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" 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 the difference of the same angles. "
Practical Surveying: A Text-book for Students Preparing for Examinations Or ... - Side 127
av George William Usill - 1889 - 272 sider
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volum 2

1801 - 658 sider
...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 the sum of their opposite...angles : • To the tangent of half their difference.* Then * DEMONSTRATION. By the first problem, the sides' are as the sines of their- opposite angles,...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 464 sider
...to find the rest. SR.ULE. As the sum of any two sides of a plane triangle, is to their difference, so is the tangent of half the sum of their opposite angles, to the tangent of half their difference. Then the half difference of these angles, added to their half sum, gives the greater angle, and subtracted...
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A Course of Mathematics in Two Volumes for the Use of Academies as Well as ...

Charles Hutton - 1807 - 464 sider
...angles ; then divide that by 2, which will give the half sum of the said unknown angles. Then say, As the sum of the two given sides, Is to the difference of the same sides -, So is the tang, of half the sum of their op. angles, To the tang, of half the diff....
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - 1811 - 442 sider
...angles ; then divide that by 2, which will give the half sum of the said unknown angles. Then say, As the sum of the two given sides, Is to the difference of the same sides ; So is the tang, of half the sum of their op. angles, To the tang, of half the diff....
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - 1822 - 616 sider
...angles ; then divide that by 2, which will give the half the sum of the said unknown angles. Then say, As the sum of the two given sides, Is to the difference of the same sides ; So is the tans- of half the sum of their op. angles. To the tang, of half the diff....
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A treatise on navigation, and nautical astronomy

Edward Riddle - 1824 - 572 sider
...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 the 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 ...

1829 - 196 sider
...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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Southern Review, Volum 3

1829 - 530 sider
..." the sum of two sides of a triangle is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half their difference.'" This half difference added to half the sum, gives the greater, and subtracted from the half sum, gives the less. When all the angles...
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Crocker's Elements of land surveying. To which are added, Tables of six ...

Abraham Crocker - 1841 - 486 sider
...and AC, by the scale. Ansr. Z. A = 47o 15'. CB = 622-9. AC = 591-9. CASE II Rule for the Second Case. As the sum of the two given sides is to the difference...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 Encyclopædia of Architecture: Historical, Theoretical, and Practical

Joseph Gwilt - 1842 - 1114 sider
...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 the 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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