| Francis Nichols - Plane trigonometry - 1811 - 162 pages
...| C : tan. | (A+ B), that is, in any spherical triangle the cosine of half the sum of any two sides **is to the cosine of half their difference, as the cotangent of half the included angle** is to the tangent of half the sum of the other two angles. 78. Remark. From this proposition and cor.... | |
| 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 - 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...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.... | |
| Charles William Hackley - Trigonometry - 1838 - 338 pages
...cot \ c : tan \ (A — B) . . . (9) That is, the cosine of half the sum of two sides of a spherical **triangle is to the cosine of half their difference, as the cotangent of half the included angle** is to the tangent of half the sum of the other two angles. The second may be repeated in a similar... | |
| 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
...Napier's Analogies. Proof. This theorem is at once obtained by applying § 79 to the polar triangle. 91. **Theorem. The cosine of half the sum of two sides of...difference, as the cotangent of half the included angle** is to the tangent of half the sum of the other two angles, or in (figs. 32 and 33), соз4(а^с)... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...Napier's Analogies. Proof. This theorem is at once obtained by applying § 79 to the polar triangle. 91. **Theorem. The cosine of half the sum of two sides of...difference, as the cotangent of half the included angle** is to the tangent of half the sum of the other two angles, or in (figs. 32 and 33), cos.£(a— c)... | |
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