 In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of...  Elements of Trigonometry, Plane and Spherical - Pàgina 51per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pàginesVisualització completa - Sobre aquest llibre
 | McGill University - 1865 - 332 pàgines
...latter formula, determine tan. 15°, first finding tan. 30°. 5. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the base angles is to the tangent of half the difference. 6. Prove that if A" be the number of seconds... | |
 | Gerardus Beekman Docharty - 1867 - 474 pàgines
...cos. A— sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)... | |
 | James Pryde - 1867 - 506 pàgines
...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,... | |
 | William Mitchell Gillespie - 1868 - 530 pàgines
...triangle, the sines of the angles are to each other as the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference...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... | |
 | Boston (Mass.). School Committee - 1868 - 508 pàgines
...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,... | |
 | Eli Todd Tappan - 1868 - 444 pàgines
...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 - 550 pàgines
...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 - 1869 - 698 pàgines
...£(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 - 1869 - 1192 pàgines
...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 - 1870 - 392 pàgines
...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:... | |
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