# De utilitate mathematicae 80

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 80. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/80

ἐπιμερὴς δέ ἐστι λόγος, ὅταν ὁ μείζων ὅρος ἅπαξ ἔχῃ τὸν ἐλάττονα καὶ ἔτι πλείω μέρη αὐτοῦ τοῦ ἐλάτ- τονος], εἴπε ταὐτὰ καὶ ὅμοια εἴτε ἕτερα καὶ διάφορα· ταὐτὰ μὲν οἷον δύο τρίτα ἢ δύο πέμπτα καὶ εἴ τινα ἄλλα οὕτως· ὁ μὲν γὰρ τῶν εʹ ἀριθμὸς τοῦ τῶν γʹ δὶς ἐπίτριτος, ὁ δὲ τῶν ζ τοῦ τῶν εʹ δὶς ἐπίπεμπτος, ὁ δὲ τῶν ηʹ τοῦ τῶν εʹ τρὶς ἐπίπεμπτος, καὶ οἱ ἑξῆς ὁμοίως· ἕτερα δὲ καὶ διάφορα οἷον ὅταν ὁ μείζων αὐτόν τε ἔχῃ τὸν ἐλάττονα καὶ ἔτι ἢμισυ αὐτοῦ καὶ τρίτον, οἷον ἔχει λόγον ὁ τῶν ιαʹ πρὸς τὸν τῶν Ϛʹ, ἢ πάλιν ἥμισυ καὶ τέταρτον, ὅς ἐστι λόγος τῶν ζ πρὸς δʹ, ἢ νὴ Δία τρί- τον καὶ τέταρτον, ὅν ἔχει λόγον τὰ ιθʹ πρὸς τὰ ιβ΄. παραπλησίως δὲ θεωρείσθωσαν καὶ οἱ λοιποὶ ἐπιμερεῖς δυσὶν ὑπερέχοντες μέρεσιν ἢτρισὶν ἢπλείοσι, καὶ ὁμοίοις ἢ ἀνομοίοις. ὑπεπιμερὴς δέ ἐστιν [ὁ] ἀνάπαλιν ὁ ἐν τῷ προειρημένῳ λόγῳ ἐλάσσων πρὸς τὸν μείζονα ἐξετα- ζόμενος.

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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/.