 | Jeremiah Day - Logarithms - 1815 - 172 pages
...radius. (Art. 11 9.) THEOREM II. ..* 144. In a plane triangle, Jl 3 the sum of any two of the sides, To their difference; So is the tangent of half the...opposite angles, To the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is to their difference ; as the tangent of half the sum of the... | |
 | Jeremiah Day - Measurement - 1815 - 388 pages
...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, !£o the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is to their difference... | |
 | Olinthus Gregory - Plane trigonometry - 1816 - 278 pages
...Take the given angle from 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 - Plane trigonometry - 1816 - 276 pages
...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... | |
 | Robert Gibson - Surveying - 1818 - 502 pages
...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... | |
 | Nautical astronomy - 1821 - 708 pages
...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 - Natural history - 1821 - 356 pages
...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... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...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... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...will be as BE : BD ;; AE : DF ; that is, as the sum of the sides is to the difference of the sides, so is. the tangent of half the sum of the opposite angles, to the tangent of half their difference. EXAMPLE J. In the plane triangle ABC, i AB .145 yards Given < AC 174-07 yards I Z. A 37° 20' Required... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...and the sides of the 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... | |
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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. 
