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

1838

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Values of the cotangent	28

Values of the cosecant	29

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 t for the cosecant	34

Corollaries from these	36

Mercators sailing	145

Example of the last	147

NAUTICAL ASTRONOMY 103 Introductory	149

Definitions	150

Corrections to be applied to the observed altitudes of celestial objects	152

Dip or depression of the horizon	153

Refraction	155

Parallax	157

Relation of tangent and cotangent FORMULE FOR THE SOLUTION OF RIGHTANGLED TRIANGLES	37

Derivation of formulae	38

39 40 and 41 Applications of these formulae	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 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

ARTICLE Page	72

PART II	81

Three angles being given to find the sides	94

RIGHT ANGLED TRIANGLES	105

Astronomical example	112

Introduction	124

PRINCIPLEs of NAVIGATION ARTICLE Page 96 Definitions	125

Plane sailing	129

Traverse sailing	132

Parallel sailing	138

Middle latitude sailing	141

Examples of corrections	158

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

Examples	166

On finding the longitude by the lunar observations	171

Variation of the compass	177

Formulae for the tangent of the sum and difference of two arcs	180

Value of the sine and cosine of 45	181

Sine of 30 and secant of 60	182

Construction of table of sines c	183

PART VI	185

Use of the arithmetical complement	189

Quadrantal triangles	195

Formulae to be employed instead of Napiers rules in certain cases where great accuracy is required	199

Two sides and the included angle of a spherical triangle being given to find the third side directly	201

Two angles and the interjacent side being given to find the third angle	202

Rules relative to ambiguous cases	203

Determination of the effect of minute errors in data	205

A side and the opposite angle being two of the given parts 65 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	67

Derivation of a formula for the cosine of an angle in terms of the three sides of a triangle	68

and 70 Derivation of formulae 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 half the arc Page 56 57 59	71

62	72

Droits d'auteur

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 logarithmical, trigonometrical, and nautical tables
Publié	1838
Original provenant de	The British Library
Numérisé	7 sept. 2015

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