| 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,... | |
| 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° — C; hence... | |
| 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 triangle,... | |
| 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.... | |
| 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 triangle,... | |
| 1869
...we have the principle. When two sides and their included angles are given : The sum of the two sides **is to their difference as the tangent of half the sum of the** other two angles is to the tangent of half their difference. This young man also worked out a problem... | |
| 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,... | |
| 1870 - 319 sider
...0 : sin B. Theorems. THEOREM II. 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. Let ACB be a triangle: then will AB + AC:... | |
| 1871
...we have the principle. When two sides and their included angles are given : The sum of the two sides **is to their difference as the tangent of half the sum of the** other two angles is to the tangent of half their difference. This young man also worked out a problem... | |
| Elias Loomis - 1871 - 58 sider
...^(A+B) . sin. A-sin. B~sin. ^(AB) cos- ^(A+B)~tang. ^(AB) ' that is, The sum of the sines of two arcs **is to their difference, as the tangent of half the sum of** those arcs is to the tangent of half their difference. COS f*fvt Dividing formula (3) by (4), and considering... | |
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