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sects the curve mentioned in the four points, in which / is touched 
by surfaces a°, and-in the 12 points, in which the plane V is 
touched by surfaces a’. 
The planes zr, in which the curves c° lie which belong to 
the points of the line /, envelop a developable surface of class five, 
These planes are the tangent planes in the points P of the straight 
line / at the surfaces a° passing through these points. Four of these 
tangent planes pass through /, because / touches at four surfaces a“; 
through an arbitrary point of / pass therefore altogether five of 
these planes. 
Through an arbitrary point of one of the above mentioned curves 
o° and 9° pass therefore five planes 2, consequently five curves c’. - 
These curves are therefore 5-fold curves of the surface 4. A surface 
I now intersects the surface A along these fivefold curves and 
along the curve c° lying on 11°, consequently, together, along a 
curve of order 5 X 9 45 X16H5==130; the order of A is 
therefore 26. . 
Any point of A belongs evidently to a group of S*, of which 
one of the points lies on the line /. A second line m, intersects the 
surface A in 26 points. There are consequently 26 groups of S*, of 
which two points lie on two given straight lines. 
§ 9. A plane V intersects the surface 4°° along a curve c°° of 
order 26. Any point of this curve belongs to a group, of which 
cne of the points lies on the line /; the other points of these groups 
form a curve 2, the order of which we shall determine. 
To this end we try to find the intersections of this curve 4 with 
the plane |. They are the following: 
1. The straight line / intersects the plane V in a point P. 
The curve c’, belonging to this point P, has a node in P, and 
further intersects the plane VV in three points that lie on the curve 
c*°. The line connecting one of these points with the point P con- 
tains two points of the curve 7, which points lie in the plane V; 
so 6 intersections of 2 with the plane V are found. 
2. If a point Q describes the plane WV, two coincidences of S* 
will’ lie in Q; the remaining points belonging to these coincidences, 
describe, as appeared in § 5, a surface of order 21; it is intersected 
in 21 points by the line / The coincidences belonging to one of 
these intersections, are evidently points of the curve c*", which have 
coincided with one of the associated points of the curve 4. In this 
way 21 intersections of the curve 4 with the plane V are found. 
3. The plane J” intersects the base-curve og’ in 9 points Q. 
