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πεπεισμένοι ἔστων. See on 499 E. Plato's attempt to conciliate the Many is obviously half-hearted. The Multitude can never be philosophers (494 A), and are not likely to believe in the Philosopher-king. But it was necessary to prove or postulate some degree of assent or at least quiescence on their part in order to demonstrate the possibility of the perfect city. Cf. 502 C note τις . τίς is read by A, but Adimantus's reply makes it probable that the indefinite pronoun is correct. βασιλέων ἔκγονοι. See on 499 B.
The Republic of Plato. James Adam. 1902. Cambridge. Cambridge University Press.
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