# De utilitate mathematicae 81

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 81. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/81

πολλαπλασιεπιμόριος δέ ἐστι λόγος, ὅταν ὁ μείζων ὅρος δὶς ἢ πλεονάκις ἔχῃ τὸν ἐλάττονα καὶ ἔτι μέρος αὐτοῦ, ὡς ὁ μὲν τῶν ζʹ δὶς ἔχει τὸν γʹ καὶ ἔτι τρίτον αὐτοῦ, καὶ λέγεται αὐτοῦ διπλασιεπίτριτος, ὁ δὲ τῶν θʹ δὶς ἔχει 〈τὸν〉 τῶν δʹ καὶ ἔτι τὸ τέταρτον· αὐτοῦ, λέγεται δὲ διπλασιεπιτέταρτος, ὁ δὲ τῶν ιʹ τρὶς ἔχει τὸν τῶν γʹκαὶτὸτρίτον αὐτοῦ, καὶ λέγεται τριπλασιεπίτριτος. παραπλησίως δὲ θεωρείσθωσαν καὶ οἱ λοιποὶ πολλα- πλασιεπιμόριοι. τοῦτο δὲ συμβαίνει, ὅταν δυεῖν προ- τεθέντων ἀριθμῶν ὁ ἐλάττων καταμετρῶν τὸν μείζονα μὴ ἰσχύσῃ ὅλον καταμετρῆσαι, ἀλλʼ ἀπολείπῃ μέρος τοῦ μείζονος, ὅ ἐστιν αὐτοῦ τοῦ ἐλάσσονος μέρος· οἷον ὁ τῶν κϚʹ τοῦ τῶνηʹ πολλαπλασιεπιμόριος λέγεται, ἐπειδή- περ 〈ὁ〉 ηʹτρὶς καταμετρήσας τὸν κςʹ οὐχ ὅλον ἀπήρτι- σεν, ἀλλὰ μέχρι τῶν κδʹ ἐλῦών δύο ἐκ τῶν κςʹ ἀπέλι- πεν, ὅ ἐστι τῶν ηʹ τέταρτον.

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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/.