# Fragmenta 6.33

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.33

λγ΄. Κύκλος περὶ διάμετρον τὴν ΑΒ, καὶ ἐκβεβλήσθω ἡ ΑΒ καὶ ἔστω ἐπὶ τυχοῦσαν τὴν ∠Ε κάθετος, καὶ τῷ ὑπὸ ΑΖΒ ἴσον κείσθω τὸ ἀπὸ ΖΗ τετράγωνον· ὅτι, οἷον ἐὰν ληφθῇ σημεῖον ὡς τὸ Ε, καὶ ἀπ᾿ αὐτοῦ ἐπὶ τὸ Η ἐπιζευχθεῖσα ἐκβληθῇ ἐπὶ τὸ Θ, γίνεται καὶ τὸ ὑπὸ ΘΕΚ ἴσον τῷ ἀπὸ ΚΗ τετραγώνῳ. ἐπεζεύχθωσαν αἱ ΑΕ, ΒΛ ὀρθὴ ἄρα ἐστὶν ἡ Θ Λ γωνία. ἔστιν δὲ καὶ ἡ Ζ ὀρθή· τὸ ἄρα ὑπὸ ΑΕΛ ἴσον ἐστὶν τῷ τε ὑπὸ ΑΖΒ καὶ τῷ ἀπὸ ΖΕ τετραγώνῳ. ἀλλὰ τὸ μὲν ὑπὸ ΑΕΛ ἴσον ἐστὶν τῷ ὑπὸ ΘΕΚ, τὸ δὲ ὑπὸ ΑΖΒ ἴσον ἐστὶν τῷ ἀπὸ τετραγώνῳ· τὸ ἄρα ὑπὸ ΘΕΚ ἴσον ἐστὶν τοῖς ἀπὸ τῶν ΕΖ, ΖΗ τετραγώνοις, τουτέστιν τῷ ἀπὸ ΕΗ 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/.