Note 794 — Chapter VII · THE PYTHAGOREANS

We learn from Plato, Theaet. 148 b 1, that Theaitetos called surds, what Euclid calls δυνάμει σύμμετρα, by the name of δυνάμεις, while rational square roots were called μήκη. Now in Tim. 31 c 4 we find a division of numbers into ὄγκοι and δυνάμεις, which seem to mean rational and irrational quantities. Cf. also the use of ὄγκοι in Parm. 164 d. Zeno in his fourth argument about motion, which, we shall see (§ 163), was directed against the Pythagoreans, used ὄγκοι for points. Aetios, i. 3, 19 (R. P. 76 b), says that Ekphantos of Syracuse was the first of the Pythagoreans to say that their units were corporeal. Probably, however, “Ekphantos” was a personage in a dialogue of Herakleides (Tannery, Arch. xi. pp. 263 sqq.), and Herakleides called the monads ἄναρμοι ὄγκοι (Galen, Hist. Phil. 18; Dox. p. 610).