# Fragmenta 6.9

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.9

θ΄. Ἔστω τρίγωνον τὸ ΑΒΓ καὶ ἐν αὐτῷ διήχθωσαν αἱ Α∠, ΑΕ, καὶ τῇ ΒΓ παράλληλος ἤχθω ἡ ΖΗ, καὶ κεκλάσθω ἡ ΖΘΗ, ἔστω δέ, ὡς ἡ ΒΘ πρὸς τὴν ΘΓ, οὕτως ἡ ∠Θ πρὸς τὴν ΘΕ ὅτι παράλληλός ἔστιν ἡ ΚΛ τῇ ΒΓ. ἐπεὶ γάρ ἐστιν, ὡς ἡ ΒΘ πρὸς τὴν ΘΓ, οὕτως ἡ ∠Θ πρὸς τὴν ΘΕ, λοιπὴ ἄρα ἡ Β∠ πρὸς λοιπὴν τὴν ΓΕ ἐστιν, ὡς ἡ ∠Θ πρὸς τὴν ΘΕ. ὡς δὲ ἡ Β∠ πρὸς τὴν ΕΓ, οὕτως ἐστὶν ἡ ΖΜ πρὸς Ν καὶ ὡς ἄρα ἡ ΖΜ πρὸς ΝΗ, οὕτως ἐστὶν ἡ ∠Θ πρὸς τὴν ΘΕ. ἐναλλάξ ἔστιν, ὡς ἡ ΖΜ πρὸς τὴν ∠Θ, οὕτως ἡ ΝΗ πρὸς τὴν ΘΕ. ἀλλʼ ὡς μὲν ἡ ΖΜ πρὸς τὴν ∠Θ, οὕτως ἐστὶν ἐν παραλλήλῳ ἡ ΖΚ πρὸς τὴν ΚΘ, ὡς δὲ ἡ ΗΝ πρὸς τὴν ΘΕ, οὕτως ἐστὶν ἡ ΗΛ πρὸς τὴν ∠Θ καὶ ὡς ἄρα ἡ ΖΚ πρὸς τὴν Κ Θ, οὕτως ἐστὶν ἡ ΗΛ πρὸς τὴν ∠Θ. παράλληλος ἄρα ἐστὶν ἡ ΚΛ τῇ ΗΖ· ὥστε καὶ τῇ ΓΒ.

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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/.