# De utilitate mathematicae 93

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 93. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/93

τὸ δὲ λεῖμμα γίνεται ἐν λιγῶ ὅν ἔχει τὰ σνςʹ πρὸς σμγ΄. εὑρίσκεται δʼ οὕτω· δυεῖν ἐπογδόων ληφθέντων καὶ τούτων τρὶς πολλαπλασιασθέντων καὶ τῷ δὶς ἐπ- ογδόῳ προστεθέντος ἐπιτρίτου. οἷον εἶς μὲν ἐπόγδοος λόγος ὁ τῶν θʹ πρὸς τὰ η. ἐκι δὲ τούτων γίνονται δύο ἐπόγδοοι οὕτω· τὰ θʹ ἐφʼ ἑαυτὰ γίνεται πα, εἶτα τὰ θʹ ἐπὶ τὰ ηʹ γίνεται οβʹ, ἔπειτα τὰ ηʹ ἐφʼ ἑαυτὰ γίνεται ξδ΄, καὶ ἔστι τὰ μὲν παʹ τῶν οβʹ ἐπόγδοα, τὰ δὲ οβʹ τῶν ξδ΄ ἐπόγδοα. ἂν δὴ τρὶς ταῦτα λάβωμεν, τὰ μὲν παʹ γίνεται τρὶς σμγʹ, τὰ δὲ οβʹ γίνεται σιςʹ, τὰ δὲ ξδ΄ τρὶς γίνεται ρ̣?β΄. τούτων ἐπίτριτα τὰ σνϚ΄, ἅτινα πρὸς σμγ΄ ἔχει τὸν τοῦ λείμματος λόγον, ὅς ἐστι πλείων ἢ ἐποκτωκαιδέκςατος.

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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/.