CIDE DICTIONARY
hyperbolical, a. [L. hyperbolicus, Gr. : cf. F. hyperbolique.].

Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster]

Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression. 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.
ROGET THESAURUS
hyperbolical
Exaggeration
N
exaggeration, expansion, hyperbole, stretch, strain, coloring, high coloring, caricature, caricatura, extravagance, Baron Munchausen, men in buckram, yarn, fringe, embroidery, traveler's tale, fish story, gooseberry, storm in a teacup, much ado about nothing, puff, puffery, rant, figure of speech, facon de parler, stretch of fancy, stretch of the imagination, flight of fancy, false coloring, aggravation, exaggerated, overwrought, bombastic,
hyperbolical, on stilts, fabulous, extravagant, preposterous, egregious, outre, highflying, hyperbolically, excitabat enim fluctus in simpulo.