 | 1867 - 120 pages
...two considerations that, if from any two points on a parabola perpendiculars be drawn to the axis, the distance between their feet is equal to the difference of the focal radii of the points, and that, if from the two foci of an hyperbola perpendiculars be drawn to either asymptote,... | |
 | Luigi Cremona - Geometry, Projective - 1885 - 434 pages
...parabola -— ^ = o , so that FL = 2 FA. 353. THEOREM. In the ellipse the sum, and in the hyperbola the difference, of the focal radii of any point on the curve is constant*. Let M be any point on a central conic (Figs. 214, 215) whose * APOLLONIUS, loc. eit.,... | |
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The latter, therefore, are parallel to the axes of the parabolas, since both are perpendicular to the same two lines. [Mr. TOWNSEND gives the proof as follows : — " The property appears immediately from the two considerations that, if from any two points... 