| 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
...IG being parallel to AC ; AH : 1H : : CH : GH. (by Cor. i. Theo. 20. Sect, i.) But the Wholes are as **their Halves, ie AH : IH : : CE : ED, that is, as...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... | |
| 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 to half... | |
| 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... | |
| 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 to half... | |
| 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
...co-sine AC : : tang. C : co-tang. A. £>. E, D. LEMMA. As the sum of the sines of two unequal arches **is to their difference, so is the tangent of half the sum of** those arches to the tangent of half their difference : and, as the sum of* the co-sines is to their... | |
| George Adams - 1813 - 534 sider
...angle ; and when an angle is wanted, it must begin with a side. As the sun, of the two given sides **is to their difference ; so is the tangent of half the sum of the two** 3. When two sides of a triangle and the included angle are given, to find the other angles and side.... | |
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