 | John Playfair - 1836 - 488 pàgines
...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. QE.D. PROP. Vv ' •.: I . <.••«,! If a perpendicular... | |
 | John Playfair - 1836 - 148 pàgines
...triangle, any three being given, the fourth is also given. PROP. III. In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent' of half their difference. Let ABC be a plane triangle, the sum of any... | |
 | John Gummere - 1836 - 412 pàgines
...therefore since BC, FG are parallel, EB : BF : : EC : CG (2.6.:) that is, the sum of the sides AC, AB, is to their difference, as the tangent of half the sum of the angles ABC, ACB, is to the tangent of half their difference. To demonstrate the latter part of the rule, let... | |
 | Jeremiah Day - 1836 - 418 pàgines
...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°)::tanri(ACB +... | |
 | Andrew Bell - 1837 - 290 pàgines
...demonstrated that AB : BC = sin C : sin A. PROPOSITION VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. From A as a centre, with the radius AC, describe... | |
 | John Playfair - 1838 - 342 pàgines
...sin. AC—sin. AB : : R : tan. Í (AC—AB). 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. CA+AB : CA—AB : : tan.} (B+C) : tan. J (BC). For (2.) CA... | |
 | Euclid - 1838 - 470 pàgines
...three being given, the fourth is also given. PROP. III. FIG. 8. IN a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let ABC be a plane triangle; the sum of any two... | |
 | Charles William Hackley - 1838 - 328 pàgines
...: tan ^ (A -f- B) : tan ^ (A — B) That is to say, the sum of two of the sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the. tangent of half their difference. This proportion is employed when two sides... | |
 | Charles William Hackley - 1838 - 338 pàgines
...: : tan ^ (A -fB) : tan \ (A — B) That is to say, the sum of two of the sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. This proportion is employed when two sides... | |
 | Thomas Keith - 1839 - 498 pàgines
...chords of 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... | |
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in any triangle, the sum of two sides 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. 
