# An Elementary Treatise on Plane and Spherical Trigonometry: With Their Applications to Navigation, Surveying, Heights and Distances, and Spherical Astronomy, and Particularly Adapted to Explaining the Construction of Bowditch's Navigator, and the Nautical Almanac

J. Munroe, 1861 - Trigonometry - 359 pages

### Contents

 General Principles of Plane Trigonometry 3 Sines Tangents and Secants 6 Right Triangles 14 General Formulas 17 Values of the Sines Cosines Tangents Cotangents Secants and Cosecants of Certain Angles 30 Oblique Triangles 39 Logarithmic and Trigonometric Series 53 NAVIGATION AND SURVEYING 63
 17 170 II 171 22 172 30 175 39 177 53 189 72 204 75 215

 Plane Sailing 65 Traverse Sailing 72 Parallel Sailing 75 Middle Latitude Sailing 78 Mercators Sailing VI Surveying 84 Heights and Distances 106 SPHERICAL TRIGONOMETRY 115 Definitions 117 Right Triangles 120 Oblique Triangles 138 PAGE 164 3 167 6 168
 Precession and Nutation 229 78 231 84 238 Time 243 97 246 Longitude 255 Aberration 279 106 280 117 286 121 292 Parallax 301 Eclipses 317

### Popular passages

Page 40 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 37 - To find a side, work the following proportion: — as the sine of the angle opposite the given side is to the sine of the angle opposite the required side, so is the given side to the required side.
Page 105 - PROBLEM III. To find the height of an INACCESSIBLE OBJECT above a HORIZONTAL PLANE. 11. TAKE TWO STATIONS IN A VERTICAL PLANE PASSING THROUGH THE TOP OF THE OBJECT, MEASURE THE DISTANCE FROM ONE STATION TO THE OTHER, AND THE ANGLE OF ELEVATION AT EACH. If the base AB (Fig.
Page 121 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Page 162 - ... are called hour circles. Small circles parallel to the celestial equator are called parallels of declination. The sensible horizon is that circle in the heavens whose plane touches the earth at the spectator; The rational horizon is a great circle in the heavens, passing through the earth's centre, parallel to the sensible horizon.
Page 142 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 68 - Call the differences of latitude corresponding to the 1st, 2d, 3d, and 4th tracks, the 1st, 2d, 3d, and 4th differences of latitude ; and call the corresponding departures the 1st, 2d, 3d, and 4th departures.
Page 121 - NAPIER'S CIRCULAR PARTS. Thus, in the spherical triangle A. BC, right-angled at C, the circular parts are p, b, and the complements of h, A, and B. 167. When any one of the five parts is taken for the middle part, the two adjacent to it, one on either side, are called the adjacent parts, and the other two parts are called the opposite parts. Then, whatever be the middle part, we have as THE EULES OF NAPIER.
Page 95 - Now the sum of the areas of the triangles is the area of the polygon, and the sum of the angles of the triangles is the sum of the angles of the polygon.
Page 155 - ... two sides of a spherical triangle, is to the sine of half their difference as the cotangent of half the...