Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The curve that satisfies the following property: That segment of the tangent line that lies between the point of tangency and a fixed line has length independent of the point of tangency chosen.
from the GNU version of the Collaborative International Dictionary of English
 n. A curve such that the part of the tangent between the point of tangency and a given straight line is constant;  so called because it was conceived as described by the motion of one end of a tangent line as the other end was drawn along the given line.
from The Century Dictionary and Cyclopedia
 n. A transcendental curve invented by Christian Huygens (1629–95), the property of which is that the distances along the different tangents from the points of contact to the intersections of a certain line are all equal.
Etymologies
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Examples

I found by experiment that it is neither, but an approximation to the tractrix (a modification of the catenary), if anything definite; as indeed one, on thinking over the matter, might feel certain it would be  the tractrix being the curve of least friction.

This had led, through the work of Leonardo (on the catenarytractrix matter), into the work of Kepler, which, in turn, led into Leibniz's uniquely original discovery of the principle of the calculus, and the revision of that discovery by Leibniz, based upon the work of Pierre de Fermat, which was carried out by Leibniz's collaboration with Jean Bernouilli in defining a universal physical principle of least action.

Santa Maria del Fiore, and the development of the pairing of the catenary and tractrix relationship by Leonardo da Vinci.

De Docta Ignorantia; Leonardo da Vinci (e.g., the use of the relatively leastaction physical curve, the catenarytractrix, as a principle of construction
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fbharjo commented on the word tractrix
to a point
February 12, 2012