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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... "
Academic Trigonometry: Plane and Spherical - Page 25
by Thomas Marcus Blakslee - 1888 - 35 pages
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

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...
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An Elementary Treatise of Spherical Geometry and Trigonometry

Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...triangles. In 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...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852 - 268 pages
...the various positions of the lines of the diagram. 5. In a spherical triangle, the cosine of any side is equal to the 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',...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...cot.BC Or, cot. 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,...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...the sine of C. (147) (148) (149) TRIGONOMETRY. 149. In any 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 two sides into the cosine of their included angle. Let A BC be any spherical triangle,...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...of B1 Ö D is still equal to the sine of G. 149. In any 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 two sides into the cosine of their included angle. Let ABC be any spherical triangle,...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...«till equal to the sine of C. 7* TRIUONOMETRY. 1 49. In any 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 two sides into the cosine of their included angle. Let ABC be any spherical triangle,...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 444 pages
...Trigonometry 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...
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Elements of Trigonometry: Plane and Spherical

Edward Olney - Trigonometry - 1885 - 222 pages
...thought sufficient for the general student] 143- Prop- — In a 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 cos c...
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