( 206 ) 
as point of unity of the homogeneous system of coordinates and by 
following for the rest the notation of fig. 2 we obtain the following 
table of proportions of coordinates of the points the knowledge of which 
is sufficient for the determination of the equations of the lines of 
the double four: 
Peas A, 4050.0 gO (0; 0; A OR 
Pr ate led RORE 0,4... (0, 0,1, 2 Oe 
B ie! 0, SOE OR... . (0,0, Ore 1, 05 
te elk 0, 1,0,0,1), este (0, Of 0, —1,1). 
So the equations of the two quadruples of lines are 
Obee idd 0 5 2,0 
Ag ee ee « Lg — Uy == F5 9 m0 9 ta = 0 
is Jo ae at's i toe tp 0 5 ==) 
Aita ee an ande da 0, Hd 
br ot Og ne eee ety ee Og eg EO 
Doneer ta 0, Md 
ba oe POG 2 eng to Og) tg = 0 
DERDE It ER 
So the equations of the spaces (a: b;), i= 1, 2,3, 4, through the 
opposite sides of the double four are 
CEN 
(aarbop nnn. a — % — Dg + 4%, + 4, = 9 
(âbent eg eee eee 0 
abd ot aarde 0 
and these four spaces have evidently the right line 
EE A) 
in common. 
