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" A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a. "
Elements of Geometry and Trigonometry from the Works of A.M. Legendre ... - Page 323
by Charles Davies - 1854 - 432 pages
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Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - Astronomy - 1833 - 286 pages
...; 1 ' ^ cos. b cos. c . . , . , cos. 6 cos. c . Hence multiplying by , and transposing, we have Hi cos. a = cos. b cos. c + sin. b sin. c cos. A ; which is a general expression for the cosine of any side in terms of the other two sides, and their...
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Elements of Spherical Trigonometry

Augustus De Morgan - Spherical trigonometry - 1833 - 40 pages
...c = cot. A sin. B ....... O,, reduced as before to tan. ds = tan. a cos. B and C is determined from cos. A = — cos. B cos. C + sin. B sin. C cos. a tan. B sin. (c — <4) = -- sin. tan. A O,' or tan. 0 = cot. B cos. a . ,r. ..N Cos- A. . sin. (C —...
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Repertorium der gesammten deutschen Literatur

German literature - 1834 - 810 pages
...sphärischtrigonometrischen Formeln durch Constructioa ist bei weitem nicht so einfach , als wenn bloss eine Formel (cos. a = cos. b cos. c + sin. b sin. c. cos. A) durch Construction gefunden wird und aus dieser dann die übrigen hergeleitet .werden. Unter den trigonometrischen...
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Géodésie, ou Traité de la figure de la terre et de ses parties: comprenant ...

Louis Benjamin Francoeur - Geodesy - 1835 - 542 pages
...c'est-à-dire, changeant a en 180° — A, A en 180° — a, etc., nous avons ':'**' "•'>•'* — cos A = cos B cos C — sin B sin C cos a. . .'. (7) Ces théorèmes suffisent à la résolution de tous les triangles sphériques, ainsi qu'on...
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Cours complet de mathématiques pures, Volume 2

Louis-Benjamin Francœur - Mathematics - 1837 - 634 pages
...supplémentaire (équ. i et 2), c'est-à-dire, changeant a en 180° — A, A en 180°— a, etc., nous avons — cos A = cos B cos C — sin B sin C cos a. . . (7). Ces théorèmes suffisent à la résolution de tous les triangles sphériques , ainsi qu'on...
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Aperçu historique sur l'origine et le développement des méthodes en ...

Michel Chasles - Geometry - 1837 - 868 pages
...arcs doubles 4. » Albategnius est parvenu à la formule fondamentale de la trigonométrie sphérique cos. a =cos. b cos. c. -+- sin. b. sin. c. cos. A , dont il a fait diverses applications 5. On trouve dans ses ouvrages la première idée des tangentes...
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An Introduction to Astronomy: Designed as a Textbook for the Use of Students ...

Denison Olmsted - Astronomy - 1839 - 504 pages
...triangle right angled at C, Formula 1. sin a =sin c sin A. In an oblique angled triangle, Formula 2. cos a — cos b cos c + sin b sin c cos A. All the known methods employed by astronomers, in investigating rigorously the theory of occultations,...
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Exercises d'Analyse et de Physique Mathématique, Volume 3

Augustin Louis Baron Cauchy - 1844 - 408 pages
...équations, savoir, trois équations semblables à la formule (22), qui pourront s'écrire comme il suit : r cos a = cos b cos c -+- sin b sin c cos a, (26) - cos b = cos c cos a -+- sin c sin a cos 6, ' cos c = cas a cos b -f- sin a sin b cos y , ( 325...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...spherical triangle in terms of the sines and cosines of the angles. By (/3) we have, cos. a= .'. 1+cos. a= cos. A + cos. B cos. C sin. B sin. C cos. A + cos. B cos. C+sin. B sin. C sin. B sin. C cos. A+cos. (B— C) sin. B sin. C A+B— C A+C— B 2cos. x cos. Let...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845 - 542 pages
...triangle, in terms of the sines of the sides of the triangle. By (a) we have, cos. A = •. 1+cos. A — cos. a — cos. b, cos. c sin. b sin. c cos. a— cos. b cos. c+sin. b sin. c sin. b sin. c cos, a— (cos, b cos. c — sin. 5 sin. c) sin. b sin. c cos, a —...
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