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 - 372 páginas

PLANE TRIGONOMETRY	2

Circular protractor	8

Definition of the sine	15

Of formulas for sin a and cos	16

243	19

Trigonometric lines have the same signs in pairs	23

Mode of computing the spherical excess	25

Area of a plane triangle in terms of any three parts	27

166	166

89	162

90	156

Definitions	203

Examples and exercises	210

Rule for adding or rejecting 10 in the introduction of radius for homogeneity	215

THEORY OF MERCATORS SAILING	217

THEORY OF MIDDLE LATITUDE SAILING	219

Application of the formulas to practical examples	33

Method of finding the logarithm of a number beyond the limit of	39

latitude are taken	52

Exercise	63

Various problems admitting particular solutions	81

APPENDIX I	87

Demonstration of a formula for sin n + 1	97

Use of subsidiary angles	108

Forms for finding the trigonometric lines and their logarithms for very small	110

Resolution of quadratic equations trigonometrically	115

Demonstration of sine proportion for right angled triangles	122

Blank form for the application of one of these formulas	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 computing its effect on the time of meridian transit	160

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

Questions on logarithms	173

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	193

Título	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
Autor	Charles William Hackley
Editor	G.P. Putnam, 1851
Procedencia del original	Biblioteca Pública de Nueva York
Digitalizado	21 Jun. 2006
Largo	372 páginas

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Trigonometric lines of negative arcs	224

APPENDIX III	227

Use of the arithmetical complement	229

Surveying by offsets	237

Derivation of series for calculating the logarithmic sines cosines c	244

Map and field book	247

SURVEY OF ROADS RAILWAYS AND CANALS	253

Definitions	267

Correction for refraction	273

General account of triangulation	276

Example of corrections for the moons altitude	279

Example	285

Description and use of the sextantNote	294

MEASUREMENT OF BASES	315

Formula for reduction of phase in tin cones	321

Examples of the above method	333

LATITUDE BY ASTRONOMIC OBSERVATIONS	340

General formula including all the corrections	348

173	352

APPENDIX TO PART VI	361

Table of formulas expressing the most useful general relations of arcs	109

Form for recording its observations	127