446 ANTIENT METAPHYSICS. Book V. 



thence follow that thofe animals do a£lually exifl:. Nor, indeed, are 

 Euclid's definitions, properly fpeaking, definitions, except upon the 

 fuppofition of the exiftence of the things defined ; for, otherwife, they 

 are not definitions of things^ but explanations of ivords^ becaafe 

 a definition exprefles the nature and eifence of the thing defined ; 

 and, therefore, of a non-entity, or nothings there can be no definition. 

 But I may give a name to a thing that has no exigence, luch as a 

 Hippocentaur, or a Chimaera, and 1 may explain what notion or idea 

 I affix to the word *. It is evident, therefore, that, upon the fuppofi- 

 tion of a material world not exiting, Euclid's fcience is merely no- 

 tional and nominal, without any foundation in the nature of things : 

 So that it is neceilary, in order to eftablifh the reality ot geometry and 

 other fciences, to prove the exiftence of a material world. This I have, 

 endeavoured to do in a preceeding chapter ; .and, if I have fucceeded, 

 the confcquence is, that magnitude^ the fubjedt ot geometry, is not a 

 mere notion, but a thing actually exifting ; and fo is, likewife, inag- 

 mtude limit edy ox figure. For, though, perhaps, there is not to be 

 found a perfed geometrical figure, yet they all exift in the way that 

 Michael Angelo faid the ftatue exifted in the block of marble, 

 « which,' fays he, * the ftatuary does no more than produce, by taking 

 ' away what is fuperfluous.' 



Arithmetic, too, w^ould be merely a notional fcience, if there were 

 no material world exifting j for then there would be nothing that 



could 



* This (lifl:in£lion betwixt the definition of a thing, and the explanation of a name, 

 is dated by Ariftotle, in his La(l Analytics^ lib. 2. cap. 7. and is explaineil, at preat 

 length, by Philoponus and Eullratlus, in their commentaries upon the pailage, where 

 they have fliown, that wc n.ay give a defcription of the notion we exprt-fs by any 

 word which will be fuflicient for making our meaning underflood, but will not be a 

 definition of the thing. For example, when I fpeak of a man, I may fay that I de- 

 note by that word an animal that walks eredt, looks up, and fpt-aks. This will fuffi- 

 ciently explain what animal I mean, but it is far from the definition ot a man. 



