 In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of...  Elements of Trigonometry, Plane and Spherical - Pàgina 51per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pàginesVisualització completa - Sobre aquest llibre
 | Charles Davies - 1839 - 376 pàgines
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angk, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of haJ/ their difference. 58. Let ACB be a triangle : then will AB+AC:... | |
 | Adrien Marie Legendre - 1839 - 372 pàgines
...— 6=2p — 2b; hence THEOREM V. fit every rectilineal triangle, the sum of two sides is to tlieir 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 A (Theorem III.).... | |
 | Charles Davies - 1841 - 414 pàgines
...AC : : sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:... | |
 | John Playfair - 1842 - 332 pàgines
...difference between either of them and 45°. PROP. IV. THE OR. 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 ofhalftlteir difference. Let ABC be any plane triangle... | |
 | Enoch Lewis - 1844 - 234 pàgines
...being suited to any radius whatever (Art. 27). QED ART. 30. In any right lined triangle, the sum of any two sides is, to their difference, as the tangent...half the sum of the angles, opposite to those sides, to the tangent of half their difference. Let ABC be the triangle; AC, AB, the sides. From the centre... | |
 | Nathan Scholfield - 1845 - 542 pàgines
...sin. A ' b a sin. B sin. A c sin. C sin. B b PROPOSITION III. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle, then, by Proposition... | |
 | Nathan Scholfield - 1845 - 894 pàgines
...a c b sin. B sin. A sin. C sin. B sin. C. 68 PROFOSITION in. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle, then, by Proposition... | |
 | Nathan Scholfield - 1845 - 506 pàgines
...sin. A^ 6 a sin. B sin. A c 6 sin. C sin. B 08 PROPOSITION III. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference, Let ABC be any plane triangle, then, by Proposition... | |
 | William Scott - 1845 - 288 pàgines
...b : a — b :: tan. | (A + в) : tan. ¿ (A — в).* Hence the sum of any two sides of a triangle, is to their difference, as the tangent of half the sum of the angles oppo-* site to those sides, to the tangent of half their difference. SECT. T. EESOLUTION OF TRIANGLES.... | |
 | Scottish school-book assoc - 1845 - 278 pàgines
...a — 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— DC)... | |
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