 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.  Elements of Surveying - Página 25por Charles Davies - 1830 - 300 páginasVista completa - Acerca de este libro
 | Nathan Scholfield - 1845 - 542 páginas
...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,... | |
 | William Scott - 1845 - 288 páginas
...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... | |
 | Nathan Scholfield - 1845 - 244 páginas
...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,... | |
 | Euclid, James Thomson - 1845 - 382 páginas
...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,... | |
 | Benjamin Peirce - 1845 - 498 páginas
...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:... | |
 | Benjamin Peirce - 1845 - 498 páginas
...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... | |
 | Nathan Scholfield - 1845 - 894 páginas
...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,... | |
 | Charles Davies - 1846 - 386 páginas
...similar manner, we should find, AB : AC :: sin C : sin B. 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. 58. Let ACB be a triangle : then will AB+AC:... | |
 | Euclid, John Playfair - 1846 - 334 páginas
...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... | |
 | Dennis M'Curdy - 1846 - 168 páginas
...triangle EFG, BC is drawn parallel to FG the base EC : CF : : EB : BG; that is, the sum of two sides is to their difference, as the tangent of half the sum of the angles at the base ia to the tangent of half their difference. * Moreover, the angles DBF, BFE are... | |
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