| Euclides - 1860
...demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle **is to their difference as the tangent of half the sum of the** angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and... | |
| War office - 1861 - 12 sider
...=2 tan 2 A. 5. In any triangle, calling one side the base, prove that the sum of the other two sides **is to their difference as the tangent of half the sum of the** angles at the base is to the tangent of half their difference. 6. Observers on two ships a mile apart... | |
| Benjamin Greenleaf - 1862 - 490 sider
...^ (A — B) f(\7\ sin A — sin B ~ wt~i (A + B) ; ( ' that is, The sum of the sines of two angles **is to their difference as the tangent of half the sum of the** angles is to the tangent of half their difference, or as the cotangent of half their difference is... | |
| Charles Davies - 1862 - 393 sider
...AC . : sin C : sin B. THEOREM IL In any triangle, the sum of the two sides containing either angle, **is to their difference, as the tangent of half the sum of** tt1e two oif1er angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will... | |
| Benjamin Greenleaf - 1863 - 320 sider
...a sin A sin B sin C' (89) (90) (91) (92) (93) 112. 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. For, by (90), a : b : : sin A : sin B;... | |
| 1863 - 256 sider
...proposition is therefore general in its application.* 118. The »urn of any two side» of a plane triangle ie **to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =»... | |
| 1864
...the first proportion in Theorem I. THEOREM III. 41. 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. Let ABC be a triangle ; then AB + BC:BC—... | |
| 1865
...latter formula, determine tan. 15°, first finding tan. 30°. 5. The sum of the two sides of a triangle **is to their difference as the tangent of half the sum of the** base angles is to the tangent of half the difference. 6. Prove that if A" be the number of seconds... | |
| James Pryde - 1867 - 458 sider
...the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides **is to their difference as the tangent of half the sum of the** remaining angles to the tangent of half their difference. The half sum and half difference being added,... | |
| Gerardus Beekman Docharty - 1867 - 283 sider
...sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides **is to their difference as the tangent of half the sum of the** ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)... | |
| |