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" TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Page 69
by Thomas Simpson - 1810 - 125 pages
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...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: With the Use of the Compass and ...

Alfred Wilks Drayson - Military topography - 1861 - 236 pages
...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 formulŠ of Plane and ...

William Thomas READ - 1862 - 144 pages
...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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Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - 1863 - 482 pages
...latter. 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. 16. In any plane triangle it will be,...
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A Treatise on Surveying: In which the Theory and Practice are Fully ...

Samuel Alsop - Surveying - 1865 - 440 pages
...: the remainder will be the sum of the remaining angles. Then, 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. This half difference added to the half sum...
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The Theory of Navigation and Nautical Astronomy: Together with the Elements ...

William Thomas Read - Nautical astronomy - 1869 - 176 pages
...1. Sin В Or Sin A : sin B : : a : Ъ. (2) In any plane triangle, as the sum of any two sides is to their difference, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. From the preceding, we have, a^_ sin A Ъ...
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Key to Robinson's New Geometry and Trigonometry, and Conic Sections and ...

Horatio Nelson Robinson - 1875 - 288 pages
...71░ 50' 48" Here we will apply the following theorem in trigonometry. As the sum of two sides 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. Let x= the half difference between D and...
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - Railroad engineering - 1880 - 362 pages
...opposite to the latter. 3. In any plane trianf/le, 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. 4. In any plane triangle, as the cosine...
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Elements of Plane and Spherical Trigonometry with Logarithmic and Other ...

Simon Newcomb - Trigonometry - 1882 - 372 pages
...convenient method founded on the following theorem : THEOREM IV. As the sum of any two sides is to their difference, so is the tangent of half the sum of the angles opposite these sides to the tangent of half their difference. Proof. From the equation b : o...
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Philosophical Transactions, Giving Some Account of the Present Undertakings ...

Meteorology - 1828 - 490 pages
...at the pole is obtained by the following method : As the tangent of half the sum of the co-latitudes is to the tangent of half their difference ; so is the tangent of half the sum of the observed angles, to the tangent of half their difference. The triangle is thus reduced to a spherical...
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