# Fragmenta 6.23

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.23

κγ΄. Ἔστω τὸ ὑπὸ ΑΒΓ ἴσον τῷ ἀπὸ Β∠ τετραγώνῳ· ὅτι γίνεται γ, τὸ μὲν ὑπὸ συναμφοτέρου τῆς Α∠Γ καὶ τῆς Β∠ ἴσον τῷ ὑπὸ Α∠, ∠Γ, τὸ δὲ ὑπὸ συναμφοτέρου τῆς Α∠Γ καὶ τῆς ΒΓ ἴσον τῷ ἀπὸ ∠Γ τετραγώνῳ, τὸ δὲ ὑπὸ συναμφοτέρου τῆς Α∠Γ καὶ τῆς ΒΑ ἴσον τῷ ἀπὸ Α∠ τετραγώνῳ. ἐπεὶ γὰρ τὸ ὑπὸ ΑΒΓ ἴσον ἐστὶν τῷ ἀπὸ Β∠, ἀνάλογον καὶ ὅλη πρὸς ὅλην καὶ ἀνάπαλιν καὶ συνθέντι· ἔστιν ἄρα, ὡς συναμφότερος ἡ Γ∠, ∠Α πρὸς τὴν ∠Α, οὕτως ἡ Γ∠ πρὸς τὴν ∠Β· τὸ ἄρα ὑπὸ συναμφοτέρου τῆς Α∠, ∠Γ καὶ τῆς Β∠ ἴσον ἐστὶ τῷ ὑπὸ τῶν Α∠Γ. πάλιν, ἐπεὶ ὅλη ἡ Α∠ πρὸς ὅλην τὴν ∠Γ ἐστιν, ὡς ἡ ∠Β πρὸς τὴν ΒΓ, συνθέντι ἐστίν, ὡς συναμφότερος ἡ Α∠Γ πρὸς τὴν ∠Γ, οὕτως ἡ ∠Γ πρὸς τὴν ΓΒ· τὸ ἄρα ὑπὸ συναμφοτέρου τῆς Α∠Γ καὶ τῆς ΓΒ ἴσον ἐστὶν τῷ ἀπὸ ∠Γ. πάλιν, ἐπεὶ ὅλη ἡ Α∠ πρὸς ὅλην τὴν ∠Γ ἐστιν, ὡς ἡ ΑΒ πρὸς τὴν Β∠, ἀνάπαλιν καὶ συνθέντι ἐστίν, ὡς συναμφότερος ἡ Γ∠Α πρὸς τὴν ∠Α, οὕτως ἡ ∠Α πρὸς τὴν ΑΒ· τὸ ἄρα ὑπὸ συναμφοτέρου τῆς Α∠Γ καὶ τῆς ΑΒ ἴσον ἐστὶν τῷ ἀπὸ Α∠ τετραγώνῳ.

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Euclid, Fragmenta, ed. Heinrich Menge. 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/tlg1799.tlg016.local001/.