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

Wiley & Putnam, 1838 - 307 pages

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PLANE TRIGONOMETRY	1

Engineers method	7

TRIGONOMETRICAL LINES	13

Its definition and changes of value	19

THS COTANGENT AND COSECANT	21

Its Algebraic sign	25

Values of the cotangent	28

Values of the cosecant	29

Example in the measurement of distances Solution of obliqueangled triangles by logarithms	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 sum and difference of two arcs	69

Derivation of formula for the sine and cosine of an arc in terms of 56 57 59	71

Derivation of formulæ for the sum and difference of the sines of	74

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 24 24 24 25 25 26 27 27 27 88	37

Derivation of formulæ	38

39 40 and 41 Applications of these formulæ	39

Advantage of logarithms 31	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

Rules to find the logarithmic secant and cosecant of any given arc Solution of rightangled triangles with the aid of logarithms	59

Examples	61

Use of the arithmetical complement	62

Titre	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
Auteur	Charles William Hackley
Éditeur	Wiley & Putnam, 1838
Original provenant de	The British Library
Numérisé	7 sept. 2015
Longueur	307 pages

Exporter la citation	BiBTeX EndNote RefMan

65	80

PART II	81

Formula for the cosine of an angle in terms of the three sides	88

Three angles being given to find the sides	94

RIGHT ANGLED TRIANGLES	105

Astronomical example	112

APPLICATION OF PLANE AND SPHERICAL TRIGONOMETRY	123

ARTICLE	125

66	129

Traverse sailing	132

Parallel sailing	138

Example of the last	147

Dip or depression of the horizon	155

Method of determining the latitude at sea by the meridian altitude	161

On finding the longitude by the lunar observations	171

Variation of the compass	177

69	179

half the arc	182

PART VI	185

Quadrantal triangles	195

Rules relative to ambiguous cases	201