| 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,... | |
| 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,... | |
| 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... | |
| 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,... | |
| 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... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...^(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... | |
| William Frothingham Bradbury - Geometry - 1872 - 268 pages
...each other, have the same sine, and BD = a sin. BCD = a sin. C (41) B 102. 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 (Art. 103) be a plane triangle... | |
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