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which bear at the same time the points of intersection of the nodal 
tangents 
Se. and ws Bee 
The remaining points of intersection of the two fourrays lie on 
the conic 
Gt, = & — (a,%a,? + ¢’) 2,7 = 0 
This is immediately ae if we eliminate out of the equations 
(aren Ne —a;72,°) = 9, 
(a?o, — Pa) (c,* —4,7z,7) = 0 
the quantity «,* 
The coincidences on /, and 4, here also originate from the tangents 
out of H, and H,. Indeed we find for the polar curves of H, and H, 
awe,’ — aw, t°) + a,(2,72, — a,°4,2,") = 0, 
or 
(are, Ears =e 22,2, Nd. 
From this is evident at the same time that the conics 
PE ddr == 
generate the points of contact of ihe double oe meeting in 
A. and. A. 
By combining the equation 
7a. a, 6, 2,° == 0 
with the equation of C, we find that the eight points of contact 
of the four double tangents are situated on the conic 
21 ar = (a,7a,* + &) a,’ 
7. The curve of Hess is represented by 
(a,?2,7+ a,?x,”) eer, ie ee Za De. ve — (a,72,7+4,7u,7)} 
+ (a,2a,?— 2c?) (a,7#,?+-a,°2,7) x," (SUR ea 
If we eliminate w,*v,° out of en equation and the equation of C,, 
“a7 — (a,72,7 + 0e) ez, Hea, = 0, 
it is evident that the points which the two curves have in common 
besides 0, and Q, are situated on the conic 
(da daj dee. 
The eight points of injleaion of a C, with two bifleenodal points are 
points of intersection with a conic. 
They lie two by two on four right lines through the point of 
intersection OV, of the four double tangents of the first group. 
The polarcurve 7, of the Ee (y) is represented by 
(yey EY, )eyety—Y ay 2ey? Harte stad ag) + ery, =O. 
