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 Practical Surveying, ... - Side 94av Robert Gibson - 1808 - 440 siderUten tilgangsbegrensning - Om denne boken
| Andrew Bell - 1837 - 240 sider
...demonstrated that AB : BC = sin C : sin A. PROPOSITION VI. THEOREM. The sum of two sides of a triangle **is to their difference as the tangent of half the sum of** me angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and... | |
| Charles William Hackley - 1838 - 307 sider
...tan £ (A -f- 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. This proportion is employed when two sides... | |
| Jeremiah Day - 1838
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, **is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. This is the second theorem applied to the... | |
| Robert Gibson, James Ryan - 1839 - 412 sider
...ike rtum of Ijte two given sides AB and BC, including a given angle ARC, it to their difference aa **the tangent of half the sum of the two unknown angles A and C is** lathe tangent of half their difference. Produce AB, and make HB=BC, and join HCi let fall th« perpendicular... | |
| Charles Davies - 1839 - 334 sider
...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:... | |
| Charles Davies - 1839 - 261 sider
...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:... | |
| Jeremiah Day - 1839 - 370 sider
...THE OPPOSITE ANGLES J To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) **is to their difference ; as the tangent of half the sum of the** angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making... | |
| Thomas Keith - 1839
...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... | |
| Charles Davies - 1841 - 359 sider
...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:... | |
| John Playfair - 1842 - 317 sider
...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... | |
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