 | Benjamin Martin - 1736 - عدد الصفحات: 414
...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 - عدد الصفحات: 658
...$ 07 21 feet. 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...difference : : So is the tangent of half the sum of their opposite angles : • To the tangent of half their difference.* Then * DEMONSTRATION. By the... | |
 | Robert Gibson - 1806 - عدد الصفحات: 486
...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 - عدد الصفحات: 464
...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 - عدد الصفحات: 476
...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... | |
 | Robert Gibson - 1808 - عدد الصفحات: 482
...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 - عدد الصفحات: 466
...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,... | |
 | Nicolas Pike - 1808 - عدد الصفحات: 470
...given. RULE 2. — As the sum of any two sides is to their difference ; so 5s the tangent of the half sum of the two opposite angles, to the tangent of half the difference of those two opposite angle* ; which hah" difference being added to the half sum, gives the greater... | |
 | William Nicholson - 1809 - عدد الصفحات: 722
...9.74198 To the sine DC .56.88 ................ 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 - عدد الصفحات: 168
...(AC + BC) : : BH (AC — BC) : BG (2ED), by 4. 6. ^ ED THEOREM V. In any plane triangle, it will be, as the sum of any two sides is to their difference,...of the two opposite angles, to the tangent of half their difference, For, let ABC (fig. 5.) be the triangle, and AB, AC the two proposed sides ; and from... | |
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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. 
