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" C = sin. A sin. B sin. C; dividing both sides of this equation by cos. A cos. B cos. C, we have sin. A sin. B sin. C _ sin. "
An introduction to the theory ... of plane and spherical trigonometry ... - Page 116
by Thomas Keith - 1839
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - Trigonometry - 1806 - 464 pages
...,. . rsut since - — = -r— = - — , we shall have sin B sin A sin c Sin c (sin Af-sin B) = sin c (sin a +sin b ) Sin c (sin A — sin B) = sin c (sin a — sin b) Which two equations being divided by the preceding Sin A + sin B sin c sin a + sin...
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Éléments de géométrie: avec des notes

Adrien Marie Legendre - Geometry - 1806 - 482 pages
...cette proposition, sin A : sin a :: sin B : sin b :: sin C : sin c; ce qui donne la double équation : sin A sin B sin C sin a ~~ sin b sin c LXXVI. Dans tout triangle sphérique le cosinus d'un angle est 'égal au quarré du rayon multiplié...
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Elements of Plane and Spherical Trigonometry

Olinthus Gregory - Plane trigonometry - 1816 - 278 pages
...(In + 1 ) 90°. 35. Substituting for tan, its value : — , in equa. (4) preceding, it becomes • sin A sin B sin c sin A sin B sin c. COS A COSB COSC COS A COS B COS C* whence, taking away the denominators, there results, sin A cos B...
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Éléments de géométrie, avec des notes

Adrien Marie Legendre - Geometry - 1817 - 474 pages
...aura donc - , RZ sin C RZ Sin C = —. r— r , Ou :— : r— t, uu — : — — : ; — 7 — : . sin a sin b sin c sin a sin b sin c Les valeurs de cos A et de cos B donneraient semHablement sin A. RZ sin B RZ . sin a " sin a sin b...
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Alma Mater, Or, Seven Years at the University of Cambridge, Volume 1

John Martin Frederick Wright - 1827 - 344 pages
...the sphere = 1. Prove the following theorems: I. Cos. C = II. cos. c—cos. ax cos. b sin. ax sin. b sin. A sin. B sin. C sin. a sin. b sin. c IV. sin. I -- a) x sin. ( -- o) . /S . /S S in.'i C= - - 5£_, - ^ sm. ax sin. 6 sm. -) x sm. --c)...
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Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - Astronomy - 1833 - 286 pages
...these equations gives sin. A cos. B cos. C + cos. A sin. B cos. C + cos. A cos. B sin. C = sin. A sin. B sin. C ; dividing both sides of this equation by...have sin. A . sin. B . sin. C sin. A sin. B sin. C "~ nna It ' nrtu I™i cos. A cos. B cos. C cos. A cos. B ' cos. C ' that is, tan. A + tan. B .f- tan....
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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
...dans cette équation A et a, en B et b, en C et ct comme M reste constant, on en tire cette équation sin A sin B sin C „ sin a sin b sin c" " " " " Dans tout triangle sphérique , les sinus des angles sont proportionnels aux sinus des côtés...
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New Series of The Mathematical Repository, Volume 6

Thomas Leybourn - Mathematics - 1835 - 682 pages
...triangle ABC is cut so that (putting a, b, c for radii of A, i sin a : sin c : sin a sin b : sin c sin a : sin b sin c : sin a sin b : sin c . ,.(6) •(7) .(8) -(9). Compounding these in threes, we obtain the following equations, (4t5»9)give,...
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Éléments de géométrie: avec des notes

Adrien Marie Legendre - Geometry - 1838 - 446 pages
...proposition, sin A : s in a : : sin B : sin b : : sin C : sin c ; ce qui donne la double équation : sin A sin B sin C sin a sin b sin c LXXVI . Dans tout triangle sphérique le cosinus d'un angle est égal au quarré du rayon multiplié...
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Elements of Plane and Spherical Trigonometry: With it Applications to the ...

John Radford Young - Nautical astronomy - 1848 - 412 pages
...these equations gives sin. A cos B cos. C + cos. A sin. B cos. C + cos. A cos. B sin. C = sin. A sin. B sin. C; dividing both sides of this equation by cos. A cos. B cos. C, we have sin. A sin. B sin. C _ sin. A sin. B sin. C cos. A cos. B cos. C ~~ cos. A ' cos. B ' cos. C' that is, tan. A + tan. B +...
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