Plato Seeks the G (ometry) Spot

Plutarch, Convivial Questions (718f):

Geometry being especially, according to Philolaos, the beginning and the metropolis of other studies, it excites and turns one’s intellect, such that it is purified and loosened from the objects of perception. For this reason, Plato himself dislikes those like Eudoxus and Archytas and Menaichmos who undertake to apply the squaring of the cube to instrumental or mechanical uses. Thus the good of geometry perishes and is wasted when it rushes back to the realm of the visible, and is not born upward, and does not take hold of the unseen and incorporeal forms, existing in respect to which God is always God.

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μάλιστα δὲ γεωμετρία κατὰ τὸν Φιλόλαον (Vorsokr. 44 A 7a) ἀρχὴ καὶ μητρόπολις οὖσα τῶν ἄλλων ἐπανάγει καὶ στρέφει τὴν διάνοιαν, οἷον ἐκκαθαιρομένην καὶ ἀπολυομένην ἀτρέμα τῆς αἰσθήσεως. διὸ καὶ Πλάτων αὐτὸς ἐμέμψατο τοὺς περὶ Εὔδοξον καὶ ᾿Αρχύταν καὶ Μέναιχμον εἰς ὀργανικὰς καὶ μηχανικὰς κατασκευὰς τὸν τοῦ στερεοῦ διπλασιασμὸν ἀπάγειν ἐπιχειροῦντας· ἀπόλλυσθαι γὰρ οὕτω καὶ διαφθείρεσθαι τὸ γεωμετρίας ἀγαθὸν αὖθις ἐπὶ τὰ αἰσθητὰ παλινδρομούσης καὶ μὴ φερομένης ἄνω μηδ’ ἀντιλαμβανομένης τῶν ἀιδίων καὶ ἀσωμάτων εἰκόνων, πρὸς αἷσπερ ὢν ὁ θεὸς ἀεὶ θεός ἐστιν’ (Plat. Phaedr. 249c).

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