| 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... | |
| 1880
...apparent from the true direction. Now, the sum of the two sides of a triangle is to their difference, i **the tangent of half the sum of their opposite angles is to the** at of half their difference. B the sum of the angles opposite to v and r mast be the at direction of... | |
| 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... | |
| Euclid, Robert Simson - 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,... | |
| 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... | |
| 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 :... | |
| John Playfair - 1837 - 318 páginas
...because 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... | |
| Euclid - 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,... | |
| Andrew Bell - 1837 - 240 páginas
...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** me angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and... | |
| 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... | |
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