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ASYMPTOTE
A line which approaches nearer to some curve than assignable distance, but, though infinitely extended, would never meet it. Asymptotes may be straight lines or curves. A rectilinear asymptote may be conceived as a tangent to the curve at an infinite distance.
Origin: Gr. Not falling together; priv. + to fall together; with + to fall. Cf. Symptom.
Source: Websters Vocabulary