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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 New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 81
by Peter Nicholson - 1823 - 596 pages
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - Surveying - 1839 - 376 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. 53. Let ACB be a triangle : then will AB+AC:...
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - Surveying - 1839 - 380 pages
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angk, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of haJ/ their difference. 58. Let ACB be a triangle : then will AB+AC:...
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An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839 - 498 pages
...double their opposite angles. PROPOSITION IV. (115) In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of their opposite angles is to the tangent of half their difference, Let ABC be any triangle ; make BE...
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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
...to the tangent of the 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
...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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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...part, therefore, of that 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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Plane Trigonometry and Mensuration for the Use of the Royal Military College

William Scott - Measurement - 1845 - 290 pages
...tan. (A — в)' or, a + 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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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...12"; to solve the 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
...equal to 5528' 12"; to 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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