| Charles Davies - 1841 - 414 pages
...AC : : sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angle, **is to their difference, as the tangent of half the sum of** the two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will... | |
| John Playfair - 1842 - 332 pages
...parallel to FG, CE : CF : : BE ; BG, (2. 6.) that is, the sum of the two sides of the triangle ABC **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. PROP. V. THEOR. If a perpendicular... | |
| Enoch Lewis - 1844 - 240 pages
...to any radius whatever (Art. 27). QED ART. 30. In any right lined triangle, the sum of any two sides **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 the triangle;... | |
| William Scott - 1845 - 288 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... | |
| Nathan Scholfield - 1845 - 542 pages
...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,... | |
| Nathan Scholfield - 1845 - 244 pages
...proposition, a sin. A.~ c b sin. 68 FROPOSITION 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,... | |
| Benjamin Peirce - 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.)... | |
| Nathan Scholfield - 1845 - 894 pages
...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,... | |
| Benjamin Peirce - 1845 - 498 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.)... | |
| Euclid, James Thomson - 1845 - 382 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,... | |
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