| Benjamin Martin - 1736
...Sides, Is to the Sine of their Difference, ( So is the Sine of the Sum of the Angles, to the Sine of **their Difference ; ) So is the Tangent of half the Sum of the Angles,** To the Tangent of halt their Différence. 14. That is, IK : IH: : AP :AO. Therefore IK+IH m IK-IH .... | |
| 1801 - 426 sider
...and the angle included by them ; to find the rest. In a plane triangle, As the sum of any two sides : **Is to their difference : : So is the tangent of half the sum of** their opposite angles : • To the tangent of half their difference.* Then * DEMONSTRATION. By the... | |
| Abel Flint - 1804 - 168 sider
...this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; **Is to their Difference ; So is the Tangent of half the Sum of the** two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference... | |
| Robert Gibson - 1806 - 452 sider
...wholes are as their halves, ie 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 104 PLANE TRIGONOMETRY. Plate... | |
| John Bonnycastle - 1806 - 419 sider
...included angle are given, to find the rest. SR.ULE. As the sum of any two sides of a plane triangle, **is to their difference, so is the tangent of half the sum of** their opposite angles, to the tangent of half their difference. Then the half difference of these angles,... | |
| Euclid, Robert Simson - 1806 - 518 sider
...Let ABC be a plane triangle, live sura of any two sides, AB, AC will be to their difiV.-rt.-nce as **the tangent of half the sum of the angles at the base** ABC, ACB to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
| Isaac Dalby - 1807
...triangles DRA, DGB will be similar; whence we have, DG : DR :: GB : RA; That is, as the sum of the sides, **is to their difference, so is the tangent of half the sum of the** unknown or opposite angles, to the tangent of half the difference of those angles. Examp. 1. Let CD... | |
| Abel Flint - 1808 - 168 sider
...this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; **Is to their Difference ; So is the Tangent of half the Sum of the** two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference... | |
| Robert Gibson - 1808 - 440 sider
...wholes areas their halves, ie 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 Plate V. THEO. III. In any... | |
| Sir John Leslie - 1809 - 493 sider
...consequently AB: BC:: S,C: S,A. PROP.X. THEOR. In any triangle, the sum of two sides, is to the difference, as **the tangent of half the sum of the angles at the base, to the tangent of half their difference.** In the triangle ABC, AB + AC : AB— AC : : T, : f ., ( ,— [ t 2 -For, by the last proposition, AB... | |
| |