| William Mitchell Gillespie - Surveying - 1855 - 436 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... | |
| Elias Loomis - Trigonometry - 1855 - 192 pages
...BC, or sin. A : sin. B :: BC : AC. 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... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...(2.) In the same way it may be shown that THEOREM II. 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. By Theorem I., we have 5 : c : : sin.... | |
| William Mitchell Gillespie - Surveying - 1856 - 478 pages
...to each other a* 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... | |
| Peter Nicholson - Cabinetwork - 1856 - 518 pages
...+ BC :: AC-BC : AD — BD. TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Let ABC be a triangle 4 then, of... | |
| William Mitchell Gillespie - Surveying - 1857 - 538 pages
...to each other at the opposite sides. THEOREM II.— 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... | |
| Elias Loomis - Trigonometry - 1859 - 218 pages
...(AB)~tang4(AB) ' that is, The sum of the cosines of two arcs is to their difference, as the cotangent of half the sum of those arcs is to the tangent of half their difference. From the first formula of Art. 74, by substituting A+B for a, we have gin 2 sin4(A+B)xco84(A+B) XV... | |
| Elias Loomis - Logarithms - 1859 - 372 pages
...BxBC, or sin. A : sin. B : : BC : AC. THEOREM II. (50.) 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 any triangle ; then will... | |
| George Roberts Perkins - Geometry - 1860 - 472 pages
...it may be shown that §«.] TRIGONOMETRY. THEOREM It In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the op? posite angles is to the tangent of half their difference. By Theorem I., we have o : c : :... | |
| Euclides - 1860 - 288 pages
...demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B... | |
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