# Commentarius in dimensionem circuli 112

Eutocius, Commentarius in dimensionem circuli, Εἰς τὸ γ΄ θεώρημα.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/eutocius/commentarius-in-dimensionem-circuli/112

Ἔτι δίχα ἡ ὑπὸ ΚΑΓ γωνία τῇ ΑΛ | Διὰ τὰ αὐτὰ δή ἐστιν ὡς συναμφότερος ἡ ΚΑ, ΑΓ πρὸς ΚΓ, ἡ ΑΛ πρὸς ΛΓ. Καὶ ἔστιν ἡ μὲν ΑΚ ἐλάσσων ἢ αζ, ἡ δὲ ΑΓ ἐλάσσων ἢ αθ Ϛ΄, ἡ δὲ ΚΓ ξϚ. Συναμφότερος ἄρα ἡ ΚΑ, ΑΓ πρὸς ΚΓ ἐλάσσονα λόγον ἔχει ἤπερ βιϚ Ϛ΄ πρὸς ξϚ. Καὶ ἡ ΑΛ ἄρα πρὸς ΛΓ ἐλάσσονα λόγον ἔχει ἤπερ βιϚ Ϛ΄ πρὸς ξϚ. Καὶ ἐπεὶ ἡ ΑΛ ὑπόκειται βιϚ Ϛ΄ καὶ τὸ ἀπʼ αὐτῆς δϡκη λϚ, ἡ δὲ ΛΓ ξϚ καὶ τὸ ἀπ᾿ αὐτῆς δτνϚ, ἴσον δὲ αὐτοῖς ἐστι τὸ ἀπὸ ΑΓ, ἔσται ἄρα Μ θσπδ λϚ΄· ὧν πλευρὰ τετραγωνική ἐστι βιζ δ΄ ἔγγιστα· ὑπερέχει γὰρ τὸ ἀπʼ αὐτῆς τοῦ ἀκριζοῦς μιγ L΄ κ΄. Ὥστε ἡ ΑΓ πρὸς ΓΑ ἐλάσσονα λόγον ἔχει ἤπερ βιζ δ΄ πρὸς ξϚ, Οἱ δὲ πολλαπλασιασμοὶ ὑπόκεινται·

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Eutocius, Commentarius in dimensionem circuli, ed. Charles Mugler. 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/tlg4072.tlg002.local001/.