 | William Nicholson - 1809 - 722 pages
....56.88 ................ l .75486 Axiom III. In every plane triangle it will bn as the sum of any two sides is to their difference; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference. Which lialf difference, being added... | |
 | Thomas Simpson - Trigonometry - 1810 - 168 pages
...— BC) : BG (2ED), by 4. 6. ^ ED THEOREM V. In any plane triangle, it will be, as the sum of any two sides is to their difference, so is the tangent of half the sum of the two opposite angles, to the tangent of half their difference, For, let ABC (fig. 5.) be the triangle,... | |
 | 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... | |
 | Charles Hutton - Mathematics - 1811 - 442 pages
...willbe^ 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 I. In the plane triangle ABC, f AB 345 yards Given j AC 174-07 yards I / A 37° 20' Required... | |
 | Charles Hutton - Mathematics - 1811 - 494 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 th«ir difference. EXAMPLE I. In the plane triangle ABC, f AB 345 yards Given } AC 174-07 yards C /A... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | John Gummere - Surveying - 1814 - 398 pages
...remain' 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... | |
 | 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... | |
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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. 
