| 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
...sine of A ; these sines 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 of half the sum of the** angles, opposite to those sides, to the tangent of half their difference. Let ABC be the triangle;... | |
| Nathan Scholfield - Conic sections - 1845 - 542 pages
...have, by the proposition, a sin. A ' b 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,... | |
| Nathan Scholfield - Conic sections - 1845 - 244 pages
...According to this, we shall have, by the proposition, a sin. A.~ c b sin. 68 FROPOSITION 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,... | |
| Nathan Scholfield - 1845 - 896 pages
...proposition, sin. A' a ~b a c b sin. B sin. A sin. C sin. B sin. C. 68 PROFOSITION in. 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,... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...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,... | |
| William Scott - Measurement - 1845 - 290 pages
...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... | |
| Dennis M'Curdy - Geometry - 1846 - 168 pages
...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... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 332 pages
...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... | |
| Roswell Park - 1847 - 622 pages
...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,... | |
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