| Charles Davies - 1830 - 390 pages
...should obtain, THEOREM. 44. In any plane triangle, the sum of tfte two sides containing either angle, **is to their difference, as the tangent of half the sum of** the other two angles, to the tangent of half their difference. Let ABC (PI. I. Fig. 3) be a triangle... | |
| Alexander Ingram - 1830 - 458 pages
...sura. PROP. XXXIX. In any triangle ABC, of which the sides are unequal, the sum of the sides AC + AB **is to their difference as the tangent of half the sum of** the opposite angles B and C, to the tangent of half their difference. CA + AB : CA — AB : : tan.... | |
| Charles Hutton - 1831 - 656 pages
...lui(A-fB) sinx+sins v * This equation is readily converted into a very useful proportion, viz. Tin' **sum of the sines of two arcs or angles, is to their...angles, is to the tangent of half their difference.** 26. Operating with the third and fourth formula- of the preceding article, as we have already done... | |
| Jeremiah Day - 1831 - 394 pages
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, **is to their difference ; as the tangent of half the sum of** the opposite angles, to the tangent of half their difference. This is the second theorem applied to... | |
| Jeremiah Day - 1831 - 520 pages
...a - sin6~tan J(a — 6) ' sin a + sin b I sin a — sin b'. ;tan J(a+6) : tan J (a— b.) That is, **The sum of the sines of two arcs or angles, is to** the difference of those sines ; as the tangent of half the sum of the arcs or angles, to the tangent... | |
| John Radford Young - 1833 - 286 pages
...4 tan. a — 4 ~~ tan. J(A — B) ' that is to say, in any plane triangle the sum of any two sides **is to their difference as the tangent of half the sum of** the opposite angles is to the tangent of half their difference. By help of this rule we may determine... | |
| Euclid - 1835 - 540 pages
...difference ; and since BC, FG are parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the sides **is to their difference, as the tangent of half the sum of** the angles at the base to the tangent of half their difference. * PROP. IV. FIG. 8. In a plane triangle,... | |
| John Playfair - 1836 - 148 pages
...three being given, the fourth is also given. PROP. III. i In a plane triangle, the sum of any two sides **is to their difference, as the tangent of half the sum of** the angles at the base, to the tangent of half their difference. Let ABC be a plane triangle, the sum... | |
| Adrien Marie Legendre - 1836 - 394 pages
...c=2p — 2c, a+c — 6=2p — 26; hence THEOREM V. In every rectilineal triangle, the sum of two sides **is to their difference as the tangent of half the sum of** the angles opposite those sides, to the tangent of half their difference. For. AB : BC : : sin C :... | |
| 1836 - 488 pages
...difference of two arcs, is equal to the product of the cosines of the arcs + the product of their sines. **The sum of the sines of two arcs or angles, is to** the difference of those sines ; as the tangent of half the. sum of the arcs or angles, to the tangent... | |
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