James Adam, The Republic of Plato

γεγονώς=‘produced,’ ‘a product of,’ is cancelled by Hartman; but φύς is too far away, and γίγνεσθαι (‘to be produced’) is sufficiently accurate: cf. γένηται in 461 C.

ἀνέγγυον: ‘unauthorised,’ because the child of an irregular union. An ἀνέγγυος γάμος is a marriage without an ἐγγύη or contract between the parents of the betrothing parties (Blümner Privatalt. p. 262 note 2).

ᾧ. ᾗ is read by Ξ, Vind. E and Eusebius (Praep. Ev. XIII 19. 18); but αὐτούς includes both sexes, and in such cases the masculine is preferred to the feminine. Hartman strangely thinks ᾧ neuter.

θυγατρὶ κτλ. The cases enumerated are all in the direct line, and nothing is said forbidding unions between ‘brothers’ and ‘sisters.’ See however 461 E note Greek law permitted the marriage of uncles with nieces, aunts with nephews, and even half-brothers and halfsisters, provided they were not ὁμομήτριοι (Becker's Charicles E. T. p. 478, with the passages there cited). Some of Plato's contemporaries, notably the Cynics, entertained peculiarly revolting views on this subject, and the question was frequently agitated in his time: see Dümmler Proleg. zu Pl. St. pp. 52 ff. The Stoics agreed with the Cynics: see the authorities cited in Henkel Stud. zur Geschichte d. Gr. Lehre vom Staat p. 30.