By a Cut shall be understood to mean a self-returning linear separation (naturally represented by a fine-drawn or peculiarly colored line) which severs all that it encloses from the sheet of assertion on which it stands itself, or from any other area on which it stands itself. The whole space within the cut (but not comprising the cut itself) shall be termed the area of the cut.

A cut is not a graph-replica. A cut drawn upon the sheet of assertion severs the surface it encloses, called the area of the cut, from the sheet of assertion; so that the area of a cut is no part of the sheet of assertion.