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in (4, 4)-correspondence with the traces B and C' of 8° and y’ lying 
outside g as vertices. So A** is cut according to g and to a curve 
of order eight with fourfold points in B and C. 
So, the triplets of points associated to the points of one of the base 
curves lie on a surface of order sixteen, passing eight times through 
g and four times through each of the other two base curves. 
§ 9. Any point G of g also belongs to ow quadruples. If G is 
to be a point common to three cubic curves (a*b*), (67c*), (a’c*) the 
surfaces a?, 6®,c? must admit in G the same tangential plane. 
We now consider in the first place the locus * of the curve 
(a°b°), intersection of surfaces a’, 4° touching one another in G. 
Any plane p through g cuts these projective pencils (a*), (0°) accord- 
ing to two projective pencils, the vertices of which are the traces 
A and B of a’ and §* outside g. These pencils of lines generate a 
conic passing through G, the lines AG and BG determining with g 
two surfaces a®,b® touching p in G. So g is double line and G is 
threefold point of #*. 
In the same way the pencils (@*) and (c*) determine a second 
monoid y*. The monoids #* and y* have the base curve e and 
the line g to be counted four times in common; the residual inter- 
section, locus of the three points associated to G, is of order nine. 
The cubic cones touching the monoids in G intersect in g and in 
five other edges; so G is jivefold point of the curve (G)’. Any plane 
through g cuis ®* and yw‘ according to two conics passing through 
G and a point A; in each of the two other points of intersection 
three homologous rays of three projective pencils with vertices A, B, C 
concur. So g is cut, besides in G, in two more points G*, each of 
which forms with G a pair of associated points. So the pairs of 
the J* lying on g are arranged in an involutory correspondence 
(2,2), i. e. g bears four coincidencies. This proves moreover that 
g is a sevenfold line of the locus G of the curves (G)’; for in the 
first place any point G is fivefold on the corresponding (G)’ and it 
lies furthermore on two suchlike curves corresponding to other 
points of g. 
The curve (a?l?) meeting y* in a point C rests in two points G 
on g; so C lies on two curves (G)’, Le. y° is double curve of G. 
The curve (a°b?) contains the two triplets of points associated to the 
points of intersection G with g. Moreover it has in common with 
the surface G in each of these two points G seven points and two 
points in each of the eight points in which it rests on a’ and @°. 
So we find that G is of order 12. So, the points associated to the 
