Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 162
holds for conjugate diameterswhose slopes to the major axis are 7n and m respectively(§124); therefore— Theorem VIII. If any chord of an ellipse is parallel to adiameter, the supplemental chord is parallel to the conjugatedifljneter. Relation of the Ellipse and Circle. 131. Let a circle be… … Comparing (a) and (b), we have y? = ^^ b ye whence a TEE ELLIPSE. 147 that is, the ordinate of the ellipse at any point is found bymultiplying the ordinate of the circle by the constant factor -. Hence we havea Theorem IX. If all the ordinates of a circle he dimin-ished in the same proportion^ the…
Geometry, Analytic
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