( 261 ) 
into which the system 
EN Ld == Li st 
J 
passes by means of the relation 
Pa = Pit + po te + pg ta + Pa Ta + Ps % =O 
between the coordinates x; of points and the coordinates p;, of spaces, 
can be completed by 
Ps + po =O 
and from this is evident, that each of the fifteen lines of SEGRE'’s 
configuration is represented by a triplet of equations of the form 
Pitpe=—9, pz dpa=0, ps t+ pp = 9 
and that the lines are situated six by six in ten spaces with the 
coordinates 
Nn eet, A GE ne end 
So the six lines 
(14, 25, 36), (15, 24, 36), (16, 23, 45) 
(14, 26, 35), (15, 23, 46), (16, 24,-35) 
are situated in the first of those ten spaces, etc. 
In the quoted treatise CasTELNUOVO has represented the fifteen 
planes of the dualistically opposite figure by the system of the 
fifteen corresponding triplets of equations 
a t+ ag=0, e2+%,=0, 2 +%— 0. 
Though the connection between the above-mentioned treatise and 
these considerations have already hereby been indicated, yet I desire 
to acknowledge that not until the existence of that treatise had 
been brought to my notice by Srare did I succeed in deducing 
from my considerations founded upon the double four the above- 
given simple representation. 
