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" The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. "
A Practical Application of the Principles of Geometry to the Mensuration of ... - Page 105
de Jeremiah Day - 1815 - 96 pages
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1896 - 274 pages
...The proposition is therefore general in its application.* 118. The sum of any two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. For, by the preceding article, a : b = sin A : sin В whence,...
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New Plane and Spherical Trigonometry

Webster Wells - 1896 - 238 pages
...B : sin C, (48) and с : a = sin С : sin A. (49) 108. /n a»?/ triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By (47), a : b = sin A : sin B. Whence by composition and...
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Treatise on Surveying

William Mitchell Gillespie - 1896 - 594 pages
...to each other as the opposite sides. THEOREM H. — In every plane triangle, the sum of two sides u to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. TE1EOBEM III. — In every...
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Pamphlets in Philology and the Humanities, Volume 2

1897 - 726 pages
...triangle are proportional to the sines of the opposite angles. That is, a : b = sin A : sin B The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles opposite is to the tangent of half their difference. That is, a -f J : a — I = tan £ ( A...
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A Treatise on Surveying: Comprising the Theory and the Practice, Volume 1

William Mitchell Gillespie - 1897 - 618 pages
...are to each other at the opposite sides. THEOREM II.—In every plane triangle, the turn of two rides is to their difference as the tangent of half the sum of the angles opporite those sides is to the tangent of half their difference. THEOBBM HI.—In every plane...
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Elements of Plane and Spherical Trigonometry

James William Nicholson - 1898 - 186 pages
...[58] is called the Law of Tangents. Translation : The sum of any two sides of any triangle is to then. difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 101. Relation of the half of one angle to the three sides....
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Plane and Spherical Trigonometry: An Elementary Text-book

Charles Hamilton Ashton, Walter Randall Marsh - 1900 - 184 pages
...other vertices, similar expressions may be found for the other sides. 42. Law of the tangents. — The sum of any two sides of a triangle is to their difference as the tangent of one-half of the sum of the opposite angles is to the tangent of onehalf their difference. From formula...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1901 - 278 pages
...thereton; general in its application.' 118. The sum of ang two sides of a plane triangle is to thcir difference as the tangent of half the sum of the opposite angles is to the tangent of half thcir difference. For, by the preceding article, a : b = sin A : sin В whence,...
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The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - 1902 - 1204 pages
...formulas enable us to transform a sum or difference into a product. The sum of the sines of two angles is to their difference as the tangent of half the sum of those angles is to the tangent of half their difference. sin A + sin K _ 2 sin \^(A + B) cos J£C4...
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Plane Trigonometry

James Morford Taylor - 1904 - 192 pages
...logarithms, we must deduce other formulas, one of which is the law of tangents below. Law of tangents. The sum of any two sides of a triangle is to their difference as the tangent of half the sum of their opposite angles is to the tangent of h (1ff their difference. From the law of sines, we have...
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