 | Nathan Scholfield - 1845 - 894 σελίδες
...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 - 1845 - 506 σελίδες
...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,... | |
 | Nathan Scholfield - 1845 - 542 σελίδες
...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,... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...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 σελίδες
...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 - 1845 - 288 σελίδες
...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 - 1845 - 498 σελίδες
...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... | |
 | Scottish school-book assoc - 1845 - 444 σελίδες
...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 - 1845 - 498 σελίδες
...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:... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...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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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... 
