 | 1801 - 658 Seiten
...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...their opposite angles : • To the tangent of half their difference.* Then * DEMONSTRATION. By the first problem, the sides' are as the sines of their-... | |
 | Abel Flint - 1804 - 226 Seiten
...solution of 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... | |
 | John Bonnycastle - 1806 - 464 Seiten
...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...sum of their opposite angles, to the tangent of half their difference. Then the half difference of these angles, added to their half sum, gives the greater... | |
 | Robert Gibson - 1806 - 486 Seiten
...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.... | |
 | Isaac Dalby - 1807 - 476 Seiten
...their included angle arc given. The tv.-o remaining angles will be found from the following Theorem : As the sum of the given sides, Is to their difference, So is the tungcnlof half the sum of the two unknown angles, To the tangent of half their difference. Demonstration.... | |
 | Samuel Webber - 1808 - 466 Seiten
...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...of their opposite angles : To the tangent of half their difference.* * DEM0NSTRATI0N. By the first problem, the sides are as the sines of their opposite... | |
 | Abel Flint - 1808 - 190 Seiten
...solution of 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... | |
 | Robert Gibson - 1808 - 482 Seiten
...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... | |
 | William Nicholson - 1809 - 722 Seiten
....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 - 168 Seiten
...— 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, so is the tangent of half the sum of the two opposite angles, to the tangent of half their difference, For, let ABC (fig. 5.) be the triangle,... | |
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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. 
