 In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of...  Easy Introduction to Mathematics - Página 353por Charles Butler - 1814Vista completa - Acerca de este libro
 | Scottish school-book assoc - 1845 - 278 páginas
...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 - 1845 - 498 páginas
...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 - 1845 - 498 páginas
...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 - 1846 - 168 páginas
...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... | |
 | Euclid, John Playfair - 1846 - 334 páginas
...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 - 854 páginas
...: 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... | |
 | Roswell Park - 1847 - 632 páginas
...an oblique angled triangle, the sides are proportional to the sines of the opposite angles : also, the sum of any two sides is to their difference, as the tangent of the half sum of the two opposite angles, is to the tangent of their half difference : and finally,... | |
 | Jeremiah Day - 1848 - 354 páginas
...THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half then- difference. Demonstration. Extend CA to G, making AG equal... | |
 | Charles Davies - 1849 - 372 páginas
...2 (/i 2 +c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. * For. AB : BC : : sin C : sin A (Theorem... | |
 | Jeremiah Day - 1851 - 418 páginas
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R : tan (ACH— 45°) : : tan... | |
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