 | William Scott - 1845 - 288 páginas
...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... | |
 | Euclid, James Thomson - 1845 - 382 páginas
...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,... | |
 | Nathan Scholfield - 1845 - 542 páginas
...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,... | |
 | 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... | |
 | Euclid, John Playfair - 1846 - 334 páginas
...BC is 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... | |
 | Dennis M'Curdy - 1846 - 168 páginas
...triangle EFG, BC is drawn parallel to FG the base EC : CF : : EB : BG; that is, the sum of two sides is to their difference, as the tangent of half the sum of the angles at the base ia to the tangent of half their difference. * Moreover, the angles DBF, BFE are... | |
 | 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... | |
 | Charles Davies - 1849 - 372 páginas
...+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... | |
 | Sir Henry Edward Landor Thuillier - 1851 - 826 páginas
...C : AB : : the Sine of A : BC, etc. QED H THEO. II. In any plane triangle ABC, the sum of the tivo given sides AB and BC, including a given angle ABC, is to their difference, as theJangent of half the sum of the two unknown angles A and C is to the tangent of half their difference.... | |
 | Jeremiah Day - 1851 - 418 páginas
...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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C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 
