| Euclid - 1835 - 513 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,... | |
| 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... | |
| 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... | |
| Surveys - 1837 - 249 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:... | |
| John Playfair - Geometry - 1837 - 318 pages
...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. 325 PROP. V. THEOR. If a perpendicular... | |
| Euclid, James Thomson - Geometry - 1837 - 390 pages
...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,... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...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... | |
| Jeremiah Day - Geometry - 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... | |
| Charles William Hackley - Trigonometry - 1838 - 307 pages
...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... | |
| Charles Davies - Surveying - 1839 - 261 pages
...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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