( 2097) 
ar | by bg by Cy ez dy || bj | ag ag ay Cg C3 da || cy | a, ag as bj bg ay 
as | bi bg by cy ¢g dy || ba | a ag ay cy ¢3 dy | Cg | ar ag as bj be ey 
ag | bi ba ba ci cq & || bg | a ag ag Cy Cg @ || dy | ag ag ag ba dg Ca 
ag, bi by bs dy dy € ba a, dg ag dy dy € dy a, ay As by by Cj 
A5 | Ci Ca ¢g dy dg e || ej | dg az as bg bz dy || ej | ag ag as bg ba Cy 
From this it is easy to deduce that the fifteen lines are situated 
six by six in ten spaces of which four pass through each line, 
according to the following table: 
aj ay | bg by cg ei az a4 | by bg cg ey 
aj a3 | ba by ea ay ay as | b ea di dy 
aj aa | ba bg e, do ag as | bg a dy da 
ag as | bj by ci da dz as | bg cy Ca ey 
ag a4 | by bg ez dy ay as | by dy dy ei 
As follows from the first table each of these sextuples of right 
lines consists of two triplets of generatrices of the two systems of 
rays lying on the same quadratic surface. 
With this the configuration of SEGRE is found back analytically. 
We now point to another particularity which will soon be of 
service. Out of the first table follows that the fifteen triplets 
ai ba ez, ag bj C3, as By ea, ay 0) dg, a5 Cy dy, 
a, bg Ca, ag bs Ce}, As Dz C1, ay bg ds, a5 Cy dy, 
a, by dg, az by dis ay by ej» aa bg @5 Gs Cg & 
consist of three lines intersecting each other two by two. The 
question whether the three lines of a triplet le in a same plane, 
pass through a same point or show both particularities of situation 
is analytically easy to answer. We immediately find that the lines 
of a triplet always pass through a same point but never lie in a 
same plane. So we find fifteen new points connected with the 
configuration and in accordance with this fifteen “spaces through 
three lines.” 
