Note 27 — V. Algebraical Functions

We suppose in what follows that the singularities of the curve are all ordinary nodes. The necessary modifications when this is not the case are not difficult to make. An ordinary multiple point of order may be regarded as equivalent to ordinary double points. A curve of degree which has an ordinary multiple point of order , equivalent to ordinary double points, is therefore unicursal. The theory of higher plane curves abounds in puzzling particular cases which have to be fitted into the general theory by more or less obvious conventions, and to give a satisfactory account of a complicated compound singularity is sometimes by no means easy. In the investigation which follows we confine ourselves to the simplest case.