| John Radford Young - 1833 - 264 páginas
...of their aum and difference . / .19 ARTIcLE. PAGE. 19. In a plane triangle the sum of any two sides **is to their difference as the tangent of half the sum of the opposite angles** to the tangent of half their difference . . . .21 •20. Formulas for determining an angle in terms... | |
| Euclid - 1835 - 513 páginas
...difference ; and since BC, FG are parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the sides **is to their difference, as the tangent of half the sum of the** angles at the base to the tangent of half their difference. * PROP. IV. FIG. 8. In a plane triangle,... | |
| John Playfair - 1836 - 114 páginas
...three being given, the fourth is also given. PROP. III. i In a plane triangle, the sum of any two sides **is to their difference, as the tangent of half the sum of the** angles at the base, to the tangent of half their difference. Let ABC be a plane triangle, the sum of... | |
| Adrien Marie Legendre - 1836 - 359 páginas
...c=2p — 2c, a+c — 6=2p — 26; hence THEOREM V. In every rectilineal triangle, the sum of two sides **is to their difference as the tangent of half the sum of the** angles opposite those sides, to the tangent of half their difference. For. AB : BC : : sin C : sin... | |
| Euclid, James Thomson - 1837 - 390 páginas
...to the definitions of this book, the sine of a right angle is equal to the radius. 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,... | |
| John Playfair - 1837 - 318 páginas
...difference as the radius to the tangent of the 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... | |
| Andrew Bell - 1837 - 240 páginas
...same manner, it may be 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... | |
| 1837 - 249 páginas
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithet 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:... | |
| Jeremiah Day - 1838
...THE OPPOSITE ANGLES ; 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... | |
| Charles Davies - 1839 - 334 páginas
...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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