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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. "
A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ... - Pàgina 68
per Jeremiah Day - 1815 - 126 pàgines
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 pàgines
...difference between either of them and 45°. PROP. IV. THE OR. 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 ofhalftlteir difference. Let ABC be any plane triangle...
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A Treatise on Plane and Spherical Trigonometry: Including the Construction ...

Enoch Lewis - 1844 - 240 pàgines
...to any radius whatever (Art. 27). QED ART. 30. In any right lined triangle, the sum of any two sides 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 the triangle; AC, AB,...
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Plane Trigonometry and Mensuration for the Use of the Royal Military College

William Scott - 1845 - 288 pàgines
...b : a — b :: tan. | (A + в) : tan. ¿ (A — в).* Hence the sum of any two sides of a triangle, is to their difference, as the tangent of half the sum of the angles oppo-* site to those sides, to the tangent of half their difference. SECT. T. EESOLUTION OF TRIANGLES....
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - 1845 - 244 pàgines
...proposition, a sin. A.~ c b sin. 68 FROPOSITION 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, then,...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 pàgines
...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, a, b any...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - 1845 - 542 pàgines
...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, then,...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pàgines
...B sin. A sin. C sin. B sin. C. 68 PROFOSITION in. 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, then,...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - 1845 - 498 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:...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - 1845 - 498 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...
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Key to System of practical mathematics. 2 pt. No.xvii

Scottish school-book assoc - 1845 - 278 pàgines
...6 tan. 4(A — B) opposite to the angles A and B, the expression proves, that the sum of the sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference, which is the rule. (7.) Let (AD— DC)...
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