| Robert Gibson - Surveying - 1811 - 508 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... | |
| Abel Flint - Surveying - 1813 - 168 pages
...its opposite Angle, 0.72537; the other given side 240. As 200' : 0.72337 : : 240 : 6.87044=50° 3<X. **CASE III. Two Sides and their contained Angle given,...the Angles and you will have the greater Angle; and** substract the half Difference Sfom the half Sum and you will have the lesser Angle. In the Triangh... | |
| George Adams - Geometry - 1813 - 534 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 - 534 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 - 346 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 - Electronic books - 1814 - 508 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 - 126 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 - 96 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 - 244 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 - 244 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... | |
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