| Francis Nichols - Plane trigonometry - 1811 - 162 pages
...PROP. XVIII. . 76. In any spherical triangle the sine of half the sum of any two sides is to the sine of half their difference, as the cotangent of half the included angle is to the tangent of half the difference of the other two angles. Let the two sides AC, BC, and the included angle C be proposed;... | |
| John Playfair - 1819 - 354 pages
...difference of th£ angles opposite to them : ;UM! also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained between them, to the tangent of half the sum of the angles opposite to them. COR. 2.... | |
| William Galbraith - Astronomy - 1827 - 412 pages
...half the difference of the angles opposite to them : And the cosine of half the sum of these sides is to the cosine of half their difference, as the cotangent of half tne angle contained between them, is to the tangent of half the sum of the angles opposite to them,t... | |
| William Galbraith - Astronomy - 1834 - 454 pages
...half the difference of the angles opposite to them : And the cosine of half the sum of these sides is to the cosine of half their difference as the cotangent of half the angle contained between them is to the tangent of half the sum of the angles opposite to them, t or... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...substituted in (847), gives t sin. % (a -\- c) cotan. ¿ B (8M) MÏ.~j (a — с) ~ tang. ¿ (Л — C)' 77. Theorem. The cosine of half the sum of two sides of...difference, as the cotangent of half the included angle (852) is to the tangent of half the sum of the other two angles, or in (figs. 4. and 5.), cos. ¿ (a... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...gives sin. J (a -\- c) cotan. ¿ В sin. à (a — c) = tang. J (A^~C)J which is the same as (845). 77. Theorem. The cosine of half the sum of two sides of...cosine of half their difference, as the cotangent of hit If the included angle (852) is to the tangent of half the sum of the other two angles, or in (figs.... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...difference of the angles opposite to them : and also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained between them, to the tangent of half the sum of the angles opposite to them. COR. 2.... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...difference of the angles opposite to them : and also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained between them, to the tangent of half the sum of the angles opposite to them. COR. 2.... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...53° 8'. 90. Theorem. The sine of half the sum of two sides of a spherical triangle is to the sine of half their difference, as the cotangent of half the included angle is to the tangent of half the difference of the other two angles, that is, in ABC (figs. 32 and 33), sin.¿(ajc) :sin.i(a— c)=cotan.... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...difference of the angles opposite to them : and also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained between them, to the tangent of half the sum of the angles opposite to them. COR. 2.... | |
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