 | Charles Davies - Navigation - 1841 - 414 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 as the radius 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... | |
 | Joseph Gwilt - Architects - 1842 - 1114 pages
...as BE I BD : I AE ; DF ; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. It is to be observed, that in the third term of the proportion the cotangent of half the given angle... | |
 | Enoch Lewis - Conic sections - 1844 - 240 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;... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...1. The first 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,... | |
 | William Scott - Measurement - 1845 - 288 pages
...в) a — b~ 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... | |
 | Benjamin Peirce - Plane trigonometry - 1845 - 498 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 : b = sin. A : sin.... | |
 | 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: 6 = sin. A : sin.... | |
 | Scottish school-book assoc - 1845 - 278 pages
...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) =d then, с —... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...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,... | |
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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. 
