emch: projective groups. 7 



The same result is also obtained by starting from the two conies 

 K and Ri which determine the collineation. Fig. 3 represents the 

 involutoric position of the conies (CADA^ )=CBEBi)=— i. 



The polars of C in regard to the conies K and K^ intersect each 

 other in S on 1. The polars of S in regard to K and K^ pass 

 therefore through T, the common point of tangency of the conies 

 with 1, and through C, i. e., they are identical. Hence the point T 

 is the intersection-point of AB^andA" (SETD)= — i. Thus, 

 designating the points of tangency of the common tangents to the 

 conies by A, A 1 and B, B^ the conies are in involutoric position, 

 if their common point of tangency with 1, T, coincides with the 



intersection-point of AB^ and A'B. 



Besides involution we have to consider those collineations which 

 result from special positions of the centre and axis of perspective 

 collineation, or what is the same, from special positions of the 

 conies K and K^. 



In the following development it would not be necessary 

 to take conies K and Ri into consideration. We shall do it 

 here in order to show how the representation of special collineations 



