 | Jeremiah Day - 1831 - 520 pàgines
...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 tangent of half the sum of ibe opposite angles, to the tangent of half their difference. Therefore, R : tan(ACH-45°)::tand(ACB... | |
 | Charles Hutton - 1831 - 656 pàgines
...is readily converted into a very useful proportion, viz. The sum of the sines of two arcs or angles, is to their difference, as the tangent of half the sum of those arcs or angles, is to the tangent of half their difference. 26. Operating with the third and... | |
 | Charles Hutton - 1831 - 662 pàgines
...is readily converted into a very useful proportion, viz. The sum of the sines of two arcs or angles, is to their difference, as the tangent of half the sum of those arcs or angles, is to the tangent of haJftJteir difference. 26. Operating with the third and... | |
 | John Playfair - 1832 - 358 pàgines
...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. QED PROP. V. THEOR. If a perpendicular be drawn from any angle... | |
 | John Playfair - 1833 - 346 pàgines
...isparallel 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. Q,. ED PROP. V. THEOR. If a perpendicular be drawn from any... | |
 | John Radford Young - 1833 - 240 pàgines
...- tan. J (A + B) 0 — 6 ~ "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... | |
 | John Radford Young - 1833 - 286 pàgines
...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... | |
 | Thomas Charles Robson - 1834 - 326 pàgines
...This case is resolved by the following PROPOSITION. (Fig. 16.) 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 a triangle, the sum of AB and AC, any two sides,... | |
 | Euclides - 1834 - 518 pàgines
...their difference; and since BC, FG are parallel *, 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. PROPOSITION IV. In any plane triangle BAC, whose... | |
 | Adrien Marie Legendre - 1836 - 394 pàgines
...Hence 1f(a+b + c)=p, or a + b + c=2p; we have a + 6 — c=2p — 2c, THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference...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 III.).... | |
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in any triangle, the sum of two sides 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. 
