| Robert Gibson - 1818 - 478 páginas
...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
...same angle*. Thus, in the triangle ABC, if we call AB the base, it will he as the sum of AC and CB **is to their difference, so is the tangent of half the sum of the** angles ABC, BAG', to the tangent of half their difference. Dem. With the longest leg CB as radius,... | |
| 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 - 551 páginas
...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... | |
| Nathaniel Bowditch - 1826 - 617 páginas
...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 (by art. u'J, Geom.) THEOREM IV. As the base of any plane triangle is to... | |
| Nathaniel Bowditch - 1826 - 617 páginas
...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 páginas
...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 - 120 páginas
...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... | |
| Jeremiah Day - 1831 - 370 páginas
...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... | |
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