| Charles Hutton - Measurement - 1788 - 728 pages
...the fum of any two fides is to their difference, fo is the tangent of half the fum of their oppofite **angles, to the tangent of half their difference. Then the half difference** added to the half fum of the angles, gives the greater ; and fubtracled, leaves the let's angle*. Then,... | |
| Mathematics - 1801 - 658 pages
...and the angle included by them ; to find the rest. In a plane triangle, As the sum of any two sides : **Is to their difference : : So is the tangent of half...• To the tangent of half their difference.* Then** * DEMONSTRATION. By the first problem, the sides' are as the sines of their- opposite angles, wnd consequently... | |
| Samuel Webber - Mathematics - 1808 - 470 pages
...and the angle include^ by them; to fmd the rest. In a plane triangle, As the sum of any two sifts : **Is to their difference " : : So is the tangent of...angles : To the tangent of half their difference.*** * DEM0NSTRATI0N. By the first problem, the sides are as the sines of their opposite angles,aml consequently... | |
| Edward Riddle - Nautical astronomy - 1824 - 572 pages
...Or the angles opposite the given sides may be determined as follows. As the sum of the given sides **is to their difference, so is the tangent of half...sum of their opposite angles to the tangent of half** the difference of the same angles, (Trig. Prop. 6.) And this half difference of the angles added to... | |
| Arithmetic - 1829 - 180 pages
...the remaining side and angle, 1! i ii. As the SUM of the TWO GIVEN SIDES, is to THEIR DIFFERBNCE ; **so is the TANGENT OF HALF THE SUM OF THEIR OPPOSITE ANGLES to the tangent of HALF** THE DIFFERENCE of those angles. Then if we add the half difference of the angles, so found, to their... | |
| Abraham Crocker - 1841 - 490 pages
...II Rule for the Second Case. As the sum of the two given sides is to the difference of those sides, **so is the tangent of half the sum of their opposite angles, to the tangent of** hajf their difference. This half-difference, added to the half sum, will give the greater angle * :... | |
| Joseph Gwilt - Architects - 1842 - 1114 pages
...said unknown angles ; and using the following ratio, we have — As the sum of the two given sides **Is to their difference, So is the tangent of half...sum of their opposite angles To the tangent of half** the difference of the same angles. Now the half sum of any two quantities increased by their half difference... | |
| James Hann - Plane trigonometry - 1854 - 136 pages
...sides are given. m A n By An. 19, ^4 = г ? : R; • a - b tan £ ( A - B) Hence the following rule : **As the sum of any two sides of a plane triangle is...opposite angles to the tangent of half their difference.** By Art. 16, cos A = — -т ; Л a' - 6" = c" - 26c cos A = C(c'- 26 cos A), (a -f 6) (a - Ķ) = С... | |
| Frederick Augustus Griffiths - 1859 - 422 pages
...their contained angle, are given. As the sum of the two sides, is to the difference of the sides ; **so is the tangent of half the sum of their opposite angles, to the tangent of half** the difference of the same angles. Then by adding half the sum to half the difference the greater angle... | |
| Frederick Augustus Griffiths - Artillery - 1859 - 426 pages
...their contained angle, are given. As the sum of the two sides, is to the difference of the sides ; **so is the tangent of half the sum of their opposite angles, to the tangent of half** the difference of the same angles. Then by adding half the sum to half the difference the greater angle... | |
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