448 ANTIENT METAPHYSICS. Book V. 



But, if Euclid has been unfortunate in this definition, he has been 

 remarkably fortunate in his definitions of the feveral kinds of numbers, 

 and their feveral properties and affedions, which are exprefled with a 

 clearnefs, and a brevity at the fame time, that are really wonderful. 

 Of this kind, particularly, is his definition of proportion in numbers, 

 which is as fliortly exprefTed as his definition of proportion in magLii- 

 tudes prefixed to his fifth book, but much more clearly. 



Ariftotle has obferved *, that the point, as well as the monad, is- 

 indivifible ; but the difference betwixt them is, that the monad is not 

 only indivifible, but it has no fite or pofition ; whereas the point has sn 

 fite. And, indeed, the monad is one of the moft abftra£l ideas that 

 we have ; for it feparates from the thing every affedlion or quality ex- 

 cept exiftence and unity ; which, with refped: to fingle things, arc 

 truly the fame ; for we never have the idea of a fingle thing, but we 

 confidcr it as one. And, accordingly, in common language, we fay 

 oneftngle thing. 



As to the compofitlon o^ monads, or number, befides being multitude 

 defned, it has order ; for it has not only a regular progreffum up- 

 wards, but in all its compofitions by multiplication, and in its ratios^, 

 that is, the relation of one number to another, there is a wonderful 

 regularity, very little known to our modern mathematicians, but which 

 was very much fludied by the antients, as is evident from the treatife. 

 upon arithmetic of Nicomachus, a Pythagorean philolopher of later 

 times. 



And here we may obferve the reafon why the Pythagoreans made 

 number the fymbol of immaterial and divine things ; for, befides that 

 they are the mod abftracSt of all ideas derived from fenfible objeds, 

 being divefted of all the common properties of material ihings, even 

 time and place, they have order and proceffion, luch as the Pythago- 

 reans 

 • Metaph. lib. 5- cap- 6. 



