[249]. For these stories and a criticism of them, see Max C. P. Schmidt, Kulturhistorische Beiträge, i. pp. 78 sqq. The smith’s hammers belong to the region of Märchen, and it is not true either that the notes would be determined by the weight of the hammers, or that, if they were, the weights hung to equal strings would produce the notes. These inaccuracies were pointed out by Montucla (Martin, Études sur le Timée, i. p. 391).
[250]. Arist. Met. Μ, 4. 1078 b 21 (R. P. 78); Zeller, p. 390, n. 2. The Theologumena Arithmetica, wrongly attributed to Nikomachos of Gerasa, is full of fanciful doctrine on this subject (R. P. 78 a). Alexander in Met. p. 38, 8, gives a few definitions which may be old (R. P. 78 c).
[251]. Arist. Phys. Δ, 6. 213 b 22 (R. P. 75).
[252]. Diog. ix. 19 (R. P. 103 c). It is true that Diogenes is here drawing from a biographical rather than a doxographical source (Dox. p. 168), but this touch can hardly be an invention.
[253]. Arist. Met. Μ, 3. 1091 a 13 (R. P. 74).
[254]. Arist. Phys. Δ, 6. 213 b 23 (R. P. 75 a). The words διορίζει τὰς φύσεις have caused unnecessary difficulty, because they have been supposed to attribute the function of limiting to the ἄπειρον. Aristotle makes it quite clear that his meaning is that stated in the text. Cf. especially the words χωρισμοῦ τινος τῶν ἐφεξῆς καὶ διορίσεως. The term διωρισμένον is the proper antithesis to συνεχές. In his work on the Pythagorean philosophy, Aristotle used instead the phrase διορίζει τὰς χώρας (Stob. i. p. 156, 8; R. P. 75), which is also quite intelligible if we remember what the Pythagoreans meant by χώρα (cf. p. 115, [n. 240]).
[255]. Cf. Arist. Phys. Δ, 6. 213 a 27, οἱ δ’ ἄνθρωποι ... φασὶν ἐν ᾦ ὅλως μηδέν ἐστι, τοῦτ’ εἶναι κενόν, διὸ τὸ πλῆρες ἀέρος κενὸν εἶναι; de Part. An. Β, 10. 656 b 15, τὸ γὰρ κενὸν καλούμενον ἀέρος πλῆρές ἐστι; de An. Β, 10 419 b 34, δοκεῖ γὰρ εἶναι κενὸν ὁ ἀήρ.
[256]. Arist. Met. Α, 3. 984 a 7 (R. P. 56 c).
[258]. Arist. Met. Α, 5. 986 a 25 (R. P. 66).