The Collaborative International Dictionary of English v.0.48:

Hyperbolic \Hy`per*bol"ic\, Hyperbolical \Hy`per*bol"ic*al\, a.
   [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
   1. (Math.) Belonging to the hyperbola; having the nature of
      the hyperbola.
      [1913 Webster]

   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." --Fuller.
      [1913 Webster]

   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.
      [1913 Webster]