Chap.vrrr. antient metaphysics. 447 



could be numbered^ as there would be nothing, in the other cafe, that 

 could be meaj'ured. 



It may be further obferved on this head, that, upon the fuppofition 

 of no material world exifting, not only thofe faiences of geometry and 

 arithmetic would have been merely notional, but they never could 

 have exifted ; for it is from the material world that both the geometer 

 and arithmetician take their ideas of magnitudes and numbers. 



As to Arithmetic, Euclid, in his book upon arithmetic, has defined 

 well enough, for his purpofe, the monads which is the principle of 

 number. He has faid it is that by which every thing is faid to be 

 one ; for it was not his bufinefs, as an arithmetician or geometer, to 

 enter into a metaphyfical difquifition concerning the one-t and to fhow 

 that it is neceflarily connected with exiflence ; and that the ens and the 

 ununiy as the fchoolmen fpeak, are truly one and the fame thing. But 

 he has not been fo fortunate in his definition of number^ which, he 

 fays, is a multitude compofed of monads *; by which he has plainly 

 confounded two ideas, which are not only dlftin£t, but, in fome fort, 

 oppofite ; for multitude^ as well as number^ confifts oi monads ^ that is, 

 of feparate and detached things, not of one continued body. And, 

 accordingly, the barbarous nations, when their arithmetic fails them, 

 and they want to denote multitude that they cannot number, they 

 point not to the earth or fea, but to the hairs of their head, which are 

 feparated and detached one from another. Euclid, therefore, ought 

 to have defined number, as Ariftotle does, to be * multitude defined 

 *or limited t.' 



But, 



* Ex. ftoixtuy c-v/KifiLtivav ■^X^Seg. 2cl defin. lib. 2. 



f n^jiJef iriTTu^xs-ixiyovy and TrXnSoi he defines to be ro oKet^inv tvyc({.t'.t ti{ fiii p'4"'«;tH| that 

 is, monads. Metaph. lib. 5. cap. 13. 



