Dowling, L. Wayland (Linnaeus Wayland), b. 1867, Turneaure, F. E. (Frederick Eugene), 1866- · New York, H. Holt and company · leaf 125
to F and D^E, to F,. 92. A fundamental theorem. If the length of the focal radius toany point on an ellipse or an hyperbola is divided by the distanceof the point from the corre-sponding directrix, then the ratioso formed is constant and equalto the eccentricity of the curve. We are to prove (Figs.… … Hence, + x a X e • = e. Arts. 91-93] CONSTRUCTION OF AN ELLIPSE 109 . The theorem is proved for the hyperbola in the same way,making use of the lengths of the focal radii (Art. 52) and Fig. 68. 93. Construction of an ellipse or an hyperbola. The theorem inthe preceding article furnishes a…
Geometry, Analytic
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