 | Jeremiah Day - 1831 - 398 pages
...the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 1 44.) the sum of the sides is to their difference ; as the tangent of half the...opposite angles, to the tangent of half their difference. Therefore, R : tan(ACH-45°)::tani(ACB+B) : tan^(ACB^B) Ex. In the triangle ABC, (Fig. 30.) given the... | |
 | Jeremiah Day - 1831 - 418 pages
...angle greater than 45° : And radius is to the tangent of the excess of this angle abort 45° ; os the tangent of half the sum of the opposite angles, to the tangent of ha1f their difference. In the triangle ABC, (Fig. 39.) let the sides AC and AB, and the an<rle A be... | |
 | Jeremiah Day - 1831 - 522 pages
...THE OPPOSITE ANGLES; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making... | |
 | John Playfair - 1832 - 356 pages
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV. The sum of any two sides of a triangle is to their difference, at the tangent of half the sum of the angles opposite to those sides, to the tangent of half their... | |
 | John Playfair - 1833 - 348 pages
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV.. 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... | |
 | John Radford Young - 1833 - 288 pages
...4 tan. a — 4 ~~ tan. J(A — B) ' that is to say, in any plane triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By help of this rule we may determine the remaining parts... | |
 | William Galbraith - 1834 - 454 pages
...sides and contained angle are given. I. As the sum of the given sides Is to their difference; So is the tangent of half the sum of the opposite angles To the tangent of half their difference. Half the difference added to half the sum of those angles gives the greater, and subtracted from half... | |
 | Euclid - 1835 - 540 pages
...difference ; and since BC, FG are parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base to the tangent of half their difference. * PROP. IV. FIG. 8. In a plane triangle,... | |
 | 1836 - 488 pages
...an angle great, er than 45° : and radius ia to the tangent of the excess of this angle above 45° ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. In a plane triangle, twice the product of any two sides, is to the difference between the sum of the... | |
 | John Playfair - 1836 - 148 pages
...three being given, the fourth is also given. PROP. III. i In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let ABC be a plane triangle, the sum of... | |
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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. 
