| Benjamin Peirce - Plane trigonometry - 1845 - 498 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:... | |
| 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... | |
| Euclid, James Thomson - Geometry - 1845 - 380 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,... | |
| 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,... | |
| John Playfair - Euclid's Elements - 1846 - 332 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... | |
| Dennis M'Curdy - Geometry - 1846 - 168 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... | |
| 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... | |
| Charles Davies - Trigonometry - 1849 - 384 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... | |
| Sir Henry Edward Landor Thuillier - Surveying - 1851 - 828 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.... | |
| Charles William Hackley - Trigonometry - 1851 - 524 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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