PYTHAGOREAN WRITINGS. 533 



But, fetting alide hiftorical teftimony, this is very 

 eafily demonftrable from the very nature of the cafe. 

 This proof could not poffibly have efcaped the penetra- 

 tion of fo accurate a judge of the interior pythagorean 

 philofophy, as our anonymous critic. According to 

 the teftimony of Ariftotle, Pythagoras reprefented 

 every thing by numbers, and ftrove to reprefent juftice 

 and all the other virtues, under the fimilitude of num- 

 bers. Numbers, therefore, were with him what defi- 

 nitions are with us, and ideas with Plato. It is farther 

 proved, that the Pythagoreans held all entities to be 

 impreffions of numbers, and numbers therefore to be 

 the originals of all things. The platonic ideas, and the 

 pythagoric numbers are -therefore effentially the fame, 

 and Plato can no otherwife have borrowed his ideas 

 than from the pythagorean fyftem. 



The fame thing is alfo expreflly affirmed by other 

 pythagoric fragments. Archytas of Tarentum delivers 

 himfelf thus : All things are either intellectual, or fub- 

 ject to conjecture, or fenfible. Senfible are bodies, 

 conjectural are fuch things as participate in the ideas, 

 pde'XpvIa, toqv idwv ; and intellectual the necefiary frames 

 of the ideas, as the properties of figures in geometry; 

 farther, the ideas themfelves, m uhot, avlcc * The fame 

 word alfo appears in a fragment of Ariftaaus^> 



Accordingly, there were not only two, there were 

 even, from the little that is come down to us, four 

 authors who held the ideas for a pythagoric invention. 

 I know that this conclulion may be evaded by declaring 



* Stobaeus, eclog. phyf. lib. i. p. 92. 

 f Id. ib. p c 24, 



m m 3 all 



