Elements of trigonometry, plane and spherical: adapted to the present state of analysis : to which is added, their application to the principles of navigation and nautical astronomy : with logarithmic, trigonometrical, and nautical tables, for use of colleges and academies (Google eBook)

Front Cover
Wiley & Putnam, 1838 - Trigonometry - 307 pages
0 Reviews
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

TRIGONOMETRICAL LINES 13 Their use
13
Its definition
14
Variations in the value of the sine
15
Sines of other quadrants derived from the first
16
Algebraic sign ofthesine
17
THE TANGENT 19 Its definition and changes of value
18
Recapitulation of the values of the tangent
20
Algebraic sign of the secant
21
Its definition
22
Its variations of value
23
Article P 28 Values of the cotangent
24
Algebraic notation of the trigonometrical lines
25
Expression for the secant
27
Relation of tangent and cotangent
28
40 and 41 Applications of these formulae
31
Advantage of logarithms
35
Logarithms of the base and unity
36
Method of calculating tables of logarithms
37
Theory of the characteristic
39
Explanation of the Tables
40
Rule to find the logarithm of any number between 1 and 10000
41
Logarithms of decimal numbers
43
Rule to find the logarithms of numbers greater than 10000
48
Examples in multiplication and division by logurithms
49
Formation of powers by logarithms
51
Extraction of roots by logarithms
52
Table of logarithmic sines tangents c
53
To find the degrees minutes and seconds corresponding to any given logarithmic sine tangent c
54
Rules to find the logarithmic secant and cosecant of any given arc
57
Solution of rightangled triangles with the aid of logarithms 61 Examples
59
Use of the arithmetical complement
60
Example in the measurement of distances
61
A side and the opposite angle being two of the given parts
62
Two angles and the interjacent side being given
64
Example in the measurement of heights the bases of which are in accessible 66
66

Common terms and phrases

Popular passages

Page 201 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 126 - The latitude of a place is its distance from the equator, measured on the meridian of the place, and is north or south according as the place lies north or south of the equator.
Page 78 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 35 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 83 - An oblique equator is a great circle the plane of which is perpendicular to the axis of an oblique projection.
Page 17 - The minutes in the left-hand column of each page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right.hand column, belong to the degrees below.
Page 14 - SINE of an arc, or of the angle measured by that arc, is the perpendicular let fall from one extremity of the arc, upon the diameter passing through the other extremity. The COSINE is the distance from the centre to the foot of the sine.
Page 174 - A' . cos z = .- ;t cos A cos A ' and in the triangle mzs, cos d sin sin a' cos z = cos a cos a hence, for the determination of D, we have this equation, viz., cos D sin A sin A' cos d sin a sin a
Page 66 - FH is the sine of the arc GF, which is the supplement of AF, and OH is its cosine ; hence, the sine of an arc is equal to the. sine of its supplement ; and the cosine of an arc is equal to the cosine of its supplement* Furthermore...
Page 162 - S"Z and declination S"E, and it is north. We have here assumed the north to be the elevated pole, but if the south be the elevated pole, then we must write south for north, and north for south. Hence the following rule for all cases. Call the zenith distance north or south, according as the zenith is north or south of the object. If the zenith distance and declination be of the same name, that is, both north or both south, their sum will be the latitude ; but, if of different names, their difference...

Bibliographic information