Math. [ad. (ultimately) Gr. ἀσύμπτωτος not falling together, f. ἀ priv. + σύν together + πτωτ-ός apt to fall. Cf. F. asymptote.]
A line that approaches nearer and nearer to a given curve, but does not meet it within a finite distance. A rectilinear asymptote may be considered as a tangent to the curve when produced to an infinite distance. Also fig.
1656. trans. Hobbes’ Elem. Philos. (1839), 200. Asymptotes … come still nearer and nearer, but never touch.
1796. Hutton, Math. Dict., I. 162. Two parabolas, placed with their axes in the same right line, are asymptotes to one another.
1860. Farrar, Orig. Lang., 117. Language, in relation to thought, must ever be regarded as an asymptote.
1867. Denison, Astron. without Math., 238. [A hyperbola’s] legs continually approach two straight lines called asymptotes which are in fact the outline of the cone itself, but never reach them.
b. attrib. quasi-adj.
1701. Grew, Cosmol. Sacra, II. v. 55 (J.). Asymptote Lines, though they may approach still nearer together, till they are nearer, than the least assignable Distance: Yet being still produced Infinitely, will never meet.
