James Adam, The Republic of Plato

ἥ τε δίκη κτλ. Cf. VI 487 A where οὐδ᾽ ἂν ὁ Μῶμος, ἔφη, τό γε τοιοῦτον μέμφαιτο similarly concludes the earlier enumeration of qualities necessary to the philosophic ruler.

καὶ πράξομεν . καί (which some inferior MSS omit) is “paullo insolentius positum, sed ita ut τἀναντία πάντα partim ad civitatis conditionem—partim ad opinionem hominum atque existimationem philosophiae, quam sequi errorem istum oporteat, spectare et utramque contra, quam dictum optandumque sit, casuram esse significet” (Schneider).

γελοῖον takes up γέλωτα just before, hence καί. My extreme προθυμία, says Socrates in effect, was fitted to provoke a smile (cf. VI 506 D).

ἐν τῷ παρόντι. The reference is to 535 C and VI 495 C—496 A. After παρόντι Burnet adds <τι>, needlessly: see on III 388 D.

536B - 537C After apologising for his excessive zeal in defence of Philosophy, Socrates lays down his ordinances. We must select our pupils while they are young, and put before them in their boyhood all the propaedeutic studies, taking care to avoid compulsion. At the same time they will be brought on the field of battle and receive their baptism of fire. From eighteen to twenty, gymnastic exercises claim their undivided attention. At twenty, those who have proved themselves the best will enter on a systematic comparative study of mathematics etc., lasting ten years.