| Jeremiah Day - 1831 - 370 sider
...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 AG equal... | |
| Jeremiah Day - 1831 - 370 sider
...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... | |
| John Radford Young - 1833 - 264 sider
...4 tan. a — 4 ~~ tan. J(A — B) ' that is to say, 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. By help of this rule we may determine the... | |
| Euclides - 1834
...given, the fourth is also given. PROPOSITION III. In a plane triangle, the sum of any two sides in **to their difference, as the tangent of half the sum of the** angle at Ihe base, to the tangent of half their difference. PROPOSITIONS III. IV. of the angles at... | |
| Euclid, Robert Simson - 1835 - 513 sider
...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, the cosine... | |
| Adrien Marie Legendre - 1836 - 359 sider
...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 A (Theorem... | |
| John Playfair - 1836 - 114 sider
...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 any two... | |
| John Playfair - 1837 - 318 sider
...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... | |
| Euclid - 1837 - 390 sider
...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, a, b any... | |
| 1837 - 249 sider
...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:... | |
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