200 ANTIENT METAPHYSICS. Book IV. 



I have, in a preceding Chapter *, explained in what fenfe Ariftotle, 

 and his Commentators, fpeak of Ideas by Abjlr action^ or in Abjirac- 

 tion, which laft is the expreflion Ariftotle commonly uies f. By 

 fuch expreflion, they did not denote all Ideas, as our modern pliilo- 

 Ibphers do, but only the Ideas of certain Accidents of Subitances, 

 confidered by the Mind as feparated and abftradted from the Sub- 

 ftances in which they are inherent. Of this kind are ma- 

 thematical Ideas, fuch as the Ideas of Magnitude, Figure, and 

 Number, which the Mind contemplating by themfelves, and as 

 abftradled from the Natural Subftances, of which they are Accidents, 

 has formed out of them the Sciences of Geometry and Arithmetic J. 

 And hence it is, that Mathematics are faid to be in the middle, be- 

 twixt Material Subftances, and Subftances Immaterial : For thefe, 

 both in Idea, and real exiftence, are entirely without Matter ; where- 

 as the Subjedls of Mathematics, Figures, and Numbers, do really ex- 

 ift in Matter, and are only feparated from it by our manner of con- 

 ceiving them and thinking of them. 



The procefs by which thofe Ideas are abftraded I have minutely 

 defcribed in Volume Firft ||, It is no more than an analyfis made 

 by Science, of that operation of the Human Mind. It may be com- 

 pared to the analyfis, which Ariftotle has made in his books of Ana- 

 lytics, 



• P. 75- 



t His commentators commonly fay that thofe Ideas arc J/ «^«({i5-(«f, which, I 

 think, is not fo good an expreffion, as importing that they are formed from 

 Material Obje£ls, which, I am perfuaded, Ariftotle did not believe ; but Ari- 

 Ilotle's own expreffion is, t» i» w^aijirH Afyo«i»*. Lib. 3. De Anima, cap. 8. in fine, 

 et cap, 9. 



\ See the Commentary of Simplicius, p 77. upon the eighth Chapter of Ariftotle'* 

 Third Book, De Anima, where ail this is moft accurately explained, and at great 

 length. 



II P. 1 03. et feq^. 



