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" C' (89) (90) (91) (92) (93) 112. 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. "
The Theory and Practice of Surveying: Containing All the Instructions ... - Page 108
by Robert Gibson - 1811 - 508 pages
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 449 pages
...triangle. j , C> ~! ' ' Ans. The question is impossible. 81. Theorem. The sum of 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. [B. p. 13.] Proof. We have (fig. 1.) a:...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 449 pages
...solve the triangle. -4n'. The question is impossible. 81. Theorem. The sum of 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. [B. p. 13.] Proof. We have (fig. 1.) a...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...proposition is a particular case of this PROP. III. THEOR. — 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, is to the tangent of half their difference. Let ABC be a triangle,...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845
...a sin. B sin. A c sin. C sin. B b PROPOSITION III. In any plane triangle, the sum of any two sides, is to their difference, as the tangent of half the sum of the angles opposite to them, is to the tangent of half their difference. Let ABC be any plane triangle,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...BC is parallel to FG, CE : CF : : BE : BG, (2. 6.) that is, the sum of the two sides of the triangle ABC 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. PROP. V. THEOR. If a perpendicular...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...triangle EFG, BC is drawn parallel to FG the base EC : CF : : EB : BG; that is, the sum of two sides is to their difference, as the tangent of half the sum of the angles at the base ia to the tangent of half their difference. * Moreover, the angles DBF, BFE are...
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A Treatise of Plane Trigonometry, and the Mensuration of Heights and ...

Jeremiah Day - Logarithms - 1848 - 153 pages
...THE SUM OF THE OPPOSITE ANGLES ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half then- difference. Demonstration. Extend CA to G, making...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 359 pages
...+c 2 —a 2 ) = R x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. * For. AB : BC : : sin C : sin...
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A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Ralph Smyth, Sir Henry Edward Landor Thuillier - Surveying - 1851 - 718 pages
...C : AB : : the Sine of A : BC, etc. QED H THEO. II. In any plane triangle ABC, the sum of the tivo given sides AB and BC, including a given angle ABC, is to their difference, as theJangent of half the sum of the two unknown angles A and C is to the tangent of half their difference....
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A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - Trigonometry - 1851 - 372 pages
...: tan (A + B) : tan ^ (A — B) That is to say, the sum of two of the 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. 76 This proportion is employed when two...
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