| Francis Nichols - Plane trigonometry - 1811 - 128 pages
...tangent of half the difference of the other two sides: also, the cosine of half the sum of any two angles **is to the cosine of half their difference, as the tangent of half the** included side is to the tangent of half the sum of the other two sides. Fig. page 80. Let the angles... | |
| Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...half the difference of t,he sides opposite to them; and the cosine of half the sum of the same angles **is to the cosine of half their difference, as the tangent of half the side** adjacent to them, to the tangent of half the suai of the sides opposite. LetC+B=2S, CB=2D, the base... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...(M-\-N) : cos. (M — N) : : y — x : y+x; which may be written as in (744). 60. Theorem. The sine **of half the sum of two angles of a spherical triangle is to the** sine of half their difference, as the tangent of half the side to (749) which they are both adjacent... | |
| Charles William Hackley - Trigonometry - 1838 - 328 pages
...: : tan \ c : tan ^ (a — 6) The last one may be translated into ordinary language thus: The sine **of half the sum of two angles of a spherical triangle is to the** sine of half their difference as tfc.e tangent of half the interjacent side is to the tangent of half... | |
| Charles William Hackley - Trigonometry - 1838 - 336 pages
...(a — 6) : : 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... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...half the difference of the sides opposite to them; and the cosine of half the sum of the same angles **is to the cosine of half their difference, as the tangent of half the side** adjacent to them, to the tangent of half the sum of the sides opposite. LetC+B=2S, C— B=2D, the base... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...TV) : cos. (M — TV) z= y — x : y -f- ж ; which may be written as in (349). 79. Theorem. The sine **of half the sum of two angles of a spherical triangle is to the** sine of half their difference, as the tangent of half the side to which Napier's Analogies. they are... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 449 pages
...-{- N) : cos. (M — N) = y — x : y -\-x ; which may be written as in (349). 79. Theorem. The sine **of half the sum of two angles of a spherical triangle is to the** sine of half their difference, as the tangent of half the side to which Napier's Analogies. they are... | |
| John Playfair - Euclid's Elements - 1846 - 332 pages
...half the difference of the sides opposite to them ; and the cosine of half the sum of the same angles **is to the cosine of half their difference, as the tangent of half the side** adjacent to them, to the tangent of half the sum of the sides opposite. 260 the segments of the base,... | |
| Charles William Hackley - Trigonometry - 1851 - 538 pages
...difference of the other two angles. The third may be translated into ordinary language thus : The sine **of half the sum of two angles of a spherical triangle is to the** •ine of half their difference as the tangent of half the interjacent side is to the tangent of half... | |
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