| Andrew Bell - 1837 - 240 páginas
...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 páginas
...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 páginas
...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 - 261 páginas
...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 páginas
...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... | |
| John Playfair - 1842 - 317 páginas
...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... | |
| Enoch Lewis - 1844 - 228 páginas
...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;... | |
| Nathan Scholfield - 1845
...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,... | |
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