 | John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...the beginning and end are equal. 2. Extract the square root of 4<1 — 24^2. 3. In a plane triangle, the sum of the sides is to their difference, * as the tangent of the semi-sum of the angles at the base, to the tangent of their semi-difference. 4. An equation, which... | |
 | John Radford Young - Astronomy - 1833 - 286 pages
...above, n + 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 remaining parts... | |
 | William Galbraith - Astronomy - 1834 - 454 pages
...sides and contained angle are given. I. As the sum of the given sides Is to their difference; So is the tangent of half the sum of the opposite angles To the tangent of half their difference. Half the difference added to half the sum of those angles gives the greater, and subtracted from half... | |
 | Euclid - 1835 - 540 pages
...and CF their 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,... | |
 | Robert Simson - Trigonometry - 1835 - 544 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,... | |
 | Jeremiah Day - Measurement - 1836 - 418 pages
...construction, equal to the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the sides is to their difference ; as the...the tangent of half their difference. Therefore, R : tan(ACH-45°)::tanri(ACB + B) : tan J(ACB^B)' Ex. In the triangle ABC, (Fig. 30.) given the angle... | |
 | John Playfair - Geometry - 1836 - 148 pages
...and CF their difference ; and since BC, FG are parallel, (3. 5.) 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. In any plane triangle BAC, whose... | |
 | Mathematics - 1836 - 488 pages
...an angle great, er than 45° : and radius ia to the tangent of the excess of this angle above 45° ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. In a plane triangle, twice the product of any two sides, is to the difference between the sum of the... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 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... | |
 | Charles Davies - Navigation - 1837 - 342 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:... | |
| |
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 Theorem II. we have a : b : : sin. A : sin. B. 
