| Charles Davies - Surveying - 1839 - 261 pages
...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. 53. Let ACB be a triangle : then will AB+AC:... | |
| Jeremiah Day - Geometry - 1839 - 370 pages
...THE OPPOSITE ANGLES J 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... | |
| Thomas Keith - 1839
...double their opposite angles. PROPOSITION IV. (115) In any plane triangle, the sum of any two sides **is to their difference, as the tangent of half the sum of** their opposite angles is to the tangent of half their difference, Let ABC be any triangle ; make BE... | |
| Charles Davies - Navigation - 1841 - 359 pages
...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 - Euclid's Elements - 1842 - 317 pages
...BC is parallel to FG, CE : CF : : BE ; BG, (2. 6.) that is, the sum of the two sides of the triangle **ABC 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. PROP. V. THEOR. If a perpendicular... | |
| Enoch Lewis - Conic sections - 1844 - 228 pages
...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 of half the sum of the** angles, opposite to those sides, to the tangent of half their difference. Let ABC be the triangle;... | |
| William Scott - Measurement - 1845 - 237 pages
...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... | |
| Nathan Scholfield - 1845
...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,... | |
| Scottish school-book assoc - 1845
...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)... | |
| Nathan Scholfield - Conic sections - 1845 - 232 pages
...proposition, a sin. A.~ c b sin. 68 FROPOSITION 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,... | |
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