# De utilitate mathematicae 137

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 137. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/137

ἐπὶ μέρους δὲ ἀριθμητικὴ μέν ἐστι μεσότης ἡ τῷ αὐτῷ ἀριθμῷ τῶν ἄκρων τοῦ μὲν ὑπερέχουσα, ὑφʼ οὗ δὲ ὑπερεχομένη· οἷον γ΄ β΄ α΄ ὁ γὰρ τῶν β΄ ἀριθμὸς μονάδι ὑπερέχει τοῦ ἑνὸς καὶ μονάδι ὑπερέχεται ὑπὸ τοῦ γ΄. συμβέβηκε δὲ ταύτῃ τῇ μεσότητι πρὸς τὴν τῶν ἄκρων σύνθεσιν ὑποδιπλασίῳ εἶναι· ἥ τε γὰρ τριὰς καὶ ἡ μονὰς συντεθεῖσαι τὴν τετράδα ἐποίησαν, ἥτις δι- πλασία ἐστὶ τοῦ μέσου ἀριθμοῦ τῆς δυάδος.

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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/.