Osgood, William F. (William Fogg), 1864-1943, Graustein, William Caspar, 1888-1941, joint author · New York, The Macmillan company · leaf 125
or. 9. The Parabola as the Limit of Ellipses. We have provedthat, when e < 1, equation (3), § 7, represents an ellipse with eccentricity e — e. Weknow that, if e = 1, theequation represents aparabola. If, then, in theequation we allow e toapproach 1 through values< 1, the ellipse which… … Fig. 14 m, but having values for cas their limit, viz. e == -J-, which along the axis of y, and the focus F: (m, 0) are the same forall the ellipses. But the center 0 and the right-hand vertex THE ELLIPSE 119 A of each successive ellipse are farther away from 0. andtheir distances from 0, namely,…
Geometry, Analytic
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