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1 Cf. 3.14.
2 e.g. Empedocles, Fr. 62 (Diels).
5 For the probable connection between the Atomists and the Eleatics see E.G.P. 173, 175, and cf. De Gen. et Corr. 324b 35-325a 32.
6 i.e., of the atoms.
7 Cf. R.P. 194.
8 These letters will convey Aristotle's point better to the English reader, but see critical note.
9 Aristotle seems to have regarded Pythagoras as a legendary person.
10 Pythagoras himself (fl. 532 B.C.) is said by Aristoxenus (ap. Stobaeus 1.20.1) to have been the first to make a theoretical study of arithmetic.
12 Apparently (cf. infra, Aristot. Met. 1.17） they identified these not only with properties of number but with numbers themselves. Thus justice (properly=squareness)=4, the first square number; soul or mind=1, opportunity=7 (Alexander).
13 Pythagoras himself is credited with having discovered the ratios of the octave (2 : 1), the fifth (3 : 2) and the fourth (4 : 3). Burnet, E.G.P. 51.
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