| Nathaniel Bowditch - 1826 - 617 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,... | |
| William Galbraith - 1827 - 322 sider
...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
...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 - 284 sider
...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 - 370 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.) is to... | |
| Olinthus Gregory - 1833 - 427 sider
...the tangent of the sum or difference of the arcs. 11. As the sum of the sines of two unequal arcs, **is to their difference ; so is the tangent of half the sum of** those two arcs to the tangent of half their difference. 12. Of any three equidifferentarcs,it will... | |
| William Galbraith - 1834 - 428 sider
...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 - 334 sider
...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 - 472 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 the... | |
| Abel Flint, George Gillet - 1838 - 334 sider
...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... | |
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