 | 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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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 sine of half the sum of two sides of a... 
