# De utilitate mathematicae 128

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 128. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/128

ἐκ δὲ τῶν πολλαπλασίων ἀνάπαλιν τεθέντων [α΄ α΄ α΄] καὶ ὁμοίως πλαττομένων οἱ ἐπιμόριοι λόγοι 〈καὶ αἱ〉 ἐν τούτοις συστήσονται ἀναλογίαι, ἐκ μὲν τῶν διπλασίων ἡμιόλιοι, ἐκ δὲ τῶν τριπλασίων οἱ ἐπίτριτοι, ἐκ δὲ τῶν τετραπλασίων ἐπιτέταρτοι, καὶ ἀεὶ ἑξῆς οὕτως. οἷον ἔστω ἀναλογία κατὰ τὸν διπλάσιον λόγον ἐν τρισὶν ὅροις, τοῦ μείζονος κειμένου πρώτου, καὶ πεπλάσθωσαν ἕτεροι τρεῖς ἐκ τούτων τὸν εἰρημένον τρόπον· δ΄ β΄ α΄ οἱ δὲ ἐξ αὐτῶν γενήσονται δʹ Ϛʹ θ΄· γίνεται ἀνάλογον ἐν ἡμιολίοις. πάλιν ἔστωσαν τρεῖς ὅροι ἀνάλογον ἐν τριπλασίοις θ΄ γ΄ α΄· συστήσονται τὸν αὐτὸν τρόπεον ἐκ τούτων ὅροι τρεῖς ἀνάλογον ἐν ἐπιτρίτοις θ΄ ιβ΄ ιϛ΄. ἐκ δὲ τῶν τετραπλασίων συστήσονται ἐν ἐπιτετάρτοις ιϚ΄ κ΄ κε΄, καὶ οὕτως ἀεὶ ἐκ τῶν ἐχομένων οἱ ἑξῆς ὁμώνυμοι.

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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/.