# De utilitate mathematicae 86

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 86. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/86

Ἐρατοσθένης δὲ ἐν τῷ Πλατωνικῷ φησι, μὴ ταὐ- τὸν εἶναι διάστημα καὶ λόγον, ἐπειδὴ λόγος μέν ἐστι δύο μεγεθῶν ἡ πρὸς ἄλληλα ποιὰ σχέσις· γίνεται δʼ αὕτη καὶ ἐν διαφόροις 〈καὶ ἐν ἀδιαφόροις〉. οἷον ἐν φ λόγῳ ἐστὶ τὸ αἰσθητὸν πρὸς τὸ νοητόν, ἐν τούτῳ δόξα πρὸς ἐπιστήμην, καὶ διαφέρει καὶ τὸ νοητὸν τοῦ ἐπιστητοῦ ᾧ καὶ ἡ δόξα τοῦ αἰσθητοῦ. διάστημα δὲ ἐν διαφέρουσι μόνον, ἢ κατὰ τὸ μέγεθος ἢ κατὰ ποιό- τητα ἢ κατὰ θέσιν ἢ ἄλλως ὁπωσοῦν. δῆλον δὲ καὶ ἐντεῦθεν, ὅτι λόγος διαστήματος ἕτερον· τὸ γὰρ ἢμισυ πρὸς τὸ διπλάσιον 〈καὶ τὸ διπλάσιον πρὸς τὸ ἢμισυ〉 λόγον μὲν οὐ τὸν αὐτὸν ἔχει, διάστημα δὲ τὸ αὐτό.

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Theon Smyrnaeus, De utilitate mathematicae, ed. Eduardus Hiller. Text: The Greek Library, from the Perseus Digital Library and other open sources, CC BY-SA 4.0. Changes: apostrophes normalised and the text divided into reading sections by Interlinea.
License: CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/). Source: https://thegreeklibrary.pages.lisn.upsaclay.fr/works/tlg1724.tlg001.local001/.