66 



As through an arbitrary point /-• of F^ there pass 2 more planes 

 of symmetr3^ i^for the conic of the double lines of {k^)^ defined by 

 y' and (P), sends two of them Ihrongh /*), we find also in this 

 way, that the planes of symmetry in consideration envelop a 

 developable snrface of the sixth class with V^ as a 4-fold tangent 

 plane. 



^ 16. In order to find the planes of symmetry through seven 

 given points, we consider a group of six and a group of five of 

 these points that have 4 points in common. The corresponding 

 surfaces have 3 . 6 = 18 tangent planes m common. If we subtract 

 from them 2.4 = 8 times V^ and further 6 planes through the 

 centre of the sphere through the 4 common points, it appears 

 again that : 



through seven given points there pass 4 quadratic surfaces of 

 revolution. 



(Cf. §§ 7 and 8). 



