( ?55 ) 
.wangles are at the same time polar triangles of a selfsame conic v 
if a mL* / TS ar0 " nd Pair of ' nv °l u, ion triangles’;’ 
‘,“ “ C ft ' 3 descnb3d a«>™d two of these triangles, then the 
curve 0 conjugate to it will have 6 nodes in its circumference. 
Also the remaining points of intersection of ft and S’ are easilv 
indicated; they are the four points of intersection of ft and -/ 7 
t-l 6 , kD °" “ 01 T er * hat “ C ° niC desorited around •» involution 
taang e and through two of the vertices of an other involution 
triangle must also contain the third vertex of the latter. 
6. It is also clear, that we can easily construct conics described 
around three involution triangles; to that end we make a conic 
pass through the vertices of an arbitrary involution triangle and 
through two singular points not lying on each other’s polar line • for 
this we choose S lt and S lt . As a, is described around a polar 
triangle of y 2 , it is described around an infinite number of these 
triangles; further each polar triangle of y, having one of the 
singular points as vertex is at the same time an involution triangle 
so that «, is described around three involution triangles. 
Now the curve « s will have in the circumference of a, nine nodes • 
so it must degenerate and must be one of the parts into which 
it breaks up. If P 1 is an arbitrary point of a, then always one of 
the two points P t and P t forming with P, an involution triangle 
will also lie on «„ so also the third vertex lies on «, (5). If now 
we let P, describe the conic « 2 , then P t and P s will describe the 
same curve; every time however that coincides with one of the 
singular points on «„ P, and P, will be bound to no other 
condition, than that they must lie on the polar line of that point and 
must form with P, a polar triangle of y,. So the parts into which 
« 8 degenerates are: 
1. the conic a, to be counted double; 
2. as many lines as there are singular points lying on a t . 
From this ensues that besides S lt and S lt 2 more singular points 
lie on a,. 
This last we can prove still in another way; we construct a 
second conic described around an involution triangle Q l Q, Q 
and through S lt and S lt ; it will cut « 2 in two points more/which 
being both the vertices of two, i.e. of an infinite number of in volution 
triangles, are therefore singular points. If we construct another conic 
£ described around a triangle of involution R, R t R t and through 
« lt and S lt> then this, must still cut a, in two singular points; these 
