| Euclid - 1835 - 540 pages
...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 of half... | |
| John Playfair - Geometry - 1836 - 114 pages
...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 sides, AB,... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...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... | |
| Euclid - Geometry - 1837 - 410 pages
...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, a, b any... | |
| John Playfair - Geometry - 1837 - 332 pages
...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 ; CA+AB... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...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... | |
| Charles Davies - Navigation - 1837 - 336 pages
...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 - Geometry - 1838 - 416 pages
...opposite angles. It follows, 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... | |
| Charles William Hackley - Trigonometry - 1838 - 336 pages
...— b : : 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 - Geometry - 1839 - 432 pages
...opposite angles. It follows, 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... | |
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