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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... "
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 68
by Nathan Scholfield - 1845 - 232 pages
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Elements of Surveying, and Navigation: With a Description of the Instruments ...

Charles Davies - Navigation - 1841 - 406 pages
...AC : : sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...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 - Conic sections - 1844 - 228 pages
...sine of A ; these sines being suited to any radius whatever (Art. 27). QED ART. 30. In any right lined triangle, the sum of any two sides is, to their difference,...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, the sides. From...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

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, a, b any two of its...
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Plane Trigonometry and Mensuration for the Use of the Royal Military College

William Scott - Measurement - 1845 - 290 pages
...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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Key to System of practical mathematics. 2 pt. No.xvii

Scottish school-book assoc - 1845 - 278 pages
...a — 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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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

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:...
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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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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 168 pages
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1846 - 332 pages
...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...
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