# Commentarius in dimensionem circuli 69

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/eutocius/commentarius-in-dimensionem-circuli/69

Τετμήσθω δίχα ἡ ὑπὸ ΒΑΓ τῇ ΑΖΗ. Ἐπεὶ οὖν ἴση ἐστὶν ἡ ὑπὸ ΒΑΗ τῇ ὑπὸ ΗΓΒ, ἐπὶ γὰρ τῆς αὐτῆε περιφερείας βεβήκασιν, ἀλλὰ καὶ τῇ ὑπὸ ΗΑΓ, καὶ ἡ ὑπὸ ΗΓΒ ἄρα τῇ ὑπὸ ΗΑΓ ἐστὶν ἴση. Καὶ κοινὴ ἡ ὑπὸ ΑΗΓ ὀρθή· καὶ λοιπὴ ἄρα ἡ ὑπὸ ΗΖΓ λοιπῆ τῇ ὑπὸ ΑΓΗ ἐστὶν ἴση. Ἰσογώνιον ἄρα ἐστὶ τὸ ΑΗΓ τρίγωνον τῷ ΓΗΖ τρινώνῳ· ἔστιν ἄρα ὡς ἡ ΑΗ πρὸς ΗΓ, ἡ ΓΗ πρὸς ΗΖ καὶ ἡ ΑΓ πρὸς ΓΖ. Τῶν γὰρ ἰσογωνίων τριγώνων ἀνάλογόν εἰσιν αἱ πλευραί, καὶ ὁμόλογοι αἱ τὰς ἴσας γωνίας ὑποτείνουσαι.

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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/.