with .
The above equation represents the third class of Newton's classification of cubic
curves, which Newton divided into five species depending on the roots
of the cubic in on the right-hand side of the equation. Newton described these
cases as having the following characteristics:

1. "All the roots are real and unequal. Then the Figure is a diverging Parabola of
the form of a Bell, with an Oval at its Vertex.

2. Two of the roots are equal. A parabola will be formed, either Nodated by touching an Oval, or Punctate, by having the Oval
infinitely small.