 | Robert Gibson - Surveying - 1811 - 580 pages
...ABC, the sum of the two given sides AB and BC, including a given angle ABC, is to their difference, as the tangent of half the sum of the two unknown angles A and C is to Che tangent of half their difference. Produce AB and make HB=BC, and join HC : let fall the perpendicuktt... | |
 | George Adams - Geometry - 1813 - 648 pages
...angle ; and when an angle is wanted, it must begin with a side. As the sun, of the two given sides is to their difference ; so is the tangent of half the sum of the two 3. When two sides of a triangle and the included angle are given, to find the other angles and side.... | |
 | Robert Gibson - Surveying - 1814 - 558 pages
...theo. 20. sect. 4.) But the 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...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 lined filane triangle... | |
 | John Gummere - Surveying - 1814 - 398 pages
...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,... | |
 | 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
...PROP. XV. •. 15. In any plane triangle it will be, as the sum of the sides about the vertical angle, is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. By the preceding prop. AC : BC :: sin... | |
 | 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... | |
 | John Gummere - Surveying - 1817 - 384 pages
...remainder will be the sum of the two unknown angles. Then ; • ' I . 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.* This -half difference of the two unkn'own angles, added'... | |
 | 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,... | |
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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. 
