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)

Pilēsin

Ἰστέον δέ, ὅτι ὁ μὲν Ἀριστοτέλης αἴτιον λέγει τῆς εἰς ὕδωρ μεταβολῆς τὴν ψύξιν μόνον· Θεόφραστος δὲ οὐ μόνον τὴν ψύξιν αἰτίαν φησὶ τῆς τοῦ ὕδατος γενέσεως, ἀλλὰ καὶ τὴν πίλησιν. ἰδοὺ γὰρ ἐν Αἰθιοπίᾳ μὴ οὔσης ψύξεως ὅμως ὑετὸς κατάγεται διὰ τὴν πίλησιν· φησὶ γὰρ ὄρη εἶναι ἐκεῖσε ὑψηλότατα, εἰς ἃ τὰ νέφη προσπταίουσι, καὶ εἶθ’ οὕτως καταρρήγνυται διὰ τὴν γινομένην πίλησιν. ἀλλὰ μὴν καὶ ἐπὶ τῶν λεβήτων ὑγρότης, φησίν, ἀντικαταρρεῖ, ἔτι δὲ καὶ ἐπὶ τῶν θόλων τῶν λουτρῶν μὴ παρούσης ψύξεως, διὰ τὴν πίλησιν δηλονότι τούτου γινομένου.
(Olympiodorus, In Aristotelis Meteorologica 1.9 346b30 (CAG t.12.2 p.80.30-81.1 Stüve)

One should know that Aristotle says that the cause of the change to water is the cooling only; but Theophrastus says that not only cooling is the cause of the coming-to-be of the water, but also compression. For consider; there is no cooling in Ethiopia, but nevertheless rain falls because of compression. For he says that there are very high mountains there, against which the clouds strike, and then in this way rain bursts out because of the compression that takes place. Moreover, in the case of cauldrons too moisture, he says, runs down again, and also in the case of the domed rooms in baths, where there is no cooling, this clearly coming about because of the compression. (tr. William W. Fortenbaugh, Pamela M. Huby and/or Robert W. Sharples)