 | 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,... | |
 | John Charles Snowball - 1837 - 322 pages
...conversely. 13 CHAPTER II. FORMULAE CONNECTING THE SIDES AND ANGLES OF A SPHERICAL TRIANGLE. ART. PAUB 28. Sin A sin B sin C sin a sin b sin c 29. Cos A . sin b . sin c = cos a — cos b. cos c 30,31. Sin c . cos A = cos a . sin b — sin a.... | |
 | 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 gle C, par exemple, cos L. = : LXXVI . Dans tout triangle sphérique le cosinus d'un angle est égal... | |
 | Adrien Marie Legendre - Geometry - 1839 - 372 pages
...have sin c (cos A+cos B)=(R—cos C) sin (a+b) But since -—~=-—r — -—T5i we shall have sin C sin A sin B sin c sin a sin b sin c (sin A + sin B)=sin C (sin a + sin b), and sin c (sin A—sin B)=sin C (sin a—sin b). Dividing these... | |
 | Thomas Keith - 1839 - 498 pages
...sin b . sin A sin b . sin c sin a sin c sin c . sin A sin c . sin B sin a sin b sin b . sin A sin c . sin A sin B sin c sin a . sin B sin c . sin B sin A sin c sin a . sin c sin b . sin c sin A sin B (420) The general expressions for the cosines,... | |
 | David Hewitt - Trigonometry - 1840 - 156 pages
...(^—5— Jj. (1) = 4 cos — . cos — . cos — (42) ; С Л В XZ Я sin 2 A + sin 2 В + sin 2 С sin A + sin B + sin C sin A . sin B . sin C cos - . cos 2 . cos 2 sin - . cos - . 2 sin - . cos - . 2 sin - . cos . А А .В В . С С COS 2 ' C... | |
 | Education - 1840 - 468 pages
...= A'B. B'C. C'A, and the product of the areas of the triangles A'BC', B'CA', CAB' (A'K. B'C'. C'A' sin A' sin B' sin C')' . sin A sin B sin C 4. If a point (C') be taken in any one (as AB) of three indefinite straight lines that intersect in... | |
 | Geometry - 1843 - 376 pages
...have sin c (cos A+cos B)=(R—cos C) sin (a+b) But since -—?q=-—r — -—5, we shall have sin C sin A sin B sin c sin a sin b sin c (sin A+sin B)=sin C (sin a+sin b), and sin c (sin A—sin B)=sin C (sin a—sin b). one; we shall have... | |
 | Adrien Marie Legendre - Geometry - 1843 - 476 pages
...a cosb cos c), on aura donc Sin L = -: :—r , OU . „ RZ sin C RZ -—: : fï wtc . — :—; : . sin a sin b sin c sin a sin b sin c Les valeurs de cos A et de cos B donneraient semblablement sin A RZ sin B_ RZ sin a sin a sin b sin... | |
 | John Radford Young - Nautical astronomy - 1848 - 412 pages
...the equations (3), page 49, we have sin. A sin. c = sin. a sin. C sin. B sin. c = sin, b sin. C .'. (sin. A ± sin. B) sin. c = (sin. a ± sin. b) sin. C . . (2). Dividing (2) by (1) there results sin. A ± sin. B sin. a ± sin. b sin. C cos. A -f cos.... | |
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Oblique spherical triangles sin A sin B sin C sin a ~~ sin b sin c cos a = • cos b 
