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such a projective relation exists that the rays d and & through H 
correspond to the double-elements of the involution, the first of 
which is composed of the right lines d and &. The locus of the 
points of intersection of corresponding elements thus consists of the 
line d and a C, with cusps O,, O,. 
The polar line k of point A (6,,— 6,, 0) with respect to the conic A,, 
ut, Ha — Abe, + bz, + bez) oo 
has as equation b,(w,—àb,r,) — b,(x7,—Ab,x,) = 0 or 
be =br 
On the line A lie the points Q,, Q,, which are connected with 
the pair of points P,, P, of F, generated by A, in such a way 
that we have 
Q, = (O,P,; OF) and Q, (O,2;; O,P,). 
The fundamental involution #, is thus projected out of O, and 
out of O, in the same involutory system of points (Q,, Q,). Now 
Q, is the projection of two points P, and P,’ of C,, so it is conjugate 
to two points, Q, and Q,’, by means of /,. Therefore the pairs 
Q,, Q, form on kh an involutory correspondence (2,2). 
2. The points of C, are projected out of O, and O, by two 
pencils in correspondence (2,2); the line # is for both systems a 
branch-ray, because it is conjugate to the two cuspidal tangents 
k, and k,; the remaining branch-rays are the tangents out of O, 
and” O10 1: 
These tangents are represented by 
2b,e,* + 26,272, — Abr, — be, =, 
abe, en 2b,2° 2, => 26,0,0," EN bin — 0. 
Through the points of intersection of these two three-rays passes 
the figure, represented by 
(b°z*—b re’) + ber, (6,7x,*—b,?2,7)—},b,2,’ (0,4, —6,2,) = 0. 
It is composed of the line h, 
bri =O 
and the conic 
(b,c, + 6,a,) br — b,b, (‚rs 4+ #,°) = 0. 
The tangents 7,, 8, t, out of O, can thus be conjugated to the 
tangents 1,,8,,t, out of O, in such a way that the points of inter- 
section R=r,r,, S=s,s,, T=t,t, le with the point of intersection 
of the cuspidal tangents on a right line h. 
At the same time a new proof has been given for the well-known 
