 | George Clinton Whitlock - Mathematics - 1848 - 340 pages
...A + sin5 : sinlA — sin 7?, or (333) a + b : a—b : : tani(A+B) : tan^(^-S) ; ie PROPOSITION VI. The sum of any two sides of a triangle is to their dif- (396) ference, as the tangent of the half sum of the angles opposite to the tangent of half their... | |
 | Charles Davies - Trigonometry - 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 : sin... | |
 | Charles William Hackley - Trigonometry - 1851 - 536 pages
...— 6 : : 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...angles is to the tangent of half their difference. 76 This proportion is employed when two sides and the included angle of a triangle are given to find... | |
 | Jeremiah Day - Geometry - 1851 - 418 pages
...THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making... | |
 | William Smyth - Plane trigonometry - 1852 - 198 pages
...AC : : tang — - — - tang ; "•" /^ a proportion, which we may thus enunciate : the sum of tioo sides of a triangle is to their difference, as the...angles is to the tangent of half their difference. parts. Subtracting the angle C 45° from 180°, and dividing the remainder by 2, we have = 67° 30',... | |
 | William Chauvenet - 1852 - 268 pages
...The 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...angles is to the tangent of half their difference. For, by the preceding article, a : b = sin A : sin В whence, by composition and division, a + b :... | |
 | Adrien Marie Legendre - Geometry - 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 AJ3... | |
 | Charles Davies - Geometry - 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... | |
 | Jeremiah Day - Mathematics - 1853 - 288 pages
...of their opposite angles. It follows, therefore, from the preceding proposition, (Alg. 38'.>.) that the sum of any two sides of a. triangle, is to their difference ; as the tangent of half the sum of tin; opposite angles, to the tangent of half their difference. This is the second theorem npplied to... | |
 | Horatio Nelson Robinson - History - 1853 - 334 pages
...point without a circle, by theorem 18, book 3, we have, Hence, . . AB : AE=AF : AG QED PROPOSITION 7. The sum of any two sides of a triangle, is to their difference, as the tangent of the half sum of the angles opposite to these sides, to the tangent of half their difference. Let ABC... | |
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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. 
