 | George Adams - Geometry - 1813 - 648 pages
...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
...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
...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... | |
 | 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... | |
 | 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... | |
 | Olinthus Gregory - Plane trigonometry - 1816 - 278 pages
...•. 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 B : sin... | |
 | Olinthus Gregory - Plane trigonometry - 1816 - 276 pages
...remainder will !>e the sum of the 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... | |
 | Robert Gibson - Surveying - 1818 - 502 pages
...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... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...sine DC 56.88 1.75485 Axiom III. In every 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 angles opposite there, to the tangent of half their difference. Which half difference, being added to half... | |
 | Nautical astronomy - 1821 - 708 pages
...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, describe... | |
| |
TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. 
