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Πόλεις τε οὖν δή που λάμπουσιν αἴγλῃ καὶ χάριτι καὶ ἡ γῆ πᾶσα οἷον παράδεισος συγκεκόσμηται· καπνοὶ δ’ ἐκ πεδίων καὶ φρυκτοὶ φίλιοι καὶ πολέμιοι, οἷον πνεύματος ἐκριπίσαντος, φροῦδοι, γῆς ἐπέκεινα καὶ θαλάττης· ἀντεισῆκται δὲ θέας πᾶσα χάρις καὶ ἀγώνων ἄπειρος ἀριθμός. ὥστε οἷον πῦρ ἱερὸν καὶ ἄσβεστον οὐ διαλείπει τὸ πανηγυρίζειν, ἀλλὰ περίεισιν ἄλλοτε εἰς ἄλλους, ἀεὶ δέ ἐστι πού· πάντες γὰρ ἀξίως τούτου πεπράγασιν· ὥστε μόνους ἄξιον εἶναι κατοικτεῖραι τοὺς ἔξω τῆς ὑμετέρας, εἴ τινές πού εἰσιν ἄρα, ἡγεμονίας, οἵων ἀγαθῶν στέρονται. καὶ μὴν τό γε ὑπὸ πάντων λεγόμενον, ὅτι γῆ πάντων πήτηρ καὶ πατρὶς κοινὴ πάντων, ἄριστα ὑμεῖς ἀπεδείξατε. νῦν γοῦν ἔξεστι καὶ Ἕλληνι καὶ βαρβάρῳ καὶ τὰ αὑτοῦ κομίζοντι καὶ χωρὶς τῶν αὑτοῦ βαδίζειν ὅποι βούλεται ῥαδίως, ἀτεχνῶς ὡς ἐκ πατρίδος εἰς πατρίδα ἰόντι· καὶ οὔτε Πύλαι Κιλίκιοι φόβον παρέχουσιν οὔτε στεναὶ καὶ ψαμμώδεις δι’ Ἀράβων ἐπ’ Αἴγυπτον πάροδοι, οὐκ ὄρη δύσβατα, οὐ ποταμῶν ἄπειρα μεγέθη, οὐ γένη βαρβάρων ἄμικτα, ἀλλ’ εἰς ἀσφάλειαν ἐξαρκεῖ Ῥωμαῖον εἶναι, μᾶλλον δὲ ἕνα τῶν ὑφ’ ὑμῖν. καὶ τὸ Ὁμήρῳ λεχθὲν “γαῖα δέ τοι ξυνὴ πάντων” [cf. Hom., Il. 15.193] ὑμεῖς ἔργῳ ἐποιήσατε, καταμετρήσαντες μὲν πᾶσαν τὴν οἰκουμένην, ζεύξαντες δὲ παντοδαπαῖς γεφύραις ποταμούς, καὶ ὄρη κόψαντες ἱππήλατον γῆν εἶναι, σταθμοῖς τε τὰ ἔρημα ἀναπλήσαντες καὶ διαίτῃ καὶ τάξει πάντα ἡμερώσαντες.
(Aelius Aristides, Or. 26.99-101)

Cities gleam with radiance and charm, and the whole earth has been beautified like a garden. Smoke rising from plains and fire signals for friend and foe have disappeared, as if a breath had blown them away, beyond land and sea. Every charming spectacle and an infinite number of festal games have been introduced instead. Thus like an ever-burning sacred fire the celebration never ends, but moves around from time to time and people to people, always somewhere, a demonstration justified by the way all men have fared. Thus it is right to pity only those outside your hegemony, if indeed there are any, because they lose such blessings. It is you again who have best proved the general assertion, that Earth is mother of all and common fatherland. Now indeed it is possible for Hellene or non-Hellene, with or without his property, to travel wherever he will, easily, just as if passing from fatherland to fatherland. Neither Cilician Gates nor narrow sandy approaches to Egypt through Arab country, nor inaccessible mountains, nor immense stretches of river, nor inhospitable tribes of barbarians cause terror, but for security it suffices to be a Roman citizen, or rather to be one of those united under your hegemony. Homer said, “Earth common of all,” and you have made it come true. You have measured and recorded the land of the entire civilized world; you have spanned the rivers with all kinds of bridges and hewn highways through the mountains and filled the barren stretches with posting stations; you have accustomed all areas to a settled and orderly way of life. (tr. James H. Oliver)

Ageōmetrētos

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Ἐπεγέγραπτο ἔμπροσθεν τῆς διατριβῆς τοῦ Πλάτωνος ὅτι ἀγεωμέτρητος μηδεὶς εἰσίτω· ἀντὶ τοῦ ἄνισος καὶ ἄδικος. ἡ γὰρ γεωμετρία τὴν ἰσότητα καὶ τὴν δικαιοσύνην τηρεῖ. (Scholia in Aelii Aristidis Πρὸς Πλάτωνα ὑπὲρ τῶν τεττάρων 125.14)

In front of Plato’s school had been inscribed, “Let noone enter un-geometried” rather than “unequal” or “unjust,” for geometry maintains equality and justness. (tr. Dennis McHenry)

Διὰ τούτων μὲν οὖν καὶ διὰ πλειόνων ἑτέρων δῆλον ὅτι ἄλλα τινὰ ᾐνίττοντο ἐκεῖνοι. εἰ γὰρ μάλιστα πάντων τῆς τῶν μαθημάτων γνώσεως ἐπεμελοῦντο οἱ Πυθαγόρειοι (Πυθαγόρειος δὲ ὁ Πλάτων, οὗ καὶ πρὸ τῆς διατριβῆς ἐπεγέγραπτο ‘ἀγεωμέτρητος μὴ εἰσίτω’) οὐδεὶς δ’ οὐδ’ ἄκρῳ δακτύλῳ γεωμετρήσας τοιοῦτό τι λέγειν ἀνέξεται, τίς οὕτως ἠλίθιος ὡς οἴεσθαι τὸν Πλάτωνα ταῦτα οὕτω κατὰ τὸ φαινόμενον λέγειν; ἴσως δὲ οὐκ ἄκομψον ἐπὶ ὀλίγων συντόμως τῶν συμβόλων τὴν διάνοιαν δηλῶσαι.
(Joannes Philoponus, In Aristotelis De Anima 1.3 (Arist. p. 406b25))

For these reasons therefore, and for many others, it is clear that they [Timaeus, Plato and the Pythagoreans] hinted at other things. Indeed, given that nobody was more concerned about (acquiring) the knowledge of mathematics than the Pythagoreans (and Plato was a Pythagorean: in front of his school he had inscribed: “let no one enter un-geometried”), and that nobody who has practised geometry with more than the tip of his finger would tolerate such a manner of speaking, who would be so foolish as to think that what Plato says here is limited to the visible? (tr. David Bauwens)

Οἱ δὲ τὴν φυσιολογικὴν λέγοντες προηγήσασθαι φασιν ὅτι δεῖ ἀπὸ τῶν φυσικῶν ἄρξασθαι, ἐπειδὴ ταῦτα σύντροφα ἡμῖν ἐστι καὶ συνήθη. οἱ δὲ λέγοντες τὴν μαθηματικὴν ἔφασαν διὰ τοῦτο δεῖν προηγήσασθαι τὰ μαθηματικὰ διὰ τὸ ἐπιγεγράφθαι ἐν τῷ τοῦ Πλάτωνος μουσείῳ ‘ἀγεωμέτρητος μηδεὶς εἰσίτω.’ (Olympiodorus, Prolegomena et in Categorias commentarium 8v (Comm. in Arist. Gr. vol. 12.1 (Busse) 8.37-9.1)

Those who say the study of nature comes first, say that one has to start from the natural elements, because these are innate and familiar to us. But those who say that the study of mathematics takes precedence, say that this needs to be of primary importance, because in Plato’s school the words “Let no one unversed in geometry enter” were inscribed. (tr. David Bauwens)

Ὁ μὲν οὖν Πλάτων εἰς φυσιολογικὸν καὶ θεολογικὸν αὐτὸ διαιρεῖ· τὸ γὰρ μαθηματικὸν οὐκ ἠβούλετο εἶναι μέρος τῆς φιλοσοφίας, ἀλλὰ προγύμνασμά τι ὥσπερ ἡ γραμματικὴ καὶ ἡ ῥητορική· ὅθεν καὶ πρὸ τοῦ ἀκροατηρίου τοῦ οἰκείου ἐπέγραψεν ‘ἀγεωμέτρητος μηδεὶς εἰσίτω’. τοῦτο δὲ ὁ Πλάτων ἐπέγραφεν, ἐπειδὴ εἰς τὰ πολλὰ θεολογεῖ καὶ περὶ θεολογίαν καταγίνεται· συμβάλλεται δὲ εἰς εἴδησιν τῆς θεολογίας τὸ μαθηματικόν, οὗτινός ἐστιν ἡ γεωμετρία.
(Pseudo-Galen, De partibus philosophiae 6.2-7 (Wellmann))

Plato divided [theoretical philosophy] into physiology and theology. In fact, he did not want mathematics to be a part of philosophy, but a sort of progymnasma like grammar and rhetoric. That’s why, before his private lecture-room, he inscribed “Let no one enter un-geometried.” He inscribed this since he discoursed on theology in all matters and dwelt on theology, and included mathematics, of which geometry is a part, into theology’s forms of knowledge. (tr. Dennis McHenry)

Πρὸ τῶν προθύρων τῶν αὑτοῦ γράψας ὑπῆρχε Πλάτων· “Μηδεὶς ἀγεωμέτρητος εἰσίτω μου τὴν στέγην.” (Joannes Tzetzes, Chil. 8.972-973)

Over his front doors Plato wrote: “Let no one unversed in geometry come under my roof.” (tr. Ivor Thomas)