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" A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B... "
Correspokndance sur l'École impériale polytechnique, par m. Hachette - Page 239
by Paris école polytechn - 1813
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Leçons de geométrie analytique: comprenant la trigonométrie rectiligne et ...

Lefébure de Fourcy (M., Louis Etienne) - Geometry, Analytic - 1859 - 520 pages
...cos b cos c En chassant le dénominateur, et (ransposant cos « dans le premier membre , il vient [1] cos a = cos b cos c + sin b sin c cos A. Telle est la formule fondamentale de la trigonométrie sphérique. 94. Dans la figure les côtés b...
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Briefwechsel zwischen C.F. Gauss und H.C. Schumacher, herausg ..., Volumes 3-4

Carl Friedrich Gauss - 1861
...völlig eben so gut siod. Sie mögen z. B. eben so gerne die vierte Fundamentalformel so schreiben cos A + cos B cos C = sin B sin C cos a Dergleichen gehört zu den vollkommen indifferenten Dingen, womit jeder es halten mug, wie er Lust...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 490 pages
...plus the cosine of the second side into the cosine of the included angle. By (150) and (152) we have cos a = cos b cos c -\- sin b sin c cos A, cos c = cos a cos b -\- sin a sin b cos C; and by means of (147), sin C sin c = sin a --. — -.. sin...
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Military Schools and Courses of Instruction in the Science and Art of War ...

Henry Barnard - Military education - 1862 - 399 pages
...cot. a sin. i — cot. A sin. C = cos. i cos. C, and by the consideration ofthe supplementary triangle cos. A = — cos. B cos. C + sin. B sin. C cos. a. Right-angled triangles.—Formulas cos. a=cos. i cos. c; sin. J = sin.'a sin. B; tang. c—tang, a...
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Elemente der Vermessungskunde

Karl Maximilian von Bauernfeind - Scientific apparatus and instruments - 1862 - 839 pages
...Zur Lösung der vorliegenden Aufgabe dient die bekannte Grundformel der sphärischen Trigonometrie : cos a = cos b cos c + sin b sin c cos A , in welcher A = w' , a = w und b = c = 90° — i zu setzen ist. Hiernach erhält man zunächst cos...
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Zeitschrift für Mathematik und Physik, Volume 7

Mathematics - 1862
...seinen Nebenwinkel ansehen, so erhalten wir für das Dreieck auf der Kugel sofort die Beziehungen : I. cos a = cos b cos c + sin b sin c cos a , II. sin a sin ß = sin b sin a , III. cot a sin b = — cos 6 cos y + sin y cot et, denen als duale...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 490 pages
...Applying (150) to A' BC', we have cos a1 = cos b1 cos c' -j- sin b' sin c' cos A' ; or, by (46), — cos A =. cos B cos C — sin B sin C cos a ; whence, cos A = sin B sin C cos a — cos B cos C. (153) In like manner may be deduced cos -Z?=sin...
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Zeitschrift für Mathematik und Physik, Volume 7

Mathematics - 1862
...seinen Nebenwinkel ansehen, so erhalten wir für das Dreieck auf der Kugel sofort die Beziehungen: I. cos a =. cos b cos c -|- sin b sin c cos a , II. sin a sin ß = sin b sin a , III. cot a sin b — — cos b cos y + si>» y cot a , denen als...
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Popular and Mathematical Astronomy, with the principal formulæ of Plane and ...

William Thomas READ - 1862
...2 OP . OE, OD . OD PD . DE . c0sa = op7oE + pcrroE-cosA = cos b . cos c + sin b . sin c cos A ; and cos a — cos b . cos c = sin b . sin c cos A. Therefore f*>»«-«»ft•«>•« = cos A. sin b . sin c NB — Compare this with the value of cos...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...cos a = -^OC* + ~W "* A' ' Substituting the functions derived from the triangles 0 A' O A' O, we have cos a = cos b cos c -)- sin b sin c cos A. In like manner may be deduced cos b = cos c cos a -)- sin c sin a cos B, cos c = cos a cos b -)- sin...
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