| James Pryde - Navigation - 1867 - 506 pages
...add 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) - Trigonometry - 1868 - 346 pages
...a + I _ 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 J(A+ B) =... | |
| William Mitchell Gillespie - Electronic book - 1868 - 530 pages
...angles are 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, the... | |
| Eli Todd Tappan - Geometry - 1868 - 436 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 : sin.... | |
| Boston (Mass.). School Committee - Boston (Mass.) - 1868 - 508 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. 3. Given two sides and an opposite angle,... | |
| William Mitchell Gillespie - Surveying - 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 plane triangle, the... | |
| New-York Institution for the Instruction of the Deaf and Dumb - Deaf - 1869 - 698 pages
...£(CB); whence 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... | |
| Boston (Mass.). City Council - Boston (Mass.) - 1869 - 1192 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,... | |
| Charles Davies - Geometry - 1870 - 398 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 + AC:... | |
| New-York Institution for the Instruction of the Deaf and Dumb - Deaf - 1871 - 370 pages
...(CB); whence 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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