| Olinthus Gregory - 1816 - 244 sider
...180°, the remainder will be the sum of th£ other two angles. Then say, — As the sum of the given **sides, Is to their difference ; So is the tangent of half the sum of the** remaining angles, To the tangent of half their difference. Half the difference added to half the sum... | |
| Olinthus Gregory - 1816 - 244 sider
...AC; whence the proposition is manifest. PROP. XI. 1 1 . 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. Let AE and AB be two unequal arcs, of which... | |
| Abel Flint - 1818 - 168 sider
...Side. Fig. 49. 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...Tangent of half the Sum of the two opposite Angles ; To** th« Tangent of half the Difference between them. Add this half difference to half the Sum of the Angles... | |
| Robert Gibson - 1818 - 478 sider
...wholes are as their halves, ie AH : IH : : CE : ED, that is, as the snm of the two sides AB and BC, **is to their difference ; so is the tangent of half the sum of the two** unknown angles A and C, to the tangent of half their difference. QED THEOREM HI. In any right-lined... | |
| 1821
...opposite angle, so is either of the other sides to the sine of its opposite angle. THEOREM III. In every **plane triangle, it will be, as the sum of any two sides is to their difference, so is the** tangtnt of half the sum of the two opposite angles to the tangent 'of half their difference (by art.... | |
| William Nicholson - 1821
...of either angle to the co-tangent of the other angle. As the sum of the sines of two unequal arches **is to their difference, so is the tangent of half the sum of** those arches to the tangent of half their difference : and as the sum of their co-sines is to their... | |
| William Nicholson - 1821
...of either angle to the co-tangent of the other angle. As the sum of the sines of two unequal arches **is to their difference, so is the tangent of half the sum of** those arches to the tangent of half their difference : and as the sum of their co-sines a to their... | |
| Edward Riddle - 1824
...triangle. 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 - 241 sider
...Side. Fig. 49. 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... | |
| Nathaniel Bowditch - 1826 - 617 sider
...opposite angle, so is either of the other sides to the sine of its opposite angle. THEOREM HI. . In every **plane triangle, it will be, as the sum of any two sides is to their difference,** su is the tangent of half the sum of the two opposite angles to the tangent 'tif half their difference... | |
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