( 754 ) 
This point forms an involution triangle with aS 1s and with another 
point of s 12 and an other one with S lt and with a point of (an 
“other one”, as S lt and S l9 which do not lie on each other’s polar 
line cannot be vertices of a selfsame involution triangle); so the point 
of intersection of s lt and s lt is also a singular point and S 19 S lt a 
singular line. 
Each line connecting two singular points not lying on each other's 
polar line is a singular line ; each point which is the point of inter¬ 
section of two singular lines not passing through each other's pole is a 
singular point. 
On s l9 , the polar line of S tt , lie 3 singular points; the remaining 
6 are connected with S 12 by 3 singular lines. So each line connecting 
S 19 with one of the singular points on s lt is not a singular line, 
as only 3 of these lines pass through S lt . 
We can indicate the position of the singular points by the following 
diagram, where the indices have been chosen in such a way that 
always the points Sm , Su and Su lie on a selfsame line, that the 
lines sat, $ki and su intersect each other in a selfsame point, and 
that the point Sat and the line S& are each other’s pole and polar 
line with respect to y,. 
5. We make a point describe a conic «, and an other point 
a line b x the two points which are conjugated to the former describe 
a curve those which are conjugated to the latter a curve ft 4 . 
As ft* and « s intersect each other in 8 points, b x and a n must have 
8 points in common, so a” is a curve of order eight; we shall call 
it in future « 8 . As intersects all singular lines twice, a B will have 
in each of the 10 singular points a node. 
If a, is described around an involution triangle, then a 8 has also 
ilouble points in the vertices of this triangle. As all involution 
