 | 1820 - 496 pages
...same demonstration will consequently serve for both methods. Since in every spherical triangle (ABC), cos. a = cos. b cos. c + sin. 6 sin. c cos. A, if we call the angle at the moon A and consequently the zenith distance of the sun or star a, that... | |
 | Augustus De Morgan - Spherical trigonometry - 1833 - 40 pages
...preceding, by treating the remaining angles in a similar manner, we get the following formuls : — cos. a = cos. b cos. c + sin. 6 sin. c cos. A cos. 6 = cos. c cos. a + sin. c sin. a cos. B cos. c = cos. a cos. 6 + sin. a sin. b cos. C . . O, or cos.... | |
 | Cork city, univ. coll - 1851 - 208 pages
...of a, 6, and c, adapted to logarithmic computation. 3. Show how the second member of the equation, cos. a = cos b cos c + sin 6 sin c cos A, may be adapted to logarithmic computation by the introduction of a subsidiary arc 9, and exhibit the... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...substituting these values, we have, cos a — sin b sin c cos J. = cos b cos c; and by transposing, cos a = cos b cos c + sin 6 sin c cos A. A similar equation may be deduced for the cosine of either of the other sides : hence, cos a = cos... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...substituting these values, we have, cos a — sin b sin c cos A = cos J cos c ; and by transposing, cos a = cos b cos c + sin 6 sin c cos A. A similar equation may be deduced for the cosine of eithe1 of the other sides : hence, cos a = cos... | |
 | Isaac Todhunter - Spherical trigonometry - 1859 - 156 pages
...triangle, and a' and A' similar quantities for the other. Then cos a = cos b cos c + sin b sin c cos A, cos a'= cos b cos c + sin 6 sin c cos A! ; therefore cos a - cos a = sin 6 sin c (cos A — cos A") ; that is, sin ^ (a + a") sin ^ (a — a')... | |
 | Isaac Todhunter - Spherical trigonometry - 1863 - 182 pages
...2AD . AE cos A - 2OD . OE cos a; ,, , OA OA AE AD therefore, cos« = — . — + _._ COSA; that is, cos a — cos b cos c + sin 6 sin c cos A . cos a — cos 6 cos c Therefore, cos A = • 38. "We have supposed, in the construction of the preceding... | |
 | Georg Christian Konrad Hunäus - Mathematical instruments - 1864 - 716 pages
...geringsten Einflufs auf die Bestimmung der Zeit hat. Differenziert man die erste Formel der Gleichungen [2] cos a = cos b cos c -\- sin 6 sin c cos A nach den Regeln des Differenziirens der trigonometrischen Functionen , imlera man darin alle Gröl'scii... | |
 | Georg Christian Konrad Hunäus - Mathematical instruments - 1864 - 732 pages
...geringsten KinHufs auf die. Bestimmung der Zeit hat. Differenziert man die erste Formel der Gleichungen [2J cos a -- cos b cos c -\- sin 6 sin c cos A nach den Regeln des Differcnzürcus der trigoiioinctris&lien Funeti^nen, indem man darin alle Gröi'sen... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...more from 90° than another side, is of the same species as its opposite angle. For, by (150), we have cos a = cos b cos c -\- sin 6 sin c cos A ; whence, cos a — cos 6 cos c cos A = -. — j• - , sin b sm c in which the denominator is always... | |
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... sin c cos A cos a ; adding sin2a and transposing, 1 — cos a cos b cos c... 
