The Collaborative International Dictionary
Hyperbolic \Hy`per*bol"ic\, Hyperbolical \Hy`per*bol"ic*al\, a.
(Math.) Belonging to the hyperbola; having the nature of the hyperbola.

(Rhet.) Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression. ``This hyperbolical epitaph.''
Fuller.Hyperbolic functions (Math.), certain functions which have relations to the hyperbola corresponding to those which sines, cosines, tangents, etc., have to the circle; and hence, called hyperbolic sines, hyperbolic cosines, etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which is, that the distance from the pole to the generating point varies inversely as the angle swept over by the radius vector.