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remaining lines however is to be indicated by an a with two indices 
derived from those two of the original quintuple which does not 
cut it. Then the ten lines 
become 
Qin 9 G95 5» G35 9 G45 9 Fu » G94 9 G34 2 413 9 G3 2» Qs 
If moreover we add to each of the lines of the original quintuple 
the index 6 and if we allow az to be written ars, then the previous 
determinant passes after a quarter of rotation into the entirely 
regular form: 
A 43 M4 a5 a6 
da, | | 423 Ag, das dag 
a3) 439 | O34 EE 436 
re 
dar | bag 443 M45 A456 
Os) | as9 | 53 M54 | 456 
a | 
der dez | 463 des M65 
Ren 
In this entirely regular notation two different lines a cross or 
intersect each other according to their having an index in common 
or not. In the first place we of course think here of the fifteen 
lines of the three-dimensional space which are left when from the 
27 right lines of a cubic surface a double six is set aside; for, these 
lines behave in regard to the crossing and cutting in quite the 
same way with corresponding notation. However, we must not lose 
sight of the fact, that in the configuration three lines cutting each 
other two by two pass through a point without lying in a plane, 
whilst with an arbitrary surface of order three they lie in a plane 
without passing through a point. If however we polarize the surface 
of order three to a surface of class three, for instance with respect 
to a sphere lying in the same space, then the 27 right lines, bearers 
of points and of double tangent planes, pass into 27 right lines, 
