( 210 ) 
If the 15 “points in three lines” and the 45 “planes through 
two lines” are considered as parts of the configuration, we then 
find that each of the points lies in three lines, in fifteen planes and 
in seven spaces, each of the lines 
lies in six planes and in three spaces 
and each of the planes lies in three 
spaces, whilst reversely each of 
the lines passes through three 
points, each of the planes passes 
through five points and through 
Fig. 3. two lines, each of the spaces passes 
through seven points, through three lines and through nine planes. 
This all is given summarily in the symbol 
Of (16, 3, 15/7.) 502 55%6,3 | 5,2, 45) 3° | 7/329, 165), 
by which we represent the configuration extended in this way. 
For clearness’ sake we assemble in fig. 3 the elements of the 
configuration lying in the space (aj 2); the nine lines not lying in 
it are represented by their points of intersection. 
3. The fifteen found lines are written as follows in the form of 
a determinant which with respect to a diagonal, here the diagonal 
of the missing elements, is symmetric 
dy ag dz da a, 
LN GE LMES 
bi ba bs bs as 
po ee he 
Ci Ca cs | bs a, 
ee ENEN ERE | 
dy dy C3 bs as 
a dy Ca ba da 
ey d, Cy dy ay 
and the following laws are proved: 
