The Imaginary in Geometry 51 



and a horizontal projection of an element of 



x 2 -f y- = b-, 



the two elements from the auxiliary circles being collinear with 

 the origin so that if (.\\, y\) is from the first circle while 

 (x. 2 , 3',) is from the second, then 



5>i 



The elements divide into two sets, viz : Those which are deter- 

 mined by radial elements of the circles as shown in fig. 46, A, B, 

 P, Q et al. Those which are determined by non-radial elements 

 of the circles as shown by the P's, other than P 3 and P 8 , in fig. 47. 



The determination of P e , P s , P by their end points is shown. 



v 



