| John Playfair - Euclid's Elements - 1842 - 332 pages
...half the 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.£(a+ c) :sin. |(a— c)=cotan.... | |
| 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
...half the 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 - 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...the tangent of half the sum of the other two angles. The second may be repeated in a similar manner, changing cosine into sine and tangent of the half sum... | |
| Charles William Hackley - Trigonometry - 1851 - 540 pages
...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...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 manner, changing cosine into... | |
| Benjamin Peirce - Trigonometry - 1852 - 398 pages
...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...angle is to the tangent of half the sum of the other tico angles, or in (figs. 32 and 33), cos. J (a + c) : cos. J (a — c) = cotan. \ B : tang. J ( A... | |
| Horatio Nelson Robinson - Geometry - 1860 - 468 pages
...sum of any two sides of a spherical triangle is to the sine of the half difference of the same sides, as the cotangent of half the included angle is to the tangent of the half difference of the other two angles. The half sum, and the half difference of two angles of... | |
| Benjamin Peirce - Trigonometry - 1861 - 396 pages
...to the polar triangle. »• jf 91. Theorem. The cosine of half the sum of two sides of a triangle. is to the cosine 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... | |
| S. M. Saxby - Nautical astronomy - 1861 - 140 pages
...two sides is to the cosine of half their difference, so is the cotangent of half the contained angle to the tangent of half the sum of the other two angles. And half the difference thus found added to half the sum gives the greater angle ; and half the difference... | |
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