These lines are attributed to Solon by Plutarch, in the tract πῶς ἄν τις ὑπ᾽ ἐχθρῶν ὠφελοῖτο, but they occur among the elegiac “gnomæ” of Theognis, lines 316–318.  Fronton du Duc in his notes on the Homilies points out that they are also quoted in Plutarch’s life of Solon.  Basil was well acquainted with Plutarch.  (cf. references in the notes to the Hexaemeron.)