| Nathan Scholfield - Conic sections - 1845
...sin. A ' b a sin. B sin. A c sin. C sin. B b PROPOSITION III. In any plane triangle, the sum of any **two sides, is to their difference, as the tangent of half the sum of the angles** opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle, then,... | |
| Nathan Scholfield - 1845 - 896 pages
...a c b sin. B sin. A sin. C sin. B sin. C. 68 PROFOSITION in. In any plane triangle, the sum of any **two sides, is to their difference, as the tangent of half the sum of the angles** opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle, then,... | |
| Nathan Scholfield - Geometry - 1845 - 506 pages
...sin. A^ 6 a sin. B sin. A c 6 sin. C sin. B 08 PROPOSITION III. In any plane triangle, the sum of any **two sides, is to their difference, as the tangent of half the sum of the angles** opposite to them, is to the tangent of half their difference, Let ABC be any plane triangle, then,... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...proposition is a particular case of this PROP. III. THEOR. — The sum of any two sides of a triangle **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. Let ABC be a triangle, a, b any... | |
| Scottish school-book assoc - 1845 - 278 pages
...a — 6 tan. 4(A — B) opposite to the angles A and B, the expression proves, that the sum of the **sides is to their difference, as the tangent of half the sum of the** opposite angles is to the tangent of half their difference, which is the rule. (7.) Let (AD— DC)... | |
| William Scott - Measurement - 1845 - 290 pages
...b : a — b :: tan. | (A + в) : tan. ¿ (A — в).* Hence the sum of any two sides of a triangle, **is to their difference, as the tangent of half the sum of the angles** oppo-* site to those sides, to the tangent of half their difference. SECT. T. EESOLUTION OF TRIANGLES.... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...triangle. j ¿ , C> ~! ' ' Ans. The question is impossible. 81. Theorem. The sum of two sides of a triangle **is to their difference, as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. [B. p. 13.] Proof. We have (fig. 1.) a:... | |
| Scottish school-book assoc - 1845 - 434 pages
...difference of the segments of the base made by a perpendicular upon it from the vertex, as the cosine **of half the sum of the angles at the base, is to the** cosine of half their difference. Also, that the sum of the sides, is to the lifference of the segments... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 449 pages
...solve the triangle. -4n'. The question is impossible. 81. Theorem. The sum of two sides of a triangle **is to their difference, as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. [B. p. 13.] Proof. We have (fig. 1.) a... | |
| John Playfair - Euclid's Elements - 1846 - 332 pages
...difference between either of them and 45°. PROP. IV. THEOR. The sum of any two sides of a triangle **is to their difference, as the tangent of half the sum of the angles** opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle ; CA+AB... | |
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