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. Footnote 839: _Tim._ 39 a 5-b 2, especially the words τὰ τάχιστα περιιόντα ὑπὸ τῶν βραδυτέρων ἐφαίνετο καταλαμβάνοντα καταλαμβάνεσθαι (“they appear to be overtaken, though they overtake”). Footnote 840: Plato, _Laws_, 822 a 4 sqq. The Athenian says of the theory that he had not heard of it in his youth nor long before (821 e 3). If so, it can hardly have been taught by Philolaos, though it may have been by Archytas. [Sidenote: Things likenesses of numbers.] 153. We have still to consider a view, which Aristotle sometimes attributes to the Pythagoreans, that things were “like numbers.” He does not appear to regard this as inconsistent with the doctrine that things _are_ numbers, though it is hard to see how he could reconcile the two.[841] There is no doubt, however, that Aristoxenos represented the Pythagoreans as teaching that things were _like_ numbers,[842] and there are other traces of an attempt to make out that this was the original doctrine. A letter was produced, purporting to be by Theano, the wife of Pythagoras, in which she says that she hears many of the Hellenes think Pythagoras said things were made _of_ number, whereas he really said they were made _according to_ number.[843] It is amusing to notice that this fourth-century theory had to be explained away in its turn later on, and Iamblichos actually tells us that it was Hippasos who said number was the exemplar of things.[844] Footnote 841: Cf. especially _Met._ Α, 6. 787 b 10 (R. P. 65 d). It is not quite the same thing when he says, as in Α, 5. 985 b 23 sqq. (R. P. _ib._), that they perceived many likenesses in things to numbers. That refers to the numerical analogies of Justice, Opportunity, etc. Footnote 842: