# De utilitate mathematicae 20

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 20. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/20

περισσάκις δὲ ἄρτιοί εἰσιν ὧν ὁ πολλαπλασιασμὸς ἐκ δυεῖν ὡντινωνοῦν περισσοῦ καὶ ἀρτίου γίνεται, καὶ πολλαπλασιασθέντες εἰς ἴσα μὲν ἄρτια μέρη δίχα διαι- ροῦνται, κατὰ δὲ τὰς πλείους διαιρέσεις ἃ μὲν ἄρτια μέρη, ἃ δὲ περισσὰ ἔχουσιν· ὡς ὁ ιβ΄ καὶ κ΄· τρὶς γὰρ δ΄ ιβ΄, καὶ πεντάκις δ΄ κ΄· καὶ τὰ μὲν ιβ΄ διχῆ διαιρεῖ- ται 〈εἰς〉 ϛ΄ καὶ ϛ΄, τριχῇ δὲ εἰς δ΄ καὶ δ΄ καὶ δ΄, τετραχῆ δὲ εἰς τετράκις γ΄· τὰ δὲ κ΄ διχῆ μὲν εἰς ι΄, τετραχῆ δὲ εἰς ε΄, πενταχῆ δὲ εἰς 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/.