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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. "
An Easy Introduction to the Mathematics: In which the Theory and Practice ... - Page 405
by Charles Butler - 1814
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Electronic book - 1868 - 530 pages
...angles are 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 plane triangle,...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 436 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 : sin....
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Annual Report of the School Committee of the City of Boston

Boston (Mass.). School Committee - Boston (Mass.) - 1868 - 508 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. 3. 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 - Deaf - 1869 - 698 pages
...(CB); whence 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 - Surveying - 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 plane triangle,...
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Documents of the City of Boston, Volume 3

Boston (Mass.). City Council - Boston (Mass.) - 1869 - 1192 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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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 398 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 + AC:...
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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 - Deaf - 1871 - 370 pages
...(CB); whence 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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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...^(A+B) . sin. A-sin. B~sin. ^(AB) cos- ^(A+B)~tang. ^(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. COS f*fvt Dividing formula (3) by (4), and considering...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 268 pages
...each other, have the same sine, and BD = a sin. BCD = a sin. C (41) B 102. 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. Let ABC (Art. 103) be a plane triangle...
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