8 



KANSAS UNIVERSITY QUARTERLY. 



is made by means of those conies. For the arrangement we refer 

 to the book of Fiedler already mentioned. 



(a). The conies K and K^ have two parallel common tangents, 

 such that the centre C is at infinity (Fig. 4). There is 



k=( 00 LAAi)=(claai), or 



the corresponding point ranges are similar with the point of simili- 

 tude in the axis. 



For the counter-points there is 



k=( OD L 00 Qi)=( OD LR 00), 



i. e., Qi and R are at infinity. The counter-axes q^ and r form 

 two coincident point-ranges of which the centre and the point at 

 infinity of the axis are the double-points. Parallel straight lines 

 have parallel corresponding lines. Such a collineation is called 

 affinity, or dilation.* 



*The word affinity is used in Mobius' " Barycentrisclier Calcul." 



