 | Daniel Cresswell - Geometry - 1816 - 352 pages
...complemental triangle. PROP. I. (230.) Theorem. The cosine of any one of the sides, of a spherical triangle, is equal to the product of the cosines of the other two sides, together with the continued product of the sines of those two sides, and the cosine of the angle contained... | |
 | Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...the form of a theorem it may be stated thus : The cosine of one of the sides of a spherical triangle^ is equal to the product of the cosines of the other two sides, increased by the product of their sines multiplied into the cosine of the included angle. There are three equations answering to... | |
 | George Clinton Whitlock - Mathematics - 1848 - 340 pages
...= QTP + RTd — RTP PROPOSITION III. The cosine of any side of a spherical triangle is equal (535) to the product of the cosines of the other two sides increased by that of their sines multiplied into the cosine of the angle opposite the first-mentioned side. For,... | |
 | William Chauvenet - 1852 - 268 pages
...without requiring a special examination of the various positions of the lines of the diagram. 5. In a spherical triangle, the cosine of any side is equal...the product of the cosines of the other two sides, plus the continued product of the sines of those sides and the cosine of the included angle. Let the... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...AC : cot.BC = cos. ACD : cos.BCD. PROPOSITION VII. The cosine of any side of a spherical triangle, is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides multiplied by the cosine of the included angle. Let ABC... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...an angle and its supplement are the same, the sine of B1 Ö D is still equal to the sine of G. 149. In any spherical triangle, the cosine of any side...the product of the cosines of the other two sides, plus the product of the sines of those two sides into the cosine of their included angle. Let ABC be... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...the same, the sine of B' G'D is still equal to the sine of C. (147) (148) (149) TRIGONOMETRY. 149. In any spherical triangle, the cosine of any side...the product of the cosines of the other two sides, plus the product of the sines of those two sides into the cosine of their included angle. Let A BC... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...supplement are the same, the sine of B' C?D is «till equal to the sine of C. 7* TRIUONOMETRY. 1 49. In any spherical triangle, the cosine of any side...the product of the cosines of the other two sides, plus the product of the sines of those two sides into the cosine of their included angle. Let ABC be... | |
 | Benjamin Greenleaf - 1867 - 188 pages
...angle and its supplement are the same, the sine of B' O'D is still equal to the sine of G. 7* 149. Jn any spherical triangle, the cosine of any side is...the product of the cosines of the other two sides, plus the product of the sines of tliose two sides into the cosine of their included angle. Let AB 0... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...in Space. THREE 8IDE8 AND AN ANGLE. 878. Theorem. — The cos)ne of any side of a spherical triangle is equal to the product of the cosines of the other...two sides, increased by the product of the sines of those sides and the cosine of their included angle. 315 Let ABC be a spherical triangle, O the center... | |
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Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides... 
