A Treatise on Trigonometry, Plane and Spherical: With Its Application to Navigation and Surveying, Nautical and Practical Astronomy and Geodesy, with Logarithmic, Trigonometrical, and Nautical Tables for the Use of Schools and Colleges

G. P. Putnam, 1853 - Trigonometry - 372 pages

PART I	1

Conversion of the two modes of division	8

Area of a plane triangle in terms of any three parts	9

Definition of the sine	15

Expressions for the tangent cotangent secant and cosecant in terms of	16

sine and cosine	23

Application of the formulas to practical examples	29

EXPLANATION OF THE TABLE	39

Theory of traverse sailing and use of the traverse table	209

Exercises in ditto	210

Variation of the sine for values of the arc from zero to 360	215

THEORY OF MERCATORS SAILING	217

66	220

19	221

Examples and exercises	224

General principles	234

Raising of powers and extraction of roots by logarithms	45

Demonstration of formulas for the sine and cosine of the surn and difference	50

Exercise	63

Of formulas for the sine and cosine of twice an arc	67

Example under the above formula	74

Blank form for this case	80

Mode of solution when two angles and the included side the unknown	86

APPENDIX I	87

Demonstration of a formula for sin n+1	110

nearly equal	114

Demonstration of sine proportion for right angled triangles	122

Demonstration of the formula for the cosine of an angle in terms of	128

66	135

sides of a spherical triangle	136

Astronomical example from the suns right ascension and declination	143

Rules for determining the meridian altitude of a star	149

Conversion of siderial into mean solar time and vice versâ	164

On the resolution of right angled plane triangles	171

given log sine tangent c	174

ON UNLIMITED SPHERICAL TRIANGLES AND THEIR SOLUTION	177

Mode of using the Gauss equations	184

SOLUTION OF QUADRANTAL TRIANGLES	194

Rule for adding or rejecting 10 in the introduction of radius for homogeneity	195

Definitions	203

Theory of the vernier	242

Mode of computing the spherical excess	250

Contour of ground	251

By reduction of irregular to regular boundaries	257

Forms for finding the trigonometric lines and their logarithms for very small	262

Questions on logarithms	267

Correction for refraction	273

Example of geodetic determination of latitude	278

DETERMINATION OF THE LATITUDE AT SEA BY MERIDIAN ALTITUDE	279

Example	285

Variation of the compass	295

THE REFLECTING CIRCIE	303

61	304

Definitions	315

Formula for reduction of phase in tin cones	321

PROJECTION OF MAPS	334

LATITUDE BY ASTRONOMIC OBSERVATIONS	340

Longitude by celestial observations	348

Astronomical determination of azimuth	352

The inclination	358

Form for recording its observations	364

Description of the Pulkova and Washington instruments	370

Table of formulas expressing the most useful general relations of arcs	111

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Title	A Treatise on Trigonometry, Plane and Spherical: With Its Application to Navigation and Surveying, Nautical and Practical Astronomy and Geodesy, with Logarithmic, Trigonometrical, and Nautical Tables for the Use of Schools and Colleges Michigan Historical Reprint Series
Author	Charles William Hackley
Edition	4
Publisher	G. P. Putnam, 1853
Original from	the University of Virginia
Digitized	Oct 27, 2010
Length	372 pages

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