The headword and primary gloss are adverbial forms created from the perfect participle passive of the verbs ἅγω and παιδεύω respectively.
[1] This gloss has been taken from (or at least influenced by) Timaeus Sophista, Lexicon Platonicum: ἠγμένος: πεπαιδευμένος “guided: educated”.
[2] (For ἀγωγή cf. alpha 320 and esp. alpha 321.) This second gloss seems to be a simplification of a definition taken from some lexicographic text. See for example Ammonius Grammaticus, De adfinium vocabulorum differentia 379.4: παιδεύσις δὲ παιδείας καὶ αρετῆς παραδόσις καὶ ἐκ παιδὸς ἐπ’ ἀρετὴν ὀδηγοῦσα “and education [παιδεύσις ] is transmission of erudition and excellence, and guidance [ἀγωγή ] leading out of childhood in the way to excellence”.