| Charles Davies - Navigation - 1841 - 418 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 AB+AC:... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...difference between either of them and 45°. PROP. IV. THE OR. 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 ofhalftlteir difference. Let ABC be any plane triangle... | |
| Enoch Lewis - Conic sections - 1844 - 240 pages
...sine of A ; these sines being suited to any radius whatever (Art. 27). QED ART. 30. In any right lined **triangle, the sum of any two sides is, to their difference,...tangent of half the sum of the angles, opposite to** those sides, to the tangent of half their difference. Let ABC be the triangle; AC, AB, the sides. From... | |
| Euclides, James Thomson - Geometry - 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, a, b any two of its... | |
| William Scott - Measurement - 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 OF TRIANGLES.... | |
| 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)... | |
| 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:... | |
| Benjamin Peirce - Plane trigonometry - 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.) a... | |
| Dennis M'Curdy - Geometry - 1846 - 168 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... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 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 : CA-AB... | |
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