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" In any plane 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. "
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811
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James Pryde - 1867 - 506 pages
...the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half difference being...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1868 - 444 pages
...BA-cos. A. That is, b = a cos. C -J- e cos. A. 869. Theorem — The sum of any two sid.es of a triangle is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference. By Art. 867, a : b : : sin. A :...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1868 - 530 pages
...to each other as 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 every...
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Elements of Trigonometry, Plane and Spherical

Lefébure de Fourcy (M., Louis Etienne) - 1868 - 350 pages
...tang } (A + B) a — b tang} (A — B) *• ; which shows that, in any triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. We have A + B=180°...
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Documents of the City of Boston, Volume 3

Boston (Mass.). City Council - 1869 - 1194 pages
...and cosecant. 2. Demonstrate that, in any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 8. Given two sides and an opposite angle,...
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Annual Report and Documents of the New York ..., Volume 50, Parts 1868-1873

New-York Institution for the Instruction of the Deaf and Dumb - 1869 - 698 pages
...we have the principle. When two sides and their included angles are given : The sum of the two sides is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their difference. This young man also worked out a problem...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1869 - 550 pages
...to each other at the opposite sides. THEOREM EL — In every plane triangle, the turn of two tides 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 every...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1870 - 392 pages
...0 : sin B. Theorems. THEOREM II. In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. Let ACB be a triangle: then will AB...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1871 - 302 pages
..., sin. A : sin. B : : BC : AC. B THEOREM II. (50.) In any plane triangle, the sum of any tico sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Let ABC be any triangle ; then will...
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Annual Report and Documents of the New York Institution for the Instruction ...

New-York Institution for the Instruction of the Deaf and Dumb - 1871 - 370 pages
...we have the principle. When two sides and their included angles are given : The sum of the two sides is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their difference. This young man also worked out a problem...
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