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From: Webster's Revised Unabridged Dictionary (1913)

 Hy·per·bo·loid n.  Geom. A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface.
 Hyperboloid of revolution, an hyperboloid described by an hyperbola revolving about one of its axes. The surface has two separate sheets when the axis of revolution is the transverse axis, but only one when the axis of revolution is the conjugate axis of the hyperbola.