 | Daniel Cresswell - Geometry - 1816 - 352 pages
...complemental triangle. PROP. I. (230.) Theorem. The cosine of any one of the sides, of a spherical triangle, is equal to the product of the cosines of the other two sides, together with the continued product of the sines of those two sides, and the cosine of the angle contained... | |
 | Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...the form of a theorem it may be stated thus : The cosine of one of the sides of a spherical triangle^ is equal to the product of the cosines of the other two sides, increased by the product of their sines multiplied into the cosine of the included angle. There are... | |
 | William Chauvenet - 1852 - 268 pages
...without requiring a special examination of the various positions of the lines of the diagram. 5. In a spherical triangle, the cosine of any side is equal...product of the cosines of the other two sides, plus the continued product of the sines of those sides and the cosine of the included angle. Let the plane B'A'С',... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...AC : cot.BC = cos. ACD : cos.BCD. PROPOSITION VII. The cosine of any side of a spherical triangle, is equal to the product of the cosines of the other...two sides, plus the product of the sines of those sides multiplied by the cosine of the included angle. Let ABC be a spherical triangle, and CD a perpendicular... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...its supplement are the same, the sine of B' G'D is still equal to the sine of C. (147) (148) (149) TRIGONOMETRY. 149. In any spherical triangle, the...sides into the cosine of their included angle. Let A BC be any spherical triangle, 0 the centre of the sphere. Draw the plane B' A' C' perpendicular to... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...sine of an angle and its supplement are the same, the sine of B1 Ö D is still equal to the sine of G. 149. In any spherical triangle, the cosine of any...sides into the cosine of their included angle. Let ABC be any spherical triangle, O the centre of the sphere. Draw the plane B1 A1 O perpendicular to... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...supplement are the same, the sine of B' C?D is «till equal to the sine of C. 7* TRIUONOMETRY. 1 49. In any spherical triangle, the cosine of any side...sides into the cosine of their included angle. Let ABC be any spherical triangle, 0 the centre of the sphere. Draw the plane B1 A' O perpendicular to... | |
 | Benjamin Greenleaf - 1867 - 188 pages
...In like manner, by means of (153), sinJB = ^°3^. (197) cos p ^ 161. T^e cosine of the hypothenuse is equal to the product of the cosines of the other two sides. By means of (152) we have cos A = cos p cos b -\- sin p sin b cos C, which, by making O = 90°, becomes... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...in Space. THREE 8IDE8 AND AN ANGLE. 878. Theorem. — The cos)ne of any side of a spherical triangle is equal to the product of the cosines of the other two sides, increased by the product of the sines of those sides and the cosine of their included angle. 315 Let... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...of an angle and its supplement are the same, the sine of B CPD is still equal to the sine of (7. 7* 149. In, any spherical triangle, the cosine of any...sides into the cosine of their included angle. Let ABC be any spherical triangle, 0 the centre of the sphere. Draw the plane B1 A' O perpendicular to... | |
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Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b... 
