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" A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a. "
Elements of Geometry and Trigonometry from the Works of A.M. Legendre ... - Page 323
by Charles Davies - 1854 - 432 pages
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Briefwechsel zwischen C.F. Gauss und H.C. Schumacher, herausg ..., Volumes 3-4

Carl Friedrich Gauss - Astronomers - 1861 - 952 pages
...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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Zeitschrift für Mathematik und Physik, Volume 7

Mathematics - 1862 - 586 pages
...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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Military Schools and Courses of Instruction in the Science and Art of War ...

Henry Barnard - Military education - 1862 - 410 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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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...c; Applying (150) to A'BC', we have cos ai = cos & cos ci -)- sin V sin c' cos A' ; or, by (46), — cos A = cos B cos C — sin B sin C cos a ; whence, cos .4 = sin B sin C cos a — cos B cos C. (153) In like manner may be deduced cos .Z?=:sin...
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Elemente der Vermessungskunde

Carl Maximilian von Bauernfeind, Karl Maximilian von Bauernfeind - Scientific apparatus and instruments - 1862 - 876 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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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 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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Popular and Mathematical Astronomy, with the principal formulæ of Plane and ...

William Thomas READ - 1862 - 144 pages
...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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Zeitschrift für Mathematik und Physik, Volume 7

Mathematics - 1862 - 600 pages
...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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Elements of Geometry and Trigonometry;: With Practical Applications

Benjamin Greenleaf - Geometry - 1863 - 502 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 (7; and by means of (147), sin c sm a sin C sin A* , . ^ 7 sin...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 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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