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Turorem I. — The M;-20f L situated in the Sp, passing through 
a fixed Spy generate a variety yet of r—1 dimensions and of 
order n + 1. 
Let d be a linear space Sp,—s, Each Sp,—; passing through d 
contains a J/;~». Space d belongs to the variety generated by these 
M;"», for » =1. We deduce from it the above theorem. 
f n r . 
Tueorem I]. — A Vo of the system K’ contains generally but 
n ? r a os oye 
one My» of L. Let us suppose a V;_, of K’ containing two My» 
of Z and let us denote by «, 8 the Sp, containing these two Ms. 
The M5 > of which the Sp,—; pass through the Sp,—2 common to « 
, yn-+l ° 3 
and 2 generate a Vet! on which the points common to a, 8 and to 
the two Mf-2 are multiple of order two. 
From this ensues that through a point of the Sp, > common to 
a, B generally no M'_» of ZL will pass of which the Sp, would 
pass through this Sp‚—s, which is contrary to the hypothesis y= 1; 
hence the theorem. 
ConcLusion : We see that 
1. An Sp, contains a single M;» of L, thus to an Sp 
corresponds a single V;. of A’. 
9. A Vi. of K' contains a single M‚ > of L, thus to a 
Vs of K' corresponds a single Sp. 
Hence: 
A oe”-complex of M ;-_ with characteristics u=1, »v—=1 ss the 
intersection of the elements of two varieties in birational correspond- 
ence; one of these varieties is composed of the Sp, of the space, the 
other is a homaloid system of Vi, r=times infinite. 
Liege, Oct. 1908. 
