Analytic geometry and principles of algebra (1913)
Ziwet, Alexander, 1853-1928, Hopkins, Louis Allen, joint author, Hedrick, E. R. (Earle Raymond), 1876-1943 · New York, The Macmillan Company · leaf 229
ANALYTIC GEOAIETRY [X, § 225 Just as in the case of the circle, so for the ellipse the locusof the midpoints of any system of parallel chords is a diameter.This follows from the corresponding property of the circlebecause the ellipse can be regarded as the projection of acircle (§211). But this… … Fig. 92 To find the diameter conjugate to a given diameter y — mxof the ellipse (1), let y= mx +Z: be any parallel to the givendiameter. If this parallel intersects the ellipse (1) at the realpoints (iCj, ^i) and {xo, yo), the midpoint has the coordinates^(xi -\- x^, J(?/i H- ^/o). The quadratic…
Geometry, Analytic
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