 | Charles Davies - 1839 - 376 pàgines
...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:... | |
 | Adrien Marie Legendre - 1839 - 372 pàgines
...a + 6 — c=2p — 2c, THEOREM V. fit every rectilineal triangle, the sum of two sides is to tlieir 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 III.).... | |
 | John Gummere - 1841 - 468 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... | |
 | Charles Davies - 1835 - 388 pàgines
...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 tico other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:... | |
 | 1843 - 376 pàgines
...brevity, put £ (a+b+c)=p, or a+b+c=2p; we have a + b — c=2p — 8c, THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference...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 III.).... | |
 | Enoch Lewis - 1844 - 240 pàgines
...being suited 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...half the sum of the angles, opposite to those sides, to the tangent of half their difference. Let ABC be the triangle; AC, AB, the sides. From the centre... | |
 | John Playfair - 1844 - 338 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. PROP. V. THEOR. If a perpendicular be drawn from any angle... | |
 | Euclid, James Thomson - 1845 - 382 pàgines
...proposition is a particular case of this one. PROP. III. THEOK.—The sum of any two sides of a triangle is to their difference, as the tangent of half the...sides, is to the tangent of half their difference. Let ABC be a triangle, a, b any two of its sides, of which a is the greater, and A, B the angles opposite... | |
 | Nathan Scholfield - 1845 - 506 pàgines
...sin. A 1 sin. B sin. A sin. C sin. B sin. CJ 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, then, by Proposition... | |
 | Nathan Scholfield - 1845 - 244 pàgines
...have, by the proposition, a sin. a c b sin. PROPOSITION III. In any plane triangle, the stun 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, then, by Proposition... | |
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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. 
