προσθεῖναι
From LSJ
οὗτος μὲν ὁ πιθανώτερος τῶν λόγων εἴρηται, δεῖ δὲ καὶ τὸν ἧσσον πιθανόν, ἐπεί γε δὴ λέγεται, ῥηθῆναι → this is the most credible of the stories told; but I must relate the less credible tale also, since they tell it
προσθεῖναι: απαρ. αορ. βʹ του προστίθημι· μτχ. προσθείς.