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Conicoid

Conicoid, or Quadric Surface, is a surface any section of which is a conic. Of such surfaces the sphere is an example, every section of this figure being a circle. An ellipsoid is another case; it somewhat resembles an egg in shape, but has three perfectly symmetrical axes at right angles to each other. Every section of an ellipsoid is an ellipse or oval, but there are two directions in every ellipsoid in which circular cuts may be made. The ordinary cone is another case of quadric surface; in fact, every conic section is so called because it may be made by cutting a cone. Among other quadrics we have the paraboloid or the hyperboloid. Certain special quadrics are obtained by rotating a conic about an axis of symmetry. These are termed conoids, or quadrics of revolution, and it is evident that all sections of such surfaces at right angles to the axis are circular. Of such we have the oblate spheroid if an ellipse rotate about its minor axis; the prolate spheroid if it rotate about its major axis; the sphere if a circle rotate about its diameter; and the cone if a line pair rotate about the bisector of the angle between the lines, the cylinder being a special case of cone. There are other conoids also.

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