# Fragmenta 6.11

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.11

ια΄. Τρίγωνον τὸ ΑΒΓ. καὶ τῇ ΒΓ παράλληλος ἡ Α∠, καὶ διαχθεῖσα ἡ ∠Ε τῇ ΒΓ συμπιπτέτω κατὰ τὸ Ε σημεῖον· ὅτι ἐστίν, ὡς τὸ ὑπὸ ∠Ε, ΖΗ πρὸς τὸ ὑπὸ ΕΖ, Η∠, οὕτως ἡ ΓΒ πρὸς τὴν ΒΕ. ἤχθω διὰ τοῦ Γ τῇ ∠Ε παράλληλος ἡ ΓΘ, καὶ ἐκβεβλήσθω ἡ ΑΒ ἐπὶ τὸ Θ. ἐπεὶ οὖν ἐστιν, ὡς ἡ Γ πρὸς τὴν ΑΗ, οὕτως ἡ ΓΘ πρὸς τὴν ΖΗ, ὡς δὲ ἠ Γ πρὸς τὴν ΑΗ, οὕτως ἐστὶν ἡ Ε∠ πρὸς τὴν ∠Η. καὶ ὡς ἄρα ἡ Ε∠ πρὸς τὴν ∠Η, οὕτως ἐστὶν ἡ ΘΓ πρὸς τὴν ΖΗ τὸ ἄρα ὑπὸ τῶν ΓΘ, ∠Η ἴσον ἐστὶν τῷ ὑπὸ τῶν Ε∠, ΖΗ. ἄλλο δέ τι τυχὸν τὸ ὑπὸ ΕΖ, Η∠ ἔστιν ἄρα, ὡς τὸ ὑπὸ ∠Ε, ΖΗ πρὸς τὸ ὑπὸ ∠Η, ΕΖ, οὕτως τὸ ὑπὸ ΓΘ, ∠Η πρὸς τὸ ὑπὸ ∠Η, ΕΖ, τουτέστιν ἡ ΓΘ πρὸς ΕΖ, τσυτέστιν ἡ ΓΒ πρὸς ΒΕ. ἔστιν οὖν, ὡς τὸ ὑπὸ ∠Ε, ΖΗ πρὸς τὸ ὑπὸ ΕΖ, Η∠, οὕτως ἡ ΓΒ πρὸς ΒΕ. τὰ δʼ αὐτά, κἂν ἐπὶ τὰ ἕτερα μέρη ἀχθῇ ἡ Α∠ παράλληλος, καὶ ἀπὸ τοῦ ∠ ἐκτὸς ὡς ἐπὶ τὸ Γ διαχθῇ ἡ εὐθεῖα.

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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/.