Chap. VII. ANTIENT METAPHYSICS. 77 



nature of the fubjeds that we join together in propofitions : For 

 unlefs we know with the greateft accuracy the meaning of the words 

 that we employ to exprefs our ideas, it is impoflible that we can 

 demonftrate. And here we return again to the doQrine of ideas, 

 and the divifion of them into genus and fpecies, fubftance and ac- 

 cident ; one of which two divifions muft be expreffed in the defini- 

 tion, according to the nature of the fubjed. 



And here it is to be obferved, that a fingle predicate or fubjeft of a 

 propofition may be expreffed by feveral words. Of this the firft Ax- 

 iom of EucHd, and which one may think fhould be a very fimple 

 propofition, That things, ivhich are equal to the fame thing, are equal 

 to one another, may furnifh us an example. For there the equality 

 of things to one another, is predicated of things equal to the fame 

 thing : Where both the predicate and the fubjed are ideas com- 

 pounded of fevera! ideas, and expreffed by feveral words*. 



Thus it appears, that definitions, as well as axioms, are neceffary 

 for fcience ; and, therefore, Euclid has prefixed to his Syftem of 

 Geometry, both definitions and axioms. 



And here I would advife a man, who defires to learn the art of 

 reafoning, to ftudy the Elements of Euclid, before he applies to the 

 Logic of Ariftotle : For in Euclid he will readily perceive the pro^ 

 grels of the mind from propofitions felf- evident to propofitions 

 that need to be demonftrated ; and this upon fubjeds the moft fimr 

 pie of any that are the fubjed of fcience and the lead removed 

 from the perceptions of fenfe, being lines and figures, which are re- 

 prefented to the fight, not like other fubjeds of fcience to be com- 

 prehended only by intelled. The method Euclid follows in his de- 

 monftrations is called the Synthetic Method, by which he proceeds 

 from felf-evident propofitions, or propofitions before demonftrated, 



to 



• Vol. I. p. 391. and following. 



