6 THE THEORY OP ROLLING CURVES. 



He employs the same method of finding the one curve from the other 

 which is used here, and he attributes it to Euler (see the Acta Petropolitana, 

 Vol. v.). 



Thus, nearly all the simple cases have been treated of by different authors; 

 but the subject is still far from being exhausted, for the equations have been 

 applied to very few curves, and we may easily obtain new and elegant proper- 

 ties from any curve we please. 



Almost all the more notable curves may be thus linked together in a great 

 variety of ways, so that there are scarcely two curves, however dissimilar, 

 between which we cannot form a chain of connected curves. 



This will appear in the list of examples given at the end of this paper. 



Let there be a curve KAS, whose pole is at C. 



