| Jeremiah Day - 1839 - 370 páginas
...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... | |
| Charles Davies - 1839 - 261 páginas
...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:... | |
| 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 - 1841 - 359 páginas
...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 - 317 páginas
...difference as the radius to the tangent of the 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 - 228 páginas
...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;... | |
| Euclid, James Thomson - 1845 - 352 páginas
...1. The first part, therefore, of that proposition is a particular case of this PROP. III. 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, is to the tangent of half their difference. Let ABC be a triangle,... | |
| William Scott - 1845
...в) a — b~ tan. ¿ (A — в)' or, a + 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,... | |
| Nathan Scholfield - 1845
...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,... | |
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