 | Nathaniel Bowditch - 1826 - 764 σελίδες
...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,... | |
 | William Galbraith - 1827 - 412 σελίδες
...45. In 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... | |
 | Alexander Ingram - 1830 - 458 σελίδες
...180°, 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... | |
 | Abel Flint - 1830 - 322 σελίδες
...side. Fig. 48. The 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 TANQENT OF HALF THE SUM OF THE TWO OPPOSITE ANGLES TO THE TANGENT OF HALF THE DIFFERENCE BETWEEN THEM.... | |
 | Jeremiah Day - 1831 - 520 σελίδες
...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 σελίδες
...45. In 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 - 368 σελίδες
...and side. The solution of this CASE depends on the following PROPOSITION. ' IN EVERY PLANE TRIANGLE, AS THE SUM OF ANY TWO SIDES IS TO THEIR DIFFERENCE,...OF THE TWO OPPOSITE ANGLES TO THE TANGENT OF HALF THE DIFFERENCE BETWEEN THEM. ADD THIS HALF DIFFERENCE TO HALF THE SUM OF THE ANGLES AND YOU WILL HAVE... | |
 | 1836 - 488 σελίδες
...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... | |
 | Abel Flint - 1838 - 348 σελίδες
...CASE depends on the following PROPOSITION. IN EVERY PLANE TRIANGLE, AS THE SUM OF ANY TWO SIDES ISTO 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 HALF THE SUM OF THE ANGLES, AND YOU WILL HAVE... | |
 | Thomas Holliday - 1838 - 404 σελίδες
...the 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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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. 
