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all conics of the net |v*| pass through this point. The involution 
mentioned becomes then parabolic and the two double points coincide 
in the point Bz. 
§ 2. From this it ensues that any straight line ¢, passing through 
a point A; is tangent of a curve @*, which has a point of inflexion 
in By. These straight lines ¢ connect the point Bj with the vertices 
of the cones of the net; as they le on the curve 0°, those straight 
lines form therefore a cone of order six. 
Let now the order be required of the surface «, formed by the 
points of inflexion of the curves 9%. This surface has multiple points 
in the points B}; the tangents in such a point are the tangents of 
the curves e*, which have a point of inflexion im this base-point ; 
so they form a cone of order six, so that the points Bj are seatuple 
points of the surface «. A g* intersects this surface, besides in the 
points Br, moreover in its 16 points of inflexion; so it is to be 
seen that this surface is of order sixteen. 
Through an arbitrary point P of a straight line / pass + cones 
of the net, which cut / moreover in 4 other points P’. The corre- 
spondence (4, 4) of the points P and P’ has eight coincidences, 
consequently there are ezght cones that touch /, therefore also eight 
planes zr, passing through /. 
The stationary planes envelop therefore a surface of the eighth class. 
§ 3. In the base-point B, the osculating plane may be laid to 
each of the curves 9%; this plane intersects the curve once more in 
a point 7, which we shall call the tangential point of B,. These 
points 7’ form a surface rt, of which we shall determine the order. 
If the curve of has a point of inflexion in B,, the point 7” will 
coincide with 5. The surface + consequently passes through B, and 
the tangents in this point are the tangents of the curves e*, which 
have a point of inflexion in 5,; B, is therefore a sertuple point of r. 
A straight line / passing through B, intersects r in the first place 
in this point. Let 7’ be one of the other intersections. The curve 
* passing through this point 7’ has / as bisecant; it is base-curve 
of a pencil (®*). The surface ®* from it, passing through a point 
of /, has / as generatrix. Now there is only one ®* in the net [*| 
for which this is the case, viz. the surface determined by two points 
of /; consequently @* must in any case lie on this D°. 
All curves g* lying on one and the same #& touch in B, the 
plane of contact V of ®? in B. They intersect V moreover each 
in two points, lying on the two generatrices of ®*, which pass 
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