| 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... | |
| Robert Gibson - 1795 - 319 sider
...ie AH : IH : : CE : ED, that is, as the Sum of the two Sides AB and BC, is to their Difference ; fo **is the Tangent of half the Sum of the two unknown Angles** A and C, • to the Tangent of half their Difference. QED THEO. Plate V. <THE 0. III. In any right-lined... | |
| 1801
...sides 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
...solution of 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 to half... | |
| 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 V. THEOREM JII.... | |
| 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,... | |
| 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... | |
| 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 right-lined plane... | |
| Abel Flint - 1808 - 168 sider
...solution of 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 to half... | |
| Samuel Webber - 1808
...and the angle include^ by them; to fmd the rest. In a plane triangle, As the sum of any two sifts : **Is to their difference " : : So is the tangent of half the sum of** their opposite angles : To the tangent of half their difference.* * DEM0NSTRATI0N. By the first problem,... | |
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