An elementary treatise on analytical geometry : embracing plane co-ordinate geometry, and an introduction to geometry of three dimensions (1869)
Johnson, William Woolsey, 1841-1927 · Philadelphia : J.B. Lippincott · leaf 143
ti-tuting the value of Y in A2Y2 -f B2X2 = A2B2, and dividing by the coefficient of X2, we have the quadratic ~^ :• A2m2 + B2 A2m2 -f B2 12* 138 THE ELLIPSE. completing the square, etc., — A2mb ± ABl/AV + B2 — b2 X = A2m2 + B2 and Y = B2b ± m ABl/AW -f B2 — VA2m2 + B2 the values of Y being derived… … are the co-ordinates of M, the mid-dle point of the chord PP. Sup-pose now the value of m to remainfixed while that of b varies, both co-ordinates of M will vary, but Y B2 their ratio, which is — = — -—, is constant. Therefore theX mA2 middle points of all chords parallel to PP, in the figure, are…
Geometry, Analytic
Internet Archive · Library of Congress · Public Domain Mark 1.0. Free to use for anything.
