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, 1851 - Trigonometry - 372 pages

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Derivation of formulas similar to cos a	1

PLANE TRIGONOMETRY	2

EXPLANATION OF THE TABLE	39

Rules for finding the log sin tan c of any given arc expressed	48

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

Of formulas for the sine and cosine of twice an arc	72

Blank form for the same	79

APPENDIX I	87

Semicircular protractor	215

THEORY OF MERCATORS SAILING	217

THEORY OF MIDDLE LATITUDE SAILING	219

APPENDIX III	227

76	229

Theory of the vernier	242

levelling staves	249

Mode of computing the spherical excess	250

An angle and the logarithms of the sides containing it being given to solve	108

Demonstration of formula for solution of a triangle when two sides	114

Demonstration of sine proportion for right angled triangles	122

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

three angles of a spherical triangle	134

Mode of solution when two angles and the included side the unknown	140

DESCRIPTION OF THE TRANSIT INSTRUMENT	147

Example of this reduction	154

Mode of solution when two sides and the included angle are given and	163

Conversion of siderial into mean solar time and vice vers�	164

On the resolution of right angled plane triangles	171

Description and mode of using the trigonometric tables of Callet	174

ON UNLIMITED SPHERICAL TRIANGLES AND THEIR SOLUTION	177

Mode of using the Gauss equations	184

SOLUTION OF QUADRANTAL TRIANGLES	193

35	160

Derivation of series for calculating the logarithmic sines cosines c	184

Definitions	207

Theory of traverse sailing and use of the traverse table	209

96	260

Formula for computing parallax in altitude	276

ON FINDING THE LONGITUDE	287

heavenly body	293

APPENDIX TO PART V	299

VARIOUS MODES OF DETERMINING LATITUDE	301

Definitions	315

The heliotrope	321

Example of geodetic determination of latitude	330

Use of blank maps by plane table parties	337

Correction for refraction in zenith telescopes	343

Rule when the meridian is distant from that of Greenwich	351

Astronomical determination of azimuths	352

The inclination	358

Form for recording its observations	365

Description of the Pulkova and Washington instruments	372

98	111

299	125

329	131

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
Author	Charles William Hackley
Publisher	G.P. Putnam, 1851
Original from	the New York Public Library
Digitized	21 Jun 2006
Length	372 pages

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