improperly
From LSJ
Δύο γὰρ, ἐπιστήμη τε καὶ δόξα, ὧν τὸ μὲν ἐπίστασθαι ποιέει, τὸ δὲ ἀγνοεῖν → Two different things are science and belief: the one brings knowledge, the other ignorance (Hippocrates)
adv. P. ἀπρεπῶς. Shamelessly: P. and V. ἀναιδῶς. Incorrectly: P. and V. οὐκ ὀρθῶς.