 | Thomas Simpson - Trigonometry - 1810 - 152 pages
...co-sine AC : : tang. C : co-tang. A. £>. E, D. LEMMA. 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* the co-sines is to their... | |
 | Robert Gibson - Surveying - 1811 - 580 pages
...wholes are as their halves, that is, AH: Iff : : CE : ED, that ia as the sum 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. 2. E. DK THEO. III. fig. 12. In any... | |
 | George Adams - Geometry - 1813 - 576 pages
...triangle and the included angle are given, to find the other angles and side. As the sum of the two given sides is to their difference ; so is the tangent of half the sum of the two unknown angles, to the tangent of half their difference. Half the difference thus found, added to half... | |
 | George Adams - Geometry - 1813 - 648 pages
...the angle CDB, and the side CD: to find CDB we use this proportion; as the sum of the two given aides is to their difference, so is the tangent of half the sum of the two unknown angles to the tangent of half their difference; the angle C'DB being found; the following projwrtion... | |
 | John Gummere - Surveying - 1814 - 398 pages
...der will be the sum of the two unknown angles. Then ; • * * * * • * As the sum of the two given sides, „• Is to their difference ; ,. % So is the tangent -of half the sum of the two uuknown angles, To the tangent of half their difference.* This half difference of the two unknown angles,... | |
 | Robert Gibson - Surveying - 1814 - 558 pages
...wholes are as their halves, that is, AH : IH: : CE : ED, that is as the sum 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 G, to the tangent of half their difference. QED THEO. III. Fig. 12. In any right... | |
 | 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 sum of the opposite angles, To the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is to... | |
 | 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... | |
 | Olinthus Gregory - Plane trigonometry - 1816 - 278 pages
...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... | |
| |
TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. 
