 | Benjamin Martin - 1736 - 414 σελίδες
...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... | |
 | John Potter - 1753 - 568 σελίδες
...To the Sine of its oppofite Angle. Rule 2. When any two Sides with the Angle between them are given. As the Sum of any two Sides Is to their Difference, So is the Tangent of the Half-Sum of the two oppofite Angles " To the Tangent of Half the Difference of thofe two Angles.... | |
 | 1801 - 658 σελίδες
...JROSLEM It. Given tiua 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 - 226 σελίδες
...Side. Fig. 49. The solution of this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference...of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference to half the Sum of the Angles and you will have... | |
 | Robert Gibson - 1806 - 486 σελίδες
...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... | |
 | John Bonnycastle - 1806 - 464 σελίδες
...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 σελίδες
...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 σελίδες
...Side. Fig. 49. The solution of this CASE depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference...of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference to half the Sum of the Angles and you will have... | |
 | Robert Gibson - 1808 - 482 σελίδες
...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... | |
 | Samuel Webber - 1808 - 466 σελίδες
...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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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. 
