NEWTON'S FIVE TYPES OP PLANE CUBICS 



279 



Pigr. 2 

 points is illustrated by Fig. 1, I shall now assume an entirely imag- 

 inary quadruple which is determined by the imaginary fundamental 

 points of an elliptic coaxial system of circles and the circular points 

 at infinity through which it also passes. Let P and Q be the limit- 

 ing points of the system, Fig. 2. On every ray g through an arbi- 



