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Bøker Bok 5160 av 76Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the...
" Plane Triangle, 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 the Difference between them. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Side 5
av Thomas Simpson - 1810 - 125 sider
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A new and complete epitome of practical navigation

John William Norie - 1852
...triangle. II. When two Sides and the Angle contained between them are given. As the sum of the two given sides Is to their difference, So is the tangent of half the sum of the unknown angles To the tangent of half their difference : This half difference added to half the sum...
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The Computist's Manual of Facts: And Merchant's and Mechanic's Calculator ...

Ezra S. Winslow - 1853 - 252 sider
...of that angle. That is, A being the angle — 1 — 2 sin2 of 4 A = cos A. In every plane triangle, as the sum of any two sides is to their difference, so is the natural tangent of half the sum of the angles opposite those sides to the natural tangent of half their...
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A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - 1853 - 5 sider
...radius. (Art. 119.) ff THEOREM II. /? 144. In a plane triangle, \. As THE SU^I OF ANY TWO OF THE SIDES, To THEIR DIFFERENCE ] So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITK ANGLKS; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is...
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The practical surveyor's guide: containing the necessary information to make ...

Andrew Duncan (surveyor.) - 1854 - 121 sider
...sides and their included angle are given to find the other angles and side. RULE. — As the sum of the sides is to their difference so is the tangent of half the sum of the opposite angles to the tangent of half the difference ; this half difference added to half the sum...
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The Elements of Plane Trigonometry

James Hann - 1854 - 119 sider
...+ b tan By Art. 19, —jjHence the following rule : 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. By Art. 16, .-. a2 - o2 = c2 - 2bc cos...
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A compendious course of mathematics, theoretical and practical

John Radford Young - 1855
...tanABD and this proportion expressed in words is the following rule. RULE. As the sum of the two given sides is to their difference, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. that is 0-6 (1) Two sides of a triangle are...
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Orr's Circle of the Sciences: Practical astronomy, navigation, nautical ...

William Somerville Orr - 1856
...difference. The following, therefore, is the rule :— ROLE. — As the sum of the two given sidee Is to their difference, So is the tangent of half the sum of the opposite angles To the tangent of half their difference. The half difference of the unknown angles...
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The practice of engineering field work, applied to land, hydrographic, and ...

W. Davis Haskoll - 1858 - 324 sider
...II. When the three given parts are two sides and the included angle. — As the sum of the two given sides is to their difference, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. In the triangle ABC, AB = 345, and BC = 174,...
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Practical military surveying and sketching

Alfred Wilks Drayson - 1861 - 192 sider
...quantities we proceed as follows : — Suppose AB, BC, known, and the angle ABC. Then as the sum of the two 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 their difference thus found, added to...
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Popular and mathematical astronomy, with the principal formulæ of plane and ...

William Thomas Read - 1862
...included angle, to find the rest. Proposition HI. may here be written as a rule. " As the sum of the given sides is to their difference, so is the tangent of half the sum of the opposite angles to the tangent of half their difference. And the half difference added to half the...
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