| 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... | |
| 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 páginas
...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 páginas
...the sum of the two sides AB and BC 420 is to their difference, 60 110 PLANE TRIGONOMETRY. Plate V. **So is the tangent of half the sum of) the two unknown angles** C and B j 71° 40' to the tangent of half their difference 23° 20' By Theo. 4. To half the sum of... | |
| John Bonnycastle - 1806 - 419 páginas
...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 páginas
...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 - 1808 - 440 páginas
...the sum of the two. given sides AB and £C, including a given angle ABC, is to their difference, as **the tangent of half the sum of the two unknown angles A and C** is to the tangent of half their difference. Fig. 11. PLANE TRIGONOMETRY. Plate V. Produce AB and make... | |
| 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 páginas
...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... | |
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