( 190 ) 



By comparing the square of the second of these equations with 

 the product of the two others, we find back the condition : 



(day _ 



2 dra 

 — a 



3 dx* 



If we put a = A -\- 2Bx -(- C^' 8 » m which A = a lt B = a Xi — a^ 

 and C= a x -\- a, — 2« ]S) this equation leads to : 



Br — AC 



(B + c*y + 



■1 







or 



B+C*= + [/**=+£. 



The positive sign before the radical sign is required by the condition 



da 

 that — must be positive. If x is to be real, a x a 2 must be >>«i 3 8 , 

 dx 



and the condition that x lies between and 1 is indicated by the 



construction of fig. 33. Let 00' be the #-axis, and let PQ be 



Fig. 33. 



drawn at the height of \/ — — . Let us then take OR=a li — a A 



and 0'S=a s — a lt , then the point of intersection of RS and 



