In particular if D =o, that is, if the given curve be unicursal, the transformed curve is a line, 4 is a mere linear function of 0, and the theorem is that the co-ordinates x, y, z of a point of the unicursal curve can be expressed as proportional to rational and integral functions of 0; it is easy to see that for a given curve of the order m, these functions of 0 must be of the same order m.
The theorem of united points in regard to points in a right line was given in a paper, June-July 1864, and it was extended to unicursal curves in a paper of the same series (March 1866), " Sur les courbes planes ou a double courbure dont les points peuvent se determiner individuellement - application du principe de correspondance dans la theorie de ces courbes."
However, I have decided that a unicursal maze is an abstract pattern made by a single line, or a few crossing lines.
Hence it is unicursal (see CURVE).
These curves are instances of unicursal bicircular quartics.