.
60" 50"
40"
30"
20" | 10"
-
Co-tangent of 45 Degrees.
s .
Co-tangent of 44 Degrees.
s
A 1" 2" 3" 4" 5" 6" 7" 8" 9"
p p ( 1" 2" 3" 4" 5" 6" 7" 8" 9"
.rartj 4 8 13 17 21 25 29 34 38
P.Part^ 4 g 13 17 21 25 29 34 38
70
LOGARITHMIC SINES.
d
Sine of 46 Degrees.
d
Sine of 47 Degrees.
ii
0" | 10" | 20"
i -30"
40" 50"
0" | 10" 20" [ 30"
50"
0^9. 866934 6964 6976
,6995
7016 7036 69
09.86412-7
4i47 4167 4186,4206
4226
69
i
7066 7076 7097
7117
71377168 58
i
4245
42664284
43o4!4324
4343
58
2
7178
7i98
7219
7239
7269
727967
2
4363
4383 4402
4422;444i
446 1
57
3
4
73oo
7422
7320
7442
7340 7361
7462 7482
738i 74oi 56
7603762355
3
4
448 1
4598
45oo
46i8
4620
4637
4539!4559
46574676
4579
4696
56
55
5
7543 7563
7584
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7624 7645 54
5
4716
4735
4755
4774
4794
48i3
54
6
7665J7685
7706
7726
7746 7766 53
6
4833
4853
4872
4892
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53
7
8
7786
7908
7807
7928
7827
7948
7847
7968
7867
7989
7888
8009
62
5i
8
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5o68
49704990
5o87j5io7
6009
6126
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5i46
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62
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9
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8o49 8070 8o9o
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9
5i85
6204
6224
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10
9.868161
8171
8191
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823i 82'52
49
10
9-865302
5322
534i
536i
538o
54oo
49
ii
8272
8292
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8353 8373
48
ii
5419
5439
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5478
5497
55i7
48
12
8393
84i3
8433 8454
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47
12
5536
5556 5575
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47
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85i4
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46
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46
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8635
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6770
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16
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44
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43
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39
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21
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9601
9621
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38
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38
22 9601
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9681 9701
37
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32
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28
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32
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27
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9.868785
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19
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1877
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1936 1966
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18
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47
260.0
2610
263026602669
2689
12
47
9689
9608
9627
9646 9665
9685
12
48
2709
2729
2748 2768 2788
2808
II
48
9704
9723
9742
9761
9780
9799 IJ
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2827
2847
2867 2887 2906
2926
IO
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9818
9837
9866
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99x410
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2966
2986
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9.869933
9962
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3io4 3i24
3i43
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8
61
9.87oo47
0066 0086
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62
3i83
32o3
3222
3242
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3281
7
62
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0161
0180 0199
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54
oSgo
0409
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5
55
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3557
3577
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4
55
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0623 0642
0661 0680
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4
56
3656
3676
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3734
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3
56
0618 o637 0666 o675 0694
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57
3774
3793
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2
57
o732 0761 0770 0789 0808
0827 2
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3892
3911
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395i
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58
o846;o865o884'o9o3 0922 0941 i
59
4oio
4029
4049
4069
4o88
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O
69
096009790998101710361064 °
60" 50"
40" | 30" 20"
10"
• a
60" i 50" 40" 30" 20" 10" ^
Co-sine of 43
Degrees.
S
Co-sine of 42 Degrees.
( \n 2" 3" 4"
5" 6" 7" 8" 9"
„ p. f( 1" 2" 3" 4" 5" 6" 7" 8" 9"
P. Part J 2468
10 12 14 16 18 [ "*\ 2 4 6 8 10 12 14 15 17
LOGARITHMIC TANGENTS.
71
1
Tangent of 46 Degrees.
.s
Tangent of 47 Degrees.
s
0"
10"
20"
30"
40"
50"
m
0"
10"| 20"
30"
40"
50"
o
*o.oi5i63
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6427
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6553
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6
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32
28
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7483
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7567
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29
2497
2539
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2623
2666
27o8
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29
7694
7736
7778
7821
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10.022750
2792
2834
2877
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2961
29
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8286
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28
32
3256
3298
334o
3383
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32
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27
33
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3593
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20
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26
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60"
50"
40"
30"
20"
10"
jj
60"
50"
40"
30"
20"
10"
a
Co-tangent of 43 Degrees.
s
Co-tangent of 42 Degrees.
i
p p C 1" 2" 3" 4" 5" 6" 7" 8" 9"
.( 1" 2" 3" 4" 5" 6" 7" S" 9"
(4 8 13 17 21 25 30 34 38
~ • i
lrl\ 4 8 13 17 21 25 30 34 38
72
LOGARITHMIC SINES.
.9
Sine of 48 Degrees.
d
Sine of 49 Degrees.
s
0" 10"
20" | 30" ; 40"
50"
9
0-' 10"
20" 30" | 40"
50"
0
9.87io73|io92
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2000 2019 2o38 2o57
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8
52
6899
69i8 6936
6954
69-73 6991
7
52
34o4
3422
3439
3457
3475
3493
7
53
7OIO
-7028 7o46
7o65
7o83 -7101
6
53
35io
3528
3546
3564
358i 3599
6
54
7120
7i38 7i57
7i75
7I93 72I2
5
54
36i7
3635
3652
367o
3688 37o5
5
55
723o
•7248-726-7
7286
73o3 7322
4
55
3723
374i
3759I3776 3794 38i2
4
56
57
734o
745o
73587377
7468 7487
7395
75o5
74i37432
3
2
56
57
3829
3936
3847 3865 3883 39oo 39i8
3953 39-71 3989^0064024
3
2
58
756o
7578 7597
76i5
7633 7652
I
58
4o42
4o6o 4077 4095 4n3 4i3o
I
59
767o 7688 77o77725
7743 7762
0
59
4i48
4i66 4i83 4201*4219 4236
0
60"
50" j
40" 30"
20" 10"
a
60"
50" 40" 30" 20" 10" I
Co-sine of 41 Degrees.
Jl
is
Co-sine of 40 Degrees. s
PPartJ1" 2" 3//
4" 5" 6" 7" 8" 9"
.< 1" 2" 3" 4" 5" 6" 7" 8" 9"
"1 a 4 6
7 9 11 13 15 17
irl$ 24 5 7 9 11 13 14 16
LOGARITHMIC TANGENTS.
73
1
Tangent of 48 Degrees.
.3
Tangent of 49 Degrees.
2
0"
10" 20" 1 30" 40"
50"
al
0"
10'
20"
30"
40"
50"
0
i
io.o45563
58i7
56o55647569o5732
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5774
6028
59
58
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0922
1177
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59
58
2
6071
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6240
6282
57
9
1 347
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1432
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57
3
6325
6367(64o96452
6494
6537
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1602
1 645
1688
1730
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56
4
6579
6621 6664 67o6
6748
679i
55
4
i858
I900
1943
i985
2028
2070
55
5
6833
6875i69i8J696o]7oo2
54
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2Il3
2i55
2198
224l
2283 2326
54
6
7087
7i3o 7172
7214 7257
7299
53
6
2368
2411
2453
2496
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53
7
734i
7384^426
7468
75n
7553
52
7
2623
2666
2709
275l
2794
2836
52
8
7595
7638 7680
7723
7765
78o7
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8
2879
292I
2964
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3o49
3o92
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9
785oJ7892J7934
7977
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3 1 34
3i77
3219
3262
33o4
3347
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82 3 1
8273
83i6
49
10
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3432
3475
35i7
356o
3bo2
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1 1
8358
84oo
8443
8485
8528
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48
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3645
3687
373o
3773
38i5
3858
48
12
8612
8655
8697
8739
8782
8824
47
12
39oo
3943
3985
4028
4o7o
4n3
47
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8867
89o9
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8994
9o36
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4i56
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424i
4283
4326
4368
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9i63
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9248
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4496
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97^-7
9799
9841
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4922
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42
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5i78
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42
18
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21
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21
6200
6242
6285
6328
6370
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38
22
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1198
1240
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37
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6455
6498
654i
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36
23
6711
6754
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1707
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35
24
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2216
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2301
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27
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2470
25i3
2555
2598
2640
32
27
7734
7776
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32
28
2682
2725
2767
2810
2852
2895
3i
28
799°
8o32
8o75
8117
8160
8203
3i
29
2937
2979
3O22
3o64
3io7
3i49
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29
8245
8288
833i
8373
84i6
8458
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3o
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3234
3276
33i9
336i
34o4
29
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io.o685oi
8544
8586
8629
8672
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29
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3446
3489
353i
3573
36i6
3658
28
3 1
8757
8800
8842
8885
8927
897o
28
32
3701
3743
3786
3828
387o
3gi3
27
32
9013
9o55
9o98
9i4i
9183
9226
27
33
3955
3998
4o4o
4o83
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4i68
26
33
9269
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9354
9397
9439
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26
34
4210
4252
4295
4337
438o
4422
25
34
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9567
96io
9652
9696
9738
25
35
4465
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4592
4634
4677
24
35
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9823
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47
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7564
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12
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7777
7819
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7947|7989
II
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3no
3i52
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52
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8839
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7
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4i35
4178
4220
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7
53
54
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93o6
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9476 9519
6
5
53
54
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4648
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4477
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6
5
55
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9646
9689
9732
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4
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9859
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3
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5246
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io.o6oo72
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54i7
546o
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55885631
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I
58
5673
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59
593o
5973
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60"
50"
40"
30"
20"
10"
d
60"
50"
40"
30"
W | 10"
•
Co-tangent of 41 Degrees.
•3
Co-tangent of 40 Degrees.
5
P P»rt5 l" 1" 3" 4" 5" 6" 7" S" 9"
I 4 8 13 17 21 25 30 34 38
v F .( 1" 2" 3" 4" 5" 6" 7" 8" 9"
irt} 4 9 13 17 2 X *'o 30 34 38
LOGARITHMIC SINES.
3
Sine of 50 Degrees.
-a
Sine of 51 Degrees.
4
*• ~~ [ 10" I 20"
I 30" i 40"
50"
51
0"
10"
20"
30"
40"
50"
O
9.S84254!4272|4289
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4342
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7
1217
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1261
1268
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6693 6710 6728
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6286
62o3
63o2
62I9
63i8
3
2
58
0298
o3i5o332
o349
o366o383
I
58
6335635i
6368 6384
64oo
64i7
I
59
o4oo
04170434
o45i
o468 o486
O
59
6433
645o 6466
6483
6499 65:6
0
60"
50" i 40"
30"
20" 10"
ES
60"
50" | 40"
30"
20" i 10"
G
Co-sine of 39
Degrees.
JB
s
Co-sine of 38 Degrees s
( 111 O" «J" A"
P-Part{2 3 5 7
5" 6" 7" 8" 9"
9 10 12 14 16
C 1" 2" 3" 4" 5" 6" 7" 8" 9"
1 I 2 3 5 7 8 10 12 13 15
LOGARITHMIC TANGENTS.
75
d
•fH
Tangent of 50 Degrees.
d
Tangent of 51 Degrees.
3
0"
10"
20"
30"
40"
50"
'^
0"
10"
20" 1 30" | 40"
50"
0
10.076186
6229
6272
63i5
6358
64oo
59J
o
10.091631
1674
1717
I76o
i8o3
1846
59
I
6443
6486
6529
657i
66i4
6657
58
i
1889
I932
I975
2018
2061
2IO4
58
2
6700
6742
6785
7828
687i
6913
57
2
2147
2191
2234
2277
2320
2363
57
3
6956
6999
7042
7o85
-712-7
71-70
56
3
2406
2449
2492
2535
2578
2621
56
4
7213
7256
7298
734i
7384
742-7
55
4
2664
2707
275o
2793
2837
2880
55
5
7470
7512
7555
7598
764i
7684
54
5
2923
2966
3009
3o52
3o95
3i38
54
6
77*5
7769
7812
7855
7897
794o
53
6
3i8i
3224
3267
33io
3354
3397
53
7
7983
8026
8069
8m
8i54
8197
52
7
344o
3483
3526
3569
36i2
3655
52
8
8240
8283
8325
8368
84n
8454
5i
8
3698
374i
3784
3828
387i
39i4
5i
9
8497
8539
8582
8625
8668
8711
5o
9
3957
4ooo
4o43
4o86
4i29
4172
5o
10
10.078753
8796
8839
8882
8925
8967
49
10
i 0.0942 i 5
4259
43o2
4345
4388
443 1
^9
ii
9010
9o53
9o96
9i39
9181
9224
48
ii
4474
45i7
456o
46o3
4647
4690
i8
12
9267
93io
9353
9396
9438
948 1
47
12
4733
4776
4819
4862
49o5
4948
47
i3
9524
9567
9610
9652
9695
9738
46
i3
4992
5o35
5o78
5l2I
5i64
5207
46
i4
9781
9824
9867
99°9
9952
9995
45
i4
525o
5293
5337
538o
5423
5466
45
i5
io.o8oo38
0081
0124
0166
0209
0252
44
i5
55o9
5552
5595
5638
5682
5725
44
16
0295
o338
o38i
o423
o466
oSog
16
5768
58n
5854
5897
5940
5984
43
17
o552
o595
o638
0680
0723
0766
42
17
6027
6070
6n3
6i56
6199
6242
[2
18
0809
o852
o895
o937
0980
1023
4i
18
6286
6329
6372
64i5
6458
65oi
ii
J9
1066
1 109
1162
n95
I237
1280
4o
19
6544
6588
663i
6674
671-7
6760
io
20
io.o8i323
i366
i4o9
i452
i494
i537
39
20
io.o968o3
6847
689o
6933
6976
7019
39
21
i58o
1623
1666
1-709
I752
1794
38
21
7062
7106
7i49
-7192
7235
7278
38
22
i837
1880
I923
1966
20O9
2052
37
22
7321
7365
74o8
745i
7494
7537
37
23
2094
2l37
2180
2223
2266
2309
36
23
758o
7624
7667
7710
7753
7796
36
24
2352
2395
2437
2480
2523
2566
35
24
784o
7883
7926
7969
8012
8o56
35
25
2609
2652
2695
2738
278o
2823
34
25
8099
8142
8i85
8228
8271
83i5
34
26
2866
2909
2952
2996
3o38
3o8i
33
26
8358
84oi
8444
8487
853i
8574
33
27
3i23
3i66
3209
3252
3295
3338
32
27
8617
8660
87o3
8747
879o
8833
32
28
338i
3424
3467
3509
3552
3595
3i
28
8876
8919
8963
9006
9049
9092
3i
29
3638
368i
3724
3767
38io
3853
3o
29
9i36
9179
9222
9265
93o8
9352
3o
3o
10.083896
3938
398i
4024
4o67
4no
29
So
10.099395
9438
948 1
9524
9568
9611
29
3i
4i53
4196
4239
4282
4325
4367
28
3i
9654
9697
974i
9784
9827
9870
28
32
44io
4453
4496
4539
4582
4625
27
32
99i3
9957
..43
..86
.i3o
27
33
4668
47n
4754
4797
4839
4882
26
33
10. 100173
0216
0259
o3o3
o346
o389
26
34
4925
4968
Son
5o54
5o97
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25
34
0432
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o562
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25
35
5i83
5226
5269
53i2
5355
5397
24
35
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o778
0822
o865
0908
24
36
544o
5483
5526
5569
56i2
5655
23
36
o95i
o995
io38
1081
1124
n 68
23
37
5698
574i
5784
5827
587o
59i3
22
3?
I2II
1254
I297
i34i
1 384
1427
22
38
5956
5999
6o4i
6o84
612-7
6170
21
38
1470
i5i4
i557
1600
1 643
1687
21
39
62i3
6256
6299
6342
6385
6428
20
39
1730
i773
1817
1860
igo3
i946
2O
4o
10.086471
65i4
6557
6600
6643
6686
I9
4o
10. ioi99o
2o33
2076
2119
2i63
2206
J9
4i
6729
6772
68i5
6857
6900
6943
18
4i
2249
2293
2336
2422
2466
18
42
6986
7029
-7072
7ii5
7i58
7201
17
42
25o9
2552
2596
2639
2682
2725
17
43
7244
7287
733o
7373
74i6
7459
16
43
2769
2812
2855
2899
2942
2985
16
44
7502
7588
763i
7674
7717
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44
3o29
3o72
3n5
3i58
3202
3245
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45
7760
78o3
7846
7889
7932
7975
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45
3288
3332
3375
34i8
3462
35o5
i4
46
8018
8o6l
8 10^
8i47
8i9o
8232
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46
3548
3592
3635
3678
3722
3765
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47
8275
83i8
836i
84o4
8447
849o
12
47
38o8
385i
3895
3938
3981
4o25
12
48
8533
8576
8619
8662
87o5
8748
II
48
4o68
4n i
4i55
4i98
4241
4285
II
49
8791
8834
8877
8920
8963
9006
10
49
4328
4371
44i5
4458
45oi
4545
10
5o
10.089049
9092
9i35
9i78
922I
9264
9
5o
i o.i o4588
463 1
4675
4718
4761
48o5
9'
5i
9307
935o
9393
9436
94?9
9522
8
5i
4848
489i
4935
4978
5O2I
5o65
'8
52
9565
9608
9694
9737
978o
7
52
6108
5i52
5i95
5238
5282
5325
7
53
9823
9866
9909
9952
9995
..39
6
53
5368
54i2
5455
5498
5542
5585
6
54
10.090082
0125
0168
0211
025^
0297
5
54
56a8
5672
57i5
5759
58o2
5845
5
55
o34o
o383
0426
0469
o5i2
o555
4
55
5889
5932
5975
6019
6062
6106
4
56
o598
o64i
o684
O727
o77o
o8i3
3
56
6149
6i9a
6236
62-79
6322
6366
3
57
o856
0899
0942
o985
1028
1071
a
57
6409
6453
6496
6539
6580
6626
2
58
ni4
ii57
1 200
1243
1286
i329
i
58
6669
67i3
6756
6800
6843
6886
I
59
I372
i4i6
1459
1502
1 545
1688
o
59
6980
6973
7oi7
-7060
7io3
7i47
O
60"
50"
40"
30"
20"
10"
.
60"
50"
40"
30"
20"
10"
d
Co-tangent of 39 Degrees.
i
Co-tangent of 38 Degrees.
a
p p . < 1" 2" 3" 4" 5" 6" 7" 8" 9"
irt{ 4 9 13 17 21 26 30 34 39
P. Part | 4 9 13 17 22 26 30 35 39
LOGARITHMIC SINES.
.g
Sine of 52 Degrees.
.H
Sine of 53 Degrees.
a
0"
10"
20"
30"
40" | 50"
SI
0"
10" 20" 30"
40"
50"
o
9.896532
6549
6565658i
6598 6614)59
o
9.9o2349 2364
238o
2396
24l2
2428
59
I
2
663i 6647
67296746
6664 6680
6762 6779
669-7 67i3
6-7956812
58
i
2
2444
2539
246o
2555
2475
2571
2491
2586
25o7
2602
2523
2618
58
57
3
68286844
6861
6877
6894 6910
56
3
2634
265o
2666
2681
2697
27l3
56
4
6926 6943
6959
6976
6992 -7009
55
4
2729
2745
2761
2776
2792
2808
55
5
7025
704 1
7o58
7o74
7o9o7io7
54
5
2824
2840
2856
2871
2887
29o3
54
6
7I23
7i4o
7i567i72
7i89!72o5
53
6
2919
2935
2950
2966
2982
2998
53
7
7222
7238
7254
727I
7287 73o3
52
7
3oi4
3o29
3o45
3o6i
3o77
3o93
52
8
7320
7336
7353
7369
7385 74o2
5i
8
3io8
3i24
3i4o
3i56
3i7i
3i87
5i
9
74i8
7434
745 1
7467
7483 75oo
5o
9
32o3
3219
3235
325o
3266
3282
5o
10
9.8975i6
7533
7549
7565
7582 -7598
49
10
9.903298
33i3
3329
3345
336i
3377
49
ii
76i4
763i
7647
7663
-7680 -7696
48
ii
3392
34o8
3424
344o
3455
48
12
7712
7729
7745
7761
77787794
47
12
3487
35o3
35i8
3534
355o
3566
47
i3
7810
7827
7843
7859
78767892
46
i3
358i
3597
36i3
3629
3644
366o
46
i4
79o8
7924
794i
7957
7973 799°
45
i4
3676
369i
37o7
3723
3739
3754
45
i5
8006
8022
8o39
8o55
8o7i 8088
44
i5
377o
3786
38o2
38i7
3833
3849
44
16
8io4
8120
8i368i53
8i69'8i85
43
16
3864
388o
3896
3912
3927
3943
43
17
8202
8218
8234
825o
8267|8283
42
i7
3959
3974
399o
4oo6
4021
4o37
42
18
8299
83i5
8332
8348
8364838i
4i
18
4o53
4069
4o84
4ioo
4u6
4i3i
4i
i9
8397
84i3
8429
8446
84628478
4o
i9
4i47
4i63
4178
4194
4210
4225
4o
2o|9.898494
85n
85278543
8559 8576
39
20
9.904241
4257
4272
4288
43o4
43i9
39
21
8592
8608
86248641
8657:8673
38
21
4335
435i
4366
4382
4398
44i3
38
22
8689
87o6
87228738
8754877o
37
22
4429
4445
446o
44?6
4492
45o7
37
23
8787
88o3
88i98835
8852 8868
36
23
4523
4539
4554
457o
4586
46oi
36
24
8884
89oo
89i68933
8949 8965
35
24
46i7
4632
4648
4664
4679
4695
35
25
898i
8997
9oi49o3o
9046 9062
34
25
4711
4726
4742
4757
4773
4789
34
26
9o78
9o95
9111
9I27
91439159
33
26
48o4
4820
4836
485i
4867
4882
33
27
9i76
9I92
92O8 9224
92409256
32
27
4898
49144929
4945
496o
4976
32
28
9273
9289
932I
93379354
3i
28
4992
5oo/ 5oa3
5o38
5o54
5o7o
3i
29
937o
9386
94o2 94i8
9434945o
3o
29
5o85
5ioi
5n6
5i32
5i48
5i63
3o
3o
9.899467
9483
9499 95i5
953i
9547
29
3o
9.905179
5i94
52IO
5225
524i
5257
29
3i
9564
958o
9596 96i2
9628
9644
28
3i
5272
5288
53o3
53i9
5334
535o
28
32
966o
9677
9693
9-709
9725 974i
27
32
5366
538i
5397
54i2
5428
5443
27
33
9757
9773
9789 98o6
9822 9838
26
33
5459
5474
5490
55o6
552i
5537
26
34
9854
987o
9886 9902
99i8
9935
25
34
5552
5568
5583
5599
56i4
563o
25
35
995i
9967
99839999
24
35
5645
566i
5676
5692
57o8
5723
24
36
9.9ooo47
oo63
oo79 oo96
OII2
0128
23
36
5739
5754
577o
5785
58oi
58i6
23
37
oi44
0160
01-76 0192
0208
0224
22
37
5832
5847
5863
5878
5894
59o9
22
38
0240
0256
O272
0289 o3o5
0321
21
38
5925
594o
5956
597i
5987
6002
21
39
o337
o353
o369o385
o4oi
0417
2O
39
6018
6o33 6049
6o64
6080
6o95 20
4o
9.900433
o449
o465o48i
o497
o5i3
I9
4o
9.9o6m
61266142
6i57
6i73
6188
I9
4i
0529
o545
o562o578
o594
0610
18
4i
6204
6219
6235
625o
6265
6281
18
42
0626
0642
o658o674o69o
o7o6
17
42
6296
63i2
6327
6343
6358
6374
17
43
O722
o738
o754 o77o o786
0802
16
43
6389
64o5
6420
6436
645 1
6466
16
44
O8l8
o834
o85o 0866 0882
o898
i5
44
6482
6497
65i3
6528
6544
6559
i5
45
0914
o93o
o946 o962
o978
o994
i4
45
6575
659o 66o5
6621
6636
6652
i4
46
1010
1026
1042 io58
io74
io9o
i3
46
6667
6683 6698
67i3
6729
6744
i3
47
1 1 06
I 122
n38
1 1 54
II70
1186
12
47
6760
6775
6791
6806
6821
6837
12
48
1202
1218
1234 I25o
1266
1282
II
48
6852
6868
6883
6898
69i4
6929
II
49
1298
i3i4
i33o
1 346
i362
i378
IO
49
6945
6960
6975
6991
7006
7022
IO
5o
9.901394
i4io
1426
1442
i458
i474
9
5o
9.9o7o37
7o52
-7068
7o83
7°99
7n4
9
5i
1490
i5o5
i5ai
i537
r553
i569
8
5i
7I29
7i45
7i6o
7i75
7i9i
7206
8
52
i585
1601
1617
i633
i649
i665
7
52
7222
?237
7252
7268
7283
7298
7
53
1681
i697
I7i3
I729
i745
i76o
6
53
73i4
7329
7344
736o
7375
739i
6
54
i776
I792
1808
1824
i84o
i856
5
54
7406
742i
7437
7452
7467
7483
5
55) i872
1888
i9o4
1920
i936
i95i
4
55
7498
75i3
7529
75447559
7575
4
56
196-7
i983
i999
2Ol5
2031
2047
3
56
759O
76o5
-7621
7636 765i
7667
3
57
2o63
2079
2O95
2IIO
2126
2142
2
57
7682
7697
77i3
7728 7743
7759
2
58
2i58
2I74
2I9O
22O6|2222
2238
I
58
7774
7789
78o5
782o 7835
785i
I
59
2253
2269
2285
2301 23l7
2333
O
59
7866
7881
7896
79I2 7927
7942
0
60"
50"
40'
30" | 20"
10"
O
60" 50"
40"
30" i 20"
10"
a
Co-sine of 97
Degrees.
Co-sine of 36 Degrees.
1
P PartJ l" 2" 3// *
5" 6" 7" 8" 9"
p p . < 1" 2" 3" 4" 5" 6" 7" 8" 9"
l.PartJ 2356
8 10 11 13 15
irt\ 2 3 5 6 8 9 11 12 14
LOGARITHMIC TANGENTS.
77
.5
. Tangent of 52 Degrees.
.5
Tangent of 53 DC grees.
8
0"
10"
20" | 30"
40" 50"
2
0"
10"
20"
30'
40"
50"
0
10. 107190
7234
7277(7320
7364
7407
5o
0
10.122886
2929
2973
3o £7
3o6i
3io5
59
i
745 1
7494
7537758i
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7668
58
I
3i48
3192
3236
3280
3324
3368
58
2
7711
7754
7798 784i
7885
7928
57
2
34n
3455
3499
3543
3587
363o
57
3
•79-72
8oi5 8o58
8l02
8i458i89
56
3
3674
37i8
3-762
38o6
385o
3893
56
4
8275
83i9
8362
84o6 8449
55
4
3937
398i
4o25
4069
4n3
4i57
55
5
84g3
8536
8579
8623
8666
8710
54
5
4200
4244
4288
4332
4376
4420
54
6
8753
8797
884o
8884
892-7
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53
6
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4507
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53
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9101
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52
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9275
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8
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9709
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534i
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42
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18
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1971
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2188
2232
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20
o. 112406
2449
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2623
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20
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266-7
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2841
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23
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8987
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24
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34
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34
26
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33
26
9735
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27
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4279
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32
27
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28
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28
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0307
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0439
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29
4758
4802
4845
4889
4932
4976
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29
0527
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5238
29
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0967
ion
29
3i
5281
5325
5368
54i2
5456
5499
28
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1099
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1187
1232
1276
28
32
5543
5586
563o
5674
5717
576i
27
32
1320
1 364
i4o8
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i496
i54o
27
33
58o4
5848
5892
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26
33
1 584
1628
1672
1716
1760
1804
26
34
6066
6110
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6241
6284
25
34
1 848
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1981
2O25
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35
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6372
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35
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23
36
2377
2421
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23
37
6852
6895
6939
6982
7026
7070
22
37
2642
2686
2780
2774
2818
2862
22
38
7n3
7l57
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7244
7288
7332
21
38
2906
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21
39
7375
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47
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5555
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5599
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5466
573i
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II
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10
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8
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7
52
66i5
6659
6704
6748
6792
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7
53
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1091
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11-78
1222
1266
6
53
6881
6925
6969
7oi3
7°57
7IO2
6
54
1309
i353
i397
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1 484
i528
5
54
7146
7190
723^
7279
73237367
1 f
55
l572
1616
i659
i7o3
1747
1791
4
55
74n
7455
75oo
7544
7588
7632
4
56
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1878
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1966
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2o5!:
3
56
7677
7721
7765
7809
7854
7898
3
57
2O97
2r4i
2i85
2229
2272
23i6
2
57
7942
7986
8o3i
8075
8119
8i63
2
58
236o
2404
2448
2491
2535
2^79
I
58
8208
8252
8296
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8385
8429
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59
2623
2667
2710
275/!
2798
2842
0
59
84?3
85i8
8562
8606
865o
8695
O
60"
50"
40"
30"
20"
10"
d
60"
50"
40"
30"
20"
10"
-•
Co-tangent of 37 Degrees.
1
Co-tangent of 36 Degrees.
1
A 1" 2" 3" 4" 5" 6" 7" 8" 9"
in\ 4 9 13 17 22 26 31 35 39
< 1" 2" 3" 4" 5" 6" 7" 8" 9"
l-.-farWj 4 9 13 is 22 26 31 35 40
78
LOGARITHMIC SINES.
I
Sine of 54 Degrees.
a
Sine of 55 Degrees.
i
s
0"
10"
20" 30" 40"
50"
0"
10"
20" 30" j 40"
50"
0
9.907958
7973
798880048019
8o34
59
o
9.9i3365
3379
3394
34o9 3423
3438
59
I
8o49
8o65 80808095 8111
8126
58
i
3453
3468
34S2
3497
35i2
3527
5S
2
8i4i
8156:817281878202
821-7
57
2
354i
3556
357i
3585
36oo
36i5
57
q
8233
8248 8263 82-79 8294
8309
56
3
363o
3644
3659
3674
3688
37o3
56
4
8324
834o!8355837o8385
84oi
55
4
37i8
3733
3747
3762
3777
379i
55
c
84i6
843 1
8446 8462:8477)8492
54
5
38o6
382i
3836
385o
3865
388o
54
6
8507
8523
85388553^85688584
53
6
3894
39o9
3924
3938
3953
3968
53
7
8599
86i4
86298644:86608675
52
7
3982
3997
4012
4026
4o4i
4o56
52
8
869o
87o5
8721 87368751)8766
5i
8
4070
4o85
4ioo
4n4
4129
4x44
5i
9
8781
8797
88128827884218857
5o
9
4i58
4i73
4i88
4202
4217
4232
5o
JO
9.908873
8888
89038918,8933
8949
49
10
9.914246
4261
42-76
4290
43o5
4320
49
ii
8964
8979
89949009*9025
9040
48
ii
4334
4349
4364
4378
4393
4407
48
12
9o55
90-70 9o85 9101 9116
9i3i
47
12
4422
4437
445 1
4466
448 1
4495
47
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9146
9161
9176 9192:9207
9222
46
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45io
4524
4539
4554
4568
4583
46
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9237
9252
9267 9283^9298
93i3
45
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4598
46l2
4627
464i
4656
467i
45
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9328
93439358:93-7419389
94o4
44
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4685
47oo
47i4
4729
4744
4758
44
16
9419
9434
9449 9464 9480
9495
43
16
4773
4787
4802
48i7
483i
4846
43
17
952595409555
957°
9586
42
17
486o
4875
489o
4904
4919
4933
42
18
9601
96169631 96469661
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18
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4962
4977
4992
5oo6
5021
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20
9691
9.909782
97o7972297379752
9797 9812^827 9843
9767
9858
4o
39
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20
5o35
9.915123
5o5o
5i37
5o64
5i52
5o79
5i66
5o94
5i8i
5io8
5i96
4o
39
21
9873
9888 99o3
9918 9933
9948
38
21
52IO
5225
5239
5254
5268
5283
38
22
9963
997s 9994
...9
..24
..39
37
22
5297
53i2
5326
534i
5356
537o
37
23
9.910054
0069 0084
0099 01 14
0129
36
23
5385
5399
54i4
5428
5443
5457
36
24
oi44
oi59 oi75
0190 O2o5
O22O
35
24
5472
5486
55oi
55i5
553o
5544
35
25
0235
O25o O265
0280
0295
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34
25
5559
5573
5588
56o2
56i7
563i
34
26
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0370
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33
26
5646
566o
5675
5689
57o4
57i8
33
27
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0476
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32
27
5733
5747
5762
5776
5791
58o5
32
28
o5o6
O52I
o536
o55i
o566o58i
3i
28
5820
5834
5849
5863
5878
5892
3i
29
0596
0611
0626
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06560671
3o
29
59o7
592I
5936
595o
5965
5979
3o
3o
9.910686
O7OI
0716
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o746
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29
3o
9.915994
6008
6023
6037
6o52
6066
29
3i
0776
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0806
0821
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28
3i
6081
6o95
6109
6124
K6i38
6i53
28
32
0866
0881
0896
0911
0926
0941
27
32
6167
6182
6196
6211
6225
6240
27
33
0956
09-71
0986
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1016
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26
33
6254
6268
6283
6297
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6326
26
34
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1061
1076
1091
1106
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25
34
634i
6355
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6384
6398
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25
35
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1166
1181
1196
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24
35
6427
6442
6456
6470
6485
6499
24
36
1226
1241
1256
1271
1286
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36
65i4
6528
6543
6557
6571
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23
37
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1375 139022
37
6600
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6629
6643
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22
38
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1420 i435
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21
38
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6701
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21
39
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39
6773
6787
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6845
20
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9.911584
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4o
9.916859
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6888
6902
6917
693i
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1674
1689
1704
1719
1734 1748 18
4i
6946
696o
6974
6989
7003
7017
1 8
42
1763
1778
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1808
1823 i838
17
42
7032
7046
7060
7075
7089
7104
17
43
i853
1868
i883
1897
1912 1927
16
43
7118
7l32
7147
7161
7i75
7i9o
16
44
1942
1957
1972
1987
2OO2 2017
i5
44
7204
7218
7233
7247
7261
7276
i5
45
2031
2046
2061
2076
2091 2IO6
i4
45
7290
73o4
73i9
7333
7347
7362
i4
46
2121
2i36
2i5o
2i65
2l8o 2195
i3
46
7376
739o
74o5
7419
7433
7448
i3
47
22IO
2225 224O
2255
2269 2284
12
47
7462
7476
7491
75o5
75i97534
12
48
2299
23i4
2329
2344
2358 2373
II
48
7548 7562
7576759i
76o5:76i9
II
49
2388
24o3 2418
2433
2448 2462
10
49
7634 7648
7662 7677
-7691 77o5
IO
5o
9.912477
2492 2507
2522
2537255i
9
5o
9.9177197734
7748 7762
7777 7791
9
5i
2566
258i
2596
26l I
2625 2640
8
5i
7805 7819
7834 7848
7862 7877
8
52
2655
2670 2685
2700
2-714 2-729
7
52
7891 79o5
7919 7934
7
53
2744
2759
2774
2788
28o3 2818
6
53
7976 7991 8oo5 8019
8o338o48
6
54
2833
2848
2862
2877
2892 290-7 5
54
806280768090810581198133 5
55
2922
29362951
29662981 2995 4
55
814781628176819082048219 4
56
3*oio
3o25
3o4o3o55j3o693o84 3
56
82338247:8261827682908304 3
5?
3099
3n4
3i283i43:3i583i73 2
57
83i8'83338347836i 83758389 2
58
3i87
32O2
32173232 32473261
i
58
84o4 84i8 8432 8446 846i 8475 i
59
3276
3291
33o6332o!3335335o o
59
8489 85o385i7 8532 8546856o o
60"
50"
40" 30" 20" 10" . ^
60" 50" t 40" 30" 20" 107 ^
Co-sine of 35 Degrees. i
Co-sine of 34 Degrees. ^
T.PartM' 2/ 3" 4" 5// 6// 7* 8// 9"- •'' P P^n" 2// 3// 4// 5" 6" 7" 8" 9"
J 2 3 5
6 8 9 11 12 14 ; "^ 1 3 4 6 7 9 10 12 13
LOGARITHMIC TANGENTS,
d 1 Tangent of 54 Degrees.
a
Tangent of 55 Degrees.
*
0"
10"
20"
30"
40" 1 50"
*
0"
10"
20"
30" | 40"
\5(y
0
io.i38739
8783
8828
8872
89i6
896o
5o
o
10.154773
48i8
4863
49o8
4952
4997
v
i
9oo5j9o49
9o93
9i38
9l82
9226
58
I
5042
5o87
5i32
5i77
5221
5266
58
2
9270
93i5
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60"
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40"
30"
20"
10"
d
60"
50"
40"
30"
20"
10"
c
Co-tangent of 35 Degrees.
*
Co-tangent of 34 Degrees.
3
p p . < 1" 2" 3" 4" 5" 6" 7" 8" 9"
I 4 9 13 18 22 27 31 36 40
P. Part J 5 "g 14 ig 23 27 32 36 41
LOGARITHMIC SINES.
A
Sine of 56 Degrees.
c
IS
Sine of 57 Degrees.
2
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60"
50"
40"
30" 20"
10"
d
60"
50"
40"
30" 20" 10"
e
Co-sine of 33 Degrees.
§
Co-sine of 32 Degrees.
1
.$1" 2" 3" 4" 5" 6" 7" 8" 9"
P Pnrt5 1/ ~" 3// 4// 5" 6" 7" 8" 9"
irt} 1 3 4 6 7 8 10 11 13
r.ranj i 3 4 5 7 8 9 n 12
LOGARITHMIC TANGENTS.
8)
A
Tangent of 56 Degrees.
.3
Tangent of 57 Degrees.
ji
0"
10"
20"
30"
40" | 50"
n
0"
10"
20"
30" | 40" | 50"
o
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60"
50"
40"
30"
20" 10"
j
60" 50"
40"
30"
20" 10"
j
Co-tangent of 33 Degrees.
§
Co-tangent of 32 Degrees.
§
P P t$ l" 2" 3// 4" 5" 6// 7" 8" 9"
(1" 2" 3" 4" 5" 6" 7" S" 9"
I 5 9 14 18 23 27 32 37 41
' art{ 5 9 14 19 23 28 33 37 42
LOGARITHMIC SINES.
1
.a
Sine of 58 Degrees.
c
Sine of 59 Degrees.
9
0" [ 10"
20" 30"
40"
f50"
•
0" 10"
20"
30"
40"
50"
0
9.928420(8434
8447 8460,8473
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2240 2253
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6811
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6848
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9
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52
53
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2457
2533
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2469
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2406
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257i 2584 259-7
8
6
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6921 6933
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6
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2622
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5
55
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2685
2762
2698
2774
271 1
2787
2724 2736 2749
2800 2812 2825
4
3
55
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7i65 7i78
7238 725i
7190 720217214 7226
72637275 72877299
4
3
57
2838
285o 2863
2876
2888 2901
2
57
731273247336734873607372 2
58
2914
2926
2939
2952
2964 2977
I
58
7385 7397 7409 7421 7433 7446 i
59
2990
3002
3oi5
3028
3o4o 3o53
o
59
7458 7470:7482 7494 7506:75 1 S
60"
50"
40" 30"
20"
10"
a
60" 50" 40" i 30" 20" 10" ^
Co-sine of 3 1 Degrees.
S
Co-sine of 30 Degrees. s§ !
P Part S !" ~" 3" 4" 5" 6" 7"
8" 9"
o T> -* U" 2" 3" 4" 5" 6" 7" 8" 3"
"^13456
8 9
10 12 ut) 1 2 4 5 6 7 9 10 11
LOGARITHMIC TANGENTS.
1
Tangent of 58 Degrees.
c
Tangent of 59 Degrees.
a
0"
10" 20"
30"
40"
50"
2
0"
10"
20"
30"
40"
50"
O
10.204211
4258
43o4
435i
4398
4445
5o
0
10.221226
I274
1322
i369
i4i7
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i
4492
4539
4586
4633
4679
4726
58
I
l5l2
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1608
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58
2
4773
4820
4867
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5oo8
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2
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1 846
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2037
57
3
5o54
5ioi
5i48
5i95
5242
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56
3
2o85
2i332i8i
2228
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56
4
5336
5383
543o
5477
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55
4
2372
94199467
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55
5
56i7
5664
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5758
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5852
54
5
2658
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2754
2801
2849
2807
54
6
5899
5946
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6087
6i34
53
6
2945
2993
3o4o
3o88
3i36
3i84
53
7
6181
6227
6274
632i
6368
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52
7
3232
3279
3327,
3375
3423
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52
8
6462
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665o
6697
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8
35i8
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6744
6791
6838
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8437
8484
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8578
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5529
5577
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5720
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16
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8860
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8954
43
16
58i6
5864
59I2
596o
6008
6o56
43
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9001
9048
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9i9o
9237
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17
6io4
6i52
6200
6248
6296
6344
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9284
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6392
6440
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7832
7880
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24
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32
28
2114
2161
2208
2255
23o3
235o
3i
28
9274
9322
937o
94i8
9466
95i5
3i
29
2397
2444
2492
2539
2586
2633
3o
29
9563
96n
9659
97°7
9755
98o3
3o
So
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2728
2775
2822
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29
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. .92
29
3i
2964
3OI2
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3i53
3201
28
3i
io.23oi4o
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0237
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28
32
3248
3295
3343
339o
3437
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27
32
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0622
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27
33
3532
3579
3626
3674
3721
3768
26
33
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0767
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26
34
38i6
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3910
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1008
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25
35
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4194
4242
4289
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24
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4384
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4478
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2166
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2359
2407
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5236
5284
533i
5378
5426
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5568
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2793
2842
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35i8
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4679
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7609
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497Q
5oi8
12
48
7799
7846
7894
794i
7989
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II
48
5o67
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5i64
5212
526o
53o9
II
49
8o84
8i3i
8i79
8226
8274
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10
49
5357
54o6
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555i
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10.218369
84i7
8464
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9
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10,235648
5696
5745
5793
5842
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9
5i
8654
8702
875o
8797
8845
8892
8
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5939
5987
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6o84
6i33
6181
8
52
8940
8987
9o35
9083
9i3o
9i78
7
52
623o
6278
6327
6375
6424
6472
7
53
9225
9273
9321
9368
94i6
9463
6
53
652i
6569
6618
6666
67i5
6763
6
54
95n
9559
9606
9654
97oi
9749
5
54
6812
6860
69o9
6957
7006
7o55
5
55
9797
9844
9892
9939
9987
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4
55
7io3
7i52
720O
7249
7297
7346
4
56
10.220082
oi3o
oi78
0225
0273
0321
3
56
7394
7443
7492
754o
7589
7637
3
67
o368
o4i6
o463
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0606
2
5y
7686
7734
7783
7832
7880
7929
2
58
o654
0702
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I
58
7977
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8o75
8i23
8172
8220
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59
0940
0988
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59
8*69
83i8
8366 84i5
8463
85i2
O
60"
50"
40"
30"
20"
10"
.
60" 50" 40" 30" 20"
10"
d
Co-tangent of 31 Degrees.
1
Co-tangent of 30 Degrees.
3
PPartJ1" 2" 3" 4// 5" 6" 7" 8// 9// 1 ppartJ1" 2" 3" 4// 5" 6" 7// 8// 9"
a"^ 5 9 14 19 24 28 33 38 43 | irt{ 5 10 14 19 24 29 34 39 43
LOGARITHMIC SINES.
d
Sine of 60 Degrees.
a
Sine of 61 Degrees.
s
0"
10"
20"
30"
40"
50"
Si
0"
10"
20" | 30"
40"
50"
0
9.937531
7543
7555
7567
7579
759i
59
o
9.941819
i83i
1843
i854
1866
1878
59
I
7604
7616
7628
764o
7652
7664
58
I
1889
1901
I9l3
1924
1936
1948
58
2
7676
7689
77oi
77i3
7725
7737
57
2
i959
i97i
i983
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2006
2017
57
3
7749
776i
7773
7786
7798
7810
56
3
2029
2041
2052
2064
20-76
2087
56
4
7822
7834
7846
7858
787o
7883
55
4
2099
2III
2122
2i34
2146
2157
55
5
7895
7907
79Z9
793i
7943
7955
54
5
2169
2l8o
2192
22O4
22l5
2227
54
6
7967
7979
7992 8oo4
80168028
53
6
2239
2250
2262
2273
2285
2297
53
7
8o4o
8o52
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80888100
52
7
23o8
2320
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2343
2355
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52
8
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812$
81378149
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2378
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24OI
24i3
2424
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9
8i85
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8209^221
82338245
5o
9
2448
2459
2471
2482
2494
25o6
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10
9.938258
82-70
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83o683i8
49
10
9.9425i7 2529
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2552
2563
2575
49
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48
1 1
2587 25g8
2610
2621
2633
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2679
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2-702
27i4
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2726
2737
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2864
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43
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42
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3o83
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20
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9.938980
8920
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8932
9004
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39
20
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9.943210
3i53
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3i64
3233
3i76
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3i87
3256
3i99
3268
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39
21
22
9123
9064
9i35
9o769o8790999in
9147 9159 9i7ifoi83
38
37
21
22
3279
3348
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336o
3302
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33i4
3383
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38
37
23
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9219 9231
9243
9255
36
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3532
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25
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3566
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36i2
34
26
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9422
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9458 94-70
33
26
3624
3635
3647
3658
367o
368i
33
27
9482
9494
95069518
95309542
32
27
3693
37o4
37i5
3727
3738
375o
32
28
9554
9566
95789590
9601 9613
3i
28
376i
3773
3784
3796
38o7
38i8
3:
29
9625
9637
9649 9661
9673 9685
3o
29
383o
384i
3853
3864
3876
3887
3o
3o
3i
9.939697
9768
9709
9780
9721 9733
9792 9804
97449756
98169828
29
28
3o
3i
9.943899
3967
39io
3978
3921
3990
4oov
3944
4oi3
3956
4024
29
28
32
9840
9852
9863 98-75
9887 9899
27
32
4o36
4047
4o58
4070
4o8i
4o93
27
33
9911
9923
9935 9947
9959 997°
26
33
4io4
4u5
4127
4i38
4i5o
4i6i
26
34
9982
9994
...6
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25
34
4172
4i84
4i95
4207
4218
4229
25
359.940054
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0077 0089 oioi
oii3
24
35
4241
4252
4264
4275
4286
4298
24
36 oi25
0/37
oi48 0160 oi72
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23
36
43o9
432i
4332
4343
4355
4366
23
371 0196
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22
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4377
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22
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0291
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21
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19
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9.944582
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18
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4696
4707
18
42
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17
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4752
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4820
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4843
16
44
45
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0752
0822
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44
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4854
4922
4865
4933
4877
4945
4888
4g56
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4967
4911
4979
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46
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o846
o858o87o
0881
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i3
46
4990
5ooi
5oi3
5o24
5o35
5o46
i3
47
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o9i7
0928 0940
0952
0964
12
47
5o58
5069
5o8o
5092
5io3
5n4
12
48
°975
o987
0999
' ' *
IOII
1023
io34
II
48
5i25
5i37
5i48
5i59
5171
5i82
II
49
io46
io58
10-70
1081
1093
no5
10
49
5i93
52o4
52i6
522-7
5238
525o
IO
5o
9.941117
1128
n4o
Il52
n64
u75
9
5o
9.945261
5272
5283
5295
53o6
53i7
9
5i
1187
11 99
I2II
1222 1234
1246
8
5i
5328
534o
535i
5362
5374
5385
8
52
1258
1269
I28l
i293 i3o4
i3i6
7
52
5396
54o7
54i9
543o
544i
5452
7
53
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1 34o
i35i
i363 i375
1387
6
53
5464
5475
5486
5497
55o9
5520
6
54 i398
i4io
1422
i433 i445
1457
5
54
553i
55425554
5565
5576
5587
5*
55 i469
56 i539
i48o
i55o
1492
i562
i5o4
i574
i5i5
1 586
1527
i597
4
3
55
56
5598
5666
56io562i
5677!5688
5632
5700
5643
5-7II
5655
5722
4
3
57
1609
1621
i632
1 644 1 656
1667
2
57
5733 5744|5756
57675778
5789
2
58 i679
1691
I702
I7l4 1726
1738
I
58
58oo 58125823 5834 5845
5857
I
59j *749
1761
i773
i784!i796
1808
O
59
5868:5879 589o59oi!59i3
5924
O
60" 50" | 40"
30" 20" 10"
d
60" 50" 40" | 30" 20"
10"
d
Co-sine of 29
Degrees.
§
Co-sine of 28 Degrees.
5
P TartJ J" 2" 3" 4"
5" 6" 7" 8" 9"
^ 1" 2" V 4" 5" 6" 7" 8" 9"
6 7 8 10 11
irtfc 1 2 3 5 6 7 8 9 10
LOGARITHMIC TANGENTS.
•I
Tangent of 60 Degrees.
d
£«
Tangent of 61 Degrees.
s
0"
10"
20"
30"
40" \ 50"
2
0"
10"
20"
30"
40"
50"
o
10. 23856i
8609
8658
8707
8755
88o4
59
0
10.256248
6298
6347
6397
6447
6496
59
i
8852
8901
8g5o
8998
9047
9096
58
I
6546
6596
6645
6695
6745
6794
58
2
9144
9193
9242
9290
9339
9388
57
2
6844
6894
6944
6993
7o43
7o93
57
3
9436
9485
9534
9582
963i
9680
56
3
7142
7192
7242
7291
734i
739i
56
4
9728
9777
9826
9874
9923
9972
55
4
744i
7490
754o
759°
764o
7680
55
5
10.240021
0069
0118
0167
02l5
0264
54
5
7739
7789
7839
7888
7938
7988
54
6
o3i3
o362
o4io
0459
o5o8
o557
53
6
8o38
8087
8i37
8187
82378286
53
7
o6o5
o654
0703
0752
0800
0849
52
7
8336
8386
8436
8486
85358585
52
8
0898
0947
o995
io44
1093
1142
5i
8
8635
8685
8735
8784
8834
8884
5i
9
1190
1239
1288
i337
i385
1434
5o
9
8934
8984
9o33
9o83
9i33
9i83
5o
10
io.24i483
i532
1681
1629
1678
1727
49
10
io.259233
9283
9332
9382
9432
9482
49
ii
1776
i825
i873
1922
1971
2O2O
48
1 1
9532
9582
9632
968i
973i
9781
48
12
2069
2118
2166
22l5
2264
23l3
47
12
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29
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5537
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5738
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32
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3
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2
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O
60"
50"
40"
30" \ 20" 10"
d
60" 50"
40"
30"
20" j 10"
d
Co-tangent of 29 Degrees.
•H
s
Co-tangent of 28 Degrees.
•fl
S
p pa *5 r/ 2" 3// 4" -5" 6" 7// 8" 9"
.( 1" 2" 3" 4" 5" 6" 7" 8" 9"
irl\ 5 10 15 20 25 29 34 39 44
Lrt) 5 10 15 20 25 30 35 40 45
LOGARITHMIC SINES.
N
Sine of 62 Degrees.
J
Sine of 63 Degrees.
1 *
0" 10" ' 20"
30" 40" 50"
2
0"
10"
20"
30"
40"
50"
0
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29
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32
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2710
2720
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2814
2824
2835
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3
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12
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2855
2866
2876
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2807
2907
2
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94089418
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6
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3238
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3269
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9526
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4
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3413342434343444
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3455 3465
4
3
57
9688 9698 9709 9720
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2
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3475 3485 3496 35o6;35i6 3527
2
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3537 3547'3557 3568 3578 3588 i
59
9816(982719838 9849 9859 987o
O
59
359936o936i9 3629 364o365o o
60" 50" i 40"
30" 20" 10"
.
60" 50" 40" 30" 30" 10"
Co-sine of 27
Degrees. a
Co-sine of 26 Degrees.
( 1 // O" Q" AH
P Part) ** 4
fft{ 1 2 3 4
5 7 8 9 10 P-Part| i ~2 3456789
LOGARITHMIC TANGENTS.
87
1
Tangent of 62 Degrees.
.5
Tangent of 63 Degrees.
91
0"
10"
2O'
30"
40"
50"
8
0"
10"
20"
30"
40"
50"
o
10.274326
4376
4427
4478
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59
0
10.292834
2886
2938
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3o42
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59
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4?32
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4885
58
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3i46
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33o3
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58
2
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57
2
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3563
36i5
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57
3
524o
5291
5342
5393
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5495
56
3
3772
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3876
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4o32
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4
5546
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4
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1 684
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1789
1842
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3i
29
32i5
3266
33i8
3369
3421
3472
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2106
2i58
2211
3o
3o
ic. 283523
3575
3626
3678
3729
378o
29
3o
IO. 3O2264
23i6
2369
2422
2475
2527
29
3i
3832
3883
3935
3986
4o38
4o89
28
3i
258o
2633
2686
2738
279I
2844
28
32
4i4o
4192
4243
4295
4346
4398
27
32
2897
295o
3OO2
3o55
3io8
3i6i
27
33
4449
45oi
4552
46o4
4655
4707
26
33
32i3
3266
33i9
3372
3425
3478
26
34
4?58
48io
486i
49i3
4964
5oi6
25
34
353o
3583
3636
3689
3742
3794
25
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5ii9
5170
5222
5273
5325
24
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3847
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3953
4oo6
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4270
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4482
4535
4588
464o
4693
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5995
6046
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6201
6253
21
38
4799
4852
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6562
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5276
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6924
6975
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5964
6oi7
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7234
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7337
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7344
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8837
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12
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7662
77i5
7768
7822
7875
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12
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9i48
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9407
9458
95io
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9769
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7
53
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53
9577
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54
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5
55
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4
55
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1 846
3
56
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3
57
1898
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2106
2i58
2
57
o857
0910
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1124
2
58
2210
2262
23i4
2366
2418
2470
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58
1177
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1284
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59
2522
2574
2626
2678
273o
2782
0
59
i498
i55i
i6o5
i658
i7ii
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O
60"
50"
40"
30"
20"
10"
f«
60" 50" 40" | 30"
20"
10"
.
Co-tangent of 27 Degrees.
S
Co-tangent of 26 Degrees.
i
P Part 5 l" 2" 3" 4// 5// 6// 7" 8" 9"
.< 1" 2" 3" 4" -5" 6" 7" 8" 9"
} 5 10 15 21 26 31 36 41 46
lrt{ 5 11 16 21 26 32 37 42 47
88
LOGARITHMIC SINES.
t
Sine of 64 Degrees. ,
d
Sine of 65 Degrees.
s
0"
10"
20"
30"
40"
50"
9
0" i 10" | 20" [ 30" 40"
50"
0
9.953660
3722
367o
3732
368i
3742
369i
3753
3701
3763
3712
3773
59
58
0
I
9.95727617286(7295 73o5 73i5
733573447354J7364I7374
7384
59
58
2
3783
3794
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3824
3835
67
2
7393
74o3
74i3 7423 7433
7442
57
3
3845
3855
3865 3876
3886
3896
56
3
7452
7462
7472
7482
7491
75oi
56
4
3906
39i7
3927 3937
3947
3957
55
4
75n
7521
753i
754o
755o
756o
55
5
3968
3978
3988
3998
4009
4oi9
54
5
757°
7579
7589
7599
7609
7619
54
6
4029
4o39
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4o6o
4o7o
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53
6
7628 7638
7648
7658
7667
7677
53
7
4090
4ioi
4ni
4l2I
4i3i
4i4i
52
7
7687
7697
7707
77i6
7726
7736
52
8
4i52
4162
41724182
4192
4203
5i
8
7746
7755
7765
7775
7785
7794
5i
9
4213
4223
42334243
4254
4264
5o
9
7804
78i4
7824
7833
7843
7853
5o
10
9.954274
4284
4294
43o5
43i5
4325
49
10
9.957863
7872
7882
7892
7902
79"
49
ii
4335
4345
43564366
4376
4386
48
ii
7921
793i
794o
795o
796°
7970
48
12
4396
44o6
44i7
4427
4437
4447
47
12
7979
7989
7999
8oo9
8oi8
8028
47 ,
i3
4457
4468
4478
4488
4498
45o8
46
i3
8o38
8o47
8o57
8067
8o77
8086
46
i4
45i8
4529
4539
4549
4559
4569
45
i4
8096
8106
8n5
8l2D
8i35
8i45
45
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4579
4589
46oo 46io
4620
463o
44
i5
8i54
8i64
8174
8i83
8i93
8203
44
16
464o
465o
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467i
468i
469i
43
16
8213
8222
8232
8242
825i
8261
43
17
47oi
4711
472I
4732
4742
4752
42
17
8271
8280
829O
83oo 83o9
83i9
42
18
4762
4823
4772
4833
4782'4792
4843 4853
4802
4863
48i3
4873
4i
4o
18
8329
8387
8339
8397
8348
84o6
83588368
84168426
8377
8435
4i
4o
20
9.954883
4894
49o4
49i4
4924
4934
39
20
9.958445
8455
8464
8474
8484
8493
39
21
22
4944
5oo5
4954
5oi5
4964 4974
5o25 5o35
4985
5o45
4995
38
37
21
22
85o3
856i
85i3
857i
8522
858o
8532
859o
8542
8600
855i
8609
38
37
23
5o65
5o75
5o86 5o96
5io6
5n6
36
23
8619
8628
8638
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36
24
5i26
5i36
5i46
5i56
5i66
5i76
35
24
8677
8686
8696
8706
87i5
8725
35
25
5i86
5i96
5207
5217
5227
5237
34
25
8734
8744
8754
8763
8773
8783
34
26
5247
5257
5267
5277
5287
5297
33
26
8792
8802
8812
8821
883i
884o
33
27
53o7
r)3i7
5327
5337
5348
5358
32
27
885o
8860
8869
8879
8888
8898
32
28
5368
5378
5388 5398
54o8
54i8
3i
28
8908
8917
8027
8937
8946
8956
3i
29
5428
5438
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5458
5468
5478
3o
29
8965
8975
8985
8994
9004
9013
3o
3o
9.955488
5498
55o8
55i8
5528
5538
29
3o
9.959023
9033
9042
9o52
9061
9071
29
3i
5548
5559
5569
5579
5589
5599
28
3i
9080
9090
9ioo
9109
9119
9128
28
32
5609
56i9
5629 5639
5649
5659
27
32
9i38
9i48
9l57
9167
9176
9186
27
33
5669
5679
5689 5699
57o9
57i9
26
33
9i95
9205
92l5
9224
9234
9243
26
34
5729
5739
5?49
5759
5769
5779
25
34
9253
9262
9272
9282
9291
93oi
25
35
5789
5799
58o9
58i9
5829
5839
24
35
93io
9320
9329
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24
36
5849
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5869
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5889
5899
23
36
9368
9377
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9406
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23
37
5909
59i9
5929
5939
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5959
22
37
9425
9434
9444
9453
9463
9473
22
38
5969
5979
5989
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21
38
9482
9492
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9520
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21
39
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6069
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19
18
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20
19
18
42
6208
6218
6228 6238 6248 6258
17
42
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9720
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9739
9749
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17
43
44
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6268
6327
6387
6278
6337
6397
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6347635763676377
6407641764276437
16
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43
44
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9768
9825
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9834
9891
9787
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9872
9929
16
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46
6447
6457
6466,6476 6486 6496
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9938
9948
9957
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/7
65o6
65i6
6526
6536 6546
6556
I 2
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nnn 5
5
. "4 33
43 12
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48
6566
6575
6585
6595 66o5
66i5
II
*»/
48
Vyy^
9.960052
0061
0071
0080 0090
0099 1 1
49
6625
6635
6645
6655 6665
6674
10
49
0109
0118
0128
0137 0147
oi56 10
5o
9.956684
6694
6704
6714 6724
6734
9
5o
9.960165
0175
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019410203
02 I 3
9
5i
6744
6754
6763
6773
6783
6793
8
5i
O222
0232
0241
O25o 0260
0269
8
52
68o3
68i3
6823
6833
6843
6852
7
52
0279
0288
0298
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7
53
6862
6872
6882
6892
6902
69I2
6
53
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6
54
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693i
694i
6951
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5
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0392
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55
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7000
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4
56
7040
7ODO
7°59
7069
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3
56
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3
57
7°99
7I09
7118
7128
7i38
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58
7i58
7168
7177
71877197
7207
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58
0618 0627 o636io646o655 o665 i
59
7217
7227
7236
7246 7256
7266
O
59
0674:0683 069^ 0702 071 1 071:
60"
50"
40"
30" | 20"
10"
d
60" | 50" 40" j 30" 20" j 10" i ^
Co-sine of 25
Degrees.
Co-sine of 24 Degrees. a
T PartJ l" 2" 3" 4"
I.lartJ ! 2 3 4
5" 6" 7" 8" 9"
56789
.( 1" 2" 3" 4" 5" 6" 7" fi
irt\ 1 2 3 4 5 6 7 * !>
LOGARITHMIC TANGENTS.
c
Tangent of 64 Degrees.
Jj
Tangent of 65 Degrees.
9
0"
10" 1 20"
30"
40"
50"
s
0"
10"
20"
30"
40"
50"
0
io.3n8i8
l872JI925
i979
2032
2o85
59
0
io.33i327
i382
i437
1492
1 547
1602
59
i
2l39
2I92 2246
2299
2353
2406
58
I
i657
I7I2
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1822
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1932
58
2
2460
25i3|2567
2620
2674
2727
5?
2
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2042
2097
2i53
2208
2263
57
3 2781
2834
2888
294l
2995
3o48
56
3
23i8
2373
2428
2483
2538
2593
56
A 3io2
3i55
3209
3263
33i6
337o
55
4
2648
2703
2758
28i3
2868
2924
55
5, 3423
3477
353o
3584
3637
369i
54
5
2979
3o34
3089
3i44
3i99
3254
54
6
3745
3798
3852
39o5
3959
4oi3
53
6
33o9
3364
3420
3475
353o
3585
53
7
4o66
4l2O
4i73
4227
4281
4334
52
7
364o
3695
375i
38o6
386i
39i6
52
8
4388
4442
4495
4549
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4656
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8
397i
4026
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1"
|ij. — .4 j
5i
9
4710
4764
48i7
487i
4925
4978
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5o
10
io.3i5o32
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5354
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55i5
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1 1
4965
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48
12
5676
573o
5784
5838
589i
5945
47
12
5297
5353
54o8
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55i8
5574
47
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5999
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6106
6160
6214
6268
46
1 3
5629
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45
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6016
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16
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7021
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43
16
6625
6681
6736
6792
6847
6903
43
17
7290
7344
7398
7452
75o6
756o
42
17
6958
7013
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7124
7180
7235
42
18
76i3
7667
772i
7775
7829
7883
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18
729X
7346
7402
7457
75i3
7568
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19
7937
7991
8o45
8099
8i53
8206
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7679
7735
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7846
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4o
20
10.818260
83i4
8368
8422
8476
853o
39
20
io.337957
8012
8068
8i23
81 79
8234
39
21
8584
8638
8692
8746
8800
8854
38
21
829o
8345
84oi
8456
85i2
8568
38
22
8908
8962
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60"
50" | 40"
30"
20"
10"
ej
60"
50"
40" | 30"
20"
10"
c
Co-tangent of 25 Degrees.
Z
Co-tangent of 24 Degrees.
s
,5 1" 2" 3" 4" 5" 6" 7" 8" 9"
C 1" 2" 3" 4" 5" 6" 7" 8" 9"
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00
LOGARITHMIC SINES.
a
Sine of 66 Degrees.
^c
Sine of 67 Degrees.
9
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40"
50"
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38
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60"
50"
40"
30" 20"
10"
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60" 50" | 40" 30" 20" | 10"
Co-sine of 23 Degrees.
Co-sine of 22 Degrees. s
.< 1" 2" 3" 4" 5" 6" 7" 8" 9"
llt $1234 55 67 8
.( 1" -2" 3" 4" 5/; 6" 7" 3" 9"
irt) 123345678
LOGARITHMIC TANGENTS.
91
c
Tangent of 66 Degrees.
s
Tangent of 67 Degrees.
2
0"
10"
20"
30"
40"
50"
55
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20/
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40' | 50"
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60"
50" | 40"
30" 20"
10"
d
60" | 50" 40"
30" 20"
10"
•
Co-tangent of 23 Degrees.
%
Co- tangent of 22 Degrees.
§
,(1" 2" 3" 4" 5" 6" 7" 8" 9" II p p .( I" 2" 3" 4" 5" 6" 7" 8" 9''
lrt{ 6 12 17 23 29 35 40 46 52 irt£ 6 12 18 24 30 36 42 48 54
LOGARITHMIC JSlNES.
.a
Sine of 68 Degrees.
Jj
Sine of 69 Degrees.
i
0"
10"
20" 30" 40"
50"
s
0"
10"
20"
30"
40"
50"
o
9.967166
7174
7l83 7191 7200
7208
59
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9 970152
0160
0168
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32
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2253
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2338
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236i
2369
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12
47
2385
2392
2400
2408
2416
2423
12
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9567
95759583
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9599 9608
II
48
243i
2439
2447
2454
2462
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9616
96249632
9640
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10
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96739681
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9.972524
2532
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9714
97229730
9738
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2570
2578
2586
2593
2601
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8
52
9762
9771 9779
9787
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7
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2617
2624
2632
2640
2648 2655
7
53
9811
98199828
9836
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6
53
2663
267I
2678
2686
260,4 2701
6
54
9860
98689876
9884
9893 9901
5
54
2709
2717
2725
2732
2740
2748
5
55
9909
99179925
9933
994i 9949
4
55
2755
2763
2771
2778
2786
2794
4
56
57
995799669974
9.97ooo6 ooi4 0022
9982
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999° 9998
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3
2
56
57
2802 2809
2848 2855
28172825
2863,2871
2832
2878
2840
2886
3
2
58 oo55
oo63 0071
0079
0087 oo95
I
58
2894 29OI
2909 29I7 2924 2932 I
59
oio3oiii 0119012701 36 oi 44
o
59
294o 294729552963 2970 20.78 o
60" 50"
40" i 30" 20" 10" | e.
60" i 50" : 40" 30" 20" 10" „.
Co-sine of 21 Degrees. S
Co-sine of 20 Degrees.
f ^// 2" 3"
4" 5" 6" 7" 8" 9"
D „ . < 1" 2" 3" 4". 5" 6" 7" 8" 9"
P. Part j ! o 2
345677 ul/> 1 2 2 3 4 5 fi 6 7
LOGARITHMIC TANGENTS.
1
Tangent of 68 Degrees.
A
Tangent of 69 Degrees.
X
0"
10" 1 20" | 30"
40"
50"
s
0"
10" | 20"
30" 40" | 50"
o
i
10.393590
3954
365i
4oi5
3712^772
4o76i4i36
3833
4i97
3894
4258
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58
0
i
io.4i5823
6200
5886
6263
5948
6326
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58
2
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444o 45oo
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4622
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6578
664i
6704
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6893
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4
4683
5o47
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5io8
48o4
5i69
4865
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56
55
4
6956
7335
7O20
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7083
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7i46
7524
7209
7587
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765o
56
55
c
5412
5473
5533
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5655
57i6
54
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77i4
7777
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79°3
7966
8o29
54
6
5777
5838
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6020
6081
53
6
8o93
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8282
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53
7
6142
62o3
6264
6325
6385
6446
52
7
8472
8535
8598
8661
8725
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52
9
65o7
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6629
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6812
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89i4
8978
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6873
6934
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7o56
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9
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9294
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9484
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10
10.397239
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7422
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49
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10.419611
9674
9738
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9864
9928
49
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7605
7666
7727
7788
7849
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48
II
9991
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12
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47
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8582
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8704
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9438
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9806
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. 112
42
ll
2277
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24o5
2468
2532
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42
18
10.400173
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18
2659
2723
2787
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2914
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20
10.400909
0971
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1216
39
20
10.423424
3488
355;
36i5
3679
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39
21
1278
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38
21
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3934
3998
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1953
37
22
4190
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37
23
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2261
2322
36
23
4573
4637
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4764
4828
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36
24
2384
2445
2507
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263o
2691
35
24
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5o84
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35
25
2753
28i5
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2938
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34
25
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54o4
5468
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34
26
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33o7
3369
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33
26
5724
5788
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59i6
5980
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33
27
3492
3554
36i5
3677
3739
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32
27
6108
6172
6236
63oo
6364
6429
32
28
3862
3924
3985
4o47
4io9
4170
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28
6493
6557
6621
6685
6749
68i3
3i
29
4232
4294
4356
44i7
4479
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29
6877
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7006
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7i34
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4664
4726
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4911
29
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60"
50"
40"
30"
20"
10"
.
60"
50"
40"
30"
20"
10"
.
Co-tangent of 21 Degrees.
a
Co-tangent of 20 Degrees.
a
PPartM" 2" 3" 4" 5// 6" 7" 8// 9"
.C 1" 2" 3" 4" 5" 6" 7" 8" 9"
iri$ 6 12 19 25 31 37 43 49 56
in\ 6 13 19 26 32 39 45 51 58
LOGARITHMIC SINES.
3
Sine of 70 Degrees.
|
Sine of 7 1 Degrees.
•
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60"
50"
40"
30" 20"
10"
c
60" j 50" 40" j 30" 20" | 10"
a
Co-sine of 19 Degrees.
ii
Co-sine of 1 8 Degrees.
1
pp .C 1" 2" 3" 4" 5" 6" 7" 8" 9"
irt$ 1 123 44567
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trt{ 1 1 2 3 4 4 3 ft 6
LOGARITHMIC TANGENTS
95
d
Tangent of 70 Degrees.
d
Tangent of 7 1 Degrees.
s
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20"
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50"
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3669
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22
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60"
50" 40"
30"
20"
10"
S"
60" 50" 40" 30"
20"
10"
g'
Co-tangent of 19 Degrees.
Co-tangent of 18 Degrees.
. < 1" 2" 3" 4" 5" 6" 7" 8" 9"
< 1" 2" 3" 4" 5" 6" 7" 8" 9"
llt\ 7 13 20 27 33 40 47 54 60
; ' art} 7 14 21 28 35 42 49 56 63
LOGARITHMIC SINEB.
.s
Sine of 72 Degrees.
-'
Sine of 73 Degrees.
m
0"
10"
20" 30" | 40"
50"
0"
10"
20"
30" | 40"
50"
c
9.9782o6 82i3
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1961
1967
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1986
1992
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60"
50- |
40" 30" 20" 10"
ri
60" ^ i 50" 40" 30" 20" 10- ^
Co-sine of 17 Degrees.
Co-sine of 16 Degrees.
f j// g// g//
4" 5" 6" 7" 8" 9" p p .(!" 2" 3" 4" 5" 6" 7" 8' 9"
(1 12
3 3 4 5 5 6 : r'rarM 1 12234436
LOGARITHM c TANGENTS.
4
Tangent of 7 ^ Decrees.
d
Tangent of 73 Degrees.
s
0"
10"
20"
30" | 40"J 50" |
i
0"
10"
20"
30"
40"
50"
o
10.488224
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io.54pi25
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58
3758
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59
42O9
4285
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59
2027
2106
2186
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2345
2424
O
60"
50"
40"
30"
20"
10"
g
60"
50"
40"
30"
20"
10"
j
Co- tangent of 17 Degrees.
Co-tangent of 16 Degrees.
§
p p .$ 1" 2" 3" 4" 5" 6" 7" 8" 9"
I 7 15 22 29 37 44 51 59 66
p p t f 1" 2" 3" 4" 5" 6" 7" 8" 9"
in\ 8 15 23 31 39 46 54 62 70
98
LOGARITHMIC SINES.
.9
Sine of 74 Degrees.
a
Sine of 75 Degrees.
s
0"
10"
20"
30" 1 W
50*
3 0" 10"
20"
30"
40"
50"
o
9.98a842 2848
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32
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0
60" 50" I
II
40"
30" | 20" j 10"
d
60"
50" 40"
30"
20"
10"
jft
Co-sine of 15
Degrees.
§
Co-sine of 14 Degrees.
9
( 1" 2" *V 4"
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5" 6" 7" 8" 9"
t < 1" 2" 3" 4" 5" 6" 7" 8" 9"
*l{ 1 1 8
2
33455
in\ 1 1 2 2 3 3 4 4 5
LOGARITHMIC TANGENTS.
99
d
Tangent of 74 Degrees.
_g
Tangent of 75 Degrees.
s
0"
10"
20
30"
40"
50"
9
0"
10"
20"
30"
40"
50"
o
io.5425o4
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ll
42
3636
3724
38i2
39oo
3988
4076
17
43
343o
35i2
3595
3678
3761 3844
16
43
4i64
4252
434o
4428
45i6
46o4
16
44
45
3927
4424
4oio
4507
4o93
459o
4i75
4673
4258434i
47564839
i5
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44
45
4692
5222
478i
53io
4869
5398
4957
5486
5o45
5575
5i33
5663
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i4
46
4922
5oo5
5o88
5l72
5255 5338
i3
46
575i
584o
5928
6oi7
6io5
6i93
i3
47
542i
55o4
5587
567o
57545837
12
47
6282
637o
6459
6547
6636
6724
12
48
5920
6oo3
6086
6i7o
6253^6336
II
48
68i3
69oi
699o
7o78
7167
7256
II
49
6420
65o3
6586
6669
6753:6836
IO
49
7344
7433
7522
76io
7699
7788
10
5o
10.566920
7003
-7086
7i7o
7253 7337
9
5o
io.597876
7965
8o54
8i43
823i
8320
9
5i
7420
75o4
7587
767i
7754'7838
8
5i
84o9
8498
8587
8675
8764
8853
8
52
7921
8oo5
8088
8l72
8255'8339
7
52
8942
9o3i
9I20
92O9
9298
9387
7
53
8423
85o6
859o
8674
8757;884i
6
53
9476
9565
9654
9743
9832
992I
6
54
8925
9008
9O92
9176
92609343
5
54
10.600010
OIOO
oi89
0278
o367
o456
5
55
9427
95 1 1
9595
9679
9763 9846
4
55
o545
o635
0724
o8i3
0902
O992
4
56
993o
..i4
..98
.182
.266 .35o
3
56
1081
II7O
1260
1 349
i438
i528
3
57
10.570434
o5i8
0602
0686
o77o o854
2
57
161-7
I7o6
i796
i885
i975 2064
2
58
o938
IO22
1106
1 190
i274 i358
I
58
2i54
2243
2333
2422
25l2 26OI
I
59
i442
l527
161 1
:695
i779 i863
0
59
2691 278i
287O
296o
3o5o3i39
0
60"
50" 40"
30"
20" 10"
.
60" 50"
40"
30"
20" 10"
.
To-tangei-t of 15 Degrees.
'%
Co-tangent of 14 Degrees.
§
PPartJ l" 2// 3" 4" 5" 6" 7// 8" 9//
C 1" 2" 3" 4" 5" 6" 7" 8" 9"
inl 8 16 25 33 41 49 57 65 74
irtj 9 17 26 35 43 52 61 69 78
100
LOGARITHMIC SINES.
1
Sine of 76 Degrees.
_c
Sine of 77 Degrees.
8
0"
10"
20"
30"
40"
50"
^
0" [ 10"
20"
30"
40"
50"
o
9.986904
6909
69i5
6920
6925
6930 59
o
9.988724|8729
8734
8739
8743
8748
59
i
6936
694i
6946
6951
6957
6962
58
I
8753
8758
8763
8768
8772
8777
58
2
6967
6972
6978
6983
6988
6993
57
2
8782
8787
8792
8797
8802
8806
57
3
6998
7oo4
7oo9
7014
7019
7025
56
3
8811
8816
8821 8826
883i
8835
56
4
7o3o
7o35
7o4o
7o45
7o5i
7o56
55
4
884o
8845
885o
8855
8860
8864
55
5
-7061
-7066
7072
7077
7o82
7087
54
5
8869 8874
8879
8884
8889
8893
54
6
7092
7o98
7io3
7io8
7n3
7118
53
6
8898 8903
8908
89i3
8918
8922
53
7
7124
7129
7i34
7i39
7i44
7i5o
52
7
8937
8942
8946
895i
52
8
7i55
-7160
7i65
7i7o
7i76
7181
5i
8
89568961
8966
8970
8975
8980
5i
9
10
7186
9.987217
-7191
7222
-7228
-7202
7233
720772I2
72387243
5o
49
9
10
8985
9.989014
899o
9oi8
8994
9023
8999
9028
9004
9o53
9009
9o38
5o
49
ii
7248
7253
-7259 -7264
7269!7274
48
ii
9042
9047
go52
9°57
9062
9066
48
12
7279
7284
72907295
73oo 73o5
47
12
9071
907619081
9085
9090
9o95
47
i3
U
73io
734i
73i5
7346
732i 7326
7352!7357
733i 7336
7362 7367
46
45
i3
i4
9100
9128
9io5
9i33
91099114
913819143
9119
9148
9124
9152
46
45
i5
16
7372
74o3
7377
74o8
7383;7388
74i3 -7419
•7393-7398
44
43
i5
16
9i57
9186
9162
9190
9i679i7i
9195 9200
91-76
9205
9181
9209
44
43
17
18
7434
7465
7439
747o
7444 7449
7475 748o
7454 746o
7485 -7490
42
4i
;87
92149219
9243 9247
9224
9252
9228
9257
9233
9238
9266
42
4i
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7496
75oi
75o6 75i i
75i6 752i
4o
'9
92-71
9276
9281
9285
9290
9295
4o
20
9.987526
753i
753717542
7547
7552
39
20
9.989300
93o4
93o9
93i4
93i8
9323
39
21
7557
7562
7567 7572
75777583
38
21
9328
9333
9337
9342
9347
935a
38
22
7588
7593
-7598 76o3
76o876i3
37
22
9356
936i
9366
937o
9375
9380
37
23
7618
7623
7628 7634
•76397644
36
23
9385
9389
9394
9399
94o3
9408
36
24
7649
7654
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7669,7674
35
24
94 1 3
9417
9422
9427
9432
9436
35
25
7679
7684
-7690 -7695
7700
7705
34
25
944i
9446
945o
9455
946o
9464
34
26
7710
77i5
77207725
773o
7735
33
26
9469
9474
9479
9483
9488
9493
33
27
774o
7745
775o 7756
7761
7766
32
27
9497
9502
95o7
95n
95i6
9521
32
28
7771
7776
778i 7786
7791
7796
3i
28
9525
953o
9535
9539
9544
9549
3i
29
7801
-7806
7811 7816
7821
3o
29
9553
9558
9563
9568
9572
9577
3o
3o
9.987832
7837
7842 7847
7852
?857
29
3o
9.989582
9586
9591
9596
96oo
9605
29
3i
7862
7867
7872 7877
7882
7887
28
3i
9610
9614
9619
9623
9628
9633
28
32
7892
7897
-7902 -790-7
7912
79i7
27
32
9637
9642
964-7
965i
9656
9661
27
33
7922
7927
7932 7937
7942
7947
26
33
9665
9670
9675
9679 9684
9689
26
34
7953
7958
-7963 -7968
7973
7978
25
34
9693
9698
97o3
97079719
9-716
25
35
7983
7988
7993 7998
8oo3
8008
24
35
9-721
9726
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9735974o
9744
24
36
8oi3
8018
8o23 8o288o33
8o38
23
36
9749
9753
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9772
23
37
8o43
8o48
8o53 8o58 8o63
8068
22
37
9777
9781
9786
979° 9795
9800
22
38
8o73
8078.
8o83 8o33 3o93
8098
21
38
98o4
9809
9814
98i8
9823
982-7
21
39
8io3
8108
8ii38ii88ia3
8128
2O
39
9832
9837
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9846
985o
9855
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409.988133
8i38
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8i58
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9.989860
9864
9869
9873
9878
9883
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8i63
8168
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8188
18
4i
9887
9892
9896
99oi
99o699io
18
42
43
44
8193
8223
8252
8198
8227
8257
8ao3 82088213
8232823-78242
8262'8267 82-72
8218
8247
8277
16
i5
42
43
44
99i5
9942
997°
9919,9924
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9974 9979
9929
9956
9984
9933
9961
9988
9938
9965
9993
16
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45 8282
8287
8292 8297 83o2
83o7
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45
9997
. . .2
...6
. . ii
..16
. .20
i4
46
83i2
83i7
8322'8327:8332
8337
i3
46
9.99OO25
0029
oo34
oo38
oo43
oo48
i3
4? 8342
8346
835i8356836i
8366
12
47
0052
0057
0061
0066
00-70
oo75
12
48 837i
8376
838i'8386839i
8396
II
48
oo79
oo84
0088
oo93
0098
0102
II
49 84oi
84o6
84n 84168420
8425
10
49
0107
01 II
0116
OI2O
OI25
OI29
10
509.988430
8435
844o 8445 845o
8455
9
5o
9.990134
oi38
oi43
oi48
Ol52
oi57
9
5i| 846o
8465
847o
8475 848o
8484
8
5i
0161
0166
OI7O
oi75
01-79
oi84
8
52
8489
8494
8499
85o4 85o9
85i4
7
52
0188
0193
019-7
0202
0206
02 1 1
7
53 85i9
8524
8529
85348538
8543
6
53
02l5
0220
O225
O229
0234
0238
6
54 8548
8553
8558
85638568
8573
5
54
0243
0247
O252
0256
0261
0265
5
55 8578
8583
8587
8592 8597
8602
4
55
0270
0274
0279
0283
0288
O292
4
56
86o7
8612
8617
86228626
863i
3
56
0297
o3oi
o3o6
o3io o3i5
o3i9
3
57
8636
864i
8646
865i 8656
8661
2
57
0324
o328
o333
o337o342
o346
2
58 8666
867o
8675
8680 8685
8690
I
58
o35i
o355
o36o
o364 o369
o373
I
59 8695
87oo
8704
8709 8714
8719
0
59
o378
o382Jo386
o39i o395
o4oo
0
60"
50"
40"
30" 20"
10"
d
60"
50" 40"
30" 20"
10"
d
Co-sine of 13 Degrees.
3
Co-sine of 12 Degrees.
i
.< 1" 2" 3" 4" 5" 6" 7" 8" 9"
.( 1" 2" 3" 4" 5" 6" 7" 8" 9"
in\ 1 1 2 2 3 3 4 4 5
""M 01 122 3344
LiOGARITHMIC TANGENTS.
10!
1
Tangent of 76 Degrees.
d
Tangent of 77 Degrees.
*
0"
10"
20"
30"
40"
50"
J
0"
10"
20"
30"
40"
50"
0
10.603229
33i9
34o8
3498
3588
3678
59
0
10.636636
6732
6828
6924
7020
7116
59
I
3767
3857
3947
4087
4127
4217
58
I
72l3
73o9
74o5
75oi
7597
760.4
58
2
43o6
4396
4486
4576
4666
47^6
57
2
779°
7886
7983
8o79
8i75
8272
57
3
4846
4g36
5026
5n6
5206
5296
56
3
8368
8465
856i
8657
8754
885o
56
4
5386
5477
5567
5657
5747
5837
55
4
8947
9o43
9i4o
9237
9333
943o
55
5
5927
6017
6108
6i98
6288
6378
54
5
9526
9623
9720
98i6
99i3
. . 10
54
6
6469
6559
6649
6740
683o
6920
53
6
10.640107
O2O3
o3oo
o397
o494
o59i
53
7
7011
7101
7i92
7282
7372
7463
52
7
0687
o784
0881
o978
io75
1172
52
8
7553
7644
7734
7825
79i5
8006
5i
8
I269
i366
i463
i56o
i657
17^4
5i
9
8097
8187
8278
8368
8459
855o
5o
9
i85i
i948
2046
2i43
2240
2337
5o
10
10 6o86,4o
873!
8822
89i3
9oo3
9094
4Q
10
io.642434
253i
2629
2726
2823
292I
49
ii
9i85
9276
9367
9457
9548
9639
48
1 1
3oi8
3n5
32i3
33io
34o7
35o5
48
12
973o
9821
99I2
...3
..94
.i85
47
12
36o2
37oo
3797
3895
3992
4o9o
47
i3
10.610276
o367
o458
o549
o64o
o73i
46
i3
4i87
4285
4383
448o
4578
4676
46
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0822
0913
ioo4
io95
1186
1278
45
i4
4773
487i
4969
5o66
5i64
5262
45
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1369
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i55i
1642
1734
1825
44
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536o
5458
5555
5653
575i
5849
44
16
1916
2008
2099
2I9O
2282
2373
43
16
,- 5947
6o45
6i43
6241
6339
6437
43
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2464
2556
2647
2739
283o
2922
42
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6535
6633
673i
6829
6927
7026
42
18
3oi3
3io5
3i96
3288
3379
3471
4i
18
7124
7222
7320
74i8
75i7
76i5
4i
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3562
3654
3746
3837
3929
4O2I
4o
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77i3
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79io
8008
8106
82o5
4o
20
io.6i4ii2
4204
4296
4388
4479
457I
39
20
io.6483o3
8402
85oo
8599
8697
8796
39
21
4663
4755
4847
4938
5o3o
5l22
38
21
8894
8993
9o9i
9i9o
9288
9387
38
22
52i4
53o6
5398
5490
5582
5674
37
22
9486
9584
9683
9782
988o
9979
37
23
5766
5858
595o
6042
6i34
6226
36
23
10.650078
0177
0276
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0572
36
24
63i8
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65o3
6595
6687
6779
35
24
0671
0770
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1067
1166
35
25
6871
6964
7o56
7i48
7241
7333
34
25
1265
1 364
i463
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1661
1760
34
26
7425
75i8
7610
7702
7795
7887
33
26
i859
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2o58
2l57
2256
2355
33
27
7980
8072
8i64
8257
8349
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32
27
4455
2554
2653
2752
2852
295l
32
28
8534
8627
8720
8812
89o5
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28
3o5i
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3249
3349
3448
3548
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29
9090
9183
9275
9368
946i
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29
3647
3747
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10.619646
9739
9832
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. no
29
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10.654245
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29
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28
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28
32
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27
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5542
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27
33
1319
1412
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26
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6242
6342
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25
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2624
2717
2810
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24
35
7243
7344
7444
7544
7645
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24
36
2997
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3277
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23
36
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23
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3745
3838
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22
37
8448
8549
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875o
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22
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42l3
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4494
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21
38
9o52
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21
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20
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9656
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10.625244
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10.660261
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279°
2892
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8067
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36o2
37o4
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46
8633
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44i6
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9201
9295
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9484
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9863
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48
5i29
523i
5333
5435
5537
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49
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0432
0527
0622
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0811
10
49
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10.630906
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9
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10.666354
6456
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1571
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8
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6067
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7274
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52
2047
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7
53
2618
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6
53
8i97
8299
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8607
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6
54
3190
3285
338i
3476
3572
3667
5
54
88i3
89i6
9oi8
9I2I
9224
9327
5
55
3763
3858
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4i45
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4
55
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9532
96359738
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4
56
4336
4432
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3
56
io.67oo47
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3
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57
0666 o769 o872 o975
1078
1181
2
58
5485
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5676
5772
5868
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1285 i388 i49i i595
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59
6060
6i56
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6348
6444
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0
59
I9o5 2O08 2112 22l5!23l8 2422
o
60"
50"
40"
30"
20"
10"
j
60" 50" 40" 30" 20" 10" ^
Co-tangent of 13 Degrees.
a
Co-tangent of 12 Degrees. ii
p p t5 1" 2" 3" 4" 5" 6" 7" 8" 9"
. ( 1" 2" 3" 4" 5" 6" 7" 8" 9"
I 9 19 28 37 46 56 65 74 83
lrl\ 10 20 30 40 50 60 70 80 90
0-2
LOGARITHMIC fc> i N m B.
.g
Sine of 78 Degrees.
a Sine of 79 Degrees.
s
0" 10" ! 20" 30" i 40"
50"
<=• 0" 10"
20" 30"
40"
50"
0
9.99o4o4|o4o9 o4i3 o4i8 0422
0427,59
09.991947 1951
1955 1959
1963
1967
59
I
2
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o458
o436 o44o o445 0449 O454, 58
0462 0467 0471 0476 o48o 57
2
I97i|i975
1996 2OOO
1979 i983
2004 2008
1987
2OI2
1992
2016
58
57
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56
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2O20 2024
2028
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2442
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39
21
0960
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0982
38
21
2454
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34
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34
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1094 1098
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1 107
III!
33
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2572
2576
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2584
2588
2592
33
27
iiiS
I 120 I 124
1128
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32
27
2596
2600
2604
2607
261 1
26i5
32
28
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28
2619
2623
2627
263i
2635
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29
1167
1171 1176
1180
1184
1x88
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29
2643 2647 265 1
2654
2658
2662
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3o
9.991193
I 197 1201
1206
1210
18X4
29
3o
9.992666 2670)2674
2678
2682
2686
20
3i
1218
1223 1227
I23l
1235
1240
28
3i
2690
2693 2697
2701
2705
2709
28
32
1244
1248 1253
1257
1261
1265
27
32
2?l3
2717
2721
2725
2728
2732
27
33
1270
1274 1278
1282
1287
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26
33
2736
274^
2744
2748
2752
2756
26
34
1295
1299 i3o4
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25
34
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2763
2767
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2775
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25
35
1321
i325 1329
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1 342
24
35
2783
2787
2790
2794
2798
2802
24
36
1 346
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23
36
2806
2810
2814
28l8
2821
2825
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37 i372
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1 384
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22
37
2829
2833
2837
2841
2845
2848
22
38 i397
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2860
2864
2868
2871
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1 444
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2875
2879
2883
2887
2891
2895
20
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9.991448
1452 i456
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9.992898
2902
2906
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2914
2918
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1477 1482
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1490
1494
18
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2921
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2933
2937
2941
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3028
3o32
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46
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1612
1616
1620
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3o43
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3o55
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47
1624
1628 i632
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1 645
12
47
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3o62
3o66
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3o74
3o78
12
48
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1662
1666
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II
48
3o8i
3o85
3089
3o93
3o97
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1674
1678 1682
1687
1691
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49
3io4
3io8
3lI2
3n5
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9.991699
1703 1707
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9
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9.993127
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3i34
3i38
3i42
3i46
9
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1724
1728 1732
1736
1741
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8
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3i49
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3i57
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3i65
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8
52
1749
1753x757
1761
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7
52
3172
3i76
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3i83
3i87
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7
53
1774
1778 1782
1786 i79o
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6
53
SigSjSigS
3202
3206
3210
32i3
6
54
1799
1803.1807
1811 1816
1819
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54
3217 3221 3225 3228
3232
3236
5
55
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1827 i832
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1 844
4
55 324o3s>43 3247 325i
32553258
4
56
1 848
i85ax856
1860 i865
1869
3
56
3262:3266 3270 3273 3277'328i
3
57
i873
18771881
i885
1889
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2
57
3284 3288 3292 3296^299 33o3
2
58
1897
1901 1906
i9io i9i4
1918
I
58
33o733n 33x433x83389 3325
I
59
1922
1926 1930
i934 1938
1942
O
59
3329 3333 3337334o'3344 3348 o
60" 50" |^40" 30" j 20"
10"
A
60" 50" 40" 30" ; SO" 10" . „•
Co-sine of 1 1 Degrees.
§
Co-sine of 10 Degrees. ?*
P Part* l" 2" 3" 4// 5" 6" 7//
8" 9" | .(1" 2" 3" 4" 5" 6" 7" 8" 9"
iTli 0 1 1 2 2 3 3
34 '"} 0 11222334
LOGARITHMIC TANGENTS.
103
1
Tangent of 78 Degrees.
.5
Tangent of 79 Degrees.
g
0"
10"
20"
30"
40"
50"
%
0"
10"
20"
30"
40"
50"
o
10.672525
2629
2733
2836
2940
3o43
59
o
10.711348
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1910
59
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3i4?
325i
3354
3458
3562
3666
58
i
2023
2i35
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236i
2473
2586
58
2
3769
3873
3977
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4i85
4289
57
2
2699
2811
2924
3o37
3i5o
3263
57
3
4393
4497
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47o5
48o9
49:3
56
3
3376
3488
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37i4
3827
3940
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4
5017
5l2I
5225
5329
5433
5537
55
4
4o53
4i67
4280
4393
45o6
46i9
55
5
5642
5746
585o
5954
6059
6i63
54
5
4732
4846
4959
5072
5i85
5299
54
6
6267
6372
6476
658o
6685
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53
6
54i2
5526
5639
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5866
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53
7
6894
6998
7io3
7207
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52
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6093
62O7
6320
6434
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6661
52
8
7521
7626
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7835
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8o45
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8
6775
6889
7002
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7344
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9
8149
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9
7458
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8027
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10
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8883
8988
9o93
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93o3
49
10
8142
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8484
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8712
49
ii
94o8
95i3
9618
9723
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1 1
8826
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9o55
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12
10 680039
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10.720199
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1619
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1 346
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1936
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39
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5267
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39
21
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5966
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38
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5731
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38
22
6392
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6427
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37
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7124
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7706
36
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35
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35
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34
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34
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6428
6539
7
52
7809
793o
8o52
8174
8295
8417
7
53
665o
6761
6873
6984
7°95
7207
6
53
8539
8661
8782
89o4
9026
9i48
6
54
73i8
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754i
7653
7764
7876
5
54
9270
9392
95i4
9636
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9880
5
55
7987
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8211
8322
8434
8546
4
55
io.75ooo2
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0247
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0491
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4
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8658
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8881
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3
56
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1225
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3
57
9329
944i
9553
9665
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2
$7
1470
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1715
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1961
2o83
2
58
10.710001
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58
2206
2329
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2820
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0786
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IOII
1123
1235
0
59
2943
3o66
3i89
33i2
3435
3558
O
60"
50"
40"
30"
20"
10"
d
60"
50"
40"
30"
20" | 10"
.
Co-tangent of 1 1 Degrees.
.3
s
Co-tangent of 10 Degrees.
3
p p* t$ 1" 2// 3" 4" 5" 6// 7" 8'' 9"
. ( 1" 2" 3" 4" 5" 6" 7" 8" 9"
irt} 11 22 32 43 54 65 75 86 97
in\ 12 23 35 47 59 70 82 94 106
104
LOGARITHMIC SINES.
1
Sine of 80 Degrees.
a
Sine of 6 1 Degrees.
M
0"
10"
20"
30"
40"
50"
*
0" 10" 3)» ' 30"
50"
o
9.993351
3355
3359
3363
3366
3370
59
0
9.99462o 4623 4627 463o 4633
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59
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3374
3377
338i
3385
3389
3392
58
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58
2
3
3396
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3422
34o3
3426
34o7
3429
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3433
34i4
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2
3
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468o|4683 4686 46904693
4676
4696
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56
4
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3444
3448
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3455
3459
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4
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3462
3466
3470
3473
3477
348i
54
5
4720 4723 4726 4729
4733
4736
54
6
3484
3488
3492
3495
3499
35o3
53
6
4739 4743 4746 474g 4752
4756
53
7
35o6
35io
35i4
35i7
352i
3525
52
7
4759!4762
4766
47694772
4776
52
8
3528
3532
3536
3539
3543
3547
5i
8
477u 47S-
4785
4795
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9
355o
3554
3558
356i
3565
3569
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9
4798 4802
48o5
48o8
48i2
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10
9.993572
3576
358o
3583
3587
359i
49
10
9.9948i8
4821
4825
4828483i
4834
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3594
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36o9
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484 1
4844
4848485i
4854
48
12
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36233627
363i
3634
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12
4857
486i
4864
4867
487o
4874
47
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3645
3649
3652
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488-714890
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3674 3678
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44
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43
16
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17
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3764
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18
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4977
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4984
4987
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19
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20 9.993789
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39
20
9.995oi3
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5022
5o25
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39
21
38n
38i4
38i8
3822
3825
3829
38
21
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38
22
3832
3836
384o
3843
3847
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37
22
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23
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24
3875
3879
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24
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5 1 02
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35
25
3897
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39o4
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39u
39i4
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25
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5l 12
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26
3918
392i
3925
3928
3932
3936
33
26
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5i43
33
27
3939
3943
3946
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3957
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27
5i46
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28
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28
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29
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3o
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29
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29
3i
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4o34
4o38
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28
3i
5222
5225
5228
5232
5235
5238
28
32
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27
32
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5-244
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36
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58
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58
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5732
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59
46oo
46o3
46o7
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0
59
5735 5733 574i 5744 5747 575o
0
60"
50"
40"
30" 20"
10"
S3
60" .50" 40" 30" 20" 10"
.
Co-sine of 9 Degrees.
§
Co-sine of 8 Degrees.
m
5" 6" 7" 8" 9"
p p A 1" 2" 3" 4" 5" 6" 7" 8" y '
P.PartJ Q l l l
22233
in\ 0 1 1 1 2 2 2 3 3
LOGARITHMIC TANGENTS.
105
.5
Tangent of 80 Degrees.
d
Tangent of 81 Degrees.
2
0"
10"
20"
30"
40" | 50"
*
0" 10" | 20"
30" 1 40" i 50" j
o
10- a5368i
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60" i 50" j 40" 30" | 20" i 10"
,
Co-tangent of 9 Degrees
i
Co-tangent of 8 Degrees. 3
P Pa t5 *" 2" 3// 4" 5" 6" 7" 8// 9'
J 13 26 39 52 65 78 91 103 116
. ( 1" 2" 3" 4" 5" 6" 7" 8" 9"
in) 14 29 43 58 72 86 101 115 130
00
LOGARITHMIC SINES.
g Sine of 82 Degrees.
a
Sine of 83 Degrees.
I
0" 1 10" 20"
30"
40"
50" |
s
0" 10" j 2u i )
50"
o
9.995753
5756
5759
5762
5765|576859
O
9.996751 6753 6756,675* 6761
6764
59
2
577i
5788
5773
579i
5776
5794
5779
5797
5782578558
58oo58o357
I
2
6766;6769 677i 67746777
67826784678767896792
6779
6795
58
5?
3
58o6
58o9
58i2
58i5
58i8
582i
56
3
6797 6800 6802 68o5 6807
6810
56
4
5823
5826
5829
5832
5835
583855
4
68i268i5 6818 682.
6825
55
5
584i
5844
5847
585o
5853
585654
5
6828;683o 6833 6835 6838
684i
54
6
5859
5862
5864
5867
587o
587353
6
6843 6846 6848:685i
6853
6856
53
7
5876
5879
5882
5885
5888
589ii52
7
6858,686i .6*63 6866
6869
687i
52
8
5894
5897
5899
59O2
59o5
59o8
5i
8
6874687r
6884
6886
5i
9
59n
59i4
59i7
5920
5923
5926
5o
9
6889 689 1 689 .
6899
69oi
5o
10
9.995928593i
5934
5937
594o
5943
49
10
9.9969o4;69o6 6909 69i2
6914
69i7
49
ii
5946 5949
5952
5954
5957
5960
48
ii
69i9'6922 6924 6927
6929
6932
48
12
i3
5963
5980
5966
5983
59695972
5986 5989
5975 5978
5992j5995
47
46
12
i3
69346937
6949 6952
6939 6942
6954 6957
6944
6959
6947 47
696246
i4
5998
6001
6oo36oo6
6009 6012
45
i4
6964
6967
6969
6972
6974
697745
i5
6oi5
6018
6021
6023
6026,6029
44
i5
6979
6982
6984
6987
6989
6992 44
16
6o32
6o35
6o38
6o4i
6043^046
43
16
6994
6997
6999
7002
7oo4
7oo7
43
17
6049
6o52 6o55
6o58
6061
6o63
42
17
•7009
701 1
7014
7oi6
7or9
7O2I
42
18
6066 6069 6072
6o75
6o78 6081
4i
18
-7024
7026
7029
7o3i
7o34
7o36
4i
'9
6o83 6086 6089
6o92
6095 6098
4o
19
7°39
704 1
7044
7o46
7o49
7o5i
4o
20 9.996100 6io3 6106
6io9 61 i2'6n5
39
20
9.997053
7o56
7o58
7o6i
7o63
-7066
39
21
6117
61206123
6126 6i29 6i3i
38
21
•7068
7071
7o73
7o76
7o78
7o8o
38
22
6i34
6i37
6i4o 6i43
6i466i48
37
22
7o83
7o85
7088
7o9o
7o93
7o95
37
23
6i5i
6i546i57
6160
6162
6i65
36.
2')
7098
7100
7102
7io5 7io7
7I 10
36
24
6168
6171
6i74
6177 6179 6182
35
24
71 12
7n5
7117
7120
7I22
7124
35
25
6i85
6188
6i9i
619 "> 6196 6199
34
25
7127
7I29
7i32
7i34
7i37
7i39
34
26
6202
62o5
6207
6210
62i3 6216
33
'26
7144
7i46
7149
7i5i
7i54
33
27
6219
6221
6224
6227
62306232
32
-7
7^56
7i58
7161
7i63 7166
7i68
32
28
6235
6238
6241
6244
6246 6249
3i
28
7170
7173
7i75
7178 7180
-7182
3i
29 6252 6255
6257 6260,6263 6266
3o
*9
7i85
7^7
7190
7192
7i94
7i97
3o
3o 9.996269 62-71
62746277:62806282
29
Jo
9.997199
72O2
7204
7206
72O9 72I I
29
3i
62856288
6291
6293.62966299
28
3i
7214
72l6
7218
7221
7223
•7226
28
32
63o2
63o5
63o763io63i363i6
27
32
7228
723o
7233
7235
7238
-7240
27
33
63i8
632i
6324 6327 6329 6332
26
33
7242
7245
7247
7249
7252
7254
26
34 6335
6338
634o,6343 6346 6349
25
34
7257
7259
7261
7264
7266
-7268
25
35
635!
6354
6357
63596362!6365
24
35
7271
7273
7276
7278
7280
7283
24
36
6368
6370
6,373
63766379638i
23
36
72.85
72S7
7290
7292
7294
7297
23
37
6384
6387
639o6392 6395 6398
22
37
7299
73o4
73o6
73o9
73ii
22
38
64oo
64o3
64o6
6409 64 1 1
64i4
21
38
73i3
73i6
73i8
7320
7323
7325
21
.39
6417
64i9
6422
6425 6428 643o
2O
39
7327
733o
7332
7334
7337
7339
2O
4o 9.996433
6436
6438
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6447
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4o
9 .997341
7344
7346
7348
735i
7353
19
4 1 6449
6452
6455
645764606463
18
4i
7355
7358
736o
7362
7365
7367
18
42 6465
43 6482
6468
6484
6471 6474 647616470.
6487 649o 6492'6495
17
16
42
43
7369
7383
7372
7386
7374
7376
739o
7379
7393
738i
7395
17
16
44 6498
65oo
65o3 65o6 65o8
65n
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44
7397
7399
7402
74o4
74o6
74o9
1 5
45 65i4
6517
65i9 6522 6525
6527
i4
45
74 1 1
74i3
74i6
74i8
7420
7423
i4
46
653o
6533
6535
6538654i
6543
i3
46
7425
74^7
7429
7432
7434
7436
i3
47
6546
6549
655i 65546557
6559
12
47
7439
/44i
7443
7445
7448
745o
12
48
6562
6565
6567
657o6573
6575
I I
48
7452
7455
7457
7459
746 1
7464
II
49
6578
658o
6583^586,6588
659i
IO
49
7466
7468
747i
7473J7475
7477
IO
5o
9.996594
6596
6599 6602:6604
660-7
9
5o
9.997480
7482 7484
7487 7489
749i
9
5i
6610
6612
66i5 6618 6620
6623
8
5i
7493
7496 7498
75oo
75o2
75o5
8
52
6625
6628
663i
66336636
6639
7
52
7507
7509
75ii
75i4
75x6
75i8
7
53
664 1
6644
6646
66496652
6654
6
53
7520
7523
7527
753o
7532
6
54
6657
6660
6662
6665 6667
667o
5
54 7534 7536
7539
754i
7543
7545
5
55
56
57
6673
6688
6704
6675
669i
6707
6678^681 6683
6694 6696 6699
670(^)6712 6714
6686
67oi
6717
4
3
2
55
56
57
7547755o7552|75547556
756i 75637565 7568;757o
757475777579758i7533
7559
7572
7585
4
3
2
58
6720
6722
6720
6727 6730
6733
I
58
7588 759o 7592 7594 7597 7599 i
59
6735
6738
6740
6743 6746
6748
0
59
7601 760^ -6o5 7608 7610 7612 o
60"
50"
40"
30" ; 20"
10"
c
60" 50" 40" ! 30" 20" i 10"
Co-sine of 7
Degrees.
s
Co-sine of 6 Degrees. £
( 1" 9" <* 4'
1 T» T» * 1 * -- ' *
£" 6" 7"
8" 9"
( l" 2" 3" 4" 5" 6" 7" 8
P.PartJ | ! i |
1 2 2
2 2
irt} 00111122 '
LOGARITHMIC TANGENTS.
107
1
Tangent of 82 Degrees.
.=
Tangent of 83 Degrees.
m
0" | 10"
20"
30"
40"
50"
•"
0" 10" 20" | 30" | 40"
50"
o
10.852197
235o
25o3
2656
2809
2962
5o
O
10.910856
io3o
1205
i379ii553
1727
59
i
3n5
3268
3421
3575
3728
388i
58
I
I902
2076
225l
2426
2600
2775
58
2
4o34
4i88
434:
4495
4649
4802
5?
2
295o
3i253aoo
3475
365o
3825
57
3
4g56
5no
5263
54i7
557i
5725
56
3
4ooo
4i76435i
4527
4?02
4878 56
4
5879
6o33
6i87
634i
6496
665o
55
4
5o53
5229
54o5
558i
5757
5933
55
5
68o4
6958
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7422
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54
5
6io9
6285
646 1
6638
68 1 4
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54
6
773i
7886
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8i95
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53
6
7i67
7343
7520
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53
7
8660
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9125
9280
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52
7
822-7
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2i38
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49
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2395
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2708
2864
3020
3i77
48
II
2495
2673
2852
3o3i
3210
3389
48
12
3333
3490
3647
38o3
3960
4117
4?
12
3568|3747
3926
4io5
4285
4464
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4274
443i
4588
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5o59
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1 3
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4823
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5542
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52i6
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5722
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6161
63 1 9
6476
6634
6792
695o
44
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68o3
6984
7i64
7345
7525
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44
16
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7265
7423
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7739
7898
43
16
7887
8068
8249
843o
8611
8792
43
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8o56
8214
8372
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8689
8848
42
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42
18
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9166
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18
10.930062
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33
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9.427
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32
27
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32
28
8623
8785
8947
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9271
9433
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28
10.941100
1286
1472
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1 845
2O32
3i
29
9596
9758
9921
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3o
29
2219
2406
2592
2779
2966
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10.880571
0734
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2 9
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334i
3528
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4277
29
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1 548
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28
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4465
4653
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5o28
52i6
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28
32
2528
2691
2855
3oi8
3i82
3345
27
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5593
578i
5969
6i57
6346
6534
2-7
33
35o9
3673
3837
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4i65
4329
26
33
6723
6912
7100
7289
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26
34
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4657
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53i4
25
34
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25
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5479
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24
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22
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2991
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21
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20
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10.890441
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1 106
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10.960515
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1099
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7312
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1 684
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2074
2270
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2661
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748i
765o
7819
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47
2856
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3835
12
48
8496
8665
8834
9004
9i73
9343
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48
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4227
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49
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9852
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5209
5406
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0702
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1 384
9
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6588
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7180
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9
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1-724
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2066
2236
2407
8
5i
7575
7773
7971
8169
8367
8565
8
52
2578
2749
2920
3091
3262
3433
7
52
8763
8961
9i59
9358
9556
9755
7
53
36o5
3776|3947
4119
4290
4462
6
53
9954
.i5a
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54
4633
48o5!4977
5i49
5320
5492
5
54
10.971148
1 347
1 546
i?46
1945
2i45
5
55
5664
58376oo9
6181
6353
6526
4
55
2345
2545
2745
2945
3i45
3345
4
56
5?
6698
7734
6871 ho43
790718080
7216
8253
7388
8426
756i
8599
3
2
56
57
3545
4749
3746 3946
495o5i5i
4i47
5352
4347
5553
4548
5755
3
2
58
8772
89469119
9292
9466
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58
5956j6i576359
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6762
6964
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59
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59
7i66!7368 757o
7773 7975
8i77
O
60"
50"
40"| 30" 20"
10"
c
60" 50" 40" 30" 20" 10"
a
Co-tangent of 7 Degrees.
s
Co-tangent of 6 Degrees.
§
.< 1" 2" 3" 4" 5" 6" 7" 8" 9"
I 16 33 49 65 81 98 114 130 146
. C 1" 2" 3" 4" 5" 6" 7" 8" 9"
in\ 19 37 56 75 94 112 131 150 168
108
LOGARITHMIC SINES.
.5
Sine of 84 Degrees.
.5
Sine of 85 Degrees.
a
0" ! 10" | 20" ' 30" 1 40" 50"
a
0" 10"
20"
30" 40"
50"
(
9.997^14 7617 7619 7621/7623 7626
59
o 9.998344:8346
8348
835o'8352
835j
59
I
762817630 7632 7634:7636 7639
58
8355 8357
8359
836il8363
8364
58
2
3
764 J
764376457647:76507662
7656 76687661 '76637665
56
2
8366 8368
83778379
837o
838i
83728374
83838385
8375
8386
56
4
7667
7669 7672 7674:7676 7678
55
i
8388
8390
8392
8394
8395
8397
55
5
768o
7682 7686 7687 7689 7691
54
[
8399
84oi
84o3
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22
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23
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24
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26
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27
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8268 8270 8272 8273 8276
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54
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54
8887
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55
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8290 8292 8294 8296 8298
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8923 8926 8926 892-7 8929 8930
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8932 8933 8935 8936 8938 8939
O
60" ] 50" 40" 30" 20" 10" ; .
60" 50" 40" 30" 20" 10"
Co-sine of 5 Decrees. a
Co-sine of 4 Degrees. a
P Part 5 l" ~" 3" 4" 5" 6" 7" 8" 9// »P" 2" 3// 4" 5// 6" 7" 8" *"
irtj 001111122;; irtj 0 0 0 1 1 1 1 1 1
LOGARITHMIC TANGENTS.
109
1
Tangent of 84 Degrees.
j
Tangent of 85 Degrees. |
X
0"
10"
20"
30"
40"
50"
a
0"
10"
20"
30"
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0
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60" 50"
40"
30"
20"
10"
.
60" 50" 40" 30" | 20" 10"
j
Co-tangent of 5 Degrees.
a
Co-tangent of 4 Degrees.
s
P PartJ 1//2" 3" 4" 5" G// 7" 8// 9"
( 1" 2" 3" 4" 5" 6" 7" 8" 9"
P. Part ^ 27 54 81 log 135 162 188 215 242
I 10
LOGARITHMIC SINES.
1
Sine of 86 Degrees.
«•
Sine of 87 Degrees.
H
0"
10" 1 20"
! 30" | 40"
50"
s
0"
10"
20"
30" | 40"
50"
0
I
2
3
4
9.998941
8968
8967
8976
8942|894489458947
8961 895389648955
89608961 89638964
8969 8970 8971 8973
8977 8979 89808982
8948
8967
8966
8974
8983
69
58
ll
55
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9.999404
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9418
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9432
94o7
94i3
94s6
9433
94o8
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9427
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94i5
9428
9435
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94i6
9423
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9436
59
58
56
55
5
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8986 8987 8989 899o
8992
54
5
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9438
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9oi5 9oi6J9oi7
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9464 9465
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9477
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44
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60"
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30" 20"
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.
Co-sine of 3 Degrees.
§
Co-sine of 2 Degrees.
i
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1 1 1
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in\ 000001111
LOGARITHMIC TANGENTS.
1 1 1
.5
Tangent of 86 Degrees.
d
Tangent of 87 Degrees.
*%
0"
10"
20"
30"
40"
50"
2
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20"
30"
40"
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0
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60"
50" 40"
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60" 50" | 40" 30" 20"
10"
JL
Co-tangent of 3 Degrees.
i
Co-tangent of 2 Degrees.
s
p p < 1" 2" 3" 4" 5" 6" 7" 8" 9" 1 ( 1" 2" 3" 4" 5" 6" 7" 8" 9"
} 35 69 104 138 173 207 242 276 311 | ir \ 48 97 145 193 242 290 338 387 435
112
LOGARITHMIC SINES.
1
Sine of 88 Degrees.
.a
Sine of 89 Degrees.
•
0"
10"
20"
30"
40"
50"
m
0"
10"
20"
30"
40"
50"
o
9-999735
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983i
983i
9832|9832
9833
9834
35
24
9976
9976
9977
9977
9977
9977
35
25
9834
9835
9835|9836
9836
9837
34
25
9977
9978
9978
9978
9978
9979
34
26
9838
9838
9839'9839
984o
984o
33
26
9979
9979
9979
9979
998o
9980
33
27
984i
9842
9842'9843
9843
9844
32
27
998o
9980
9980
9981
998i
9981
32
28
9844
9845
9846i9846
9847
9847
3i
28
998i
9982
9982
9982
9982
3i
29
9848
9848
9849!9849
985o
985i
3o
29
9982
9983
9983
9983
9983
9983
3o
3o
9.99985i
9852
9852:9853
9853
9854
29
3o
9.999983
9984
9984
9984
9984
9984
29
3i
9854
9855
98569856
9857
9857
28
3i
9985
9985
9985
9985
9985
9985
28
32
9858
9858
9859*9859
986o
986o
27
32
9986
9986
9986
9986
9986
9986
27
33
986i
9861
9862 9863
9863
9864
26
33
9987
9987
9987
9987
9987
9987
26
34
9864
9865
9865 9866
9866
9867
25
34
9988
9988
9988
9988
9988
9988
25
35
9867
9868
98689869
9869
9870
24
35
9989
9989
9989
9989
9989
9989
24
36
987o
9871
9871 9872
9872
9873
23
36
9989
999°
9990
999°
999°
999°
23
37
9873
9874
98749875
9875
9876
22
37
999°
999°
999 *
9991
9991
9991
22
38
9876
9877
9877,9878
9878
9879
21
38
999 i
9991
9991
9992
9992
9992
21
39
9879
9880
9880 9881
988i
0882
2O
39
9992
9992
9992
9992
9992
9993
2O
4o
9.999882
9883
98839884
9884
9885
'9
4o
9-999993
9993
9993
9993
9993
9993
*9
4i
9885
9886
98869887
9887
9888
18
4i
9993
9993
9994
9994
9994
9994
18
42
9888
9889
9889 9890
989o
9891
17
42
9994
9994
9994
9994
9994
9995
17
43
44
45
9891
9894
9897
9892
9894
9897
9892 9892 9893
989598959896
9898 9898 9898
9893
9896
9899
16
i5
i4
43
44
45
9995
9995
9996
9995
9995
9996
9995
9995
9996
9995
9996
9996
9995
9996
9996
9995
9996
9996
16
i5
i4
46
9899
9900
99oo 99oi
99oi
9902
i3
46
9996
9996
9997
9997
9997
9997
i3
47
99O2
99°3
99o3 9903 9904
99o4
12
47
9997
9997
9997
9997
9997
9997
12
48
99o5
99o5
9906 9906 9906
99°7
II
48
9997
9997
9997
9998
999s
9998
II
49
99°7
9908
9908 9909
99°9
99io
IO
49
9998
9998
9998
9998
9998
9998
10
5o
9-999910
9910
9911 9911
9912
99I2
9
5o
9-999998
9998
9998
9998
999s
9998
9
5i
52
99i3
99i5
99I3
99i5
99139914
9916 9916
99i4
9917
99i5
99i7
7
5i
52
9999
9999
9999
9999
9999
9999
9999
9999
9999
9999
9999
9999
8
7
53
99i8
99i8
9918
9919
9919
9920
6
53
9999
9999
9999
9999
9999
9999
6
54
992O
9920
9921
9921
9922
9922
5
54
9999
9999
9999
9999
9999
5
55
9922
9923
9923
9924
9924
9924
4
55
o.oooooo
oooo
oooo
oooo
oooo
oooo
4
56
9925
9925
9926
9926
9926
9927
3
56
oooo
oooo
oooo
oooo
oooo
oooo
3
57
9927
9927
9928
99289929
9929
2
57
oooo
oooo
oooo
oooo
oooo
oooo
2
58
9929
9930
993o
993i 993i
993i
I
58
oooo
oooo
oooo
oooo
oooo
oooo
I
59
9932
9932
9932
9933|9933
9933
O
59
oooo
oooo
oooo
oooo
oooo
oooo
0
60"
50"
40"
30" 20"
10"
.
60"
50"
40"
30"
20"
10"
d
Co-sine of 1 Degree.
S
Co-sine of 0 Degree.
.3
s
.( 1" 2" 3" 4" 5" 6" 7'' 8" 9"
1 $0000 00 001
p p .< 1" 2" 3" 4" 5" 6" 7" 8" 9"
irl Jo ooo oo ooo
LOGARITHMIC TANGENTS.
1
Tangent of 88 Degrees.
P. Part
7Z
0"
10"
20"
30"
40"
50"
tol".
o
11.456916
ii .457520
ii. 458i25
II.45873I
n.45|338
11.459945
59
60.6
I
46o553
46n63
46i773
462383
46^905
4636o8
58
61.1
2
464221
464836
46545i
466067
466684
4673o2
57
61.6
3
467920
46854o
469160
469782
47o4o4
47I027
56
62.2
4
47i65i
472276
472902
473528
474i56
474785
55
62. 7
5
4754i4
476044
476676
4773o8
4779^1
478575
54
63.3
6
479210'
479846
480482
481120
481759
482398
53
63.8
7
483o39
48368o
484323
484966
4856n
486256
52
64.4
8
486902
487549
488198
488847
489497
490148
5i
65.o
9
490800
49i453
492107
492762
493418
494o75
5o
65.5
10
H.494733
11.495392
ii .496052
11.496713
11.497375
11.498038
49
66.1
ii
498702
499367
5ooo33
500700
5oi368
5o2o37
48
66.8
12
502707
5o3378
5o4o5i
5o4724
5o5398
5o6o73
47
67^4
i3
506750
507427
5o8io6
5o8785
5o9466
5ioi48
46
68.0
i4
5io83o
5u5i4
512199
5i2885
5i3572
514260
45
68.6
i5
5i4g5o
5i564o
5i633i
5i7o24
517717
5i84i2
44
69.3
16
519108
519805
52o5o3
52I2O2
521903
522604
43
7o.o
J7
523307
524oio
5247i5
525421
526128
526837
42
7° -7
18
527546
528257
528969
529682
53o396
53iin
4i
7i.i
'9
53i828
532545
533264
533984
5347o5
535428
4o
72.1
20
n.536i5i
11.536876
11.537602
ii.53833o
ii. 539058
11.539-788
39
72.8
21
54o5i9
54i25i
541984
5427i9
543455
544192
38
73.5
22
54493o
54567o
5464n
547i53
547896
54864i
37
74.3
23
549387
55oi34
55o883
55i632
552384
553i36
36
75.0
24
553890
554645
5554oi
556i59
556918
557678
35
75.8
25
55844o
559203
559967
56o733
56i5oo
562268
34
76.6
26
563o38
563809
56458i
565355
566 i 3o
5669O7
33
77.5
27
567685
568464
569245
57OO27
57o8n
57i596
32
78.3
28
572382
573i7o
573959
57475o
575542
576336
3i
79.i
29
577I3i
5779*8
578726
579525
58o326
58ii28
3o
80.0
3o
11.581932
n.582737
n.583544
n.584353
n.585i63
n.585974
29
80.9
3i
586787
5876-01
5884i7
589235
590054
5908-74
28
81.8
32
591696
592520
593345
594172
595000
59583o
27
82.8
33
596662
597495
SgSSSo
599166
6oooo4
6oo844
26
83.7
34
6oi685
602528
603372
604218
6o5o66
605915
25
84. 7
35
606766
6o76i9
608474
609330
6ioi87
6iio47
24
85.7
36
611908
6i277i
6i3636
6i45o2
6i537o
616240
23
86.7
3?
617111
61-7985
618860
6i9737
620615
621496
22
87.8
38
622378
623262
624147
625o35
625924
626815
21
88.8
39
627708
628603
629500
630399
631299
6322OI
2O
89.9
4o
n.633io5
ii .634oi2
ii .634919
11.635829
n.63674i
n.637655
I9
91.1
4i
638570
639488
640407
64i329
642252
643i77
18
92.2
42
644io5
645o34
645965
646899
647834
64877i
J7
93.4
43
649711
65o652
65i595
65254i
653488
654438
16
94.6
44
655390
656343
657299
658257
6592i7
6601-79
i5
95.9
45
66u44
662110
663079
664o5o
665o23
665998
i4
97-2
46
666975
667<}55
668936
669920
67O9O7
6-71895
i3
98.5
4?
672886
673579
674874
675871
676871
677873
12
oo. 8
48
678878
679885
680894
681905
682919
683935
II
loi.S
49
684954
685975
686998
688024
689052
690083
IO
102.7
5o
ii .691 116
11.692151
ii .693189
ii .694230
11.695273
11.696318
9
104.2
5i
697366
698417
699470
700526
7oi584
-702645
8
105.7
52
703708
704774
705843
706914
707988
•709065
7
107.2
53
710144
•711226
712311
713398
714488
7i558i
6
108.9
54
716677
7i7775
718876
719980
721087
-722196
5
no. 5
55
723309
724424
725542
726663
727787
-728914
4
112 2
56
73oo44
731176
7323i2
73345i
734592
735737
3
ii4-o
5?
736885
738o35
739i89
74o346
74i5o6
-742669
2
ii5.8
58
743835
745oo4
746177
747352
74853i
74971 3
I
117.7
59
750898
752087
753279
754474
755672
756874
0
119.7
60"
50" 40"
30" 20" 10"
.
Co-tangent of 1 Degree.
§
1
114
AUXILIARY TABLE FOR SINES, & c.
1
1
0 Degree.
1
1
1 Degree.
I
1
log. sin. A—
log. A".
log. tan. A —
log. A".
log. cot A+
log. A".
1
i
log. sin. A —
log. A".
log. tan. A—
log. A".
log. cot A+
log. A".
o
0
4.685575
4.685575
i5.3i4425
60
36oo
0
4.685553
4.685619
i5.3i438i
60
60
I
575
575
425
59
366o
I
552
620
38o
59
120
2
575
575
425
58
3720
2
55i
622
378
58
1 80
3
575
575
425
57
378o
3
55i
623
377
57
240
4
575
575
425
56
384o
4
55o
625
375
56
3oo
5
575
575
425
55
3900
5
549
627
373
55
36o
6
575
575
425
54
3960
6
548
628
372
54
420
7
575
575
4*5
53
4020
7
547
63o
37o
53
48o
8
574
576
424
52
4o8o
8
547
632] 368
52
54o
9
574
576
424
5i
4i4o
9
546
6331 36?
5i
600
10
4.685574
4.685576
i5.3i4424
5o
4200
10
4.685545
4.685635
i5.3i4365
5o
660
ii
574
576
424
49
4260
ii
544
637
363
49
720
12
574
577
423
48
4320
12
543
638
362
48
780
i3
574
577
423
47
438o
1 3 542
64o
36o
47
84o
i4
574
577
423
46
444o
i4
54i
642
358
46
900
i5
573
578
422
45
45oo
i5
54o
644
356
45
960
16
573
578
422
44
456o
16
539
646
354
44
IO2O
r7
573
578
422
43
4620
17
539
647
353
43
I080
18
573
579
421
42
468o
18
538
649
35i
42
n4o
i9
573
579
421
4i
474o
'9
537
65i
349
4i
1 200
20
4.685572
4.68558o
i5.3i442o
4o
48oo
20
4.685536
4.685653
i5.3i4347
4o
1260
21
572
58o
420
39
486o
21
535
655
345
39
1320
22
572
58i
4i9
38
4920
22
534
657
343
38
i38o
23
572
58i
4i9
37
4980
23
533
659
34i
37
i44o
24
57i
582
4i8
36
5o4o
24
532
661
•339
36
i5oo
25
57i
583
417
35
5ioo
25
53i
663
337
35
i56o
26
57i
583
4i7
34
5i6o
26
53o
665
335
34
1620
27
57o
584
4i6
33
5220
27
529
668
332
33
1680
28
57o
584
4x6
32
5280
28
527
670
33o
32
1740
29
57o
585
4x5
3i
534o
29
526
672
328
3i
1800
3o
4.685569
4.685586
i5.3i44i4
3o
54oo
3o
4.685525
4.685674
i5.3i4326
3o
1860
3i
569
587
4x3
29
546o
3i
524
676
324
29
1920
32
569
587
4x3
28
5520
32
523
679
321
28
1980
33
568
588
4X9
27
558o
33
522
681
3i9
27
2O4O
34
568
589
4n
26
564o
34
521
683
3i7
26
2IOO
35
567
59o
4io
25
5700
35
520
685
3i5
25
2l6o
36
567
59i
4o9
24
576o
36
5i8
688
312
24
2220
37
566
592
4o8
23
5820
3?
5i7
690
3io
23
2280
38
566
593
407
22
588o
38
5i6
693
3o7
22
234o
39
566
593
407
21
5940
39
5i5
695
3o5
21
s4oo
4o
4.685565
4.685594
i5.3i44o6
2O
6000
4o
4.6855i4
4.685697
i5.3i43o3
2O
2460
4i
565
595
4o5
'9
6060
4i
5I2
700
3oo
'9
2520
42
564
596
4o4
18
6120
42
5n
702
298
18
258o
43
564
598
4O2
17
6180
43
5io
7o5
295
17
2640
44
563
599
4oi
16
6240
44
5o9
707
293
16
2700
45
562
600
4oo
i5
63oo
45
5o7
710
290
i5
2760
46
562
601
399
i4
636o
46
5o6
7i3
287
i4
2820
47
56i
602
398
i3
6420
47
5o5
7i5
285
i3
2880
48
56i
6o3
397
12
648o
48
5o3
718
282
12
2940
49
56o
6o4
396
II
654o
49
502
720
280
I I
3ooo
5o
4.68556o
4.6856o5
i5.3i4395
10
6600
5o
4.6855oi
4.685723
i5. 314277
10
3o6o
5i
559
607
393
9
6660
Si
499
726
274
9
3l20
52
558
608
392
8
6720
52| 498
729
271
8
3i8o
53
558
6o9
39i
7
6780
53
497 73i
269
7
8240
54
557
6x1
389
6
684o
54
495
734
266
6
33oo
55
556
612
388
5
6900
55
494
737
263
5
336o
56
556
6i3
387
4
6960
56 492
740
260
4
3420
57
555
6i5
385
3
7020
57
491
743
257
3
348o
58
554
616
384
2
7080
58
490
745
255
2
354o
59 554
618
382
I
7140
59
488
748
252
I
'log. cos. A —
log. eot A—
log. tan, A-f
*
log. co§. A — log. cot A —
log. tan. A+
•
log. c. A".
log. c. A".
log. c. A."
1
log. c. A".
log. c. A".
log. c. A".
•
s
89 Degrees.
.9
53
88 Degrees.
.3
LOGARITHMIC TANGENTS,
i
Tangent of 89 Degrees.
P. Part
H
0"
10" 20"
30"
40"
50"
tol".
0
11.758079
11.759287
II .760498
ii .761714
II .762932
n.764i54
59
121.7
i
765379
766608
767840
769076
77o3i5
77i558
58
123.8
2
772805
774o55
7753o8
776566
777826
779°9I
57
125.9
3
780359
78i63i
782907
784186
785470
786757
56
128.1
4
788047
789342
•790641
791943
79325o
79456o
55
i3o.4
5
79^874
797192
7985i5
799841
801171
8o25o6
54
132.8
6
8o3844
805187
8o6534
807885
809240
810600
53
x55.3
7
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3o46
0718
8465
6298
4228
7
54
57o9
3I73
o658 8173
5730
334o
ioi3
8761
6596
4528
6
55
6000
3465
o949 8465
6o23
3634
i3o8
9o58
6894
4828
5
56
6291
3756
1241 8758
63i6
3928
1604
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5127
4
57
6582
4o47
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66o9
4222
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6873
4338
1824
9342
69O2
45i6
2I94
9948
7788
5727
2
59
7164
463o
2116
9635
7i96
48io
2489
i 40244
8086
6027
I
89°
88°
87°
86°
85°
84°
83°
82° 81° '
80°
Natural Co-tangents.
*
to r'>85
4.85
4.86
4.87
4.88
4-89
4.9i
4-93
4-96
4.98
lib
NATURAL SINES.
i
10°
11°
12°
13°
14°
15°
16°
17°
18°
19°
o
i73648
190809
2079I2
22495l
24l922
2588i9
275637
292872
3o9oi7
325568
60
i
3935
1095
8196
5234
2204
9ioo
59i7
265o
9294
5843
59
2
4221
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848 1
55i8
2486
938i
6i97
2928
957°
6118
58
3
45o8
1666
8765
58oi
2769
9662
6476
3206
9847
6393
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4
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9o5o
6o85
3o5i
9943
6756
3484
3ioi23
6668
56
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2237
9334
6368
3333
260224
7o35
3762
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55
6 5367
2522
96l9
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73i5i 4o4o
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5653
2807
99°3
6935
3897
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7493
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5^39
3o93
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1 347
8i53
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8042
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10
176512
i93664
210756
227784
s44743
261628
278432
295l52
311782
3283i7
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6798
3949
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8068
0025
I9o8
8712
543o
2o59
8592
49
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7o85
4234
13-25
835i
53o7
2i89
899i
57o8
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0-789
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179375
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2i3599
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3i4545
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9661
6802
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8208
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i338
39
22
9947
7087
4i67
1182
8126
4995
i783
8486
5o97
1612
38
23
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7372
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i465
84o8
5276
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8763
5373
i887
37
24
0519
7657
4735
1748
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5556
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5649
2161
36
25
o8o5
7942
5oi9
2031
8972
5~837
2620
93i8
5925
2435
35
26
1091
8228
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9253
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2900
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6201
27IO
34
27
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5588
2597
9535
6397
3i79
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28
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29
1950
9o83
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29
32
2808
9938
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27
34
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8359
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4903
26
35
3665
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7859
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864o
54io
2093
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1078
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1 363
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5425
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6000
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1715
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2000
8753
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1990
8464
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222116
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762-7
4668
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8538
5358
2094
8740 5293 1747 i
79°
78°
77°
76°
75° 74°
73° ; 72° 71° 70° .
1
Natural Co-sines.
£#4.77 | 4.75
4.73
4.7i
4.69
4.67
4.65
4.62
4.6o
4.57
NATURAL TANGENTS.
1 19
J
I
10°
11°
12°
13°
14°
15°
16°
17°
18°
19°
0
i76327
i9438o
212667
23o868
249328
267949
286745
3o573i
324920
344328
60
I
6627
4682
2861
1176
9637
8261
7o6o
6o4g
6241
4653
69
2
6927
4984
3i65
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7375
6367
5563
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58
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6286
3469
1788
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5885
53o4
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7827
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55
6
8l27
6192
438i
2707
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8635
764o
685o
6281
54
7
8427
6494
4686
3oi4
1492
270133
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6607
53
8
8727
6796
4990
332i
1801
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8277
6933
62
9
9028
7099
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3627
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0767
958i
8696
7817
7269
5i
10
179328
197401
216699
233934
262420
271069
289896
308914
328139
347585
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9628
77°3
59o3
4241
2729
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2902I I
9233
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12
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6208
4548
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9662
8783
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180229
83o8
6612
4855
3348
2006
0842
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9106
8563
47
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0629
8610
6817
6162
3658
2319
1168
310189
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1 5
0829
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3256
2106
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0396
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0-718
360196
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2031
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6207
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266616
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293o52
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1829
37
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2166
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3835
1938
220169
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4632
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2979
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2810
34
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9166
7687
6385
6266
4340
3625
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33
28
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2847
1084
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7997
6698
6681
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32
29
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32
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2610
1 002
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9869
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6429
26
35
6844
4967
3221
1618
2601-70
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7796
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9063
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188349
206483
224748
243167
261-723
280460
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209618
227806
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264834
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1666
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28-70
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3i88
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8
53
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26-70
2062
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54
2670
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7476
6o79
4857
3823
2991
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1996
6
55
2871
1037
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33i2
2702
2324
5
56
3i73
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9643
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4
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1 645
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7oi4
6801
4777
3955
3352
2982
3
58
3777
1949
230266
8710
7326
6116
6096
4277
3677
33i2
2
59
4078
2253 0562
9019
7637
643i
54i3
4698 4002
364i
I
79°
78° ! 77° 76°
75° 74° 73°
72° ! 71°
70°
a
Natural Co-tangents.
i
££*•«
5.o5
6.09
5.i3
5.i7
5.22
5.27
5.33
5.39
5.46
120
NATURAL SINES.
J
X
20°
21°
22°
23°
24°
25°
26°
27°
28°
29° |
o
342020
358368
3746o7
39073i
4o6737
422618
43837i
45399o
469472
484« 10
60
I
2293
864o
4876
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7002
2882
8633
425o
9728
5o64
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2
2567
8911
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1267
7268
3i45
8894
45o9
9985
53i8
58
3
2840
9i83
54i6
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34o9
9i55
4768
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5573
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9454
5685
1802
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5027
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5827
56
5
3387
9725
5955
2070
8o65
3936
9678
5286
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55
6
366o
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5545
1012
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54
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53
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6844
52
9
4479
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9!27
499o
0723
6322
1-782
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10
344752
361082
3773o2
3934o7
4o9392
425253
44o984
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472o38
487352
5o
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5o25
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757i
3675
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55i6
1245
6839
2294
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49
12
5298
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784i
3942
9923
5779
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255i
786o
48
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1896
8110
4209
4ioi88
6042
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7357
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5844
2l67
8379
4477
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63o6
2028
76i5
3o63
8367
46
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6117
2438
8649
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07i9
6569
2289
7874
3320
8621
45
16
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6832
255o
8i33
3576
8875
44
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6663
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5278
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5368
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37
24
8572
4877
1070
7i48
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8935
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460200
5624
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36
25
8845
5i48
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74i5
3369
9i98
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34
27
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1877
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1 664
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Natural Co-sines.
££4.54
4.5i
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4 45
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4.38
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NATLRAL TANGENTS.
121
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26°
27°
28°
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69°
68°
67°
66° 65° 64°
63°
62°
61°
60°
s
Natural Co-tangenls.
P. P. 5 53
5.6o
5.68
5.76
5.85
5.95
6.o5
6 16
6.28
I
6.4o
122
NATURAL SINES.
1
i
30° 31°
32°
33°
34°
35°
36°
37°
38°
39°
0
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59°
58° ! 57°
56°
55°
54° 53°
52° 51°
50°
0
Natural Co-sines.
•9
s
P.P. ,
to I".4'18
4.i3
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3.95
3.9o
3.85 1 3.8o
3.74
NATURAL TANGENTS.
123
d
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30°
31°
32°
33°
34°
35°
36°
37°
38°
39°
o
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49°
48°
47°
46°
45°
44°
43°
42° 41°
40° .
Natural Co-tangents.
*g
P. P« Q OQ
tol".8"38
8.64
8.92
9 21
9.53
0.99 1.02 I. 06
i. 10 i.i5
126
NATURAL SINES.
A
X
50C
51°
52°
53°
54°
55°
56°
57°
58°
59°
0
766044
777146
788011
798636
809017
819152
829038
83867i
848o48
857i67
60
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2
64x8
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3
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57
4
6792
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9700
9819
9688
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5
6979
8060
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9462
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8.972
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9
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39
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8818
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6868
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59
6963
7832
846o
8846
8985
8875
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7894
7017
588o
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39°
38°
37°
36°
35°
34°
33°
32°
31°
30J
s
Natural Co-sines.
i
P P. „ t
tol//3.o8
3.02
2.95
2.88 s.8i
t.75
2.68 2.60
2.53 2.46
NATURAL TANGENTS.
12
4
x
50°
51°
52°
53°
54°
55°
56°
57°
58°
59°
o
1.19175
1.23490
1.27994
1.32704
1.37638
1.42815
1.48256
1.53986
i.6oo33
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60
I
9246
3563
8071
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2
93:6
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2865
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3
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4
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1.19882
1.24227
1.28764
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1.38484
1.43703
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1.54972
1.61074
1.67530
5o
ii
9953
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8842
3592
8568
3792
9284
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1.20024
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1.55966
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1.68643
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63i8
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I
39°
38°
37°
36°
35°
34°
33°
32° 31°
30°
a
Natural Co-tangents.
P. P.
to I".1'80
1.25
i.3i
r.37
i.44
i.5i
i.59
1.68
1.78
1.88
NATURAL SINES.
1 60°
61°
62°
63°
64°
65°
66°
67° 1 68°
69°
o
866025
8-74620
882948
89ioo7
898794
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Natural Co-sines.
i
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NATURAL
GENTS.
131
j
70°
71°
72°
73°
74°
75°
76°
77°
78°
79°
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2.74748
2.90421
3.07768
3.27o85
3.4874i
3.732o5
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4.33i48
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15° ! 14°
13° 12° 11° 10°
. '
Natural Co-tangents.
to* I"'.4'35
4.8a
5.36
6.01
6. -79
7.73
8.90
10.35
12. 2O
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!
132
NATURAL SINES.
1
H
80°
81°
82°
83°
84°
85°
86°
87°
88°
89°
O
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9°
8°
7°
6°
5°
4°
3°
2°
1°
0°
c
Natural Co-sines.
i
Jo'*;.0-80
0.72
o.63
o.55
0.46
o.38
o.3o
O.2I
o.i3
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NATURAL TANGENTS.
133
j
80° 1 81°
82°
83°
84°
85°
86°
87°
88°
89°
0
5.67128 6.3i375
7.n537
8.i4435
9.5i436
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19.0811
28.6363
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9.78817
11.8262
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81.8470
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83.8435
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5.87080
6.56o55
7.42871
8.55555
10.0780
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21.4704
34.3678
85.9398
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90.4633
38
23
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8.620-78
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92.9085
37
24
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6.61219
9465
4275
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4288
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22.0217
8006
95.4895
36
25
2283
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7.5n32
6482
2294
4742
9687
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36.i776
98.2i79
35
26
3335
383i
2806
87oi
2602
5199
i6.o435
3o8i
5627
101.107
34
27
439o
5i44
4487
8.7o93i
29l3
566o
II9O
454i
956o
104.171
33
28
5448
6463
6176
3l72
3224
6124
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6020
37.3579
107.426
32
29
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7787
7872
5425
3538; 659i
2722
75i9
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5.97576
6.69116
7.59575
8.77689
10.3854112.7062
i6.3499
22.9o38
38.1885
114.589
3o
3i
8646
6.7o45o
7.61287
9964
4172
7536
4283
23.o577
6177
118.540
29
32
9720
1789
3oo5
8.82252
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8oi4
5o75
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39.o568
122.774
28
33
6.00797
3i33
4732
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48i3
8496
5874
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5o59
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27
34
1878
4483
6466
6862
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6681
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132.219
26
35
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5838
8208
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5462
9469
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25
36
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5789
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24
37
5i43
8564
7.7i7i5
3867
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24.0263
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38
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22
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6.8i3i2
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42.4335
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21
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6.o8444
6.82694
7.77o35
9.oo983
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i3.i969
I7.i693
24.54i8
42.964i
171.885
20
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9552
4082
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3379
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2480
2558J 7i85
43.5o8i
180.932
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42
6.io664
5475
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5789
7797
2996
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44.o66i
190.984
18
43
1779
6874
2428
8211
8139
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6386
202.219
17
44
2899
8278
4242
9.10646
8483
4039
52o5| 2644
45.2261
2i4.858
16
45
4oa3
9688
6o64
3o93
8829
4566
6106
45i7
8294
229.182
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46
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6.9110^
7895
5554
9178
5o98
7oi5
64i8
46.4489
245.552
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47
6283
2525
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8028
9529
5634
7934
8348
47.o853
264.441
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48
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9.2o5i0
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286.478
12
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6.96823
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5o.5485
429. -718
8
53
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7.01174
8.oo948
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27.o566
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491.106
7
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2637
2848
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6
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8821
687.549
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56
6655
5579
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9.4o9o4
2789
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859.436
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28.1662
55.44i5
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6 30189
7.ioo38
2481
878i
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9755
3994
56.35o63437.75
I
9°
8°
7°
6°
5°
4°
3° 2°
1° 0°
A
Natural Co-tangents.
, •**
P. P. go
22. IO
28.^46
37.83
5.28
7.88
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1
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NATURAL SECANTS.
Deg.
0'
10'
20'
30'
.40'
50'
P. Part
tol'.
0
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019887
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02I095
021713
78
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12
022341
022977
023624
024280
O24945
O2562O
77
66.0
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0263o4
026998
027702
O284i5
029i38
029871
76
71.8
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o3o6i4
o3i366
032128
032900
o33682
034474
75
77-7
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035276
o36o88
036910
o37742
o38584
039437
74
83.7
16
040299
041172
o42o55
042949
o43853
044767
73
89.8
17
045692
046627
o47573
048529
o49496
o5o474
72
96.1
18
o5i462
o5246i
o5347i
054492
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71
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70
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20
1.064178
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1.069955
69
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21
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073561
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0-76024
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68
123.2
22
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079808
081094
082392
o837o3
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67
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23
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087708
089068
090441
091827
093225
66
137.9
24
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096060
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098948
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101888
65
145.6
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io3378
104881
106398
io7929
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64
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26
112602
114187
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117400
i 19028
120670
63
162.0
27
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129096
130826
62
170.7
28
132570
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139698
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61
179.7
29
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147073
148956
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152769
60
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i.i586i2
i . 160592
1.162589
I.i646o3
59
198.9
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166633
168681
170746
1-72828
17492-7
177044
58
209, i
32
179178
i8i33i
i835oi
i85689
i87895
190120
57
219.7
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192363
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196906
199205
2Ol523
2o386i
56
230.9
34
206218
2o8594
210991
2i34o6
2i5842
218298
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242.6
35
220775
223271
225789
228327
23o886
233466
54
254.8
36
236o68
23869i
24i336
244oo3
246691
249402
53
267.7
37
252i36
254892
257671
26o472
263298
266146
52
281.3
38
269018
27i9i4
274834
277779
280748
28374i
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295.6
39
286760
2898o3
292872
295967
299088
302234
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310.7
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i. 308607
i.3n833
i.3i5o87
x.3i8368
1.321677
49
326.7
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325oi3
328378
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335i92
338643
342123
48
343.6
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345633
349i72
352742
356342
359972
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47
36i.5
43
367327
37io52
3748o9
378598
382420
386275
46
38o.5
44
390164
394o86
398o42
402032
406057
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45
400.7
45 414214
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430960
435239
44
422.3
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4483o6
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457213
461-726
43
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470874
4755o9
48oi87
484907
4896-70
42
469.8
48 i 494477
499327
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509160
5i4i45
5i9i76
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496.2
49 i 524253
529377
534540
539-769
545o38
55o356
4o
524.4
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i 555724
i.56n42
i.5666i2
i.572i34
1.577708
1.583335
39
554.7
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589016
594751
6oo542
6o6388
612291
6i825i
38
587.4
52
624269
63o346
636483
642680
648938
655258
37
622.7
53
66i64o
668086
674597
68n73
6878i5
694524
36
660.9
54
701302
708148
7i5o64
722051
729110
736244
35
702.2
55
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743447
750727
758o84
7655i7
773029
780620
34
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56
788292
796045
8o388i
811801
819806
827899
33
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836o78
844348
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861159
869704
878344
32
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58
59
887080
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8959i4
95io58
9o4847
960621
9i388i
970294
923017
980081
932258
989982
3i
3o
908.5
973.o
60'
50'
40'
30'
20'
10'
Dr. 5.
Natural Co-secants.
.NATURAL SECANTS.
135
Deg.
0'
10'
30'
30'
40'
50'
P. Part
tol'.
60
2.OOOOOO
2.oioi36
2.020393
2.030772
2.041276
2.061906
29
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062665
073666
084679
096739
107036
118474
28
1123
62
i3oo54
141781
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166681
177869
190196
27
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63
202689
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228168
241168
264320
267667
26
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64
281172
294869
308760
322820
337083
35x542
26
1417
65
866202
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396137
4ix42i
426922
442645
24
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66
458593
474773
491187
5o7843
524744
641896
23
1678
67
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676976
694914
6x3x26
53x6x8
660396
22
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68
669467
688387
708614
728604
7488x4
769453
21
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69
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811747
8334x9
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877853
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2222
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2.923804
2.947372
2.971349
2.996744
3.020669
3.045835
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71
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3.097736
3.124396
3.i5x545
179198
207367
18
2740
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296123
326610
366490
388082
17
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73
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453i73
486711
620937
556871
59i536
16
3458
74
627955
666162
7o3i5x
741978
781660
822226
16
3926
75
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906126
949622
993929
4.039380
4.086913
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76
4.133565
4.182378
4.232394
4.283658
3362i5
390116
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6190
77
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602167
56o4o8
620226
681676
74482i
12
6062
78
8o9734
876491
946169
5.016862
6.088628
5.i63592
II
7171
79
5. 24o843
5.320486
5.402633
487404
674926
665333
10
8612
80
5.758770
5.855392
5.955362
6.068868
6. 166067
6.277193
9
81
6.392453
6. 612081
6.636329
6.766469
6.899794
7.039622
8
82
7.185297
7.337191
7.496711
7.661298
7.834433
8.016646
7
83
8.206609
8.404669
8.613790
8.833671
9.o65x5i
9.309170
6
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9.566772
9.839123
xo. 12762
io.43343
10.76849
ii.io455
5
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11.47371
xi.86837
12.29126
12.74549
13.23472
13.76311
4
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14.33559
14.96788
i5.63679
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17.19843
18. 10262
3
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19.10732
20.23028
21.49368
22.92669
24.66212
26.46061
2
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28.65371
31.26768
34.38232
38.20x55
42.97671
49. n4o6
I
89
57.29869
68.76736
86.94661
114.6930
171.8883
343.7762
0
60'
50'
40'
30'
20'
10'
Deg.
Natural Co-secants.
LENGTHS OF CIRCULAR ARCS.
Degrees.
Minutes.
Seconds.
o
o
0
/
H
I
!oi74533
26
.4537856
5i
.8901179
I
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27
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52
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2
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2
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3
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28
.4886922
53
.9260245
3
.0008727
3
.0000145
4
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29
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54
.9424778
4
.ooii636
4
.0000194
5
.0872665
3o
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55
.9699311
5
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5
.0000242
6
.1047198
3x
.5410621
56
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6
.0017453
6
.0000291
7
. 1221730
32
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57
•9948377
7
.0020362
7
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8
.1396263
33
.6769687
58
.0122910
8
.0023271
8
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9
.1670796
34
.6934119
59
.0297443
9
.0026180
9
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10
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35
.6108662
60
.0471976
10
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10
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ii
. 1919862
36
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65
. i 34464o
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.0031998
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12
.2094396
37
.6467718
70
.2217306
12
.0034907
12
.0000682
i3
.2268928
38
.6632261
75
.3089969
x3
.0037816
i3
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i4
.244346i
39
.6806784
80
.3962634
i4
.0040724
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.0000679
i5
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4o
.6981317
85
.4836299
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.oo43633
16
.0000727
16
.2792627
4i
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9°
.6707963
16
.0046642
16
.0000776
17
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42
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100
.7453293
17
.0049461
ll
.0000824
18
.3i4i593
43
.7604916
1X0
.9198622
18
.0062360
18
.0000873
I9
.33i6i26
44
.7679449
I2O
2.0943961
J9
.0066269
J9
.0000921
20
. 3490669
45
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x3o
2.2689280
20
.0068178
20
.0000970
21
.3665i9i
46
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x4o
2.4434610
26
.0072722
26
.0001212
22
.3839724
47
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x5o
2.6179989
3o
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'>o
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.4014267
48
.8377680
1 60
2.7926268
4o
.01x6355
40
.0001939
24
.4188790
49
.85521x3
170
2.9670697
5o
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5o
.0002424
25
.4363323
5o
-.8726646
1 80
3.1416927
60
.0174533
60
.0002909
ISC)
TRAVERSE TABLE.
Course.
Dist. I.
Dist. 2.
Dist. 3.
Dist. 4.
*
Dist. 6.
Lat
Dep.
Lat
Dep.
Lat
Dep.
Lat
Dep.
Lat
Dep.
o /
0 /
o i5
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c. oo4/4
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o.oo87
3. oooo
o.oiSi
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O.OI75
5. OOOO
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89 45
3o
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oo87
1.9999
oi75
2.9999
0262
3.9998
o349
4-9998
o436
3o
45
0.9999
oi3i
9998
0262
9997
o393
9997
o52^!
9996
o654
i5
I O
9998
oi75
9997
o349
9995
o524
9994
o698
9992
087;
89 o
16
9998
0218
1
9995
o436
9993
o654
999°
o873
0988
io9i
45
3o
9997
0262
9993
o524
999°
o785
9986
io47
5983
i3o9
3o
45
r
9995
o3o5
9991
0611
9986
o9i6
998i
1222
9977
i527
16
2 0
9994
o349
9988
o698
9982
io47
9976
i396
9970
i745
88 o
i5
9992
o393
9985
o785
9977
1178
9969
i57o
996i
i963
45
3o
9990
o436
998i
o872
997i
i3o9
9962
i745
9952
2181
3o
45
0.9988
o.o48o
i.9977
o.o96o
2.9966
o.i439
3.9954
o.i9i9
4*9942
o.2399
i5
3 o
9986
o523
9973
io47
9959
i57o
9945
2093
993i
26l7
87 o
i5
9984
o567
9968
n34
9952
I7OI
9936
2268
9920
2835
45
3o
9981
0610
9963
1221
9944
i83i
9925
2442
9907
3o52
3o
45
9979
o654
9957
i3o8
9936
I962
99i4
2616
9893
3270
i5
4 o
9976
o698
995i
i395
9927
2093
99o3
279O
9878
3488
86 o
i5
9973
o74i
9945
1482
9918
2223
989o
2964
9863
37o*
45
3o
9969
o785
9938
i569
99o8
2354
9877
3i38
9846
3923
3o
45
9966
0828
993i
i656
9897
2484
9863
33i2
9828
4i4o
i5
5 o
9962
o872
9924
i743
9886
26i5
9848
3486
98io
4358
85 o
i5
o.9958
o.o9i5
1.9916
o.i83o
2.9874
o.2745
3.9832
o.366o
4.979o
o.4575
45
3o
9954
o958
99o8
I9i7
9862
2875
98i6
3834
977°
4792
3o
45
995°
1002
9899
2004
9849
3oo6
9799
4oo8
9748
5oo9
i5
6 o
9945
io45
989o
2O9I
9836
3i36
978i
4i8i
9726
5226
84 o
i5
9941
1089
988i
2I77
9822
3266
9762
4355
97o3
5443
45
3o
9936
iiSa
987i
2264
98o7
3396
9743
4528
9679
566o
3o
45
993i
n75
986i
235l
9792
3526
9723
47oi
9653
5877
i5
7 °
9925
1219
985i
a437
9776
3656
9702
4875
9627
6o93
83 o
i5
9920
1262
984o
2524
976o
3786
968o
5o48
9600
63io
45
3o
Q9i4
i3o5
9829
2611
9743
39i6
9658
5221
9572
6526
3o
45
0.9909
0.1349
i.98i7
o.2697
2.9726
o.4o46
3.9635
o.5394
4.9543
o.6743
i5
8. o
9903
1392
98o5
2783
97o8
4i75
96n
5567
95i3
6959
82 o
i5
9897
i435
9793
2870
969o
43o5
9586
574o
9483
7175
45
3o
989o
i478
978o
2956
967o
4434
956i
59I2
945i
739o
3o
45
9884
l52I
9767
3o42
965i
4564
9534
6o85
94i8
7606
i5
9 o
9877
1 564
9754
3i29
963i
4693
95o8
6257
9384
7822
81 o
i5
987o
i6o7
974o
32 1 5
96io
4822
948o
643o
935o
8037
45
3o
9863
i65o
9726
33oi
9589
495i
945i
6602
93i4
8252
3o
45
9856
i693
97n
3387
9567
5o8o
9422
6774
9278
8467
i5
10 0
9848
I736
9696
3473
9544
52O9
9392
6946
9240
8682
80 o
i5
o.984o
o-i779
i.968i
o.3559
2.952I
0.5338
3.9362
o.7n8
[.9202
o.8897
45
. 3o
9833
1822
9665
3645
9498
5467
933o
7289
9i63
9II2
3o
45
9825
i865
9649
373o
9474
5596
9298
746 1
9I23
9326
i5
II 0
98i6
1908
9633
38i6
9449
5724
9265
7632
9o8i
954o
70 o
i5
98o8
igSi
96i6
3902
9424
5853
923l
7804
9o39
9755
45
3o
9799
1994
9598
3987
9398
598i
9197
7975
8996
9968
3o
45
979°
2o36
958i
4o73
937i
6io9
9l62
8i46
8952
1.0182
i5
12 o
978i
ao79
9563
4i58
9344
6237
9I26
83i6
89o7
o396
78 o
i5
9772
2122
9545
4244
93i7
6365
9o89
8487
8862
o6o9
45
3o
9763
2 1 64
9526
4329
9289
6493
9o52
8658
88i5
0822
3o
45
o.9753
O.22O7
i.95o7
o.44 1 4
2.926o
0.6621
3.9oi4
0.8828
4.8767
i.io35
i5
i3 o
9744
2250
9487
4499
923l
6749
8975
8998
87i9
1248
77 °
i5
9734
2292
9468
4584
920I
6876
8935
9i68
8669
i46o
45
3o
9724
2334
9447
4669
9I7I
7oo3
8895
9338
8618
l672
3o
45
97i3
2377
9427
4754
9i4o
7i3i
8854
95o7
8567
1884
-5
i4 o
97o3
2419
94o6
4838
9I09
7258
8812
9677
85i5
2O96
76 o
i5
9692
2462
9385
4923
9°77
7385
8769
9846
8462
a3o8
45
3o
968i
25o4
9363
5oo8
9o44
75n
8726
I.OOlS;
8407
25i9
3o
45
967o
2546
934i
5o92
9OII
7638
8682
0184
8352
273o
i5
i5 o
9659
2588
93i9
5i76
8978
7765
8637
o353
8296
294l
75 o
Dep.
Lat
Dep.
Lat
Dep.
Lat
Dep.
Lat. i
Dep.
Lat
Dist. 1.
Dist. 2.
Dist. 3.
Dist. 4. Dist. 5.
Couna.
TRAVERSE TABLE.
137
Course.
Dist. 6.
Dist, 7.
Dist. 8.
Dist. 9.
Dist. 10.
Lat.
Dep.
Lat.
Dep.
Lat. j Dep.
Lat i
Dep.
Lat
Dep.
o /
0 /
o i5
6.9999
.0262
•9999
o.o3o5
•9999
o.o349
•9999
O.oSgS
9-9999
o.o436
89 45
3o
9998
o524
9997
06 1 1
9997
o698
9997
o785
9996
o873
3o
45
9995
o785
9994
0916
9993
io47
9992
1178
999 T
i3oo
i5
: o
9991
1047
9989
1222
9988
i396
9986
i57i
9985
I7451
89 o
i5
9986
1 309
9983
l527
9981
i745
9979
1963
9976
2181
45
3o
9979
1571
9976
i832
9973
2094
9969
2356
9966
2618
3o
45
9972
i832
9967
2i38
9963
2443
9958
2748
9953
3o54
i5
2 0
9963
2094
99 5 7
2443
995i
2792
9945
3i4i
9939
349o
8 o
i5
9954
2356
9946
2748
9938
3i4i
993i
3533
9923
3926
45
3o
9943
2617
9933
3o53
9924
349o
9914
3926
99o5
4362
3o
45
5.993i
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.9919
0.3358
•99°8
0.3838
.9896
o.43i8
.9885
0.4798
i5
3 o
9918
3i4o
99o4
3664
989o
4i87
9877
47io
9863
5234
7 o
i5
9904
3402
9887
3968
987i
4535
9855
5l02
9839
5669
45
3o
9888
3663
9869
4273
985i
4884
9832
5494
98i3
6io5
3o
45
9872
3924
985o
4578
9829
5232
9807
5886
9786
654o
i5
4 o
9854
4 1 85
9829
4883
98o5
558i
9781
6278
9756
6976
6 o
16
9835
444?
9808
5i88
978o
5929
9753
6670
9725
74n
45
3o
9815
4708
9784
5492
9753
6277
9723
7061
9692
7846
3o
45
9794
4968
9760
5797
9725
6625
9691
7453
9657
8281
i5
5 o
9772
5229
9734
6101
9696
6972
9658
7844
96i9
8716
5 o
i5
5.9748
.549o
.9706
o.64o5
.9664
0.7320
.9622
0.8235
.958o
o.9i5o
45
3o
9724
575i
9678
67O9
9632
7668
9586
8626
954o
9585
3o
45
9698
6on
9648
7013
9597
8oi5
9547
9017
9497
.0019
i5
6 o
9671
6272
9617
73i7
9562
8362
95°7
9408
9452
o453
84 o
i-5
9643
6532
9584
7621
9525
&709
9465
9798
94o6
0887
45
3o
9614
6792
955o
7924
9486
9o56
942I
.0188
9357
1320
3o
45
9584
7052
95i5
8228
9445
94o3
9376
0578
93o7
1754
i5
7 °
9553
7312
0478
853i
94o4
975o
9329
0968
9255
2187
83 o
i5
9520
7572
944o
8834
936o
1.0096
928o
i358
92OO
2620
45
3o
9487
7832
94oi
9i37
93i6
o442
923o
1747
9i44
3o53
3o
45
.9452
o.8o9i
.936i
o.944o
7.9269
1.0788
8.9i78
1.2137
9.9o87
1.3485
i5
8 o
94i6
835o
93r9
9742
9221
n34
91*4
2526
9027
39i7
82 o
:5
9379
8610
9276
.0044
9I72
1479
9o69
2914
8965
4349
45
3o
934i
8869
923l
o347
9I2I
1825
9OI I
33o3
8902
478i
3o
45
9302
9:27
9i85
o649
9o69
2170
8953
3691
8836
5212
i5
9 °
9261
9386
9i38
o95o
9oi5
25i5
8892
4079
8769
5643
81 o
i5
9220
9645
9o9o
1262
896o
2859
883o
4467
8700
6o74
45
3o
9177
99o3
9o4o
i553
89o3
3204
8766
4854
8629
65o5
3o
45
9i33
1.0161
8989
i854
8844
3548
8700
524i
8556
6935
i5
IO O
9088
o4i9
8937
2i55
8785
3892
8633
5628
848 1
7365
80 o
i5
5.9042
1.0677
6.8883
1.2456
7.8723
1.4235
8.8564
i.6oi5
9.84o4
1.7794
45
3o
8995
o93^
8828
2756
8660
4579
8493
64oi
8325
8224
3o
45
8947
n9i
8772
3o57
8596
4922
8421
6787
8245
8652
i5
II O
8898
i449
8714
3357
853o
5265
8346
7173
8i63
9o8i
79 °
i5
884?
I7o5
8655
3656
8463
5607
8271
7558
8079
95o9
45
3o
8795
I962
8595
3956
8394
5949
8i93
7943
7992
9937
3o
45
8743
22I9
8533
4255
8324
629I
8n4
8328
79°5
2.o364
i5
12 O
8689
2475
8470
4554
8252
6633
8o33
8712
78i5
O79i
78 o
i5
8634
273l
84o6
4852
8178
6974
795i
9o96
7723
1218
45
3o
8578
2986
834i
5i5i
8io4
73i5
7867
948o
763o
1 644
3o
45
5.852
1.3242
6.8274
1.5449
7.8027
1.7656
8.7781
i.9863
9.7534
2.2070
i5
i3 o
8462
3497
8206
5747
795o
7996
7693
2.0246
7437
2495
77 °
i5
84o3
3752
8i37
6o44
7870
8336
760^
0628
7338
2920
45
3o
8342
4oo
8o6e
634
779°
8676
75i3
1010
7237
3345
3o
45
828
426
799^
6638
77°7
9oi5
742I
I392
7i34
3769
i5
i4 o
8218
45i
7921
6935
7624
9354
7327
1773
7o3o
4l92
76 o
i5
8i54
4769
784C
723
7538
9692
723l
2i54
6923
46i5
45
3o
8089
502
777c
7527
7452
2.oo3o
7i33
2534
68i5
5o38
3o
45
802^
627
769:
7822
?364
o368
7o34
29l4
6705
546o
i5
i5 o
795
552
76if
Six
727^
0706
6933
3294
6593
5882
75 o
Dep.
Lat.
Dg».
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat
Dist. 6.
Dist. 7.
Dist. 8.
Dist. 9.
Dist. 10.
Course.
138
TRAVERSE TABLE.
Course
Dist. 1.
Dist. 2.
Dist. 3.
Dist. 4.
Dist. 5.
Lat.
Dep.
Lat.
Dep.
Lat
Dep.
Lat.
Dep.
Lat
Dep.
o /
o /
i5 i
o.964£
0.263
I.9296
0.526
2.894
o.789
3.859i
1.052
4823
i.3i5
74 45
3
963e
267
9273
534
89o
801
854f
o69
Si8
336
3o
4
06-26
271^
9249
542
8874
8i4
849£
o85
812
357
i5
16 o
9613
276
9225
55i
8838
826
845c
102
806
378
74 o
i
9600
279
92OI
559
880
839
8402
II9
800
399
45
3o
9588
284
9:76
568
8765
852
8353
i36
794
420
3o
4
95?6
288
9i5i
5764
8727
864
83o3
l52
787
44 1
i5
17 o
9563
2922
9I26
584
8689
877
825a
i69
781
46i
73 o
i5
955o
2965
9ioo
593
865i
889
8201
186
775
482
45
3o
9537
3oo7
9074
6oi/
8612
9O2
8i49
202
7686
5o3
3o
45
0.9524
o.3o49
i.9o48
o.6o9
2.8572
o.9i4
3.8o96
1.219
4.7620
1.5243
i5
18 o
95n
3090
9O2I
6180
8532
927
8042
236
7553
545
72 0
i5
9497
3i32
8994
6263
849i
9395
7988
252
7485
5658
45
3o
9483
3i73
8966
6346
845o
95i9
7933
2692
74i6
5865
3o
45
9469
32i4
8939
6429
84o8
9643
7877
2858
7347
6072
i5
19 o
9455
3256
89io
65u
8366
9767
7821
3o23
7276
6278
7I 0
i5
944i
3297
8882
6594
8323
989i
7764
3i88
7204
6485
45
3o
9426
3338
8853
6676
8270.
1.0012
7706
3352
7l32
669o
3o
45
9412
3379
8824
6758
8235
oi38
7647
35i7
7o59
6896
i5
20 0
9397
3420
8794
684o
8i9i
0261
7588
368i
6985
7101
7o o
i5
o.9382
i.346i
i.8764
O.6922
2.8146
i.o384
3.7528
1.3845
i.69io
i.73o6
45
3o
9367
35o2
8733
7OO;
8100
o5o6
7467
4oo8
6834
75io
3o
45
935i
3543
87o3
7086
8o54
o629
74o5
4i7s
6757
77i5
i5
21 0
9336
3584
8672
7167
8007
o75i
7343
4335
6679
79i8
69 o
i5
9320
3624
864o
7249
796o
0873
7280
4498
6600
8122
45
3o
93o4
3665
8608
733o
79i3
o995
7217
466o
652i
8325
3o
45
9288
3706
8576
74n
7864
1117
7l52
4822
644o
8528
i5
22 0
9272
3746
8544
7492
7816
1238
7087
4984
6359
873o
68 o
15
9255
3786
85n
7573
7766
i359
7022
5i46
62-7-7
8932
45
3o
9239
3827
8478
7654
7716
i48i
6955
53o7
6r94
9i34
3o
45
0.9222
o.3867
1.8444
o.7734
3.7666
1.1601
3.6888
1.5468
4-6i 10
.9336
i5
23 0
9205
3907
84io
7816
76i5
1722
6820
5629
6o25
9537
67 o
i5
9188
3947
8376
7895
7564
1842
6762
579o
594o
9737
45
3o
9171
3987
834i
7975
75l2
I962
6682
595o
5853
9937
3o
4^
9i53
4027
83o6
8o55
7459
2082
6612
6110
5766
2.0l37
i5
,24 o
9i35
4o67
827I
8i35
74o6
22O2
6542
6269
5677
o337
66 o
i5
9118
4107
8235
8214
7353
2322
6470
6429
5588
o536
45
3o
9100
4i4?
8i99
8294
7299
244 1
6398
6588
5498
o735
3o
45
9081
4i87
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0.9045
0.4266
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i.7o63
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9026
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3o33
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74o7
9848
6111
4773
48i4
9697
35i8
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Lat 1
Dist. 1.
Dist. 2.
Dist. 3.
Dist. 4.
Dist. 5.
ourae.
TRAVERSE TABLE.
Course.
Dist. 6.
Dist. 7.
Dist. 8.
Dist. 9.
Dist. 10.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat
Dep.
o /
o /
i5 16
5.7887
1.5782
6.7535
i.84i2
7.7i83
2.IO42
8.683i
2.3673
9.6479
2.6303
74 45
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7818
6o34
7454
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6727
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6126
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72o3
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64o4
5i85
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67o6
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7454
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2.0I74
6606
3o56
6181
5938
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8820
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7378
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65o4
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6o67
63i3
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9237
73 o
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3723
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7223
8042
676o
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6297
4o56
5835
7o64
5372
3.oo7i
3o
45
5.7i44
1.8292
6.6668
2.i34i
7.6192
2.4389
8.57i6
2.7438
9.524o
3.o486
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18 o
7063
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6574
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6o85
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72 0
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8790
6479
1921
5976
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6899
9o38
6383
2211
5866
5384
5349
8557
4832
i73o
3o
45
6816
9286
6285
2501
5754
57i5
5224
893o
4693
2i44
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19 o
673i
9534
6186
2790
564i
6o45
5o97
93oi
4552
2557
7I 0
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6645
9781
6086
3o78
5527
6375
4968
9672
44o9
2969
45
3o
6558
2.0028
5985
3366
54n
67o5
4838
3.oo43
4264
338i
3o
45
6471
0275
5882
3654
5294
7o33
47o6
o4i3
4n8
3792
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20 o
6382
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5778
3941
5i75
7362
4572
0-782
3969
4202
7o o
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5.6291
2.0767
6.5673
2.4228
7.5o55
2.7689
8.4437
3.ii5i
9.38i9
3.46i2
45
3o
6200
1012
5567
45i5
4934
8oi7
43oo
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3667
5021
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45
6108
1257
5459
48oo
48n
8343
4162
1886
35i4
5429
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il 0
6oi5
i5o2
535i
5o86
4686
8669
4022
2253
3358
5837
60 o
i5
5920
1746
5 24 1
537i
456i
8995
388i
2619
3201
6244
45
3o
5825
1990
5l29
5655
4433
9320
3738
2985
3o42
665o
3o
45
5729
2233
5oi7
5939
43o5
9645
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335o
2881
7o56
16
22 O
563i
2476
49o3
6222
4i75
9969
3447
37i5
27l8
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68 o
15
5532
2719
4788
65o5
4o43
3.O292
3299
4o78
2554
7865
45
3o
5433
2961
4672
6788
39io
o6i5
3i49
4442
2388
8268
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45
5.5332
2.3203
6.4554
2.7070
7.3776
3.o937
8.2998
3.48o4
9.222O
3.867i
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23 0
523o
3444
4435
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364o
1258
2845
5i66
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5127
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7632
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5527
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5o24
3925
4i94
79I2
3365
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2535
5887
1-706
9875
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45
4919
4i65
4o72
8l92
3225
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2378
6247
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4.o275
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24 o
48i3
44o4
3948
84-72
3o84
2539
22I9
6606
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66 o
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4706
4643
3823
875o
294i
2858
2o59
6965
11-76
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45
3o
4598
4882
3697
9029
2797
3i75
i897
7322
o996
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3o
45
4489
5l20
357o
93o6
265i
3493
:733
7679
o8i4
1866
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25 0
4378
5357
3442
9583
25o5
38o9
i568
8o36
o63i
2262
65 o
i5
5.4267
2.5594
6.3312
2.986o
7.2356
3.4i25
8.i4oi
3.839i
9.o446
4.2657
45
3o
4i55
583i
3i8i
3.oi36
2207
444 1
1233
8746
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3o5i
3o
45
4042
6067
3o49
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2o56
4756
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9100
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3445
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26 o
3928
63o2
29l6
0686
i9o4
5o7o
o89i
9453
8.9879
3837
64 o
i5
38i2
6537
278l
o96o
i75o
5383
o7i9
9806
9687
4229
45
3o
3696
6772
2645
1234
i595
5696
o544
4-oi58
9493
462O
3o
45
3579
7006
25o9
i5o7
i438
6008
o368
0509
9298
5oio
i5
27 o
346o
7239
2370
1779
1281
63i9
OI9I
0859
9IOI
5399
63 o
i5
334i
7472
223l
2o5i
II2I
663o
OOI2
1209
89O2
5787
45
3o
3221
7705
209I
2322
o96i
694o
7.983i
i557
87oi
6i75
3o
45
5.3o99
a.7937
6.i949
3.2593
7-°799
3.7249
7.9649
4.1905
8.8499
4.656i
i5
28 o
2977
8168
1806
2863
o636
7558
9465
2252
8295
6947
62 o
i5
2853
8399
1662
3i32
o47i
7866
928o
2599
8o89
7332
45
3o
2729
863o
i5i7
34oi
o3o5
8i73
9o94
2944
788a
77i6
3o
45
2604
8859
i37i
3669
oi38
8479
89o5
3289
7673
8o99
i5
20 O
24?7
9089
1223
3937
6.997o
8785
87i6
3633
7462
848 1
61 o
15
235o
93i7
io75
4203
98oo
9090
8525
3976
7a5o
8862
45
3o
2221
9545
O925
447o
9628
9394
8332
43i8
7o36
9242
3o
45
2092
9773
o774
4735
9456
9697
8i38
4659
6820
9622
i5
3o o
1962
3.0000
0622
5ooo
9282
4.0000
7942
5ooo
66o3
5.0000
60 o
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat
Dist. 6.
Dist. 7.
Dist. 8.
Dist. 9.
Dist. 10.
Course.
?40
TRAVERSE TABLE.
Course.
Dist. I.
Dist. 2.
Dist. 3.
Dist. 4.
Dist. 5.
Lat.
Dep.
Lat
Dep.
Lat
Dep.
Lat
Dep.
Lat
Dep.
o /
3o i5
0.8638
o.5o38
1.7277
i.oo75
2.59l5
I.5ll3
3.4553
2.Ol5l
4.3192
2.5l89
o /
59 45
3o
8616
5o75
7233
oi5i
5849
5226
4465
0302
3o8i
5377
3o
45
8594
5n3
7l88
0226
5782
5339
4376
0452
2970
5565
i5
3i o
8572
5i5o
ai43
o3oi
57i5
545i
4287
0602
2858
5752
59 o
i5
8549
5i88
7098
o375
5647
5563
4i96
o75i
2746
5939
45
3o
8526
6226
7o53
o45o
5579
5675
4io6
o9oo
2632
6i25
3o
45
85o4
6262
7007
o524
55u
5786
4oi4
io49
25i8
63u
i5
32 0
848o
5299
6961
0598
544 1
5898
3922
H97
2402
6496
58 o
i5
845y
5336
6916
o672
5372
6008
3829
1 345
2286
6681
45
3o
8434
5373
6868
o746
53o2
6u9
3736
1492
2I7O
6865
3o
45
o.84io
o.54io
1.6821
1.0819
2.5231
1.6229
3.3642
2.1639
4.2O52
2.7o49
i5
33 o
8387
5446
6773
0893
5i6o
6339
3547
i786
1934
7232
57 o
i5
8363
5483
6726
0966
5o89
6449
345i
1932
1814
74i5
45
3o
8339
55i9
66 78
1039
5oi7
6558
3355
2077
1694
7597
3o
45
83i5
5556
6629
i ii i
4944
6667
3259
2223
i573
7779
ID
34 o
8290
6692
658i
1184
487i
6776
3i62
2368
1452
796o
56 o
i5
8266
5628
6532
1256
4798
6884
3o64
25l2
i329
8i4o
45
3o
8241
5664
6483
i328
4724
6992
2965
2656
1206
8320
3o
45
8216
5700
6433
i4oo
4649
7100
2866
2800
1082
85oo
i5
35 o
8192
5736
6383
1472
4575
7207
2766
2943
o958
8679
55 o
i5
0.8x66
0.5771
1.6333
i.i543
2.4499
i.73i4
3.2666
2.3o86
4.o832
2.8857
45
3o
8i4i
5807
6282
1614
4423
7421
2565
3228
o7o6
9o35
3o
45
8116
5842
623i
i685
4347
7527
2463
337o
o579
9212
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36 o
8090
5878
6180
i756
427I
7634
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35n
o45i
9389
54 o
i5
8o64
59i3
6l29
1826
4i93
7739
2258
3652
0322
9565
45
3o
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5948
6o77
1896
4n6
7845
2l54
3793
0193
974i
3o
45
8oi3
5983
6026
1966
4o38
795o
2o5o
3933
oo63
99i6
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3y o
7986
6018
5973
2o36
3959
8o54
1945
4o73
3.9932
3.oo9i
53 o
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7960
6o53
5920
2106
388o
8i59
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4212
9800
0265
45
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7934
6088
5867
2I75
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8263
1734
435o
9668
o438
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45
0.7907
0.6122
i.58i4
1.2244
2.372I
i.8367
3.1628
2.4489
3.9534
3.o6i i
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38 o
7880
6i57
6760
23i3
364o
8470
l520
4626
94oi
o783
52 0
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7853
6191
57o6
2382
356o
8573
i4i3
4764
9266
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45
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7826
6226
6662
245o
3478
8675
i3o4
49oi
9i3o
1 126
3o
45
7799
6259
5598
25i8
3397
8778
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5o37
8994
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3o o
7771
6293
5543
2586
33i4
8880
1086
5i73
8857
f466
5i o
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. 7744
6327
5488
2654
3232
898i
0976
53o8
8720
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45
3o
7716
636i
5432
2722
3i49
9o82
o865
5443
858i
1804
3o
45
7688
6394
5377
2789
3o65
9i83
o754
5578
8442
19-72
i5
4o o
7660
6428
532i
2856
298l
9284
0642
57I2
83o2
2139
5o o
i5
0.7632
o.646i
i.5265
1.2922
2.2897
i.9384
3.o529
a 5845
3.8162
3.23o6
45
3o
7604
6494
52o8
2989
2812
9483
o4i6
S978
8020
2472
3o
45
7576
6528
5i5i
3o55
2727
9583
o3o3
Oi 10
7878
2638
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4i o
7547
656i
5094
3l2I
2641
9682
0188
6242
7735
28o3
49 o
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75x8
6593
5o37
3i87
2555
9780
0074
6374
7592
296-7
45
3o
7490
6626
4979
3252
2469
9879
2.9958
65o5
7448
3i3i
3o
45
746 1
665g
4921
33i8
2382
9976
9842
6635
73o3
3294
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4a o
743i
6691
4863
3383
2294
2.0074
9726
6765
7i57
3457
48 o
i5
7402
6724
48o4
3447
22O7
0171
9609
6895
7OI I
36i8
45
3o
7373
6756
4746
35i2
2118
0268
9491
•7024
6864
378o
3o
45
0.7343
0.6788
1.4686
i.3576
2.2030
2.o364
2.9373
2.7l52
3.67i6
3.394o
i5
43 o
73i4
6820
462-7
364o
I94l
o46o
9254
7280
6568
4ioo
47 o
i5
7284
6852
4567
37o4
i85i
o555
9i35
74o7
64i9
4259
45
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7254
6884
45o7
3767
1761
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9oi5
7534
6a69
44i8
3o
45
7224
6916
4447
383o
1671
o745
8895
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6n8
4576
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44 o
7i93
6947
4387
3893
i58o
o84o
8774
7786
5967
4733
46 o
i5
7i63
6978
4326
3956
i489
o934
8652
7912
58i5
489o
45
3o
7i33
7009
4265
4oi8
i398
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853o
8o36
5663
5o45
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45
7102
7040
4204
4o8o
i3o6
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84o7
8161
55o9
52OI
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45 o
7071
7071
4i42
4i42
I2l3
I2l3
8284
8284
5355
5355
45 o
Dep.
Lat
Dep.
Lat.
Dep.
Lat
Dep.
Lat. |
Dep.
Lat
Dist. 1.
Dist. 2.
Dist. 3.
Dist 4.
Dist. 5.
Course.
TRAVERSE IABLE.
14
Course.
Dist. 6.
Dist. 7.
Dist. 8.
Dist. 9.
Dist. 10.
Lat.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lot.
Dep.
o /
o /
3o i5
5.i83o
3.0226
6.o468
3.5264
6.9107
4.0302
7.7745
4.5340
8.6384
5.0377
59 45
3o
1698
o452
o3i4
5528
893o
o6o3
7547
5678
6i63
o754
3o
45
1 564
0678
oi58
5791
8753
0903
7347
6016
594i
1129
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3i o
i43o
09O2
OOO2
6o53
8573
1203
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6.7283
4.3278
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0320
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4.9928
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3o82
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2611
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9281
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2426
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9497
9497
6569
6569
364o
364o
0711
0711
45 o
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dep.
Lat.
Dist. 6.
Dist. 7.
Dist. 8.
Dist. 9.
Dist. 10.
Course.
142
MERIDIONAL PARTS.
LATITUDE.
Min.
0°
1°
2°
3°
4°
5°
6°
7°
8°
9°
10°
11°
12°
Min.
O
o.o
60.0
120.0
1 80.
240.2
3oo.2j
36o.7
421. 1
48i.6
542.2
6o3.
664.
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61.0
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61.7
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43.3
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65.
26.3
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2
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62.0
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82.1
42.2
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62.7
23.1
83.6
44.3
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66.1
27.4
2
3
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63.o
23.0
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43.2
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67.1
28.4
3
4
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44.2
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68.2
29.4
4
5
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25.0
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45.2
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65.7
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5
6
6.0
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46.2
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66.7
27.1
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48.3
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70.2
3i.5
6
7
7.0
67.0
27.0
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47.2
07.4
67.7
28.1
88.6
49-3
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71.1
32.5
7
8
8.0
68.0
28.0
88.1
48.2
08.;
68.7
29.I
89.6
5o.3
II. 2
72.2
33.5
8
9
9.0
69.0
29.0
89.1
49.2
09.4
69.7
3o.i
9°-7
5i.4
12.2
73.3
34.5
9
10
10.0
70.0
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190.1
25O.2
3 io.:
370.7
43i.i
491.7
552.4
6l3.2
674.3
735.6
10
ii
I I.O
71.0
3i.o
91.1
5l.2
1 1.2
71.7
32.1
92.7
53.4
14.2
75.3
36.6
ii
12
12.0
72.0
32.0
92.1
52.2
12.2
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33.i
93.7
544
15.3
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37.6
12
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73.o
33.o
93.i
53.2
1 3.4
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14
14.0
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54.2
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17.3
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39.6
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55.2
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79-4
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16
16.0
76.0
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56.2
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58.4
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80.4
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16
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17.0
77.0
37.o
97-i
57.2
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77.8
38.2
98.7
59.4
20.3
81.4
42.7
ll
18
18.0
78.0
38.o
$8.1
58.2
i8.5
78.8
39.2
99.8
6o.5
21.3
82.4
43.7
18
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19.0
79.0
39.o
99.i
59.2
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79.8
4o.2
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6i.5
22.4
83.5
44.8
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20
2O.O
80.0
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200. i
260.2
320.5
38o.8
44i.2
5oi.8
562.5
623.4
684.5
745.8
20
21
21.0
81.0
4i.o
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61.3
21.5
81.8
42.2
02.8
63.5
24.4
85.5
46.8
21
22
22.0
82.0
42.0
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62.3
22.5
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43.2
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64.5
25.4
86.5
47-8
22
23
23.0
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43.o
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63.3
23.5
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65.5
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48.9
23
24
24.0
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44-0
04. 1
64-3
24-5
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45.2
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66.6
27.4
88.6
49-9
24
25
25.0
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45.o
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65.3
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67.6
28.5
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25
26
26.0
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06. i
66.3
26.5
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47-3
07.8
68.6
29.5
90.6
5r.9
26
27
27.0
87.0
47.o
07.1
67.3
27.5
87.8
48.3
08.9
69.6
3o.5
91.6
53.o
27
28
28.0
88.0
48.o
08. i
68.3
28.5
88.8
49.3
09.9
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92.6
54.0
28
29
29.0
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49.0
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69.3
29.5
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10.9
71.6
32.5
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29
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90.0
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2IO.I
270.3
33o.5
39o.8
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511.9
572.6
633.5
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91.0
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7i.3
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91.8
52.3
12.9
73.7
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95.7
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3i
32
32.0
92.0
52.0
12. 1
72.3
32.5
92.9
53.3
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74.7
35.6
96.7
58.i
32
33
33.o
93.0
53.i
I3.I
73.3
33.5
93.9
54.3
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75.7
36.6
97-7
59.i
33
34
34.o
94.0
54-1
14.1
74.3
34-5
94-9
55.3
<5.9
76.7
37.6
98.7
60. i
34
35
35.o
95.0
55.i
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75.3
35.5
95.9
56.3
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77-7
38.6
99.8
61.1
35
36
36.o
96.0
56.i
16.1
76.3
36.5
96.9
57.3
18.0
78.7
39.6
700.8
62.2
36
3?
37.o
97.0
57.i
17.1
77.3
37.5
97-9
58.4
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79-7
4o.7
01.8
63.2
37
38
38.o
98.0
58.i
18.1
78.3
38.5
98.9
59.4
20. o
80.8
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02.8
64.2
38
39
39.0
99.0
59.1
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79-3
39.6
99-9
60.4
21.0
81.8
42.7
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65.2
39
4o
4o.o
IOO.O
1 60. i
220.2
280.3
34o.6
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46i.4
522.0
82.8
643.7
04.9
66.3
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01. 0
61.1
21.2
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62.4
23.0
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44. 7
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67.3
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42.0
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62.1
22.2
82.3
42.6
02. 9
63.4
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45.8
06.9
68.3
42
43
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85.8
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44
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47.8
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44
45
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48
48.o
08.0
68.1
28.2
88.3
48.6
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69.5
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9°-9
5i.9
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74.5
48
49
49.0
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69.1
29.2
89.3
49.6
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7o.5
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91.9
52. 9
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75.5
49
5o
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230.2
29o.3
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47i.5
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92.9
653.9
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71.1
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52
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95.o
55.9
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52
53
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33.2
93.4
53.6
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57.o
18.2
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53
54
54.o
14.0
74.1
34-2
94.4
54.6
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75.5
36.2
97-°
58.o
19.2
80.6
54
55
55.o
i5.o
75.i
35.2
95.4
55.6
16.0
76.5
37.2
98.o
59.o
2O.2
81.7
55
56
56.o
16.0
76.i
36.2
96.4
56.6
17.0
77.5
38.2
99.o
60.0
21.2
82.7
56
5?
57.o
17.0
77.i
37.2
97-4
57.6
18.0
78.5
39.2
600.0
61.0
22.3
83.7
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58
58.o
18.0
78.1
38.2
98.4
58.6
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79.5
4O.2
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62.1
23.3
84.7
58
59
59.0
19.0
•79.1
39.2
99.4
59.7
20.0
8o.5
41.2.
02. 1
63.i
24.3
85.8
59
MERIDIONAL PARTS.
148
LATITUDE.
T
13°
14°
15°
16°
17°
18°
19°
20°
21°
22°
23°
24°
.s
0
786.8
848.5
910.5
972.7
io35.3
1098.2
n6i.5
1225. 1
1289.2
i353.7
i4i8.6
i484.i
o
i
87.8
49-5
11. 5
73.8
36.3
99.3
62.5
26.2
90.3
54-8
19.7
85.2
I
2
88.8
5o.5
12.6
74-8
37.4
i loo.S
63.6
27.3
91.3
55.8
20.8
86.3
2
3
89.9
5i.6
i3.6
75.9
38.4
01.4
64-7
28.3
92.4
56.9
21.9
87.3
3
4
90.9
52.6
i4-6
76.9
39.5
02.4
65.7
294
93.5
58.o
23.0
88-4
4
5
91.9
53.6
i5.7
78.0
4o.5
o3.5
66.8
3o.4
94.5
59.0
24*1
89.5
5
6
92.9
54.7
16.7
79.0
4i.6,
o4.5
67.8
3i.5
95.6
60.1
25-1
qo.6
6
7
94.0
55.7
17.7
80.0
42.6
o5.6
68.9
32.6
96.7
61.2
26-2
91.7
7
8
95.0
56.7
18.8
81.1
43-7
06.6
7o.o
33.6
97.8
62.3
27.3
92.8
8
9
96.0
57.8
19.8
82.1
44-7
07.7
7i.o
34-7
98.8
63.4
28.4
93.9
9
10
797.0
858.8
920.8
983.2
io45.8
1108.7
II72.I
1235.8
1299.9
i364.5
1429.5
i495.o
10
ii
98.1
59.8
21.9
84.2
46.8
09.8
73.i
36.8
iSoi.o
65.6
3o.6
96.1
ii
12
99.1
60.9
22.9
85.2
47-9
10.8
74-2
37-9
O2.O
66.6
3i.9
97-2
12
i3
800.1
61.9
23.9
86.3
48.9
11.9
75.2
39.0
o3.i
67.7
32.8
98.3
i3
i4
01.2
62.9
25. 0
87.3
49.9
12.9
76.3
4o.o
04.2
68.8
33.9
99.4
i4
i5
O2. 2
64.o
26.0
88.4
5i.o
i4-o
77-4
4i.i
o5.3
69.9
34-9
i5oo.5
i5
16
03.2
65.o
27.0
89.4
52.0
1 5.o
78.4
42.2
o6.3
70.9
36.o
01.6
16
ll
O4.2
66.0
28.1
90.4
53.1
16.1
79.5
43.2
07.4
72.O
37.i
02.7
*7
18
o5.3
67.1
29.1
9i.5
54.i
17.1
8o.5
44-3
o8.5
73.i
38.2
o3.8
18
'9
o6.3
68.1
3o.i
92.5
55.2
18.2
81.6
45.4
09.6
74.2
39.3
04.9
'9
20
807.3
869.1
931.2
993.6
io56.2
1119.2
1182.7
1246.4
i3io.6
i375.3
i44o.4
i5o6.o
20
21
08.4
70.1
32.2
94-6
57.3
20.3
83.7
47.5
11.7
76.4
4i.5
07.1
21
22
09.4
71.2
33.3
95.6
58.3
21.3
84-8
48.6
12.8
77-4
4a.6
08.2
22
23
10.4
72.2
34.3
96.7
59.4
22.4
85.8
49-6
i3.8
78.5
43.7
OQ.3
23
24
ti.4
73.2
35.3
97-7
60.4
23.4
86.9
50.7
i4«9
79.6
44-81 10.4
24
25
12.5
74-3
36.3
^8.8
6i.4
24.5
88.0
5i.8
16.0
80.7
45.8
1 1.5
25
26
i3.5
75.3
374
99.8
62.5
25.5
89.o
52.8
17.1
81.8
46.9
12.6
26
27
i4-5
76.3
38.4
1000.8
63.5
26.6
90.1
53.9
18.1
82.8
48.o
i3.7
27
28
i5.5
77-4
39.5
01.9
64.6
27.6
91.1
55.6
19.2
83.9
49.1
i4.8
28
29
16.6
78.4
4o.5
02.9
65.6
28.7
92.2
56.o
20.3
85.o
5o.2
i5.9
29
3o
817.6
879-4
94i.6
ioo4.o
1066.7
1129.7
II93.2
1257.1
i32i.4
i386.i
i45i.3
1517.0
3o
3i
18.6
8o.5
42.6
o5.o
.67-7
3o.8
94.3
58.2
22.5
87.2
62.4
18.1
3i
32
19.6
8i.5
43.6
06. i
68.8
3i.8
95.4
59.2
23.5
88.3
53.5
19.2
32
33
20.7
82.5
44-7
07.1
69.8
32.9
96.4
6o.3
24.6
89.4
54.6
20.3
33
34
21.7
83.6
45.7
08.1
70.9
34.o
97.5
61.4
25.7
90.4
55.6
21.4
34
35
22.7
84.6
46.7
09.2
72.0
35.1
98.5
62.4
26.7
9i.5
56.7
22.5
35
36
23.8
85.6
47.8
10.2
73.o
36.1
99.6
63.5
27.8
92.6
57.8
23.6
36
3?
24.8
86.7
48.8
n.3
74.i
37.2
1200.7
64-6
28.9
93.7
58.9
24.7
37
38
25.8
87.7
49-9
12.3
75.i
38.2
01.7
65.6
3o.o
94-8
60.0
25.8
38
39
26.9
88.7
5o.9
i3.4
76.2
39.3
02.8
66.7
3i.i
95.8
61.1
26.9
39
4o
827.9
889.8
951.9
ioi4«4
1077.2
n4o.3
1203.9
1267.8
i332.i
1396.9
1462.2
i528.o
4o
4i
28.9
90.8
53.o
1 5.4
78.3
4i-4
04.9
68.8
33.2
98.0
63.3
29.1
4i
42
29.9
91.8
54.o
i6.5
79.3
42.4
06.0
69.9
34.3
99.1
644
30.2
42
43
3i.o
92.9
55.i
i7.5
80.4
43.5
07.1
71.0
35.3
I4OO.2
65.5
3i.3
43
44
32.0
93.9
56.i
18.6
81.4
44-6
08.1
72.1
36.4
QI. 3
66.6
32.4
44
45
33.o
94.9
57.i
19.6
82.5
45.6
09.2
73.i
37.5
02.4
67.7
33.5
45
46
34-1
96.0
58.2
20.6
83.5
46.7
IO.2
74-2
38.6
o3.4
68.8
34.6
46
4?
35.i
97.0
59.2
21.7
84.6
47-7
n.3
75.3
39.7
o4-5
69.8
35.7
47
48
36.i
98.0
60.2
22.7
85.6
48.8
12.4
76.3
40.7
o5.6
•70.9
36.8
48
49
37.2
99.1
6i.3
23.8
86.7
49-9
1 3.4
77-4
4i.8
06.7
72.0
37.9
49
5o
838.2
900.1
962.3
1024.8
1087.7
n5o.9
i2i4-5
1278.5
i34a.9
1407.8
i473.i
iSSg.o
5o
5i
39.2
01. 1
63.4
25.9
88.8
52.O
i5.5
79.5
44.o
08.8
74.2
4o.i
5i
62
4O.2
O2. 2
644
26.9
89.8
53.o
16.6
80.6
45.i
09.9
75.3
41.2
52
53
4i.3
03.2
65.5
28.0
9° 9
54.i
17.7
81.7
46.i
II. O
76.4
42.3
53
54
42.3
o4.3
66.5
29.0
91.9
55.i
18.7
82.8
47.2
12. 1
77.5 43-4
54
55
43.3
o5.3
67.5
3o.i
93.o
56.2
19.8
83.8
48.3
13.2
78.6 44-5
55
56
444
o6.3
68.6
3i.i
94.0
57.2
20.9
84-9
49.4
i4.3
79-7 45.6
56
5?
45.4
07.4
69.6
, 32.2
95.i
58.3
21.9
86.0
5o.4
1 54
80.8 46.7
57
58
46.4
08.4
70.7
33.2
96.1
59.4
23.0
87.0
5i,5
i6.5
81.9 47.8
58
59
47-5
09.4
71.7
34.3
97.2
60.4
24.1
88.1
52.6
i7.5
83.o 48.9
59
MERIDIONAL PARTS.
LATITUDE.
Min.
25°
26°
27°
28°
29°
30°
31°
32°
33°
34°
35°
Mia.
O
i55o.o
iBi6.5
i683.5
1751.2
1819.4
1888.4
i958.o
2028.4
2099.5
2171.5
2244.3
O
I
5i.i
17.6
84.6
52.3
2O.6
89.5
59.2
29.6
2IOO.7
72.7
45.5
I
2
52.2
18.7
85.8
53.4
21.7
90.7
60.4
30.7
01.9
73.9
46.8
2
3
53.3
19.8
86.9
54.6
22.9
91.9
61.6
3i.9
o3.i
75.i
48.o
3
4
54-4
20.9
88.0
55.7
24.0
93.0
62.7
33.i
o4.3
76.3
49.2
4
5
55.5
22.O
89.1
56.8
25.2
94.1
63.9
34-3
o5.5
77.5
5o.4
5
6
56.6
23.2
9o.3
58.o
26.3
95.3
65-.0
35.5
06.7
78.7
5i.6
6
7
57-7
24.3
91.4
59.i
27.5
96.5
66.2
36.7
07.9
80.0
52. 9
7
8
58.8
25.4
92.5
60.2
28.6
97-6
67-4
37.8
09.1
81.2
54.1
8
9
59.9
26.5
93.6
61.4
29.7
98.8
68.5
39.o
io.3
82.4
55.3
9
10
i56i.o
1627.6
1694.8
1762.5
1830.9
i899.9
i969.7
2040.2
21 II. 5
2i83.6
2256.5
10
ii
62.1
28.7
95-9
63.6
32.0
I9OI.I
7°-9
4i.4
12.7
84-8
57.8
ii
12
63.2
29.8
97-°
64.8
33.2
02.3
72.0
42.6
i3.9
86.0
59.o
12
i3
644
3i.o
98.i
65.9
34.3
o3.4
73.2
43.8
87.2
60.2
i3
i4
65.5
32.1
99.3
67.0
35.5
04.6
744
44.9
i6.3
88.4
61.4
i4
i5
66.6
33.2
1700.4
68.2
36.6
05.7
75.6
46.i
!7.5
89.6
62.7
i5
16
67.7
34.3
oi.5
69.3
37.8
06. 9
76.8
47.3
18.7
9o.8
63.9
16
i7
68.8
35.4
02. 6
70.5
38.9
08.1
77-9
48.5
19.8
92.0
65.i
17
18
69.9
36.5
o3.8
71.6
4o.i
09.2
79.1
49-7
21.0
93.3
66.3
18
19
71.0
37.6
o4-9
72.7
41.2
10.4
80.2
5o.8
22.2
94-4
67.5
'9
20
1572.1
i638.8
1706.0
1773.9
1842.4
i9n.5
1981.4
2O52.O
2123.4
2i95.7
2268.8
20
21
73.2
39.9
07.1
75.o
43.5
12.7
82.6
53.2
24.6
96.9
70.0
21
22
74.3
4i.o
o8.3
76.1
44.6
i3.8
83.7
54.4
25.8
98.1
71.2
22
23
42.1
o9.4
77.2
45.8
i5.o
84-9
55.6
27.0
99.3
72.5
23
24
76.5
43.2
io.5
78.4
46.9
16.2
86.1
56.8
28.2
2200.5
73.7
24
25
77.6
44-3
n.6
79.5
48.i
I7.3
87.3
58.o
^9.4
01.7
74.9
25
26
78.7
45.5
12.8
80.6
49.2
i8.5
88.4
59.i
3o.6
o3.o
76.1
26
27
79.8
46.6
i3.9
81.8
5o.4
i9.6
89.6
6o.3
3i.8
04.2
' 77-4
27
23
8o.9
47-7
i5.o
83.o
5i.5
20.8
90.8
6i.5
33.o
o5.4
78.6
28
29
Bft.i
48.8
16.1
84-1
52.7
21.9
92.0
62.7
34.2
06.6
79-8
29
3o
i583.2
i649.9
1717.3
1785.2
1853.8
1923.1
I993.i
2o63.9
2i35.4
2207.8
2281.0
3o
3i
84.3
5i.o
18.4
86.4
55.o
24-3
94.3
65.1
36.6
09.0
82.3
3i
32
85.4
52.2
i9.5
87.5
56.i
25.4
95.5
06.2
37.8
10.2
83.5
32
33
86.5
53.3
20.7
88.6
57.2
26.6
96.6
67-4
39.o
11.4
84-7
33
34
87.6
54.4
21.8
89.8
58.4
27.8
97-8
68.6
40.2
12.7
86.0
34
35
88.7
55.5
22.9
90.9
59.6
28.9
99.0
69.8
4i-4
13.9
87.2
35
36
89.8
56.6
24.0
92.1
60.7
3o.i
2OOO.2
71.0
42.6
i5.i
88.4
36
37
9°-9
57.8
25.2
93.2
61.9
3i.3
01.3
72.2
43.8
i6.3
89-7
37
38
92.O
58.9
26.3
94.3
63.o
32.4
02.5
73.4
45.o
i7.5
9°-9
38
39
93.i
60.0
27.4
95.5
64.2
33.6
03.7
74-5
46.2
18.7
92.1
39
4o
i594.3
1661.1
1728.6
i796.6
i865.3
1934.7
2004.9
2075.7
2i47-4
2219.9
2293.3
4o
4i
95.4
62.2
29.7
97-8
66.5
35.9
06.0
76.9
48.6
21.2
94.6
4i
42
96.5
63.4
3o.8
98.9
67.6
37.i
07.2
78.1
49.8
22.4
95.8
42
43
97-6
64.5
31.9
1800.0
68.8
38.2
08.4
79-3
5i.o
23.6
97-°
43
44
98.7
65.6
33.1
OI.2
69.9
39.4
09.6
8o.5
52.2
24.8
98.3
44
45
99.8
66.7
34.2
02.3
71.1
4o.5
10.7
81.7
53.4
26.0
99.5
45
46
1600.9
67.8
35.3
o3.5
72.2
4i.7
11.9
82.9
54.6
27.2
2300.7
46
47
02.0
69.o
36.5
o4.6
73.4
42.9
84.o
55.8
28.5
02. o
47
48
o3.i
70.1
37.6
o5.7
74.5
44.o
14:3
85.2
57.0
29.7
03.2
48
49
04.2
71.2
38.7
o6.9
75.7
45.2
i5.4
86.4
58.2
3o.9
o4-4
49
5o
i6o5.4
i672.3
I739-9
1808.0
1876.8
1946.4
2016.6
2o87.6
2i59.4
2232.1
23o5.7
5o
5i
o6.5
73.4
4i.o
O9.2
78.0
47.5
17.8
88.8
60.7
33.3
06. 9
5i
52
07.6
74.5
42.1
io.3
79.2
48.7
19.0
9o.o
61.9
34.6
08.1
52
53
08.7
75.7
43.2
n.4
8o.3
49.9
2O.2
91.2
63.i
35.8
o9-4
53
54
09.8
76.8
444
12.6
8i.5
5i.o
21.3
92.4
64-3
37.o
10.6
54
55
10.9
77-9
45.5
i3.7
82.6
52.2
22.5
93.6
65.5
38.2
u.8
55
56
12.0
79-°
46.6
i4.9
83.8
53.4
23.7
94-8
66.7
39.4
i3.i
56
5?
i3.i
80.2
47.8
1 6.0
84-9
54.5
24.9
96.0
67. 9
40.7
i4.3
57
58
14.2
8i.3
48.9
17.2
86.1
55.7
26.0
97-1
69 i
41.9
i5.5 58
59
1 5.4
82.4
5o.o
i8.3
87.2
56.9
27.2
98.3
70.3
43.i 16.8 59
MERIDIONAL PARTS.
LATITUDE.
Min.
36°
37°
38°
39°
40°
41°
42°
43°
44°
45°
46°
Mill.
0
23i8.o
2392.6
2468.3
2545.o
2622.7
2701.6
2781.7
2863.1
2945.8
3o3o.o
3n5.6
0
I
19.2
93-9
69.5
46.2
24.0
02.9
83.i
64.5
47.2
3i4
I7.0
I
2
20. 5
95.i
70.8
47.5
25.3
o4-3
844
65.8
48.6
32.8
i8.5
2
3
21.7
96.4
72.1
48.8
26.6
o5.6
85.8
67.2
5o.o
34.2
19.9
3
4
23.0
97-7
734
5o.i
27.9
06.9
87.1
68.5
5i4
35.6
21.4
4
5
24.2
98.9
74-6
5i.4
29.2
o8.3
88.5
7o.o
52.8
37.0
22.8
5
6
25.4
2400.2
75.9
52. 7
3o.5
09.6
89.8
71.3
54-2
384
24.2
6
7
26.7
01.4
77.1
54.o
31.9
10.9
91.2
72-7
55.6
39.8
25. 7
7
8
27.9
02.7
78.5
55.3
33.2
12.2
92.5
74.i
57.0
4i.3
27.1
8
9
29.1
03.9
79-7
56.6
34-5
i3.5
93.8
754
58.3
42.7
28.5
9
10
233o.4
24o5.2
2481.0
2557.8
2635.8
2714.9
2795.i
2876.8
2959.8
3o44-i
3i3o.o
10
ii
3i.6
06.4
82.2
59.i
37.i
16.2
96.5
78.2
61.1
45.5
3i.5
ii
12
32.9
07.7
83.5
60.4
38.4
17.5
97-9
79.5
62.5
47.0
32.9
12
i3
34.i
09.0
84.8
61.7
39-7
18.9
99-3
8o.9
63.9
484
34.3
i3
i4
35.3
1O.2
86.1
63.o
4i.o
20. 2
2800.6
82.3
65.3
49.8
35.8
i4
i5
36.6
ii. 5
87.4
64.3
42.3
21.5
02.0
83. 7
66.7
5l.2
37.2
i5
16
37.8
12.7
88.6
65.6
43.6
22.9
o3.3
85.o
68.1
52.6
38.7
16
I7
39.0
14.0
89.9
66.9
44.9
24.2
o4-7
864
69.5
54-1
4o.i
17
18
4o.3
15.2
91.2
68.2
46.3
25.5
06.0
87.8
7°-9
55.5
4i.6
18
J9
4i.5
i6.5
92.4
69.5
47.6
26.8
o7.3
89.1
72.3
56.9
43.o
19
20
2342.8
2417-8
2493.7
2570.7
2648.9
2728.2
2808.8
2890.5
2973.7
3o58.3
3i44-5
20
21
44.o
19.0
95.0
72.0
5o.a
29.5
IO.I
91.9
76.1
59.7
45.9
21
22
45.3
20.3
96.3
73.3
5i.5
3o.8
n4
93.3
76.5
61.2
474
22
23
46.5
21.5
97.6
74-6
52.8
32.2
12.8
94.7
77-9
62.6
48.8
23
24
47-7
22.8
98.8
75.9
54-1
33.5
14.1
96.0
79-3
64-o
5o.3
24
25
49.0
24.O
2500.1
77.2
55.5
34-8
i5.5
974
80.7
654
5i.7
25
26
5o.2
25.3
01.4
78.5.
56.8
36.2
16.8
98.8
82.1
66.9
53.2
26
27
5i.5
26.5
02.7
79.8
58.i
37.5
18.2
2900.2
83.5
68.3
54.6
27
28
52.7
27.8
03.9
81.1
59.4
38.8
i9.5
0!.5
84-9
69.7
56.i
28
29
54.o
29.1
05.2
82.4
60. 7
4O.2
20. 9
02.9
86.3
71.1
57.5
29
3o
2355.2
243o.3
25o6.5
2583.7
2662.0
274l.5
2822.3
2904.3
2987.7
3072.6
SiSg.o
3o
3i
56.5
3i.6
07.8
86.0
63.3
42.9
23.6
o5.7
89.1
74-0
60.4
3i
32
57.7
32.9
09.0
86.3
64-6
44-2
25.0
o7.i
90.5
754
61.9
32
33
58.9
34.i
io.3
87.6
66.0
45.5
26.3
08.4
91.9
76.9
63.3
33
34
60.2
35.4
ii. 6
88.9
67.3
46.9
27.7
°9-7
93.3
78.3
G4.8
34
35
61.4
36.7
12.9
90.2
68.6
48.2
29.0
II. 2
94.7
79-7
66.2
35
36
62.7
37.9
14.2
9i.5
69.9
49-5
3o4
12.6
96.1
81.1
67.7
36
3?
63.9
39.2
1 5.4
92.8
71.2
50.9
3i.7
i4«o
97.5
82.6
69.1
37
38
65.2
4o.4
16.7
94.1
72.5
52.2
33.i
i5.3
98.9
84.o
70.6
38
39
66.4
4i-7
18.0
95.4
73.9
53.5
34.5
16.7
3ooo.3
854
72.0
39
4o
2367.6
2443.0
2519.3
2596.7
2675.2
2754.9
2835.8
2918.1
3ooi.8
3o86.9
3i73.5
4o
4i
68.9
44.2
20. 5
98.0
76.5
56.2
37.2
i9.5
03.2
88.3
75.o
4i
42
70.2
45.5
21.8
99.3
77.8
57.6
38.6
20.9
04.6
89.7
76.4
42
43
71.4
46.8
23.1
2600.5
•79.1
58.9
39.9
22.3
06.0
91.2
77-9
43
44
72.6
48.o
244
01.9
8o.5
60.2
4i-3
23.6
o74
92.6
79.3
44
45
73.9
49.3
25.7
03.2
81.8
6i.5
42.6
25.0
08.8
94-o
80.8
45
46
75.i
5o.6
27.0
o4.5
83.i
62.9
44.o
26.4
IO.2
95.5
82.3
46
4?
76.4
5i.8
28.3
o5.8
844
64-3
454
27.8
ii. 6
96.9
83.7
47
48
77.6
53.i
29.5
07.1
85.7
65.6
46.7
29.2
i3.o
98.3
85.2
48
49
78.9
54-3
3o.8
08.4
87.1
66.9
48.i
3o.6
i44
99-7
86.6
49
5o
238o.i
2455.6
2532.1
2609.7
2688.4
2768.3
2849.5
2932.0
3oi5.8
SlOI.2
3i88.i
5o
5i
81.4
56.9
33.4
II. O
89.7
69.6
5o.8
33.3
I7.2
02. 6
89.6
5i
52
82.6
58.i
34.7
12.3
91.0
71.0
52.2
34-7
18.7
o4.i
91.0
52
53
83.9
59.4
36.o
i3.6
92.3
72.3
53.5
36.i
20.1
o5.6
92.5
53
54
85.i
60.7
37.2
i4.9
93.7
73.7
54-9
37.5
21.5
O7.O
94.0
54
55
86.4
61.9
38.5
16.2
95.o
75.0
56.3
38.9
22-9
08.4
95.4
55
56
87.6
63.2
39.8
17.5
96.3
76.3
57.7
4o.3
24-3
o9.8 96.9 56
57
88.9
64.5
4i.i
18.8
97.6
77-7
59.o
4i,7
25. 7
ii. 2 98.4 57
58
90.2
65.8
42-4
2O.I
99.0
79-°
6o.5
43.i
27.1
12.7 998 58
59
91.4
67.0
43.6
21-4
2700.3
80.4
61.1
444
28.5
14.1^3201.3: 59
146
MERIDIONAL PARTS.
LATITUDE.
Min.
47°
48°
49°
50°
51°
52°
53°
54°
55°
56°
57°
Min.
o
3202.7
3291.5
3382.1
3474.5
3568.8
3665.2
3763.8
3864.6
3968.o
4o73-9
4182.6
o
I
O4«2
93.0
83.6
76.0
•70.4
66.8
65.4
66.3
69.7
75.7
84.5
I
2
05.7
94.5
85.i
77.6
72.O
08.4
67.1
68.0
7i.5
77.5
86.3
2
3
07.1
96.0
86.7
79.i
73.6
7O.I
68.8
69-7
73.2
79.3
88.1
3
4
08.6
97.5
88.2
80.7
75.2
71.7
7o.4
7i.5
75.0
81.1
90.0
4
5
I O.I
99.0
89.7
82.3
76.8
73.3
72.1
73.2
76.7
82.9
91.8
5
6
n.5
33oo.5
9i.3
83.8
78.4
75.o
73.7
74.9
78.4
84.7
93.7
6
7
i3.o
O2.O
92.8
85.4
79-9
76.6
75.4
76.6
80.2
86.4
95.5
7
8
i4-5
o3.5
94.3
87.0
8i.5
•78.2
77.1
78.3
82.0
88.2
97.3
8
9
i5.9
o5.o
95.8
88.5
83.i
79.8
78.7
80.0
83.7
9o.o
99.2
9
10
3217.4
33o6.5
3397.4
349o.i
3584.7
368i.5
3780.4
388i.7
3985.4
4091.8
4201.0
10
ii
18.9
08.0
98.9
91.6
86.3
83.i
82.1
83.4
87.2
93.6
02.9
ii
12
20.3
09.5
34oo.4
93.2
87.9
84.7
83.7
85.i
88.9
95.4
o4«7
12
i3
21.8
II. O
02. o
94.7
89.5
86.4
85.4
86.8
9°-7
97.2
06.6
i3
i4
23.3
12.5
o3.5
96.3
91.1
88.0
87.1
88.5
92.5
99.0
08.4
i4
l5
24.8
i4-o
o5.o
97-9
92.7
89.6
88.8
90.2
94.2
4ioo.8
io.3
i5
16
26.2
i5.5
06.6
99.4
94.3
9i.3
90.4
92.O
96.o
02.6
12. 1
16
!?
27.7
17.0
08.1
35oi.o
95.9
92.9
92.1
93.7
97-7
04.4
14.0
17
18
29.2
i8.5
o9.6
02.6
97.5
94-5
93.8
95.4
99.5
06.2
i5.8
18
*9
30.7
2O.O
n. i
04.1
99.i
96.2
95.5
97.I
4OOI.2
08.0
17.7
19
2O
3232.1
3321.5
3412.7
35o5.7
36oo.7
3697.8
3797-1
3898.8
4oo3.o
4109.8
4219.5
20
21
33.6
23.0
14.2
07.3
02.3
99.4
98.8
39oo.5
o4-7
n.6
21.4
21
22
35.i
24-5
i5.7
08.8
o3.9
37oi.i
38oo.5
O2. 2
o6.5
i3.4
23.2
22
23
36.6
26.0
i7.3
10.4
o5.5
02. 7
O2. 2
04.0
o8.3
15.2
25.1
23
24
38.o
27.5
18.8
12. 0
O7.I
o4-4
o3.8
©5.7
IO.O
17.1
27.0
24
25
39.5
29.0
20.4
i3.5
o8.7
06.0
o5.5
07.4
n.8
18.9
28.8
25
26
4i.o
3o.6
21.9
i5.i
io.3
o7.6
07.2
o9.i
i3.5
20.7
3o.6
26
27
42.5
32.1
23.5
16.7
n.9
09.3
08.9
10.8
i5.3
22.5
32.5
27
28
44-0
33.6
25. 0
i8.3
i3.6
10.9
io.5
12.5
17.1
24.3
34.4
28
29
45.4
35.i
26.5
19.8
i5.i
12.6
12.2
i4.3
18.8
26.1
36.2
29
3o
3246.9
3336.6
3428.0
3521.4
36i6.7
37i4.2
38i3.9
39i6.o
4020.6
4127.9
4238.1
3o
3i
48.4
38.1
29.6
23.0
18.4
i5.8
i5.6
17.7
22.4
29-7
4o.o
3i
32
49.9
39.6
3i.i
24.6
20.0
i7.5
i7.3
i9-4
24.1
3i.5
4i.8
32
33
5i.4
4i.i
32.7
26.1
21.6
19.1
18.9
21.2
25.9
33.3
43.7
33
34
52.8
42.6
34-2
27.7
23.2
20.8
20.6
22. 9
27.7
35.2
45.5
34
35
54.3
44-1
35.8
29.3
24.8
22.4
22.3
24-6
29.4
37.o
47-4
35
36
55.8
45.7
37.3
3o.8
26.4
24.1
24.O
26.3
3l.2
38.8
49.3
36
37
57.3
47.2
, 38.8
32.4
28.0
25.7
25-7
28.1
33.o
4o.6
5i.i
3?
38
58.8
48.7
4o.4
34.o
29.6
27.4
274
29.8
34-8
42.4
53.o
38
39
6o.3
50.2
4i.9
35.6
3i.3
29.0
29.1
3i.5
36.5
44-2
54-9
39
4o
3261.7
335i.7
3443.5
3537.1
3632.8
373o.7
383o.8
3933.2
4o38.3
4i46.i
4256.7
4o
4i
63.2
53.2
45.o
38.7
344
32.3
32.4
35.0
4o.i
47«9
58.6
4i
42
64-7
54.7
46.6
4o.3
36.i
34.0
34.i
36.7
4i.8
49.7
6o.5
42
43
66.2
56.2
48.i
4 1. Q
37.7
35.6
35.8
38.4
43.6
5i.5
62.3
43
44
67.7
57.8
49.7
43.5
39.3
37.3
*37.5
4o.2
45.4
53.4
64.2
44
45
69.2
59.3
5l.2
45.o
4o.9
38.9
39.2
41.9
47-2
55.2
66.1
45
46
70.7
60.8
52.8
46.6
42.5
4o.6
40.9
43.6
4g.o
57.o
68.0
46
47
72.1
62.3
54.3
48.2
44.i
42.2
42.6
45.4
5o.7
58.8
69.8
47
48
73.6
63.8
55.8
49-8
45.8
43.9
44.3
47.1
52.5
60.7
71.7
48
49
75.i
65.4
57.4
5i.4
474
45.5
46.o
48.8
54.3
62.5
73.6
49
5o
3276.6
3366.9
3458.9
3553.0
3649.o
3747.2
3847-7
395o.6
4o56.i
4i64.3
4275.5
5o
5i
78.!
68.4
6o.5
54.6
5o.6
48.8
49.4
52.3
57.8
66.1
77-4
5i
52
79.6
69-9
62.0
56.i
52.2
5o.5
5i.i
54-0
59.6
68.0
79.2
52
53
81.1
71.4
63.6
57.7
53.8
52.1
52.8
55.8
61.4
69.8
81.1
53
54
82.6
73.o
65.2
59.3
55,5
53.8
54-4
57.5
63.2
71.6
83.o
54
55
84.i
74-5
66.7
6o.9
57.i
55.5
56.i
59.3
65.o
73.5
84.9
55
56
85.6
76.0
68.3
62.5
58.7
57.1
57.8
61.0
66.8
75.3
86.8
56
57
87.!
77.5
69.8
64-0
6o.3
58.8
59.5
62.7
68.5
77.1
88.6
57
58
88.5
79-°
71-4
65.6
61.9
60.4
6L2
64-5
7o.3
70. o
90.5
58
59
90.0
80.6
73.o
67.2
63.6
62.1
62. 9
66.2
72.1
80.8
92.4
59
MERILIONAL PARTS.
LATITUDE.
Min.
58°
59°
60°
61°
62°
63°
64°
65°
66°
67°
68°
Min.
o
4294.3
4409.1
4527.4
4649-2
4775.0
49o4-9
5039.4
5178.8
5323.5
5474.0
563o.8
0
I
96.2
n. i
29.4
5i.3
77.1
07.1
4i.7
81.2
26.0
76.6
33.5
I
2
98.1
i3.o
3i.4
53.4
79.3
o9.4
44.o
83.5
28.4
79.1
36.2
2
3
[3oo.o
i5.o
33.4
55.4
81.4
n.6
46.3
85.9
30.9
8i.7
38.8
3
4
01.9
16.9
35.4
57.5
83.5
i3.8
48.6
88.3
33.4
84.3
4i.5
4
5
03.7
18.9
37-4
59.6
85.6
16.0
5o.9
9°-7
35.8
86.9
44-2
5
6
o5.6
20.8
39.4
61.6
87.8
18.2
53.i
93.i
38.3
89.4
46.9
6
7
oy.S
22.8
4i-4
63.7
89.9
20.4
55.4
• 95.4
4o.8
92.0
49.6
7
8
09.4
24.7
43.4
65.8
92.1
22.6
57.7
97.8
43.2
94-5
52.3
8
9
n. 3
26.7
45.4
67.8
94.2
24.8
60.0
52OO.2
45-7
97.1
54.9
9
10
43i3.2
4428.6
4547-4
4669.9
4796.3
4927.0
5o62.3
52O2.6
5348.2
5499.7
5657.6
10
ii
i5.i
3o.6
49.4
72.0
98.5
29.2
64-6
o4-9
5o.7
55o2.3
6o.3
ii
12
17.0
32.5
5i.4
74.1
48oo.6
3i.5
66.9
o7.3
53.i
04.9
63.o
12
i3
18.9
34.5
53.5
76.1
02.8
33.7
69.2
09-7
55.6
07.4
65.7
i3
i4
20,8
36.4
55.5
78.2
o4-9
35.9
7i.5
12. 1
58.i
IO.O
68.4
i4
i5
22.7
38.4
57.5
8o.3
07.1
38.i
73.8
i4.5
60.6
12.6
71.1
i5
16
24.6
4o.3
59.5
82.4
09,2
4o.3
76.1
i6.9
63.i
15.2
73.8
16
J7
26.5
42.3
6i.5
84-5
11.4
42.6
784
i9.3
65.6
17.8
76.5
J7
18
28.4
44-2
63.5
86.5
i3.5
44.8
80.7
21.6
68.0
20.4
79.2
18
:9
3o.3
46.2
65.6
88.6
i5.7
47.0
83.o
24.0
70.5
23.0
81.9
J9
20
4332.2
4448.2
4567.6
4690.7
4817.8
4949.2
5o85.3
5226.4
5373.0
5525.6
5684.6
20
21
34.1
5o.i
69.6
92.8
2O.O
$i.5
87.6
28.8
75.5
28.1
87.3
21
22
36.o
52.1
71.6
94.9
22.1
53.7
9o.o
3l.2
78.0
30.7
90.0
22
23
37.9
54.i
73.6
97.0
24-3
55.9
92.3
33.6
8o.5
33.3
92.7
23
24
39.8
56.o
75.7
99.1
26.4
58.2
94.6
36.o
83.o
35-9
95.5
24
25
4i.8
58.o
77-7
4701.1
28.6
6o.4
96-9
38.4
85.5
38.6
98.2
25
26
43.7
60.0
79-7
03.2
3o.8
62.6
99-2
4o.8
88.0
41.2
5700.9
26
27
45.6
61.9
81.7
o5.3
32.9
64.9
5ioi.5
43.2
90.5
43.8
o3.6
27
28
47-5
63.9
83.8
07.4
35.i
67.1
o3.8
45.7
93.0
46-4
o6.3
28
29
49.4
65.9
85.8
o9.5
37.3
69.4
06.2
48.i
95.5
49.0
09.1
29
3o
435i.3
4467.8
4587.8
4711.6
4839.4
4971-6
5io8.5
525o.5
5398.0
555i.6
57n.8
3o
3i
53.2
69.8
89.9
i3.7
4i.6
73.8
10.8
52. 9
54oo.5
54.2
i4-5
3i
32
55.i
71.8
91.9
i5.8
43.8
76.1
i3.i
55.3
o3.o
56.8
i7.3
32
33
57.i
73.7
93.9
17.9
45.9
78.3
i5.5
57.7
o5.5
594
20.0
33
34
Sg.o
75.7
96.0
2O.O
48.i
80.6
17.8
60. i
08. i
62.1
22.7
34
35
60.9
77-7
98.0
22.1
5o.3
82.8
20.1
62.6
10.6
64-7
25.5
35
36
62.8
79-7
46oo.o
24-2
52.4
85.i
22.4
65.o
i3.i
67.3
28.2
36
37
64,7
81.6
02. i
26.3
54.6
87.3
24.8
67.4
i5.6
69.9
30.9
37
38
66.7
83.6
o4«i
28,4
56.8
89.6
27.1
69.8
18.1
72.6
33.7
38
39
68.6
85.6
06.1
3o.5
59.o
91.8
294
72.2
2O.6
76.2
364
39
4o
437o.5
4487-6
4608.2
4732.6
486i.i
4994.1
5i3i.8
6274.7
5423.2
5577.8
5739.2
4o
4i
72.4
89.6
10.2
34-7
63.3
• 96.3
34.i
77.1
25.7
80.4
41.9
4i
42
74-3
9i.5
12.3
36.8
65.5
98.6
36.5
79.5
28.2
83.i
44-7
42
43
76.3
93.5
i4.3
39.o
67.7
5ooo.8
38.8
82.0
3o.8
85.7
47.5
43
44
78.2
95.5
16.4
4i.i
69.9
o3.i
4i.i
844
33.3
88.4
5o.2
44
45
80. i
97.5
18.4
43.2
72.0
o5.4
43.5
86.8
35.8
91.0
52.9
45
46
82.1
99.5
20.5
45.3
74.2
07.6
45.8
89.3
38.4
93.6
55.7
46
47
84.o
45oi.5
22.5
474
76.4
09.9
48.2
91.7
40.9
96.3
58.5
47
48
85.9
o3.4
24.6
49.5
78.6
12.2
5o.5
94.1
434
98.9
61.2
48
49
87.8
o5.4
26.6
5i.6
80.8
l44
52.9
96.6
46.o
56oi.6
64.0
49
5o
4389.8
4507.;
4628.7
4753.7
4883.0
5oi6.7
5i55.2
5200.0
5448.5
56o4-2
5766.8
5o
5i
91.7
09.4
30.7
55.9
85.2
18.9
57.6
53oi.5
5i.o
06.9
69.5
5i
52
93.6
II. L
32.8
58.o
87.4
21.2
59.9
03.9
53.6
o9.5
72.3
52
53
95.6
i3.4
34.8
60. i
89.5
23.5
62.3
o6.3
56.i
12.2
75.i
53
54
97.5
i5.;
36.9
62.2
91.7
25.8
64.6
08.8
58.7
i4.8
77-9
54
55
99.4
17.2
39.o
64.4
93.9
28.0
67.0
II. 2
61.2
i7.5
80.6
55
56
44oi.2
19.4
4i.o
66.5
96.1
3o.3
69.4
i3.7
63.8
20.2
834
56
57
o3.3
2.1.1.
43.o
68.6
98.3
32.6
71.7
16.1
66.3
22.9
86.2
57
58
o5.3
23.4
45.i
70.7
49oo.5
34-9
74.i
18.6
68.9
25.5
89.0
58
59
07.2
25.4
47.2
72.9
02.7
37.i
76.4
21. 1
7i.4
28.2
9i.8
59
148
MERIDIONAL PARTS.
LATITUDE.
Min.
69°
70°
71°
72°
73°
74°
75°
76°
77°
78°
79°
Min.
O
5794-6
5965.9
6145.7
6334.8
65344
674i).7
697o.3
7210.1
7467.2
7744-6
8o45. 7
O
I
97-4
68.8
48.8
38.i
37.8
49.4
74.2
14.2
71.7
49.4
5i.o
I
2
58oo.i
71.8
5i.9
4i.3
4i.3
53.o
78.1
i8.3
76.1
54-2
56.2
2
3
02.9
74-7
54-9
44-6
44-7
56.6
81.9
22.5
80.6
59.o
6i.5
3
4
o5.y
77.6
58.o
47-8
48.i
6o.3
85.8
26.6
85.o
63.9
66.7
4
5
o8.5
80.6
61.1
5i.i
5i.6
63.9
89.7
3o.8
89.5
68.7
72.0
5
6
li,3
83.5
64-2
54.3
55.o
67.6
93.6
35.o
94.0
73.5
. 77-3
6
7
l4«2
86.4
67.3
57.6
58.5
71.2
97.5
39.i
98.5
78.4
82.6
7
8
17.0
89.4
70.4
60.8
61.9
74-9
7001.4
43.3
75o3.o
83.3
87.9
8
9
19.8
92.3
73.5
64.i
65.3
78.5
o5.3
47-5
07.4
88.1
93.2
9
10
5822.6
SggS.S
6176.6
6367.4
6568.8
6782.2
7009.2
725l.7
75n.9
7793.o
8098.5
10
n
25.4
98.2
79-7
70.6
72.3
85.9
i3.i
55.8
i6.5
97-9
8io3.8
ii
12
28.2
6001.2
82.8
73.9
75.7
89.6
17.0
60.0
21.0
7802.8
09.2
12
i3
3i.o
o4-i
85.9
77.2
79.2
93.2
20.9
64.2
25.5
07-7
14.5
i3
i4
33.8
07.1
89.0
80.4
82.6
96.9
24.8
68.4
3o.o
12.6
19.9
i4
i5
36.7
IO.O
92.1
83.7
86.1
6800.6
28.8
72.6
34-5
I7.5
25.2
i5
16
39.5
1 3.o
95.2
87.0
89.6
o4.3
32.7
76.8
Sg.i
22.4
3o.6
16
I7
42.3
1 6.0
98.3
90.3
93.0
08.0
36.6
81.1
43.6
27.3
36.o
J7
18
45.i
18.9
6201.4
93.6
96.5
n.6
4o.6
85.3
48.i
32.2
4i.3
18
J9
48.o
21.9
o4.5
96.9
6600.0
1 5.4
44-5
89.5
52.7
37.2
46.7
'9
20
585o.8
6024.9
6207.7
64oo.s
66o3.5
6819.1
7048.5
7293.7
7557.3
7842.1
8i52.i
20
21
53.6
27.8
10.8
o3.4
07.0
22.8
52.4
98.0
61.8
47.i
57.5
21
22
56.5
3o.8
i3.9
06.7
!0.5
26.5
56.4
7302.2
66.4
52. 0
62.9
22
23
59.3
33.8
17.0
IO.I
i4-o
30.2
6o.3
06.4
71.0
57.o
68.4
23
24
62.2
36.8
20.2
i3.4
17.5
33.9
64.3
10.7
75.5
61.9
73.8
24
25
65.o
39.8
23.3
16.7
21.0
37.6
68.3
i5.o
80. i
66.9
79.2
25
26
67.8
42.7
26.5
20. o
24.5
4i.3
72.2
19.2
84-7
7i.9
84.7
26
87
70.7
45.7
29.6
23.3
28.0
45.i
76.2
23.5
89.3
76.9
90.1
27
28
73.5
48.7
32.7
26.6
3i.5
48.8
80.2
27.7
93.9
81.9
95.6
28
29
76.4
5i.7
35.9
29.9
35.o
52.5
84.2
32.0
98.5
86.9
8201.1
29
3o
5879.2
6o54-7
6239.0
6433.3
6638.5
6856.3
7088.2
7336.3
7603.2
789I-9
8206.6
3o
3i
82.1
57.7
42.2
36.6
42.1
60.0
92.2
4o.6
07.8
96.9
12. 1
3i
32
85.o
60.7
45.3
39.9
45.6
63.8
96.2
44-9
12.4
•7902.0
I7.6
32
33
87.8
63.7
48.5
43.2
49' i
67.5
7100.2
49-2
17.0
O7.O
23.1
33
34
90.7
66.7
5i.7
46.6
52.6
7i.3
O4.2
53.5
21.7
12.0
28.6
34
35
93.6
69.7
54.8
4y-9
56.2
75.0
08.2
57.8
26.3
I7.I
34.i
35
36
96.4
72.7
58.o
53.3
59.7
78.8
12.2
62.1
3i.o
22.1
39.7
36
37
99.3
75.7
61.2
56.6
63.3
82.6
i6.3
66.4
35.6
27.2
45.2
37
38
5902.2
78.8
64.3
60.0
66.8
86.3
20.3
70.7
4o.3
32.3
5o.8
38
39
o5.o
81.8
67.5
63.3
70.4
90.1
24.3
75.i
45.o
37.3
55.3
39
4o
5907.9
6084.8
6270.7
6466.7
6673.9
6893.9
7128.4
7379-4
7649. 7
7942.4
8261.9
4o
4i
10.8
87.8
73.9
70.0
77-4
97-7
32.4
83.7
54.3
47.5
67.5
4i
42
i3.7
90.8
77.1
73.4
81.0
6901.5
36.4
88.1
Sg.o
52.6
73.1
42
43
16.6
93.9
80.2
76.7
84-6
o5.3
4o.5
92.4
63. 7
57.7
78.6
43
44
19.4
96.9
•83.4
80.1
88.2
09.1
44.5
96.8
68.4
62.8
84-3
44
45
22.3
99.9
86.6
83.5
91.7
I2.9
48.6
74oi.i
73.2
68.0
89.9
45
46
25.2
6io3.o
89.8
86.9
95.3
I6.7
52.7
o5.5
77-9
73.i
95.5
46
47
28.1
06.0
93.0
90.2
98.9
20. 5
56.7
09.9
82.6
78.2
83oi.i
47
48
3i.o
09.0
96.2
93.6
6702.5
24.3
60.8
i4-3
87.3
83.4
06.7
48
49
33.9
12. 1
99.4
97.0
06. i
28.1
64.9
18.6
92.!
88.5
12.4
49
5o
5936.8
6n5.i
6302.6
65oo.4
6709.7
693i.9
7i69.o
7423.0
•7696.8
7993-7
83i8.i
5o
5i
39.7
18.2
o5.8
o3.8
13.2
35.7
73.i
27.4
77oi.5
98.9
23.8
5i
52
42.6
21.2
09.1
07.2
16.8
39.6
77.2
3i.8
o6.3
8004.0
29.4
52
53
45.5
24.3
12.3
10.6
20.4
43.4
81.2
36.2
n. i
09.2
35.i
53
54
48.4
27.3
i5.5
i4-o
24.0
47-2
85.3
4o.6
i5.8
i4-4
4o.8
54
55
5i.3
3o.4
18.7
i74
27.7
5x.i
89.5
45.i
20.6
19.6
46.5
55
56
54.2
33.4
21.9
20.8
3i.3
54.9
93.6
49-5
25.4
24.8
52.2
56
57
57.2
36.5
25.1
24.2
34.9
58.8
97-7
53.9
30.2
3o.o
58.o
57
58
60.1
39.6
28.4
27.6
, 38.5
62.6
7201.8
58.3
35.o
35.2
63.7
58
59
63.o
42.6
3i.6
3i.o
42.1
66.5
o5.9
62.8
39.8
4o.5
69.4
59
CORRECTIONS TO MIDDLE LATITUDE.
1
Mid.
Lat.
DIFFERENCE OF LATITUDE.
1°
2D
3°
4°
5°
6°
7°
8°
9°
10°
11°
12°
13°
14°
15°
16*
17°
18°
19° 20°
o
i5
0
2
3
5
7
9
12
i5
18
22
26
3i
36
4i
47
52
59
65
72
16
o
2
3
4
6
II
i4
18
21
25
3o
34
39
44
5o
56
62
69
17
o
2
3
4
6
8
II
i4
!7
20
24
28
33
38
43
48
54
60
66
18
o
3
4
6
8
IO
i3
16
2O
23
27
32
36
4i
46
52
58
64
I9
0
3
4
6
8
10
i3
16
19
22
26
3o
35
4o
45
5o
56
61
20
o
2
4
5
7
IO
12
i5
18
22
25
29
34
38
43
48
54
60
21
o
2
4
5
7
9
12
i5
18
21
25
29
33
37
42
47
52
58
22 ! o
2
4
5
7
9
12
i4
17
21
2/1
28
32
36
4i
46
5i
56
23
0
2
3
5
7
9
II
i4
I7
2O
23
27
3i
35
4o
45
5o
55
24
o
2
3
5
7
9
II
i4
16
20
23
27
3i
35
39
44
49
54
25
0
2
3
5
7
9
II
i3
16
I9
23
26
3o
34
39
43
48
53
26
0
2
3
5
6
8
II
i3
16
J9
22
26
3o
34
38
42
47
52
27
o
2
3
5
6
8
II
i3
16
19
22
25
29
33
37
42
47
52
28
o
2
3
5
6
8
10
i3
16
18
22
25
29
33
37
4i
46
5i
29
0
2
3
5
6
8
10
i3
i5
18
21
25
28
32
37
4i
46
5i
3o
o
2
3
5
6
8
IO
i3
i5
18
21
25
28
32
36
4i
45
5o
3i
o
2
3
5
6
8
IO
12
i5
18
21
24
28
32
36
4o
45
5o
32
o
o
2
3
4
6
8
IO
12
i5
18
21
24
28
32
36
4o
45
5o
33
0
o
2
3
4
6
8
10
12
i5
18
21
24
28
32
36
4o
45
49
34
o
o
2
3
4
6
8
IO
12
i5
18
21
24
28
32
36
4o
45
49!
35
o
0
2
3
4
6
8
IO
12
i5
18
21
24
28
32
36
4o
45
49
36
o
2
3
4
6
8
IO
12
i5
18
21
24
28
32
36
4o
45
49
37
o
2
3
4
6
8
10
12
i5
18
21
24
28
32
36
4o
45
49
38
0
2
3
4
6
8
IO
12
i5
18
21
24
28
32
36
4o
45
5o
39
o
2
3
4
6
8
IO
12
i5
18
21
24
28
32
36
4o
45
5o
4o
o
2
3
5
6
8
IO
i3
i5
18
21
25
28
32
36
4i
45
5o
4i
0
2
3
5
6
8
IO
i3
i5
18
21
25
28
32
37
4i
46
5i j
42
o
2
3
5
6
8
IO
i3
i5
18
22
25
20
33
37
4i
46
5i i
43
o
2
3
5
6
8
IO
i3
16
18
22
25
29
33
37
42
46
52
44
0
2
3
5
6
8
IO
i3
16
J9
22
25
20
33
38
42
47
52
45
o
2
3
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6
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II
i3
16
I9
22
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38
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48
53
46
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8
II
i3
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I9
22
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38
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53
47
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3
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7
9
II
i3
16
23
26
3o
35
39
44
49
54
48
o
2
3
5
7
9
II
i4
17
20
23
27
3i
35
4o
44
5o
55
*9
o
2
3
5
7
9
II
i4
17
20
23
27
3i
36
4o
45
5o
56
5o
o
9
4
5
7
9
II
i4
20
24
28
32
36
4i
46
5i
57
5i
0
2
4
5
7
9
12
i4
17
21
24
28
32
37
42
47
52
58
52
b
2
4
5
7
9
12
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18
21
25
29
33
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53
59
53
o
2
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7
IO
12
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18
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34
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60
54
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56
62
55 o
2
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16
19
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63
56
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!9
23
27
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36
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46
52
58
65
57
o
3
4
6
8
10
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16
20
24
28
32
37
42
48
54
60
66
58
0
2
3
4
6
8
II
i4
17
20
24
28
33
38
43
49
55
61
68
59
0
2
3
4
6
8
II
i4
21
25
29
34
39
45
5o
57
63
70
60
o
2
3
4
6
9
II
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18
22
26
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35
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46
52
58
65
72
61
o
2
3
5
7
9
12
i5
18
22
26
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36
42
47
53
60
67
75
62
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2
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7
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19
23
27
32
37
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49
55
62
7°
77
63
0
2
3
5
7
10
12
16
20
24
28
33
39
44
5i
57
64
72
80
64
o
2
3
5
7
10
13
16
20
24
29
34
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46
52
59
67
75
83
65
o
2
3
5
7
IO
i3
I?
21
25
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36
4i
48
54
62
69
78
86
66
0
2
3
5
8
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i4
18
22
26
32
37
43
5o
57
64
72
81
9°
67
o
2
4
6
8
II
i4
18
23
28
33
39
45
52
59
67
76
85
94
68
0
2
4
6
8
12
i5
19
24
29
34
4o
47
54
62
70
79
89
99
69
o
2
4
6
9
12
16
20
25
3o
36
42
49
57
65
74
83
93
io4
70
0
. 2
4
6
9
13
16
21
26
32
38
44
52
60
68
78
88
98
no
o
2
4
7
10
i3
17
22
27
33
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47
55
63
72
82
93
io4
116
72
o
3
5
7
IO
i4
18
23
29
35
42
49
58
67
76
87
98 in
124
150 LOGARITHMS FOR COMPUTING COMPOUND INTEREST.
In computing compound inter* st for long periods of time,
the following logarithms to more than six places.
it is necessary to have
Number.
Logarithm.
Number.
Logarithm.
.0026
.0060
.0076
.0100
.0126
.0160
.0176
.0200
.0226
.0260
.0276
,o3oo
,o325
.o35o
.P375
,o4oo
.00108 438i3
.00216 60618
.oo324 5o548
.00432 13738
.00639 60319
.00646 60422
.00763 44i79
.00860 01718
.00966 33167
.01072 38654
.01178 i83o5
.01283 72247
.01389 oo6o3
.01494 03498
.01698 81064
.01703 33393
.0426
.o45o
.0475
.0600
.0626
.0660
.0676
.0600
.0626
.0660
.0676
.0700
.0726
.0760
.0776
.0800
,01807 6o636
.01911 62904
.020i5'4o3i6
.02118 92991
.02222 21046
.02326 24696
.02428 03760
.O253o 58653
.02632 89387
.02734 96078
.0283678837
.0293837777
.o3o39 73009
.o3i4o 84643
.o324i 72788
.o3342 37555
NUMBERS OFTEN USED IN CALCULATIONS.
Circumference <
Surface of a spl
Area of a circle
Area of a circle
Capacity of a s[
Capacity of a sp
1 — 3.1416926 .
)f a circle to diameter i }
lere to diameter i >
3.1416926
.7863982
.6236988
4.1887902
0.3183099
°. 2967796
206264". 8
.0174533
.0002909
.00000486
.00000970
.ooooi454
.00001939
.00002424
.00002909
.00003394
.00003879
.oooo4363
2.7182818
.4342945
1296000
864oo
6280
Logarithms.
0.497l5o
9.896090
9.718999
0.622089
9.602860
i.758i23
5.3i4425
8.241877
6.463726
4.686676
4.986606
6.162696
5.287635
5.384545
5.463726
5.53o673
5.588665
6.639817
0.434294
9-637784
6. 112606
4.9365i4
3.722634
to radius i .... --)
to diameter i
>here to diameter i
_
>here to radius i
Arc equal to rac
Arc equal to raci
Length of i deg
Length of i mit
Sine of i secon
Sine of 2 secon<
Sine of 3 secon
Sine of 4 secon
Sine of 5 secon
Sine of 6 secon
Sine of 7 secon
Sine of 8 secon
Sine of 9 secon
Base of Napier
Modulus of the
36o degrees ex
24 hours expre
Number of feet
ius expressed in degrees
ius expressed in seconds
ree in parts of radius
— 5i
mte in parts of radius
^
i
Is
3s
is
3s
3s
3s
• "
3s
3s
s system of logarithms. . .
common logarithms . .
pressed in seconds. .
5sed in seconds
in one mile
THE
END.
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THE Course of Mathematics by Professor Loomis has now been for several years before th«
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so well adapted to the circumstances and wants of American teachers and pupils. — W. C. LAEEABEE, late Professor
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A Treatise on Algebra.
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In accordance with the expressed wish of many teachers,
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Professor Loomis's Algebra is peculiarly well adapted
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The answers to about one third of the questions are
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I have used Loomis's Elements of Algebra in my school
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ELEMENTS OF NATURAL PHILOSOPHY,
DESIGNED FOE
ACADEMIES AND HIGH SCHOOLS.
By Elias Loomis, LL.D.
12mo, 350 pages, Sheep extra, $1 00.
This volume is the result of many years of laborious study, and presents in an elementary form the fruits of
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The following are a few of the Notices of LOOMIS'S NATCRAL PHILOSOPHY which have been re-
ceived by the Publishers :
Prof. Loomis's Elements of Natural Philosophy is one
of the best and most complete works of the kind that has
been published, and possesses a clearness and conciseness
seldom equaled. I have seldom seen so much useful in-
formation in one volume.— EDWARD T. FBISTOB, Profes-
sor of Mathematics, Columbian College, D. C.
This volume has the merit of being a digest and not a
compilation. For a large class of students it is the only
suitable work on this subject that I have seen, bringing
into use, as it does, all the mathematics usually studied
in our academies, and no more.— E. W. EVANS, Profes-
sor of Natural Philosophy in Marietta College, Ohio.
Prof. Loomis's Natural Philosophy is clear, accurate,
and methodical.— DANIEL KIBKWOOD, Prof essor of Nat-
ural Philosophy in Indiana State University.
The characteristics of Loomis's Mathematical Work*,
which we so highly prize, are fully sustained in his Nat-
ural Philosophy. I am glad to find at last a text-book
on this subject so logically expressed, so complete and so
accurate.— N. B. WEBSTER, A.M., President of Virginia
Collegiate Institute, Portsmouth, Va.
This work of Prof. Loomis claims to be a philosoph-
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tration we have not met its equal. Adapted to the high-
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who do not care for demonstrations. We hope it will
crowd out of our schools the heterogeneous productions
that school boys have to stuff themselves with ; and thus
give thorough instruction that will tend to develop some
faculties besides memory. — S, J. C. SWEZEY, Marion,
Alabama.
Prof. Loomis's Natural Philosophy combines concise-
ness with very great clearness of illustration, and is the
best text-book of the kind that I have examined.— Prof.
W. FEEBEL, Nashville, Tenn.
Prof. Loomis's treatise has my decided preference as a
text-book on Natural Philosopy. It is simple and com-
prehensive in its style, and its principles are discussed
with clearness and brevity. — J. W. FERREE, A.M., Pro-
fessor of Mathematics, Dickinson Seminary, Pa.
Prof. Loomis's Natural Philosophy is the best elemen-
tary work on this subject which I have hitherto seen. It
treats is pregnant with useful knowledge.— A. W. MASON,
Jeansville, Penn.
Prof. Loomis's Natural Philosophy is the best text-
book on that subject yet published. With all its value
as a text-book, it combines a pleasing style, instructive
examples and illustrations, and is quite a readable book
for others besides school-boys.— B. W. MoDorraoLD,
Professor in Bethel College, Tenn.
While this volume requires of the pupil nothing be-
yond a knowledge of the elementary mathematics, it de-
velops the philosophy of all the leading principles of me-
chanics and physics. Its definitions are clear and con-
cise, its statement of principles methodical and accurate.
It embraces in a duodecimo volume of 350 pages, a com-
plete digest of what is usually spread over three or four
times this space. Nor by this condensation is the study*
rendered repulsive, but exactly the reverse. We com-
mend this work without qualification, as one admirably
adapted to interest the pupil, while it cultivates the habit
of philosophical reflection and observation. — New York
Observer.
This volume is not only an admirable treatise for the
use of the higher classes in schools, but is a most conve-
nient compendium of the latest discoveries in Natural
Philosophy for the instruction of adult readers. — New
York Commercial Advertiser.
This volume is an admirable compendium of the prin-
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not dull, heavy, or incomprehensible, bir
terms that all can comprehend, and that few will be una-
ble to remember.— Baltimore Dailii 7V
Among the numerous books of its class which have
originated in this country, this volume has no superior
in clearness, accuracy, and comprehensiveness. — Boston
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Prof. Loomis's works on Arithmetic, Geometry, &c., '
are models of clear and precise style, comprehensive
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ural Philosophy is marked by the same excellences. — To-
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every mechanic in his winter evenings, will FO fill his
head, as to leave no room for idle thoughts. — Newark
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The study of Prof. Loomis's work will make solid
thinkers, not smatterers. While popularizing science,
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ure to the private student. Every subject on which it | alone give it a title to that name. — a, Y. Daily Ni
Also, published by
A TREATISE ON ARITHMETIC, Theoretical and
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