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" In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... "
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 68
by Nathan Scholfield - 1845 - 232 pages
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Elementary Trigonometry, Plane and Spherical

Edwin Pliny Seaver - Trigonometry - 1889 - 306 pages
...sin AI b =2 R sin B \ ........ [117] с =2 Л sin С i 179. The sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite anyles is to the tangent of half their difference. ANALYTIC PROOF. The first two equations...
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Elements of Plane and Spherical Trigonometry: With Numerous Examples

Edward Albert Bowser - Trigonometry - 1894 - 206 pages
...since the naming of - — provided the right order is maintained, (l) 57. Law of Tangents. — In any 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 Art. 55, a : b = sin A : sin B. By composition...
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A Treatise on Plane and Spherical Trigonometry: And Its Applications to ...

Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...sides makes no difference, provided the right order is maintained. 97. Law of Tangents. — In any 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 Art. 95, a : b = sin A : sin B. By composition...
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The Ohio Educational Monthly and the National Teacher: A Journal ..., Volume 41

Education - 1892 - 754 pages
...solving triangles ? 2. Prove: — In any plane triangle, the sum of the sides including either angle is to their difference as the tangent of half the sum of the two other angles is to the tangent of half their difference. 3. Find the sine of half an angle in terms...
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Plane and Spherical Trigonometry

Alfred Hix Welsh - Plane trigonometry - 1894 - 230 pages
...- C) . . . Art. 3, Def. 2. Л. jj .-. CB + AB : CB - AB : : tan ^ (A + Cf) : tan (A - C). Hence, in any plane triangle, the sum of any two sides is...their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Scholium. — The half difference added...
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A Treatise on Plane and Spherical Trigonometry

Ephraim Miller - Plane trigonometry - 1894 - 220 pages
...(3) by — c. In like manner the others may be obtained. 64. THEORKM IV. In any triangle, the sum of two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their differenve. From the fundamental formulae [31], sin...
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Treatise on Surveying

William Mitchell Gillespie - Surveying - 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 plnne triangle,...
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Elements of Plane and Spherical Trigonometry

Charles Winthrop Crockett - Plane trigonometry - 1896 - 318 pages
...Two Sides and the Included Angle (b, c, a) . First Method. — The sum of any two sides of a 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 we have b _ sin с sin y By composition...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1896 - 274 pages
...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 =...
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A Treatise on Surveying: Comprising the Theory and the Practice, Volume 1

William Mitchell Gillespie - Surveying - 1897 - 592 pages
...angles are to each other a& the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In eve.ry plane triangle,...
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