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From: Webster's Revised Unabridged Dictionary (1913)

 Hy·per·bol·ic Hy·per·bol·ic·al a.
 1. Math. Belonging to the hyperbola; having the nature of the hyperbola.
 2. 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.”
 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.