CHAP. XII.] METHODS IN SECONDARY PROPOSITIONS. 183 



*3f* + *0-y)(l-*) = 0, (1) 



sz = 0, (2) 



* - 1, (3) 



y (i-0 = o, (4) 



wt = 0, (5) 



w =1. (6) 



Retaining x 9 I shall eliminate in succession z 9 s, y, t, and w (this 

 being the order in which those symbols occur in the above sys- 

 tem), and interpret the successive results. 

 Eliminating z from (1) and (2), we get 



M (l-y)-0. (7) 



Eliminating s from (3) and (7), 



*(l-y)-0. (8) 



Eliminating y from (4) and (8), 



*(1-0-0. (9) 



Eliminating t from (5) and (9), 



xw = 0. (10) 



Eliminating w from (6) and (10), 



x = 0. (11) 



These equations, beginning with (8), give the following 

 results : 



From (8) we have x = - y 9 therefore, If the Deity suffers 

 change. He is changed by Himself. 



From (9), x = t 9 If the Deity suffers change 9 He is changed 

 to a worse state. 



From (10), x = - (1 - w). If the Deity suffers change, He 



does not act willingly. 



From (11), The Deity does not suffer change . This is Plato's 

 result. 



Now I have before remarked, that the order of elimination 

 is indifferent. Let us in the present case seek to verify this fact 

 by eliminating the same symbols in a reverse order, beginning 

 with w. The resulting equations are, 



