 | Daniel Cresswell - Geometry - 1816 - 352 pages
...conclusions may be drawn, from the other complemental triangle. PROP. I. (230.) Theorem. The cosine of any one of the sides, of a spherical triangle, is equal...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... | |
 | 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,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...sin c cos B, L (1) cos c = cos a cos b + sin a sin b cos (7. J That is : The cosine of either side of a spherical triangle is equal to the product of the cosines of the two other sides plus the product of their sines into the cosine of their included angle, enter into... | |
 | William Chauvenet - 1852 - 268 pages
...the various positions of the lines of the diagram. 5. In a spherical triangle, the cosine of any side is equal to 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 cos.BCD cot.BC Or, cot. 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 - 518 pages
...the sine of C. (147) (148) (149) TRIGONOMETRY. 149. In any spherical triangle, the cosine of any side is equal to 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 - 1862 - 532 pages
...of B1 Ö D is still equal to the sine of G. 149. In any spherical triangle, the cosine of any side is equal to 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... | |
 | John Mulcahy - Geometry - 1862 - 252 pages
...circles whose poles are the extremities of the base. Since the cosine of the hypotenuse of a right-angled spherical triangle is equal to the product of the cosines of the sides, the locus of the vertex of such a triangle, whose hypotenuse is given, is a spherical ellipse.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...«till equal to the sine of C. 7* TRIUONOMETRY. 1 49. In any spherical triangle, the cosine of any side is equal to 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... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...would be Trigonometry in Space. THREE SIDES AND AN ANGLE. 878. Theorem. — The cosine of any side of a spherical triangle is equal to the product of...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,... | |
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Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides... 
