# Fragmenta 6.37

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.37

λζ΄. Ἡμικύκλιον τὸ ἐπὶ τῆς ΑΒ, καὶ ἀπὸ τυχόντος τοῦ Γ διήχθω ἡ Γ∠, καὶ κάθετος ἤχθω ἡ ∠Ε ὅτι τὸ ἀπὸ ΑΓ τοῦ ἀπὸ Γ∠ ὑπερέχει τῷ ὑπὸ συναμφοτέρου τῆς ΑΓ, καὶ τῆς ΑΕ. ὅτι ἄρα τὸ ἀπὸ ΑΓ ἴσον ἐστὶν τῷ τε ἀπὸ ∠Γ, τουτέστιν τοῖς ἀπὸ ∠Ε, ΕΓ καὶ τῷ ὑπὸ συναμφοτέρου τῆς ΑΓΒ καὶ τῆς ΑΕ. ὅτι ἄρα κοινοῦ ἀφαιρεθέντος τοῦ ὑπὸ ΓΑΕ λοιπὸν τὸ ὑπὸ ΑΓE ἴσον ἐστὶν τῷ τε ἀπὸ ∠Ε, τουτέστιν τῷ ὑπὸ ΑΕΒ, καὶ τῷ ἀπὸ ΓΕ καὶ τῷ ὑπὸ ΑΕ, ΓΒ. κοινοῦ ἀφαιρεθέντος τοῦ ἀπὸ ΓΕ, ὅτι λοιπὸν τὸ ὑπὸ ΑΕΓ ἴσον ἐστὶν τῷ τε ὑπὸ ΑΕΒ καὶ τῷ ὑπὸ ΑΕ, ΒΓ ἔστιν δέ.

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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/.