XVII.—The Enumeration, Description, and Construction of Knots of Fewer than Ten Crossings

Abstract

1. By a knot of n crossings, I understand a reticulation of any number of meshes of two or more edges, whose summits, all tessaraces (ἀκή), are each a single crossing, as when you cross your forefingers straight or slightly curved, so as not to link them, and such meshes that every thread is either seen, when the projection of the knot with its n crossings and no more is drawn in double lines, or conceived by the reader of its course when drawn in single line, to pass alternately under and over the threads to which it comes at successive crossings.