and lies upon 



T hile 



The Imaginary in Geometry 



r=i, 



31 



-(-i' + ^^^W+^o) 



and lies upon 



In the particular example 



x 2 + y 2 = (i — i) 2 

 these, so to speak, companions to the supplementary curve are 



and 

 »". e., 



Fig. 2 



1 The vector P= (jt, y) is normal to the first companion curve. 

 Cauchy's corresponding vector is tangent to the same and is terminated by 

 the asymptotes. 



31 



