Foundation of Constantinople according to Chronicon Paschale

In the time of the aforementioned consuls, Constantine the celebrated emperor departed from Rome, and, while staying at Nicomedia metropolis of Bithynia, made visitations for a long time to Byzantium. He renewed the first wall of the city of Byzas, and after making considerable extensions also to the same wall he joined thee to the ancient wall of the city and named it Constantinople; he also completed the Hippodrome, adorning it with works in bronze and with every excellence, and made in it a box for imperial viewing in likeness of the one which is in Rome. And he made a great Palace near the same Hippodrome, by way of the Kochlias, as it is called. And he also built a forum which was large and exceedingly fine; and he set in the middle a great porphyry column of the ban stone worthy of admiration, and he set on top of the same column a great statue of himself with rays of light on his head, a work in bronze which he had brought from Phrygia. The same emperor Constantine secretly took away from Rome the Palladium, as it is called, and placed it in the Forum built by him, beneath the column of his monument, as certain of the Byzantines say who have heard it by tradition. And after making bloodless sacrifice, he named the Tyche [the guardian spirit] of the city renewed by him Anthusa.

Chronicon Paschale, tr. M and M Whitby, Liverpool 1989, p. 15-16.

Foundation of Constantinople according to Philostorgios

Τὴν τοίνυν Θρᾴκην Κωνσταντῖνος καταλαβὼν ἐς τὰ μάλιστα δὴ τότε εὐθηνουμένην, καὶ τὸ Βυζάντιον καταμαθὼν ὡς ἄριστα γῆς τε καὶ θαλάττης ἔχοι, ἱδρύθη δὴ ἐνταῦθα· καὶ τὸν αὐχένα τῆς χερρονήσου διαλαβών (χερρόνησος γάρ ἐστι τὸ χωρίον), ἐτείχιζεν ἐκ θαλάττης εἰς θάλατταν, ἐντὸς τά τε προάστεια καὶ τοὺς πλησίον λόφους ποιούμενος, ὡς τῆς κτιζομένης πόλεως διὰ πλάτους περιβολὴν μοῖραν εἶναι μικρὰν τὴν ἀρχαίαν πόλιν. ἔνθα γὰρ νῦν ὁ πορφυροῦς καὶ μέγας ἐστὶ κίων ἑστὼς ὁ τὸν αὐτοῦ κολοττὸν φέρων, ἐντεῦθεν τὴν ἀρχὴν ποιησάμενος, τὸ λοιπὸν ἅπαν ἐπί τε ἑκατέραν θάλατταν καὶ τὴν μεσόγειον ἁπλούμενον τῆς ἑαυτοῦ παλάμης καὶ δυνάμεως ἐξήνυσεν ἔργον. ᾿Ακήκοα δὲ ἔγωγε καὶ τοῦτο τῶν πρεσβυτάτων καὶ ἀξιολόγων διηγουμένων ὡς ὁ Κωνσταντῖνος, ὁπηνίκα τὰς πύλας ὁριούμενος τοῦ τείχους ἡγεῖτο τῶν ἑπομένων ἀφ' οὗ μέτρου τὸν περίβολον ἔδει τὴν ἐργασίαν λαβεῖν, ᾔει τὸ πρόσω βάδην τε χωρῶν καὶ τὸ δόρυ τῇ χειρὶ φέρων. ὡς δὲ πρῶτον ὑπερβὰς λόφον ἐπὶ δεύτερον ᾔει, καὶ τοῦτον ὑπερελθὼν ἔτι τὸ πρόσω προὔβαινε μείζον μῆκος διαμετρούμενος ἢ τοῖς ἀκολουθοῦσιν ἐφαίνετο μετρίως ἔχειν, προσελθών <τις> ἀπὸ τῶν παρρησίαν πρὸς αὐτὸν ἀγόντων ἤρετο· «ἕως ποῦ, δέσποτα;» ὁ δὲ διαρρήδην ἀποκρινάμενος· «ἕως ἄν, ἔφη, ὁ ἔμπροσθέν μου στῇ», ὡς γενέσθαι σαφὲς ὅτι ἀγγέλων τις ἐῴκει προπορεύεσθαι τὰ μέτρα παραδώσαν, ὡς πάνυ γε δὴ θεῷ κεχαρισμένως τῆς πόλεως ταύτης οἰκιζομένης, οὐκ ἔλαττον ἢ τὸ πάλαι τῆς ῾Ιερουσαλήμ· καὶ γὰρ καὶ ἤμελλε κἀνταῦθα κοινὸν συστήσασθαι πρυτανεῖον εὐσεβείας. ἕως γοῦν ὅποι τὸ φαινόμενον εἶδος χωροῦν ἔπειτα ἔστη καὶ διαλυθὲν ἦν ἀφανές, ἐκεῖ καὶ ὁ Κωνσταντῖνος παραγενόμενος τὸ δόρυ τε ἐπήξατο καὶ ἔφη διαρρήδην· «ἕως ἐνταῦθα», ἔνθα καὶ νῦν εἰσιν αἱ μεγάλαι πύλαι τῆς πόλεως. Τὴν δὲ πόλιν κτίσας ἔνδοξον αὐτὴν ἐκάλεσε ῾Ρώμην, οὕτω κατὰ τὴν τῶν ᾿Ιταλῶν γλῶτταν «῎Αλμα ῾Ρώμα» τὴν προσηγορίαν αὐτῇ θέμενος. καὶ βουλήν τε ἐν αὐτῇ σύγκλητον ἱδρύσατο καὶ σιτηρεσίου δαπάνην πολυτελεστάτην τοῖς οἰκήτορσι κατένειμε, καὶ τὸν ἄλλον ἐν αὐτῇ τῆς πολιτείας κατεστήσατο κόσμον, ὡς ἀρκεῖν εἰς ἀντίπαλον κλέος τῇ προτέρᾳ ῾Ρώμῃ.

Vita Constantini Cod. Angelic. A f. 25r [Franchi de' Cav. 97, s. ob. S. 17, 33]
See also. [folgt Exc. Tripart. = Polyd. 268, 5—11. Theophan. 23, 22—27. Bios di Costantino ed. Guidi Rendic. Accad. Lincei 1907 S. 336, 15—19]. Ebd. f. 25v

Historia ecclesiastica (fragmenta e vita Constantini) (cod. Angelic. 22), ed. F. Winkelmann (post J. Bidez), Philostorgius. Kirchengeschichte, 3rd edn. Die griechischen christlichen Schriftsteller (Berlin: Akademie-Verlag, 1981), book. 2.9.

Engish translation

CHAP. 9.--He says that, in the twenty-eighth year of his reign, Constantine turned Byzantium into the city of Constantinople; and that, when he went to mark out the circuit of the city, he walked round it with a spear in his hand; and that when his attendants thought that he was measuring out too large a space, one of them came up to him and asked him, How far, O prince?” and that the emperor answered, “Until he who goes before me conies to a stop ;” by this answer clearly manifesting that some heavenly power was heading him on, and teaching him what he ought to do. Philostorgius adds, that Constantine, after building the city, called it “Alma Roma.,” which means in the Latin tongue, “Glorious.” He also states, that the emperor established there a senate, and distributed among the citizens a copious allowance of corn, and adorned the city in other particulars with such sumptuous magnificence, that it became a rival to ancient Rome in splen dour.

Ecclesiastical History of Philostorgius, as epitomized by Photius, Patriarch of Constantinople. Translated by Edward Walford, Late Scholar of Balliol College, Oxford. London, 1855