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4. The conics resting on seven right lines evidently form a 
surface of order 92. Each transversal of four of those right lines 
being completed to a conic by each right line cutting it and the 
remaining three given lines, this surface certainly contains 140 right 
lines. 
The locus of the conics through P, meeting five right lines /, is 
according to S 2 a surface of order 18. 
Each one of those right lines is a quadruple line, because according 
to § 1 four conics of the system can be made to pass through each 
point lying on it. 
Each line of intersection of two of the lines 4 through P is a 
double line, it being completed to conics of the system by two 
transversals of the remaining three right lines /; so there are ten 
double lines. 
In addition to the 20 indicated single right lines of the surface 
there are 20 more, originating from the pairs of lines of which one 
right line intersects four lines /, the other passing through P and 
meeting the fifth line 4. 
The section of the surface with the plane (Pl) contains the qua- 
druple right line /,, four of the double lines, two single right lines 
drawn through P and finally the conic through P and the traces of 
the remaining four lines /; this has to be counted double, as it cuts 
the lines 2, twice; in this way we also find that the surface is of 
order 18. 
By considering a right line of the pencil of rays Pl, we can 
easily understand that P is a twelvefold point. 
On the biquadratie surface of the conics through P, and P, and 
resting on four given lines, P, and P, are triple points whilst P Ps 
is a double line. 
5. The number of conics in the planes passing through a given right 
line a and cutting six given lines J, is easily found by regarding 
L.ly,l; as resting on a. In each of the planes (al,), (alg), (als) a 
proper conic must necessarily lie and each of these conies is then 
to be accounted for twice, as it meets one of the lines 4 twice; it 
is evidently determined by the traces of the remaining five. As 
moreover a forms with two transversals of J,,/;, 45 conics satisfying 
the question, there are in general eight conics, meeting the six 
lines J and intersecting a twice. In the notation of SCHUBERT «?y® = 8. 
6. Let us finally determine the number of conics intersecting 
seven right lines whilst their planes pass through a given point M. 
