ἐπ' ἀκμῆς εἶναι

From LSJ

τὸ δὲ μέλλον ἀκριβῶς οἶδεν οὐδεὶς θνατὸς ὅπᾳ φέρεται → but as for the future no mortal knows for certain where he is bound

Source

Greek > English (Woodhouse)

be on the brink of