 | Benjamin Martin - 1736 - 414 pàgines
...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 - 658 pàgines
...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 - 226 pàgines
...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 - 486 pàgines
...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 - 464 pàgines
...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 - 476 pàgines
...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 - 190 pàgines
...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 - 482 pàgines
...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 - 722 pàgines
................... 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 - 152 pàgines
...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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TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. 
