# De utilitate mathematicae 141

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 141. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/141

ἡ δὲ πέμπτη μεσότης ἐστίν, ὅταν τριῶν ὅρων ὄντων ὅν ἂν ἔχῃ λόγον ὁ τρίτος πρὸς τὸν δεύτερον, τοῦτον ἔχῃ τὸν λόγον ἡ τοῦ πρώτου ὑπεροχὴ πρὸς τὴν τοῦ δευτέρου ὑπεροχήν· οἷον εʹ δʹ βʹ τὰ μὲν εʹ τῶν δʹ μονάδι ὑπερέχει, ἀλλὰ καὶ τὰ δʹ τῶν βʹ δυάδι· ὑπο- διπλάσια δὲ τὰ βʹ τῶν δʹ· καὶ τὸ ἕν δὲ τῶν βʹ ὑπο- διπλάσιον, ἅπερ ὑπεροχαί εἰσι τοῦ τε πρώτου καὶ τοῦ δευτέρου ἀριθμοῦ.

---

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/.