emch: projective groups. 



Taking a ray s through the centre C, its corresponding ray s^ is 

 coincident with s and intersects the counter-axes q^ and 

 r in the two counter-points Q^ and R of the ray (German 

 "Gegenpunkte").* Since C and L, L being the intersection-point 

 of s with 1, correspond to themselves the following relation 

 between these points and two pairs of corresponding points A, A^, 

 and B, B^, on the ray s exists: (See Fig. 2.) 



(CLAB) = (CLAiBi), or 

 CA . CB ^CA^ . CB^ 

 LA ■ LB ~" LAI ■ LB^ 

 CA . CAi^CB . CBi 

 LA " ■ " 



or 



1. e. 



LAI LB LBi 

 (CLAAi)^(CLBBi) 

 Substituting for the pair B, B^ the pair Q, Qi, or R, R^ this 

 last projectivity becomes: 



(CLAAi)=(CLQQi)==(CLRRi), or 



(CLAAM=(CL ooQi)=(CLR 00), or 



CA . CAi_CQi . CR_ 



LA ■ LA"! ~'LQ'i ■ LR' 



=const. 



*We avail ourselves of the designation of Fiedler in his " Darstellende Geometrie," 

 I. Band, and for the following classification especially refer to §22, page 95, of this 

 book. 



