| 1801
...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... | |
| 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,... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| William Nicholson - 1809
................... l .75486 Axiom III. In every plane triangle it will bn as the sum of any two sides **is to their difference; so is the tangent of half the sum of** the angles opposite there, to the tangent of half their difference. Which lialf difference, being added... | |
| Thomas Simpson - 1810 - 125 sider
...(2ED), by 4. 6. ®. ED •f THEOREM V. In any plane triangle, it -will be, 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 their difference. For, let ABC (fig. 5.) be the triangle,... | |
| Robert Gibson - 1811 - 508 sider
...wholes are as their halves, that is, AH: Iff : : CE : ED, that ia 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. 2. E. DK THEO. III. fig. 12.... | |
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