| Euclid, John Playfair - Euclid's Elements - 1846 - 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 - 1851 - 538 pages
...: : tan 4 a : tan 4 (b — c) . . . 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 ike sum of the other two angles. The second may be repeated in a similar... | |
| Charles William Hackley - Trigonometry - 1851 - 524 pages
...: tan i (6 — c) . . . That is, the cosine of half the sum of two sides of a spherical triangle it **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... | |
| Benjamin Peirce - Trigonometry - 1852 - 400 pages
...once obtained by applying § 79 to the polar triangle. 91. Theorem. The cosine of half the sum of tico **sides of a 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 tico angles, or in (figs. 32 and 33), cos. J (a + c)... | |
| Benjamin Peirce - Trigonometry - 1861 - 400 pages
...(369) Proof. This theorem is at once obtained by applying (350) to the polar triangle. »• jf 91. **Theorem. The cosine of half the sum of two sides of...of half their difference as the cotangent of half** tJie included angle is to the tangent of half the sum of the other two angles ; or, in ABO (fig. 32... | |
| Benjamin Greenleaf - Geometry - 1861 - 628 pages
...cot £ C : tan £ (4 — B). (187) 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 sine of half the sum of two sides of... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 pages
...: cot JC : tan £ (4 — #). (187) That is, y^e 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... | |
| Benjamin Greenleaf - Geometry - 1862 - 514 pages
...the other two angles. 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 haJf the difference of the other two angles. By applying (186) and (187) to the... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...cot £ C : tan £ (4 — B). (187) 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 sine of half the sum of two sides of... | |
| Benjamin Greenleaf - 1869 - 516 pages
...: cot i C : tan £ (^ — 5). (187) 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 sine of half the sum of two sides of... | |
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