 | Edward Riddle - 1824 - 572 sider
...Or the angles opposite the given sides may be determined as follows. As the sum of the given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half the difference of the same angles, (Trig. Prop. 6.) And... | |
 | Abel Flint - 1825 - 252 sider
...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... | |
 | Nathaniel Bowditch - 1826 - 764 sider
...the tame angla. Thus, in the triangle ABC, if we call AB the base, it will be as the sum of AC and CB is to their difference, so is the tangent of half the sum of the angles ABC, ВАС, to the tangent of half their difference. Dan. With the longest leg CB as radius,... | |
 | Alexander Ingram - 1830 - 458 sider
...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,... | |
 | Jeremiah Day - 1831 - 520 sider
...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.)... | |
 | William Galbraith - 1834 - 454 sider
...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... | |
 | Abel Flint - 1835 - 366 sider
...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... | |
 | 1836 - 488 sider
...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... | |
 | Thomas Holliday - 1838 - 404 sider
...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... | |
 | Jeremiah Day - 1839 - 434 sider
...other radius. (Art. 119.) 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 J To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.)... | |
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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. 
