806 
The double conic d, of gp, corresponds to a cubic c, through 
OV, A,,....,A,. The associated pairs of points, images of the points 
of d,, are the intersections of c, with the straight lines through O; 
in the four points of contact A; of the tangents drawn out of O to 
Ca, there coincide two associated points’); the curves on ®, corre- 
sponding to these straight lines, have one cusp, hence one point of 
inflexion. 
\ 
These four straight lines OK; touch c, at K and have besides 
one free point of intersection with c,. The curves c, and c, touch 
at the points K and have no points of intersection besides these and 
they points (ASA ene yA 
If we now determine the points of intersection of A; Az with this 
c,, we find three points which have already been found in § + and § 6. 
1) The associated points of cs define together only a net out of S;. See among 
others STURM, l.c. S. 309. 
