| John Radford Young - Nautical astronomy - 1833 - 208 pages
...a -|- b _ tan. i (A + B) a — b ~ "tan. i ( A — B j ' 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... | |
| Olinthus Gregory - 1833 - 427 pages
...triangle it will be, as the sum of the sides about the vertical angle is to their difference, so is **the tangent of half the sum of the angles at the base, to the tangent of half** their difference. 16. In any plane triangle it will be, as the cosine of the difference of the angles... | |
| 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 - Geometry - 1835 - 513 pages
...difference; and since BC, FGare parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the fides **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. F1G. 8. In a plane triangle, the cosine ofhalftke difference of any two... | |
| Euclid, Robert Simson - Geometry - 1835 - 513 pages
...tangent of half their difference. Let ABC be a plane triangle, the sum of any two sides AB, AC will be **to their difference as the tangent of half the sum of the angles at the base** ABC, ACB, to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...6 — 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 - Geometry - 1836 - 114 pages
...tangent of half their difference. Let ABC be a plane triangle, the sum of any two sides, AB, AC will be **to their difference as the tangent of half the sum of the angles at the base** ABC, ACB to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
| John Playfair - Geometry - 1837 - 318 pages
...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 - 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, a, b any... | |
| 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:... | |
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