 | 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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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. 
