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

PART I	1

Conversion of the two modes of division	7

Definition of the sine	13

Of formulas for sin a and cos	16

Definition of tangent	19

Trigonometric lines have the same signs in pairs	22

Use of the tables of natural sines	28

Definitions log of the base 1 and 0	34

Definitions	203

THEORY OF PLANE SAILING	210

Mode of solution when two sides and the included angle are given and	215

THEORY OF MERCATORS SAILING	217

THEORY OF MIDDLE LATITUDE SAILING	219

Necessary modifications for the spheroidal figure	224

APPENDIX III	227

Extension of the demonstration for sine and cosine of a + b to all	229

Of finding the number corresponding to any given logarithm	42

Description of table of logarithms sines tangents c	48

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

SOLUTION OF RIGHT ANGLED TRIANGLES BY THE AID OF LOGARITHMS	54

Practical examples	60

Deduction of the formula for the cosine of an angle in terms of the three	66

Of formulas for the sine and cosine of twice an arc	71

Derivation of formulas for the sum and difference of the sines of two arcs	77

APPENDIX I	87

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

Of the sine and cosine of 45 Of the sine c of 300 and 600	110

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

PART II	121

Astronomical example of its application	127

Formulas for the sine and tangent of half an angle in terms of the three	136

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 computing its effect on the time of meridian transit	160

Solution of an oblique angled spherical triangle when two of the three given	166

On the resolution of plane triangles in general	172

ON UNLIMITED SPHERICAL TRIANGLES AND THEIR SOLUTION	177

Mode of using the Gauss equations	184

SOLUTION OF QUADRANTAL TRIANGLES	194

Mode of computing the spherical excess	200

PART IV	233

Contour of ground	251

Specimens of table from which coefficients of the formula for difference	252

By reduction of irregular to regular boundaries	257

Determination of remote points at sea	263

Mode of determining the apparent right ascension and declination of a star	269

Formula for computing parallax in altitude	275

Example and exercises	281

ON FINDING THE LONGITUDE	287

Description and use of the sextantNote	294

VARIOUS MODES OF DETERMINING LATITUDE	301

Description and use of the ghost apparatus for adjustment	307

PART VI	315

The heliotrope	321

Example of geodetic determination of latitude	329

Rule for drawing the map	335

telescopes	341

Demonstration of a formula for sin n + 1	343

General formula including all the corrections	348

Astronomical determination of azimuths	352

The inclination	358

Form for recording its observations	364

Description of the Pulkova and Washington instruments	370

by moon culminations	372

Application of the formulas for computing a table of sines c	375

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
Edition	3
Publisher	G.P. Putnam, 1851
Original from	the New York Public Library
Digitized	21 Jun 2006
Length	372 pages

Export Citation	BiBTeX EndNote RefMan