C' (89) (90) (91) (92) (93) 112. 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. A Treatise of Practical Surveying, ... - Side 94av Robert Gibson - 1808 - 440 siderUten tilgangsbegrensning - Om denne boken
| Charles Davies - 1830 - 300 sider
...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 sider
...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 sider
...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 sider
...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, Robert Simson - 1835 - 513 sider
...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 sider
...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 sider
...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 sider
...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 sider
...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 - 1837 - 390 sider
...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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