| Charles Davies - Surveying - 1839 - 376 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. 53. Let ACB be a triangle : then will AB+AC:... | |
| Charles Davies - Surveying - 1839 - 380 pages
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angk, **is to their difference, as the tangent of half the sum of the** two other angles, to the tangent of haJ/ their difference. 58. Let ACB be a triangle : then will AB+AC:... | |
| Thomas Keith - 1839 - 498 pages
...double their opposite angles. PROPOSITION IV. (115) In any plane triangle, the sum of any two sides **is to their difference, as the tangent of half the sum of** their opposite angles is to the tangent of half their difference, Let ABC be any triangle ; make BE... | |
| Charles Davies - Navigation - 1841 - 406 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
...to the tangent of the 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 - 228 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; AC, AB,... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...part, therefore, of that 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... | |
| William Scott - Measurement - 1845 - 290 pages
...tan. ¿ (A — в)' or, a + 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 - Plane trigonometry - 1845 - 498 pages
...12"; to solve the 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
...equal to 55°28' 12"; to 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... | |
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