 | Olinthus Gregory - Plane trigonometry - 1816 - 278 pages
...— = -r— : therefore, f sin a sin 4 sin A sin 11 sine , . sin a sin b sin c ' ' ' ' * "' Hence, the sines of the angles of a spherical triangle are proportional to the sines of the opposite sides. 21 . Draw CE and DF, respectively perpendicular and parallel to OB; then will the angle DCF = EOC =... | |
 | Robert Woodhouse - Geometrical optics - 1819 - 470 pages
...them, with the corresponding ones in Plane Trigonometry. íing a proposition) The sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. Right-angled spherical triangles may be considered as particular cases of oblique. The solutions... | |
 | Naval art and science - 1872 - 1120 pages
...REJIABKS. 1. The above Rules are directly deduced from the well-known analogy : the Sines of the sides of a spherical triangle are proportional to the Sines of the opposite angles. 2. I call it New, because I do not know of any author who has reduced it to practice as I have... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...sin b sin C= sin c sin B, or - — ^=- — r (1) sin B sm 6 v ' or, sin B : sin C : : sin b : sin c that is, The sines of the angles of a spherical triangle are to each other as the sines of their, opposite sides. IV. From K draw KE perpendicular to OB, and from... | |
 | Charles William Hackley - Trigonometry - 1838 - 328 pages
...written sin B sin c = sin c sin b or, sin B _ sin c sin b sin c or, sin B : sin 6 : : sin c : sin c* that is, the sines of the angles of a spherical triangle are as the sines of the opposite sides. EXAMPLE. Let z be the zenith, p the pole of the equator, and s... | |
 | Richard Abbatt - Spherical astronomy - 1841 - 234 pages
...known parts to determine the rest. SECTION VI. SPHERICAL TRIGONOMETRY. (85.) The sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. Let ABC (fig. 22.) be a spherical triangle, 0 the centre of the sphere ; join A 0, BO, CO;... | |
 | James Bates Thomson - Plane trigonometry - 1844 - 148 pages
...sin 6 sine Hence, sin a : sin A : : sin 6 : sin B : : sin c : sin C ; that is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. Hence, also, by multiplving extremes and means, we get sin A sin 6 = sin B sin a sin A sin... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...C=sm c sin B, or - — „=- — 7 ( 1 ) sin C sin c sin B sin 6 v or, sin B : sin C : : sin b : sin c that is, The sines of the angles of a spherical triangle are to each other as the sines of their opposite sides. IV. From K draw KE perpendicular to OB, and from... | |
 | James Gordon (Teacher of Navigation.) - 1849 - 260 pages
...page 42, is evidently deduced from the theorem in Spherical Trigonometry, that the Sines of the sides of a spherical triangle are proportional to the Sines of the opposite angles. From the explanation given at page 42, it appears that the limb of the Sun or Moon assumes... | |
 | James Gordon (teacher of navigation.) - 1849 - 218 pages
...page 42, is evidently deduced from the theorem in Spherical Trigonometry, that the Sines of the sides of a spherical triangle are proportional to the Sines of the opposite angles. From the explanation given at page 42, it appears that the limb of the Sun or Moon assumes... | |
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These equations may also be written in the form of proportions sin a : sin b : sin c = sin A : sin B : sin C. That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles. 
