The tractrix arises in the following problem posed to Leibniz: What is the path of an object starting off with a vertical offset when it is dragged along by a string of constant length being pulled along a straight horizontal line (Steinhaus 1999, pp. 250-251)? By associating the object with a dog, the string with a leash, and the pull along a horizontal line with the dog's master, the curve has the descriptive name "hundkurve" (dog curve) in German. Leibniz found the curve using the fact that the axis is an asymptote to the tractrix (MacTutor Archive).

From its definition, the tractrix is precisely the catenary involute described by a point initially on the vertex (so the catenary
is the tractrix evolute). The tractrix is sometimes
called the tractory or equitangential curve. The tractrix was first studied by Huygens
in 1692, who gave it the name "tractrix." Later, Leibniz, Johann Bernoulli,
and others studied the curve.

(Lockwood 1967, p. 123), where is the inverse Gudermannian.

A parameterization which traverses the tractrix with constant speed is given by

(19)

(20)

When a tractrix is rotated around its asymptote, a pseudosphere results. This is a surface of constant negativecurvature.
For a tractrix, the length of a tangent from its point
of contact to an asymptote is constant. The area between
the tractrix and its asymptote is finite.