438. ANTIENT METAPHYSICS. Book V. 



there are many, I believe, excellent geometers that never dreamed of 

 this imperfection of their fcience ; nor do I know any one in modern 

 times who has handled this matter with any accuracy, except Dr Bar- 

 row in his mathematical le(Sl:ures, who, befides being a great geome- 

 ter, was very learned in the Greek philofophy, as he has clearly fhown 

 in thofe lectures, of which I have made fome ufe in this chapter. 



In the firfl: place, if the fubje6: of any fcience is not proved to have 

 A real exiftence, that is, to be fomething in rerum natura^ and not to 

 exift merely in notion or idea, that fcience muft be altogether hypo- 

 thetical, and rather an ideal than a real fcience. Now magnitude, 

 which is the fubjed of geometry, Euclid has not only not proved to 

 have a real exiftence, but has not fo much as defined it, leaving it to 

 common fenfe to find out what it is, and alfo to be fatisfied as to its 

 reality. 



Furthermore, the fcience of geometry is founded upon definTtTons, 

 poftulates, and axioms, which accordingly Euclid has premifed to his 

 demonftrations. Now, I will (how that definitions and poftulates are 

 no more than fuppofitions, and that axioms are only propofitiona 

 founded upon thefe fuppofitions. 



Definition^ 'as Ariftotle tells us, is not a propofttion ; becaufe it af- 

 firms or denies nothing *. Neither is it the fignification of a word, ex- 

 plained by other words better known ; for, if that were the cafe, our 

 common didionaries would, under every word they explain, give u& 

 fo many definitions. But a definition ' is the unfolding or develope- 

 ' ment of a complex idea, into the feveral ideas of which it is compo- 

 ' fed j' which compofition is indeed commonly marked by one word, 



thou|;h, 



* Arift, de Interpretatlone. cap. 5^ 



