 | Jeremiah Day - Geometry - 1838 - 416 pages
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is the second theorem applied to the... | |
 | Charles Davies - Surveying - 1839 - 376 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: AB-AC: : tan ±(C+B) : tan ±(CB).... | |
 | Jeremiah Day - Geometry - 1839 - 434 pages
...THE OPPOSITE ANGLES J To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making... | |
 | 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 - 414 pages
...the same radius AD or BC. But by similar triangles, But AD being equal to BC, we have BC : sin ^ : : AC : sin B, or BC : AC : : sin A : sin B. By comparing...other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC: AB-AC; : tan ±(C+B) : tan l(C-JB). With A as a centre,... | |
 | Charles Davies - Navigation - 1835 - 388 pages
...AB : AC : : sin C : sin B. THEOREM 11. /« any triangle, the sum of the two sides containing eithe» angle, is to their difference, as the tangent of half...ACB be a triangle : then will AB+AC: AB-AC: : tan i(C+B) : tan ±(CB). With A as a centre, and a radius AC the less of the two given sides, let the semicircle... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...parallel to FG, CE : CF : : BE ; BG, (2. 6.) that is, the sum of the two sides of the triangle ABC 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. PROP. V. THEOR. If a perpendicular... | |
 | 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;... | |
 | 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... | |
 | 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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In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 
