[832]. Arist. de Caelo, Β, 13. 293 b 21, ἐνίοις δὲ δοκεῖ καὶ πλείω σώματα τοιαῦτα ἐνδέχεσθαι φέρεσθαι περὶ τὸ μέσον ἡμῖν ἄδηλα διὰ τὴν ἐπιπρόσθησιν τῆς γῆς. διὸ καὶ τὰς τῆς σελήνης ἐκλείψεις πλείους ἢ τὰς τοῦ ἡλίου γίγνεσθαί φασιν· τῶν γὰρ φερομένων ἕκαστον ἀντιφράττειν αὐτήν, ἀλλ’ οὐ μόνον τὴν γῆν.
[833]. It is not expressly stated that they were Pythagoreans, but it is natural to suppose so. Such, at least, was Alexander’s opinion (Simpl. de Caelo, P. 515, 25).
[834]. The term οἱ μαθηματικοί is that used by Poseidonios for the Chaldæan astrologers (Berossos). Diels, Elementum, p. 11, n. 3. As we have seen, the Babylonians knew the planets better than the Greeks.
[835]. Arist. de Caelo, Β, 9. 290 b 12 sqq. (R. P. 82).
[836]. Alexander, in Met. p. 39, 24 (from Aristotle’s work on the Pythagoreans), τῶν γὰρ σωμάτων τῶν περὶ τὸ μέσον φερομένων ἐν ἀναλογίᾳ τὰς ἀποστάσεις ἐχόντων ... ποιούντων δὲ καὶ ψόφον ἐν τῷ κινεῖσθαι τῶν μὲν βραδυτέρων βαρύν, τῶν δὲ ταχυτέρων ὀξύν. We must not attribute the identification of the seven planets with the seven strings of the heptachord to the Pythagoreans of this date. Mercury and Venus have in the long run the same velocity as the sun, and we must take in the earth and the fixed stars. We can even find room for the antichthon as προσλαμβανόμενος.
[837]. For the various systems, see Boeckh, Kleine Schriften, vol. iii. pp. 169 sqq., and Carl v. Jan, “Die Harmonie der Sphären” (Philol. 1893, pp. 13 sqq.). They vary with the astronomy of their authors, but they bear witness to the fact stated in the text. Many give the highest note to Saturn and the lowest to the Moon, while others reverse this. The system which corresponds best, however, with the Pythagorean planetary system must include the heaven of the fixed stars and the earth. It is that upon which the verses of Alexander of Ephesos quoted by Theon of Smyrna, p. 140, 4, are based:
γαῖα μὲν οὖν ὑπάτη τε βαρεῖά τε μέσσοθι ναίει·
ἀπλανέων δὲ σφαῖρα συνημμένη ἔπλετο νήτη, κ.τ.λ.
The “base of Heaven’s deep Organ” in Milton’s “ninefold harmony” (Hymn on the Nativity, xiii.) implies the reverse of this.
[838]. The difficulty appears clearly in Adam’s note on Republic, 617 b (vol. ii. p. 452). There the ἀπλανής appears rightly as the νήτη, while Saturn, which comes next to it, is the ὑπάτη. It is inconceivable that this should have been the original scale. Aristotle touches upon the point (de Caelo, Β, 10. 291 a 29 sqq.); and Simplicius sensibly observes (de Caelo, p. 476, 11), οἱ δὲ πάσας τὰς σφαίρας τὴν αὐτὴν λέγοντες κίνησιν τὴν ἀπ’ ἀνατολῶν κινεῖσθαι καθ’ ὑπόληψιν (ought not the reading to be ὑπόλειψιν?), ὥστε τὴν μὲν Κρονίαν σφαῖραν συναποκαθίστασθαι καθ’ ἡμέραν τῇ ἀπλανεῖ παρ’ ὀλίγον, τὴν δὲ τοῦ Διὸς παρὰ πλέον καὶ ἐφεξῆς οὕτως, οὗτοι πολλὰς μὲν ἄλλας ἀπορίας ἐκφεύγουσι, but their ὑπόθεσις is ἀδύνατος. This is what led to the return to the geocentric hypothesis and the exclusion of earth and ἀπλανὴς from the ἁρμονία. The only solution would have been to make the earth rotate on its axis or revolve round the central fire in twenty-four hours, leaving only precession for the ἀπλανής. As we have seen, Boeckh attributed this to Philolaos, but without evidence. If he had thought of it, these difficulties would not have arisen.