( 7r,fi ) 



containing the points 0^, 0^, 0^ and touching the planes «,, «,, «^ 

 is represented by 



-fiV \2v' — 3i;' (,« + 9) + r (3ft' + 2fto + So'') — 2 (,i» + 9»)), 



which in connection with the law of duality can be deduced to 

 1 . , 



(X Q 



Sftr' + 3fiV + }ivQ — 2ii'\ , 



Out of the wellknowri results (H. Schubert, "Kalkül der abzahlendcn 

 Geometrie", Leipzig, Teubner, J 879) 



^i^v'q" = 104, h'v'q' = 68, (i'vQ* = 42, ii'vq' — 34, (.i'q' = 17 

 we find that there are live quadratic surfaces satisfying the given 

 conditions. 



However it is now easy to see, that only one of those five 

 solutions furnishes four hyperboloidic lines /„ /,, /j, /, crossing each 

 other. We find namely four solutions not to be used for our purpose 

 (fig. 5) if we determine I,, /,, l^ in such a way so as to cut the given 



Fig. ti 



