[35] Aristot. Metaph. M. 6, p. 1080, b. 18. τὸν γὰρ ὅλον οὔρανον κατασκευάζουσιν ἐξ ἀριθμῶν. Compare p. 1075, b. 37, with the Scholia.
A poet calls the tetraktys (consecrated as the sum total of the first four numbers 1 + 2 + 3 + 4 = 10) πηγὴν ἀενάου φύσεως ῥιζώματ’ ἔχουσαν. Sextus Empiric. adv. Mathemat. vii. 94.
[36] Philolaus, ed. Boeckh, p. 91-95. τὸ πρᾶτον ἁρμοσθὲν, τὸ ἕν ἐν τῷ μέσῳ τῆς σφαίρας ἑστία καλεῖται — βωμόν τε καὶ συνοχὴν καὶ μέτρον φύσεως — πρῶτον εἶναι φύσει τὸ μέσον.
Aristot. Metaph. N. 3, p. 1091, a. 15. φανερῶς γὰρ λέγουσιν (the Pythagoreans) ὡς τοῦ ἑνὸς συσταθέντος — εὐθὺς τὸ ἔγγιστα τοῦ ἀπείρου ὅτι εἱλκετο καὶ ἐπεραίνετο ὑπὸ τοῦ πέρατος.
Aristot. Physic. iv. 6, p. 213, b. 21. Εἶναι δ’ ἔφασαν καὶ οἱ Πυθαγόρειοι κενόν, καὶ ἐπεισιέναι αὐτὸ τῷ οὐράνῳ ἐκ τοῦ ἀπείρου πνεύματος, ὡς ἀναπνέοντι· καὶ τὸ κενόν, ὃ διορίζει τὰς φύσεις, ὡς ὄντος τοῦ κενοῦ χωρισμοῦ τινος τῶν ἐφεξῆς καὶ τῆς διορίσεως, καὶ τοῦτ’ εἶναι πρῶτον ἐν τοῖς ἀριθμοῖς· τὸ γὰρ κενὸν διορίζειν τὴν φύσιν αὐτῶν. Stobæus (Eclog. Phys. i. 18, p. 381, Heer.) states the same, referring to the lost work of Aristotle on the Pythagorean philosophy. Compare Preller, Histor. Philos. Gr. ex Font. Loc. Context., sect. 114-115.
[37] Philolaus, p. 94. Boeckh. περὶ δὲ τοῦτο δέκα σώματα θεῖα χορεύειν, &c. Aristot. De Cœlo, ii. 13. Metaphys. A. 5.
The inhabited portion of the Earth was supposed to be that which was turned away from the central fire and towards the Sun, from which it received light. But the Sun itself was not self-luminous: it was conceived as a glassy disk, receiving and concentrating light from the central fire, and reflecting it upon the Earth, so long as the two were on the same side of the central fire. The Earth revolved, in an orbit obliquely intersecting that of the Sun, and in twenty-four hours, round the central fire, always turning the same side towards that fire. The alternation of day and night was occasioned by the Earth being during a part of such revolution on the same side of the central fire with the Sun, and thus receiving light reflected from him: and during the remaining part of her revolution on the side opposite to him, so that she received no light at all from him. The Earth, with the Antichthon, made this revolution in one day: the Moon, in one month:[38] the Sun, with the planets, Mercury and Venus, in one year: the planets, Mars, Jupiter, and Saturn, in longer periods respectively, according to their distances from the centre: lastly, the outermost circle of the fixed stars (the Olympus, or the Aplanes), in some unknown period of very long duration.[39]
[38] The Pythagoreans supposed that eclipses of the moon took place, sometimes by the interposition of the earth, sometimes by that of the Antichthon, to intercept from the moon the light of the sun (Stobæus, Eclog. Phys. i. 27, p. 560. Heeren). Stobæus here cites the history (ἱστορίαν) of the Pythagorean philosophy by Aristotle, and the statement of Philippus of Opus, the friend of Plato.
[39] Aristot. de Cœlo, ii. 13. Respecting this Pythagorean cosmical system, the elucidations of Boeckh are clear and valuable. Untersuchungen über das Kosmische System des Platon, Berlin, 1852, p. 99-102; completing those which he had before given in his edition of the fragments of Philolaus.
Martin (in his Études sur le Timée de Platon, vol. ii. p. 107) and Gruppe (Die Kosmischen Systeme der Griechen, ch. iv.) maintain that the original system proposed by Pythagoras was a geocentric system, afterwards transformed by Philolaus and other Pythagoreans into that which stands in the text. But I agree with Boeckh (Ueber das Kosmische System des Platon, p. 89 seqq.), and with Zeller (Phil. d. Griech., vol. i. p. 308, ed. 2), that this point is not made out. That which Martin and Gruppe (on the authority of Alexander Polyhistor, Diog. viii. 25, and others) consider to be a description of the original Pythagorean system as it stood before Philolaus, is more probably a subsequent transformation of it; introduced after the time of Aristotle, in order to suit later astronomical views.