| James Pryde - 1867 - 506 pages
...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... | |
| Eli Todd Tappan - 1868 - 444 pages
...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 :... | |
| William Mitchell Gillespie - 1868 - 530 pages
...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... | |
| Lefébure de Fourcy (M., Louis Etienne) - 1868 - 350 pages
...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 - 1194 pages
...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,... | |
| New-York Institution for the Instruction of the Deaf and Dumb - 1869 - 698 pages
...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... | |
| William Mitchell Gillespie - 1869 - 550 pages
...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... | |
| Charles Davies - 1870 - 392 pages
...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... | |
| Elias Loomis - 1871 - 302 pages
..., sin. A : sin. B : : BC : AC. B THEOREM II. (50.) In any plane triangle, the sum of any tico 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 any triangle ; then will... | |
| New-York Institution for the Instruction of the Deaf and Dumb - 1871 - 370 pages
...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... | |
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