ASYMPTOTE, a line which approaches continually nearer to a given curve, but which does not meet it within a finite dis tance. More precisely speaking, if a curve (c) has an infinite branch and if there be a straight line (a) such that the distance PP' to a from a point P on c approaches zero as a limit, as P moves toward infin ity, then a is called an asymptote to this curve. Geminus, writing in the first century B.C., remarked that : "Some lines exist which approach indefinitely and yet remain LuvµlrTwToL [literally, not-together-falling]." Elsewhere he gives the cases of the hyperbola and conchoid, each with its asymptote. The asymptote is often spoken of as a tangent to a curve at a point infinitely distant.