 | Société des sciences, de l'agriculture et des arts de Lille - Science - 1850 - 1106 pages
...grandeur , entre 0 et 180° ; on voil de suite jue A sera très-petit par rapport à B et à C, puisque sin. A : sin. B : sin. C :: sin. a : sin. b : sin. c. •'aisanl c — b = à , ;t représentant par ? la portion de c comprise entre l'angle adjurent ,... | |
 | Adam von Burg - Mathematics - 1851 - 684 pages
...= • —, sin B = —• , sin G = : —, sin o am c sin a «tu c «tu a st« li und daraus folgt: sin A : sin B : sin C = sin a : sin b : sin c, ein wichtiger (und jenem in §. 4(i analoger) Satz der sphärischen Dreiecke. §. 71. Aus den erwähnten... | |
 | Mathematics - 1853 - 506 pages
...du triangle sphériquc. C'est le rhomboèdre normal (C. KEOGH). Tl résulte de là, ces équations sin A sin B sin C sin a sin b sin c _ 2 v'sin/j.sin (p — a) sin (p — b) sin (p — c) sin a sin b sin c qui serviront plus loin. Il... | |
 | John Hind - Trigonometry - 1855 - 540 pages
...the angles which the sides of a triangle subtend at the centre of the inscribed circle, then will 4 sin A' sin B' sin C' = sin A + sin B + sin C". 46. The radius of the circle described through any three of the centres of the four circles that can... | |
 | Ignace-Louis-Alfred Le Cointe - Trigonometrical functions - 1858 - 420 pages
...due und angcwatttlte Démonstration. — Les relations donnent sin a siii b sin c sin A sin B sin C sin a sin b + sin c sin A ~ sin B -+- sin C et sin a _ sin b — sin c sin A sin B — sin C ' pu bien . aab -+- cb — c sin — cos — sin cos... | |
 | John Hymers - Logarithms - 1858 - 324 pages
...has a constant value for each of the angles of the triangle; hence we must have the three equations sin A sin B sin C sin a sin b sin c ' which shew, since this result is as general as the one from which it is deduced, that in any spherical... | |
 | Isaac Todhunter - Spherical trigonometry - 1859 - 156 pages
...c, and sin A are all positive. 41. From the value of sin A in the preceding article it follows that sin A sin B sin C sin a sin b sin c ' for each of these is equal to the same expression, namely, „/(! — cos 3 a — cos 2 b — cos*... | |
 | G. R. Smalley - Mathematics - 1862 - 190 pages
...— 180 = spherical ezcess. 1. cos a = cos b cos c + sin It sin c coa A. 2 SPHERICAL TRIGONOMETRY. 2. sin A : sin B : sin C = sin a : sin b : sin c. 3. cot a sin b = cot ^ sin C + cos 5 cos C'. 4. cos .4 = — cos B cos C + sin B sin (7 cos a. tan... | |
 | William Chauvenet - Trigonometry - 1863 - 272 pages
...a is given. If the sign of sin b or of sin c it given, that of sin a becomes known by the equation sin a sin b sin c sin A sin B sin C The formulae (36), (38), (39), may be used, each of which will be determinate when the sign of either... | |
 | Isaac Todhunter - Spherical trigonometry - 1863 - 182 pages
...c, and sin A are all positive. 41. From the value of sin A in the preceding article it follows that sin A sin B sin C sin a sin b sin c ' for each of these is equal to the same expression, namely, »/(! — cos2 a — cos 2 6 — cos 2... | |
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Oblique spherical triangles sin A sin B sin C sin a ~~ sin b sin c cos a = • cos b 
