# Fragmenta 6.22

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.22

κβ΄. Εὐθεῖα ἡ ΑΒ, καὶ ἐπ᾿ αὐτῆς δύο σημεῖα τὰ Γ, ∠, ἔστω δὲ τὸ δὶς ὑπὸ ΑΒ, Γ∠ ἴσον τῷ ἀπὸ ΓΒ· ὅτι καὶ τὸ ἀπὸ Α∠ ἴσον ἐστὶν τοῖς ἀπὸ τῶν Α ∠Β τετραγώνοις. ἐπεὶ γὰρ τὸ δὶς ὑπὸ ΑΒ, Γγώνοις. ἴσον ἐστὶ τῷ ἀπὸ ΓΒ, κοινὸν ἀφῃρήσθω τὸ δὶς ὑπὸ Β∠Γ λοιπὸν ἄρα τὸ δὲς ὑπὸ Α∠Γ ἴσον ἐστὶν τοῖς ἀπὸ τῶν Γ∠, ∠Β τετραγώνοις. κοινὸν ἀφῃρήσθω τὸ ἀπὸ ΓΔ τετράγωνον· λοιπὸν ἄρα τὸ θὶς ὑπὸ ΑΓ∠ μετὰ τοῦ ἀπὸ Γ∠ ἴσον ἐστὶν τῷ ἀπὸ ∠Β τετραγώνῳ. κοινὸν προσκείσθω τὸ ἀπὸ ΑΓ τετράγωνον· ὅλον ἄρα τὸ ἀπὸ Α∠ τετράγωνον ἴσον ἐστὶν τοῖς ἀπὸ τῶν ΑΓ, ∠Β τετραγώνοις.

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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/.