Chap. VIII. ANTIENT METAPHYSICS. " 439 



though that be not at all neceflary, but only convenient for the ufe of 

 fpeech. There Is, therefore, nothing affirmed concerning the idea 

 thus developed, not even that it exifts. There is one thing, however, 

 neceflarily implied in every definition, namely, that the ideas contain- 

 ed in the definition are of fuch a nature that they may confift toge- 

 ther, or, in other words, that the aflbciation and combination of them 

 is pojjzble ; for, whatever is not in its nature inconfiftent, and contra- 

 didory, is pojfihle ; whereas, what is inconfiftent, and contradidory, is 

 impoj/ibki becaufe it cannot be conceived to exift. Thus, if I fhould 

 define any figure to be a round fqiiare^ that would be no definition, be- 

 caufe it would be a definition of what is impoffible. Every definition, 

 therefore, is an hypothefis of what is pofiible. 



Before I apply this to the definitions of Euclid, I will fay fomething 

 of the fubjeift of this fcience, viz. magnitude^ which, as I have obfer- 

 v^d, Euclid has not defined, for a reafon which will appear immedi- 

 ately, namely, that it would have carried him out of the bounds of 

 the fcience ; for magnitude belongs to the genus of quantity^ which is 

 one of the categories. But it is the bufinefs of metaphyfics to explain 

 it, being one of the great conftituent principles of the univerfe, with- 

 out which no material world could have cxifted. And accordingly 

 Ariftotle, though he had faid a great deal about it, in his categories, 

 enough, as he thought, to make it underftood as a praedicate of a pro- 

 pofition, has explained it moft accurately in his metaphyfics *. There 

 he has defcribed it to be that which is divifible into parts, each of 

 which is OK^, and fomething by itfelf. And he divides it into two fpe- 

 ciefes, the one quantity difcrete^ the other quantity conthmous. The 

 former of thefe has its parts feparated and disjoined one from another, 

 and is what we call number. The latter is that which has its parts 

 contiguous, and joined together by one common" boundary. And 



it 



* Lib. 3. cap. 1. 



