( 208 ) 
so the four spaces (aj ej), (ag ¢2), (az e3), (as ba) with the equations 
(ay eh dae te 9 = 0 
(Oo. 05) earns ®3 = 0 
(ag 3) + + + + ®t] HA — 3 — da + MH = 0 
(as by) eene U = U, or drs Ly, -|- ds = 0 
really pass through the line a, with the equations 
Di (f=, fo == 0, Zs == 0. 
If we complete in the same way the remaining quadruples to 
double fours out of the five lines @ according to the notation 
dj ag ag Uy a) Ag a3 as dj Ag ay, as dg Ag dy As 
by er Saya) 84, as | 
| 
| ’ 
dy dy C3 bs | 
’ ’ 
J 
bi by bs Da Cy Cg C3 by €: dy Cg by a dy Cy by 
then it is also evident that the spaces 
(a; di), (ag da), (aa c3), (a5 03) pass through ag, 
(a, ej), (ag da)» (aa Ca)» (as bo) through a 
and (ag ej), (43 di), (44 co)» (45 41) ” aj: 
We then find for the right lines dj, do, ej the equations 
dy Lg — y= a) Tg Os, Ty, == 0 
dy ove, 1 erie a dn Tg == v5 4 Lo == 0, Lj Ze 0 ’ 
ey es pte Wk 0 
by which the equations of the fifteen lines have been indicated. 
By this we are now able to point out which of the fifteen lines 
intersect each other; it is evident that each of the fifteen lines cuts 
six of the remaining fourteen according to the following table: 
