An Elementary Treatise on Plane & 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 (Google eBook)

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J. Munroe, 1861 - Trigonometry - 358 pages
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Page 44 - 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 41 - 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 109 - 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 125 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Page 166 - ... 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 146 - 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 72 - 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 125 - 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 99 - 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 159 - ... two sides of a spherical triangle, is to the sine of half their difference as the cotangent of half the...

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