 | 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... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...triangle is equal to radius into the rectangle of the cosines of the two other sides plus the rectangle of the sines of those sides into the cosine of their included angle. V. Each of the formulas designated (2) involves the three sides of the" triangle together with one... | |
 | 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... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...triangle is equal to radius into the rectangle of the cosines of the two other sides plus the rectangle of the sines of those sides into the cosine of their included angle. V. Each of the formulas designated (2) involves the three sides of the triangle together with one of... | |
 | William Chauvenet - 1852 - 268 pages
...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 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 plane B'A'С',... | |
 | Elias Loomis - Trigonometry - 1855 - 192 pages
...either side of a spherical triangle, is equal to radius into the product of the cosines of the two other sides, plus the product of the sines of those sides into the cosine of their included angle. (226.) From equation (1) we obtain, by transposition, R " cos. a—R cos. b cos. c COS. A= : 7 : ,... | |
 | Elias Loomis - Logarithms - 1859 - 372 pages
...either side of a spherical triangle, is equal to radius into the product of the cosines of the two other sides, plus the product of the sines of those sides into the cosine of their included angle. (226.) From equation (1) we obtain, by transposition, . R2 cos. a— R cos. b cos. c COS. A= : —.... | |
 | 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...sides, plus the product of the sines of those sides multiplied by the cosine of the included angle. Let ABC be a spherical triangle, and CD a perpendicular... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...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 is equal to the product...two sides, plus the product of the sines of those two sides into the cosine of their included angle. Let A BC be any spherical triangle, 0 the centre... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...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 is equal to the product...two sides, plus the product of the sines of those two sides into the cosine of their included angle. Let ABC be any spherical triangle, O the centre... | |
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In a 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 these two sides and the cosine of their included angle. 
