| Andrew Bell - 1837 - 240 sider
...demonstrated that AB : BC = sin C : sin A. PROPOSITION VI. THEOREM. The sum of two sides of a triangle **is to their difference as the tangent of half the sum of** me angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and... | |
| Charles William Hackley - 1838 - 307 sider
...tan £ (A -f- 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. This proportion is employed when two sides... | |
| Jeremiah Day - 1838
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, **is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. This is the second theorem applied to the... | |
| Jeremiah Day - 1839 - 370 sider
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, **is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. This is the second theorem applied to the... | |
| Charles Davies - 1839 - 334 sider
...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:... | |
| Charles Davies - 1839 - 261 sider
...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 sider
...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 sider
...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 sider
...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; AC, AB,... | |
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