# De utilitate mathematicae 90

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 90. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/90

διαφέρει δὲ ἀναλογίας μεσότης, ἐπειδὴ εἰ μέν τι ἀναλογία, τοῦτο καὶ μεσότης, εἰ δέ τι μεσότης, οὐκ εὐ- θὺς ἀναλογία. ἐγχωρεῖ γάρ τι κατὰ τάξιν μέσον ὅν μὴ ἔχειν ἀναλόγως πρὸς τὰ ἄκρα· ὡς τὰ δύο μέσα ἐστὶ τῇ τάξει 〈τοῦ ἑνὸς καὶ〉 τῶν γʹ, καὶ τοῦ ἑνὸς καὶ 〈τῶν ιʹ〉 τὰ γʹ καὶ τὰ δʹ καὶ τὰ εʹ· ἀπὸ γὰρ τοῦ ἑνὸς οὐχ οἷόν τε ἐλθεῖν ἐπὶ τὰ ι΄ μὴ πρότερον ἐλθόντα ἐπὶ τὰ β΄ καὶ τὰ γ΄ καὶ τὰ δ. ἀλλʼ οὐδὲν τούτων ἀναλόγως ἔχει πρὸς τὰ ἄκρα. τὸ γὰρ ἓν οὐκ ἐν τούτῳ ἐστὶ τῷ λόγῳ πρὸς τὰ β, ἐν ᾧ τὰ β΄ πρὸς τὰ γ΄· ὁμοίως καὶ ἐπὶ τῶν β΄ καὶ γ΄ καὶ δ΄. τὰ δὲ ἐν τῷ αὐτῷ λόγῳ ὄντα καὶ μέσα ἂν εἴη, οἷον ἔν β΄ δ΄. ἀναλογία τε γάρ ἐστιν ἡ τοῦ δι- πλασίου, καὶ τά β΄ μέσα τοῦ ἑνὸς καὶ τῶν δ΄.

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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/.