# De utilitate mathematicae 48

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 48. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/48

ἐλλιπεῖς δέ εἰσιν ὧν τὰ μέρη συντεθέντα ἐλάττονα τὸν ἀριθμὸν ποιεῖ τοῦ ἐξ ἀρχῆς προτεθέντος ἀριθμοῦ, οἷον ὁ τῶν η΄· τούτου γὰρ ἥμισυ δ΄, τετάρτον β΄, ὄγδοον ἕν. τὸ αὐτὸ δὲ καὶ τῷ ι΄ συμβέβηκεν, ὃν καθʼ ἕτερον λόγον τέλειον ἔφασαν οἱ Πυθαγορικοί, περὶ οὗ κατὰ τὴν οἰκείαν χώραν ἀποδώσομεν. λέγεται δὲ καὶ ὁ γ΄ τέλειος, ἐπειδὴ πρῶτος ἀρχὴν καὶ μέσα καὶ πέρας ἔχει· ὁ δʼ αὐτὸς καὶ γραμμή ἐστι καὶ ἐπίπεδον, τρίγωνον γὰρ ἰσόπλευρον ἑκάστην πλευρὰν δυεῖν μονάδων ἔχον, καὶ πρῶτος δεσμὸς καὶ στερεοῦ δύναμις· ἐν γὰρ τρισὶ δια- στάσεσι τὸ στερεὸν νοεῖσθαι.

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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/.