| William Chauvenet - 1863 - 256 páginas
...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 =»... | |
| William Frothingham Bradbury - 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—... | |
| McGill University - 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 páginas
...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 páginas
...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.)... | |
| Boston (Mass.). School Committee - 1868
...and cosecant. 2. Demonstrate that, in any triangle, the sum of the two sides containing either angle, **is to their difference, as the tangent of half the sum of the two** other angles, to the tangent of half their difference. 3. Given two sides and an opposite angle, in... | |
| Eli Todd Tappan - 1868 - 420 páginas
...BA-cos. A. That is, b = a cos. C -J- e cos. A. 869. Theorem — The sum of any two sid.es of a triangle **is to their difference as the tangent of half the sum of the two** opposite angles is to the tangent of half their difference. By Art. 867, a : b : : sin. A : sin. B.... | |
| W.M. GILLESPIE, L.L. D., CIV. ENG. - 1868
...to each other as the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides **is to their difference as the tangent of half the sum of the** angles opposite those sides is to the tangent of half their difference. THEOREM III.— In every plane... | |
| Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 páginas
...tang } (A + B) a — b tang} (A — B) *• ; which shows that, in any triangle, the sum of two sides **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. We have A + B=180° —... | |
| Boston (Mass.). City Council - 1869
...and cosecant. 2. Demonstrate that, in any triangle, the sum of the two sides containing either angle, **is to their difference, as the tangent of half the sum of the two** other angles, to the tangent of half their difference. 8. Given two sides and an opposite angle, in... | |
| |