(The SOL headword, wrongly, is the supplementary one in the entry.)
As transmitted, the primary headword and its gloss are adverbial forms, created from the perfect participle passive of the verbs a)/gw and paideu/w respectively. (But see next note.)
[1] This gloss has been taken from (or at least influenced by) Timaeus' Platonic Lexicon: h)gme/nos: pepaideume/nos; 'guided: [meaning] educated'. (The original souce is probably Plato, Alcibiades I 124A.)
[2] (For a)gwgh/ cf. alpha 320 and esp. alpha 321.) This supplement to the entry seems to be a simplification of a definition taken from some lexicographic text. See e.g. Ammonius, De adfinium vocabulorum differentia 379.4: pai/deusis de\ paidei/as kai\ a)reth=s parado/sis kai\ e)k paido\s e)p’ a)reth\n o)dhgou=sa; 'and education [pai/deusis] is transmission of erudition and excellence, and guidance [a)gwgh/] leading out of childhood in the way to excellence'.