 | Alexander Ingram - 1830 - 458 pàgines
...and take half the remainder, to get half the sum of the unknown angles. Then as the sura of the sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference. Having thus found the half difference, add... | |
 | Jeremiah Day - 1831 - 520 pàgines
...other radius. (Art. 1 19.) THEOREM II. 144. In a plane triangle, AS THE SUM OF ANY TWO OF THE SIDES, To THEIR DIFFERENCE ; - So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25.) is to... | |
 | William Galbraith - 1834 - 454 pàgines
...a plane triangle when the two 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... | |
 | Abel Flint - 1835 - 366 pàgines
...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 TO... | |
 | Euclid - 1835 - 540 pàgines
...difference. Let ABC be a plane triangle, the sum of any two sides AB, AC will be to their difference as the tangent of half the sum of the angles at the base ABC, ACB, to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
 | 1836 - 488 pàgines
...are as their opposite sides. Theorem II. In any plane triangle, As the sum of any two of the sides, to their difference ; so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. .Theorem III. As the largest side, to the... | |
 | John Playfair - 1836 - 148 pàgines
...difference. Let ABC be a plane triangle, the sum of any two sides, AB, AC will be to their difference as the tangent of half the sum of the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
 | Andrew Bell - 1837 - 290 pàgines
...of half their difference. 3. The base of a triangle is to the difference of its sides, as the sine of half the sum of the angles at the base to the sine of half their difference. 4. The base of a triangle is to the difference of its segments, as the... | |
 | John Playfair - 1837 - 332 pàgines
...will the radius lie to the tangent of the difference between that angle and half a right angle, as the tangent of half the sum of the angles, at the base of the triangle to the tangent of half their difference.' Let ABC be a triangle, the sides of which... | |
 | Thomas Holliday - 1838 - 404 pàgines
...angle contained between them are given, to find the rest. u2 Rule.—As the sum of the two given sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference: this half difference being added to half the... | |
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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. 
