 | Robert Simson - 1835 - 544 pàgines
...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 - 1836 - 418 pàgines
...Therefore, R : tan(ACH-45°)::CG : FG. And, ai GH and DC are parallel, (Euc. 2. 6.) CG:FG::DH :FH. But DH is, by construction, equal to the sum, and...to 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 - 1836 - 148 pàgines
...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... | |
 | 1836 - 488 pàgines
...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 - 1836 - 394 pàgines
...— 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... | |
 | Euclid, James Thomson - 1837 - 410 pàgines
...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,... | |
 | John Playfair - 1837 - 332 pàgines
...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... | |
 | Charles Davies - 1837 - 342 pàgines
...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:... | |
 | Andrew Bell - 1837 - 290 pàgines
...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 William Hackley - 1838 - 338 pàgines
...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 and the included... | |
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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. 
