πρόειμι εἶμι ibo to go forward, go on, advance, Thuc., etc. of Time, προϊόντος τοῦ χρόνου as time went on, Hdt.; so, προϊόντος Xen.; προϊούσης τῆς νυκτός Xen., etc. of persons reading, προϊὼν καὶ ἀναγιγνώσκων going on reading, Plat. to go first, go in advance, Xen.:—c. gen. to go before or in advance of, τῆς στρατιῆς Hdt. to go forth, Xen. πρ. εἴς τι to pass on to, begin another thing, Xen., Arist. of an action, to go on well, succeed, Xen.