| Nathan Scholfield - Conic sections - 1845
...proposition, a 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 - Geometry - 1845 - 232 pages
...proposition, a 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,... | |
| James Thomson - Geometry - 1845 - 358 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... | |
| 1845
...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.... | |
| 1845
...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)... | |
| Benjamin Peirce - Plane trigonometry - 1845 - 449 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:... | |
| 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... | |
| Dennis M'Curdy - Geometry - 1846 - 138 pages
...AC+sin. AB : sin. AC—sin. AB : : tan. J(AC-(AB): tan. J(AC—AB). QED 4 Th. In any triangle, the sum of **two sides is to their difference, as the tangent of half the sum of the angles at the base** is to the tangent of half their difference. Given the triangle ABC, the side AB being greater than... | |
| John Playfair - Euclid's Elements - 1846 - 317 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... | |
| Nathaniel Bowditch - 1846 - 451 pages
...: DH : AF or HB ; that is, AD, the sum of the legs, AC and СЁ, is to AE, their difference, as DH, **the tangent of half the sum of the angles at the base** (the radius teing AH), is to HB, the tangent of half the difference of the same angles (to the same... | |
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