| Scottish school-book assoc - 1845 - 278 pages
...6 tan. 4(A — B) opposite to the angles A and B, the expression proves, that the sum of the sides **is to their difference, as the tangent of half the sum of** the opposite angles is to the tangent of half their difference, which is the rule. (7.) Let (AD—... | |
| Euclid, John Playfair - 1846 - 334 pages
...difference between either of them and 45°. PROP. IV. THEOR. The sum of any two sides of a triangle **is to their difference, as the tangent of half the sum of** the angles opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle... | |
| Dennis M'Curdy - 1846 - 168 pages
...triangle EFG, BC is drawn parallel to FG the base EC : CF : : EB : BG; that is, the sum of two sides **is to their difference, as the tangent of half the sum of** the angles at the base ia to the tangent of half their difference. * Moreover, the angles DBF, BFE... | |
| Jeremiah Day - 1848 - 354 pages
...THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, **is to their difference ; as the tangent of half the sum of** the angles ACB and ABC, to the tangent of half then- difference. Demonstration. Extend CA to G, making... | |
| Charles Davies - 1849 - 372 pages
...+c 2 —a 2 ) = R« x -R- x " * 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... | |
| Charles William Hackley - 1851 - 524 pages
...: tan £ (A + B) : tan ^ (A — B) That is to say, the sum of two of the sides of a plane triangle **is to their difference as the tangent of half the sum of** the opposite angles is to the tangent of half their difference. 76 This proportion is employed when... | |
| Jeremiah Day - 1851 - 418 pages
...sin 6 tan $ (a — 6)' * sin a+sin b : sin a — sin b : : tan | (a+6) : tan i (a — 6.) That is, **The sum of the sines of two arcs or angles, is to** the difference of those si?ies ; as the tangent of half the sum, of the arcs or angles, to the tangent... | |
| Charles Davies - 1886 - 340 pages
...C : sin B. Theorems. THEOREM 11. In any triangle, the sum of the two sides containing eithe1 angle, **is to their difference, as the tangent of half the sum of** (he t1eo other angles, to the tangent of half their di/ereMe. Let ACB be a triangle: then will With... | |
| Adrien Marie Legendre - 1852 - 436 pages
...AC :: sin 0 : sin jR THEOEEM II. In any triangle, the sum of the two sides containing either angle, **is to their difference, as the tangent of half the sum of** the two other angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will... | |
| William Chauvenet - 1852 - 268 pages
...proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle **is to their difference as the tangent of half the sum of** the opposite angles is to the tangent of half their difference. For, by the preceding article, a :... | |
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