| Charles Davies - 1830 - 300 páginas
...should obtain, THEOREM. 44. In any plane triangle, the sum of tfte two sides containing either angle, **is to their difference, as the tangent of half the sum of the** other two angles, to the tangent of half their difference. Let ABC (PI. I. Fig. 3) be a triangle ;... | |
| Jeremiah Day - 1831 - 370 páginas
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, **is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. This is the second theorem applied to the... | |
| Robert Gibson - 1832 - 348 páginas
...AH : IH : : CE : ED ; that is, as the sum of the two sides AB and BC is to their difference, so is **the tangent of half the sum of the two unknown angles A and C** to the tangent of half their difference. QED THEOREM III. Fig. 12. In any right-lined' plane triangle... | |
| John Radford Young - 1833 - 264 páginas
...4 tan. a — 4 ~~ tan. J(A — B) ' that is to say, 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. By help of this rule we may determine the... | |
| Euclid - 1835 - 513 páginas
...difference ; and since BC, FG are parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the 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. * PROP. IV. FIG. 8. In a plane triangle,... | |
| Adrien Marie Legendre - 1836 - 359 páginas
...c=2p — 2c, a+c — 6=2p — 26; 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... | |
| John Playfair - 1836 - 114 páginas
...three being given, the fourth is also given. PROP. III. i 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... | |
| John Playfair - 1837 - 318 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. 325 PROP. V. THEOR. If a perpendicular... | |
| 1837 - 249 páginas
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithet 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:... | |
| Euclid, James Thomson - 1837 - 390 páginas
...sine of a right angle is equal to the radius. 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,... | |
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