James Adam, The Republic of Plato

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ὑπὸ τοῦ λόγου. In this particular the analogy between the city and the soul is not quite exact, otherwise it would be the rulers in the city who prescribe τὸ δεινόν τε καὶ μή, whereas it is the legislator (see on ὁ νομοθέτης 429 C). This point is emphasized, perhaps unduly so, by Krohn (Pl. St. p. 43). Unless Plato made the Deity the οἰκιστής of the soul, as the original legislator is of the city, it was impossible for him to avoid placing the λογιστικόν in a position of even greater authority than the rulers. In Books VI and VII the inequality is redressed by making the power of the Rulers in the city commensurate with that of λόγος in the soul: see VI 497 C note

ἦρχέν τε κτλ.: ‘ruled within him and issued these instructions.’ The imperfect is used because the instructions must be given before they can be obeyed by θυμοειδές, as described in the last sentence. J. and C. say that ἦρχε refers to 428 E; but Plato is not there speaking of the individual, only of the State. Although a reference to 439 C or 441 E is barely possible, it is much simpler to regard the imperfect as real, and not ‘philosophic.’ See above on III 406 E. Schneider, to judge from his translation, takes the same view. With σμικρῷ μέρει cf. Arist. Eth. Nic. X 7. 1177^{b} 34 ff. εἰ γὰρ καὶ τῷ ὄγκῳ μικρόν ἐστι (sc. τὸ κράτιστον τῶν ἐν αὐτῷ) κτλ.

αὖ κἀκεῖνο κτλ. αὖ καί has been interpreted (1) as implying that the θυμοειδές also has a sort of knowledge: cf. 429 C and 439 E note: (2) as ‘like the rulers in the State’: cf. 428 B ff. The first view is slightly more natural on linguistic grounds, but I think Plato would hardly have attributed ἐπιστήμη in any shape to the θυμοειδές. Probably (2) is right, for the analogy between the city and the soul is in Plato's mind all through this section: see 441 C, D, and 442 D.