Fig. 58.
Any section, CD, of this cone, whose plane is oblique to the axis, but forms with it an angle greater than NOP, is an ellipse. The less the angle which the plane of the section makes with the axis, the more elongated is the ellipse.
Any section, EF, of this cone, whose plane makes with the axis an angle equal to NOP, is a parabola. It will be seen, that, by changing the obliquity of the plane CD to the axis NO, we may pass uninterruptedly from the circle through ellipses of greater and greater elongation to the parabola.
Any section, GH, of this cone, whose plane makes with the axis ON an angle less than NOP, is a hyperbola.
Fig. 59.
It will be seen from Fig. 59, in which comparative views of the four conic sections are given, that the circle and the ellipse are closed curves, or curves which return into themselves. The parabola and the hyperbola are, on the contrary, open curves, or curves which do not return into themselves.
49. A Revolving Body is continually Falling towards its Centre of Revolution.—In Fig. 60 let M represent the moon, and E the earth around which the moon is revolving in the direction MN. It will be seen that the moon, in moving from M to N, falls towards the earth a distance equal to mN. It is kept from falling into the earth by its orbital motion.
