The Nodal Cubic

The unicursal cubic must have a double point which may be a node or a cusp. The two points at the node corresponding to the different branches generally appear together in the properties of the curve and may be called the nodal points or the nodal pair. It should be borne in mind that these points are analytically distinct and have coincided only by a geometrical accident. It will be useful to remember that a nomographic correspondence exists between points on the cubic and the lines joining them to the node. The lines which correspond to the nodal points are the nodal tangents.