# De utilitate mathematicae 46

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 46. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/46

δ π β γ δ θ κε μθ αἱ δὲ διάμετροι τῶν πλευρῶν ἐναλλὰξ παρὰ μίαν ποτὲ μὲν μονάδι μείζους ἢ διπλάσιαι δυνάμει, ποτὲ δὲ μονάδι ἐλάττους ἢ διπλάσιαι ὁμαλῶς· πᾶσαι οὖν αἱ διάμετροι πασῶν τῶν πλευρῶν γενήσονται δυνάμει διπλάσιαι, τοῦ ἐναλλὰξ πλείονος καὶ ἐλάττονος τῇ αὐτῇ μονάδι ἐν πάσαις ὁμαλῶς τιθεμένῃ ἰσότητα ποιοῦντος εἰς τὸ μήτε ἐλλείπειν μήτε ὑπερβάλλειν ἐν ἁπάσαις τὸ διπλάσιον· τὸ γὰρ τῇ προτέρᾳ διαμέτρῳ λεῖπον δυνάμει τῇ ἐφεξῆς ὑπερβάλλει.

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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/.