| Francis Nichols - Plane trigonometry - 1811 - 128 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 - 317 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 - 322 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 - 428 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 - 71 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 - 71 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 - Geometry - 1837 - 318 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 - 317 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 - 449 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 - 317 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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