# hyperbolisms

Noun

- plural form of
*hyperbolism*

- Secondly, if two of the intersections coincide, say if the line infinity meets the curve in a onefold point and a twofold point, both of them real, then there is always one asymptote: the line infinity may at the twofold point touch the curve, and we have the parabolic hyperbolas; or the twofold point may be a singular point, - viz., a crunode giving the
**hyperbolisms**of the hyperbola; an acnode, giving the**hyperbolisms**of the ellipse; or a cusp, giving the**hyperbolisms**of the parabola. - As regards the so-called
**hyperbolisms**, observe that (besides the single asymptote) we have in the case of those of the hyperbola two parallel asymptotes; in the case of those of the ellipse the two parallel asymptotes become imaginary, that is, they disappear; and in the case of those of the parabola they become coincident, that is, there is here an ordinary asymptote, and a special asymptote answering to a cusp at infinity. - It is to be remarked that the classification mixes together non-singular and singular curves, in fact, the five kinds presently referred to: thus the hyperbolas and the divergent parabolas include curves of every kind, the separation being made in the species; the
**hyperbolisms**of the hyperbola and ellipse, and the trident curve, are nodal; the**hyperbolisms**of the parabola, and the cubical parabola, are cuspidal.

- hyperbolisms
- hyperbolist
- hyperbolists
- hyperbolize

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