3S8 ANTIENT METAPHYSICS. Book III. 



nothing can be demonftrated of any particular material thing, all fuch 

 things being, as I have fliown *, in conftant flux, without any (lability 

 or permanency ; and therefore incapable of being the objeds of 

 fcience. 



Having mentioned mathematics^ I will conclude this book, with 

 comparing mathematical ideas with metaphyfical ; by which we ihall 

 be able to difcover more clearly the nature of both fciences, and what 

 rank each af them ought to hold among the fubjeds of human know- 

 ledge. 



Of both, the archetype is Nature^ the original of all our ideas ; for> 

 of this book, all arts and fciences are only a tranfcript. But the dif- 

 ference is, that the mathematician takes his ideas from what is moft 

 obvious in nature, and ftands, as it were, in the title-page of this 

 book ; whereas metaphyfics go very much deeper into it, inquiring 

 into the caufes of things, confidering thofe general principles from 

 which every thing lefs general proceeds ; and, by thefe fteps, afcend- 

 ing even to that univerfal principle from which all things in the uni- 

 verfe are produced : While the fcience of mathematics takes its 

 fubjeiSls from the productions, not the principles of nature, being con- 

 verfant with the properties of the material and vifible world, and thofe 

 properties of it which, by their nature, are moft fimple and determi- 

 nate, being perfe(31y feparate and diftindt one fr6m another ; and not 

 mixing with, or running into one another, like other things ia na- 

 ture ; therefore eafy to be comprehended in an exa^ and precife defi- 

 nition*. 



The firft of this kind is number, defined by Euclid to be a multitude 

 of monads. Now, a monad is the fimpleft, that is, the leaft complex 

 of all ideas ; fcr it confiders the thing, without any quality or acci- 

 dent, even of time or ^lace^ and only as exifting, and as feparate and 



diflinft 



? Page 325V 



