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 logarithmical, trigonometrical, and nautical tables

Couverture
 

Table des matières

Their Algebraic signs
30
Algebraic notation of the trigonometrical lines
31
Expression for the tangent in terms of the sine and cosine
32
Expression for the secant
33
for the cotangent 35 for the cosecant
34
Corollaries from these
36
Relation of tangent and cotangent
37
Derivation of formulæ
38
39 40 and 41 Applications of these formulæ
39
Advantage of logarithms THEORY OF LOGARITHMS
42
Definition of logarithms
43
Logarithms of the base and unity
44
Definition of a table of logarithms
45
Method of calculating tables of logarithms
46
Theory of the characteristic Explanation of the Tables
47
Rule to find the logarithm of any number between 1 and 10000
49
Formation of powers by logarithms 55 Extraction of roots by logarithms 56 Table of logarithmic sines tangents c
53
Rule to find from the table the logarithmic sine tangent c of any given number of degrees minutes and seconds
56
To find the degrees minutes and seconds corresponding to any given logarithmic sine tangent c
58
Solution of rightangled triangles with the aid of logarithms
59
Examples
61
Use of the arithmetical complement
62
Example in the measurement of distances
63
A side and the opposite angle being two of the given parts
64
Two angles and the interjacent side being given
65
Example in the measurement of heights the bases of which are in accessible
66
Two sides and the angle opposite one of them being given an am biguous case 68 Derivation of a formula for the cosine of an angle in terms of the t...
67
and 70 Derivation of formulæ for the sine and cosine of the
69
and difference of two arcs
72
Derivation of formula for the sine and cosine of an arc in terms of half the arc
73
PART II
81
24 24
111
26
115

Expressions et termes fréquents

Informations bibliographiques