CHAP. XII.] METHODS IN SECONDARY PROPOSITIONS. 181 



It is evident that these interpretations are strictly equivalent 

 to the former one. 



Let us ascertain, in the form of a conditional proposition, the 

 consequences which flow from the hypothesis, that " Fabius will 

 perish in the sea." 



In the equation (2), which expresses the result of the elimi- 

 nation of v from the original equation, we must seek to determine 

 a: as a function of y. 



We have 



# = - = Oy + -(l-2/)on expansion, 

 or, N 



*=o(i-3/); 



the interpretation of which is, If Fabius shall die in the sea, he 

 was not born at the rising of the dog star. 



These examples serve in some measure to illustrate the con- 

 nexion which has been established in the previous sections be- 

 tween primary and secondary propositions, a connexion of which 

 the two distinguishing features are identity of process and analogy 

 of interpretation. 



6. Ex. 2. There is a remarkable argument in the second 

 book of the Republic of Plato, the design of which is to prove 

 the immutability of the Divine Nature. It is a very fine example 

 both of the careful induction from familiar instances by which 

 Plato arrives at general principles, and of the clear and connected 

 logic by which he deduces from them the particular inferences 

 which it is his object to establish. The argument is contained 

 in the following dialogue : 



" Must not that which departs from its proper form be 

 changed either by itself or by another thing ? Necessarily so. 

 Are not things which are in the best state least changed and dis- 

 turbed, as the body by meats and drinks, and labours, and every 

 species of plant by heats and winds, and such like affections ? Is 

 not the healthiest and strongest the least changed ? Assuredly. 

 And does not any trouble from without least disturb and change 

 that soul which is strongest and wisest ? And as to all made 

 vessels, and furnitures, and garments, according to the same 



