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" To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference... "
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... - Page 13
by John Bonnycastle - 1806 - 419 pages
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A Treatise on Mensuration, Both in Theory and Practice

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,...
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volume 2

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...
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Mathematics, Volume 1

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...
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A treatise on navigation, and nautical astronomy

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...
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The Practical Arithmetic: In which the Principles of Operating by Numbers ...

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...
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Crocker's Elements of land surveying. To which are added, Tables of six ...

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 * :...
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An Encyclopędia of Architecture: Historical, Theoretical, and Practical

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...
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The Elements of Plane Trigonometry

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...
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The artillerist's manual, and compendium of infantry exercise

Frederick Augustus Griffiths - 1859 - 418 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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The Artillerists̓ Manual, and British Soldiers̓ Compendium

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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