[32] Plat. Tim. p. 31 B. εἷς ὅδε μονογενὴς οὐρανός, &c.
[33] Plat. Tim. p. 35 A. Ταὐτὸν — τὸ ἀμέριστον — θάτερον — τὸ μεριστὸν — τρίτον ἐξ ἀμφοῖν οὐσίας εἶδος.
[34] Plato, Timæus, pp. 35-36. The pains which were taken by commentators in antiquity to expound and interpret this numerical scale may be seen especially illustrated in Plutarch’s Treatise, De Animæ Procreatione in Timæo, pp. 1012-1030, and the Epitome which follows it. There were two fundamental τετρακτύες or quaternions, one on a binary, the other on a ternary scale of progression, which were arranged by Krantor (Plutarch, p. 1027 E) in the form of the letter Λ, as given in Macrobius (Somn. Scip. i. 6, p. 35). The intervals between these figures, are described by Plato as filled up by intervening harmonic fractions, so as to constitute an harmonic or musical diagram or scale of four octaves and a major sixth. (Boeckh’s Untersuch. p. 19.) M. Boeckh has expounded this at length in his Dissertation, Ueber die Bildung der Welt-Seele im Timäos. Other expositors after him.
[35] Plato, Timæus, p. 36 C. τὴν μὲν οὖν ἔξω φορὰν ἐπεφήμισεν εἶναι τῆς ταὐτοῦ φύσεως, τὴν δ’ ἐντός, τῆς θἀτέρου. τὴν μὲν δὴ ταὐτοῦ κατὰ πλευρὰν ἐπὶ δεξιὰ περιήγαγε, τὴν δὲ θατέρου κατὰ διάμετρον ἐπ’ ἀριστερά.
For the meaning of κατὰ πλευρὰν and κατὰ διάμετρον, referring to the equator and the ecliptic, see the explanation and diagram in Boeckh, Untersuchungen, p. 25, also in the note of Stallbaum. The allusion in Plato to the letter χῖ is hardly intelligible without both a commentary and a diagram.
In regard to the constitution of the kosmical soul, we must note, that as it is intended to know Same, Different, and Same and Different in one — so it must embody these three ingredients in its own nature: according to the received axiom. Like knows like — Like is known by like.[36] Thus began, never to end, the rotatory movements of the living Kosmos or great Kosmical God. The invisible soul of the Kosmos, rooted at its centre and stretching from thence so as to pervade and enclose its visible body, circulates and communicates, though without voice or sound, throughout its own entire range, every impression of identity and of difference which it encounters either from essence ideal and indivisible, or from that which is sensible and divisible. Information is thus circulated, about the existing relations between all the separate parts and specialties.[37] Reason and Science are propagated by the Circle of the Same: Sense and Opinion, by those of the Different. When these last-mentioned Circles are in right movement, the opinions circulated are true and trustworthy.
[36] Aristotel. De Animâ, i. 2, 7, i. 3, 11 (pp. 404, b. 16 — 406 b. 26), with Trendelenburg’s note, pp. 227-253; Stallbaum, not. ad Timæum, pp. 136-157. See also the interpretation of Plato’s opinion by Krantor, as given in Plutarch, De Animæ Procreatione in Timæo, p. 1012 E. We learn from Plutarch, however, that the passage gave much trouble to commentators.
[37] Plato, Timæus, pp. 36-37. 37 A: λέγει κινουμένη διὰ πάσης ἑαυτῆς, ὅτῳ τ’ ἄν τι ταὐτὸν ᾗ, καὶ ὅτου ἂν ἕτερον, πρὸς ὅ, τι τε μάλιστα καὶ ὅπῃ καὶ ὅπως καὶ ὁπότε ξυμβαίνει κατὰ τὰ γιγνόμενά τε πρὸς ἕκαστον ἕκαστα εἶναι καὶ πάσχειν, καὶ πρὸς τὰ κατὰ ταὐτὰ ἔχοντα ἀεί.