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. A Treatise of Practical Surveying, ... - Side 94av Robert Gibson - 1808 - 440 siderUten tilgangsbegrensning - Om denne boken
| 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.)... | |
| 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 sider
...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 sider
...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° —... | |
| 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... | |
| William Mitchell Gillespie - 1869 - 428 sider
...to each other at the opposite sides. THEOREM EL — In every plane triangle, the turn of two tides **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... | |
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