| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...difference between either of them and 45°. PROP. IV. THEOR. The sum of any two sides of a triangle **is to their difference, as the tangent of half the sum of the angles** opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle ; CA+AB... | |
| Nathaniel Bowditch - 1846 - 854 pages
...: DH : AF or HB ; that is, AD, the sum of the legs, AC and СЁ, is to AE, their difference, as DH, **the tangent of half the sum of the angles at the base** (the radius teing AH), is to HB, the tangent of half the difference of the same angles (to the same... | |
| Roswell Park - Best books - 1847 - 626 pages
...oblique angled triangle, the sides are proportional to the sines of the opposite angles : also, the **sum of any two sides is to their difference, as the tangent of** the half sum of ihe two opposite angles, is to the tangent of their half difference : and finally,... | |
| Jeremiah Day - Logarithms - 1848 - 354 pages
...THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, **is to their difference ; as the tangent of half the sum of the angles** ACB and ABC, to the tangent of half then- difference. Demonstration. Extend CA to G, making AG equal... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...2 (/i 2 +c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of **two sides is to their difference as the tangent of half the sum of the angles** opposite those sides, to the tangent of half their difference. * For. AB : BC : : sin C : sin A (Theorem... | |
| Jeremiah Day - Geometry - 1851 - 418 pages
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the **sides is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. Therefore, R : tan (ACH— 45°) : : tan... | |
| Horatio Nelson Robinson - Mathematics - 1851 - 96 pages
...Demonstrate that radius is to the tangent of the difference between this angle and half a right angle, **as the tangent of half the sum of the angles at the base** of the triangle, is to the tangent of half their difference, To obtain that certain angle, we must... | |
| Charles William Hackley - Trigonometry - 1851 - 524 pages
...: tan £ (A + B) : tan ^ (A — B) That is to say, the sum of two of the sides of a plane triangle **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. 76 This proportion is employed when two... | |
| William Chauvenet - 1852 - 268 pages
...proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle **is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. For, by the preceding article, a : b =... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...AC :: sin 0 : sin jR THEOEEM II. In any triangle, the sum of the two sides containing either angle, **is to their difference, as the tangent of half the sum of the** two other angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will AJ3... | |
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