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

G.P. Putnam, 1852 - Plane trigonometry - 496 pages

Derivation of formulas similar to cos a	1

PLANE TRIGONOMETRY	2

Conversion of the two modes of division	8

Exposition of the different kinds of time	14

Mode of computing the spherical excess	16

Expressions for the tangent cotangent secant and cosecant in terms of	23

THEORY OF LOGARITHMS	33

EXPLANATION OF THE TABLE	39

Auxiliary angles	186

Derivation of series for calculating the logarithmic sines cosines c	196

Definitions	203

Theory of traverse sailing and use of the traverse table	209

Variations in the value of the tangent for arcs from zero up to 360	215

THEORY OF MERCATORS SAILING	217

Examples and exercises	219

Construction and use of the table of meridional parts	224

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

Raising of powers and extraction of roots by logarithms	54

Derivation of formula for the sum of half an angle in terms of the three	67

Blank form for this case	80

140	82

APPENDIX I	87

Demonstration of a formula for sin n + 1	97

Of formulas for sin a and cos	106

Application of the formulas for computing a table of sines c	110

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

sides of a spherical triangle	136

89	141

Example of this reduction	154

Mode of computing its effect on the time of meridian transit	160

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

Semicircular protractor	166

Questions on logarithms	173

tan c of any given arc expressed	174

ON UNLIMITED SPHERICAL TRIANGLES AND THEIR SOLUTION	177

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
Author	Charles William Hackley
Edition	3
Publisher	G.P. Putnam, 1852
Original from	University of Illinois at Urbana-Champaign
Digitized	9 Jan 2015
Length	496 pages

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Description and use of the plane table	234

Theory of the vernier	242

Contour of ground	251

latitude are taken	252

By reduction of irregular to regular boundaries	257

Definitions	267

Correction for refraction	273

DETERMINATION OF THE LATITUDE AT SEA BY MERIDIAN ALTITUDE	279

Variation of the compass	295

VARIOUS MODES OF DETERMINING LATITUDE	301

Reduction to the meridian of an observation with the mural	311

Description of Base Apparatus	318

Example of geodetic determination of latitude	329

Rule for drawing the map	335

By observations with zenith sector	341

Longitude by celestial observations	348

Astronomical determination of azimuths	352

INSTRUMENTS FOR EXTRA MERIDIAN OBSERVATIONS	361

Prime vertical transit	368

Table of formulas expressing the most useful general relations of arcs	375

Day Signals