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 Llibres Llibres 71 - 80 de 194 sobre In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions.... 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... Elements of Trigonometry: Plane and Spherical - Pàgina 45
per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pàgines
Visualització completa - Sobre aquest llibre ## An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - 1845 - 449 pàgines
...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...
Visualització completa - Sobre aquest llibre ## An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - 1845 - 449 pàgines
...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:...
Visualització completa - Sobre aquest llibre ## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 pàgines
...AB. Therefore the sin. AC+sin. AB : sin. AC—sin. AB : : tan. J(AC-(AB): tan. J(AC—AB). QED 4 Th. In any triangle, the sum of two sides is to their...difference, as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Given the triangle ABC, the side AB being greater...
Visualització completa - Sobre aquest llibre ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 pàgines
...difference between either of them and 45°. PROP. IV. 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, to the tangent of half their difference. Let ABC be any plane triangle ; CA+AB : CA-AB : : tan.£(B+C)...
Visualització completa - Sobre aquest llibre ## A Treatise of Plane Trigonometry, and the Mensuration of Heights and ...

Jeremiah Day - 1848 - 153 pàgines
...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 AG equal...
Visualització completa - Sobre aquest llibre ## Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - 1849 - 359 pàgines
...—^— _ R * x 2/ic-R 2 (/i 2 +c 2 —a 2 ) = R« x -R- x " * Hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference...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 A (Theorem III.)....
Visualització completa - Sobre aquest llibre ## A course of mathematics: containing the principles of plane trigonometry ...

Jeremiah Day - 1851
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R : tan (ACH— 45°) : : tan...
Visualització completa - Sobre aquest llibre ## A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - 1851 - 372 pàgines
...: 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...
Visualització completa - Sobre aquest llibre ## ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...AC :: sin 0 : sin jR THEOEEM 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. 22. Let ACB be a triangle: then will AJ3...
Visualització completa - Sobre aquest llibre ## A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852
...proposition is therefore general in its application.* 118. The sum of any two 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. For, by the preceding article, a : b =...
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