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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... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Σελίδα 117
των Dennis M'Curdy - 1846 - 138 σελίδες
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - 1868 - 420 σελίδες
...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....

Annual Report of the School Committee of the City of Boston

Boston (Mass.). School Committee - 1868
...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,...

Annual Report and Documents of the New York ..., Τόμος 50,Μέρη 1868-1873

New-York Institution for the Instruction of the Deaf and Dumb - 1869
...£(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...

A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1869 - 428 σελίδες
...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,...

Documents of the City of Boston, Τόμος 3

Boston (Mass.). City Council - 1869
...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,...

Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1870 - 319 σελίδες
...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:...

Annual Report and Documents of the New York Institution for the Instruction ...

New-York Institution for the Instruction of the Deaf and Dumb - 1871
...(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...

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1871 - 58 σελίδες
...^(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...

An Elementary Geometry and Trigonometry

William Frothingham Bradbury - 1872 - 238 σελίδες
...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...

A Treatise on Special Or Elementary Geometry, Τόμοι 1-2

Edward Olney - 1872
...horizontal parallax. PLANE TRIGONOMETRY. 86. Prop.— TJie sum of any two sides of a plane triangle is to their difference, as the tangent of half the sum of the angles opposite is to the tangent of half their difference. 1 >K\r. — Letting a and b represent any two...




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