# Fragmenta 6.Εἰς τὸ δεύτερον πόρισμα.

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.%CE%95%E1%BC%B0%CF%82%20%CF%84%E1%BD%B8%20%CE%B4%CE%B5%CF%8D%CF%84%CE%B5%CF%81%CE%BF%CE%BD%20%CF%80%CF%8C%CF%81%CE%B9%CF%83%CE%BC%CE%B1.

β΄. Καταγραφὴ ἡ ΑΒΓ∠ΕΖΗΘ, ἔστω δὲ παράλληλος ἡ ΑΖ τῇ ∠Β, ὡς δὲ ἡ ΑΕ πρὸς τὴν ΕΖ, οὕτως ἡ ΓΗ πρὸς τὴν ΗΖ ὅτι εὐθεῖά ἐστιν ἡ διὰ τῶν Θ, Κ, Ζ. ἤχθω διὰ τοῦ Η παρὰ τὴν ∠Ε ἡ ΗΛ, καὶ ἐπιζευχθεῖσα ἡ ΘΚ ἐκβεβλήσθω ἐπὶ τὸ Λ. ἐπεῖ οὖν ἐστιν, ὡς ἡ ΑΕ πρὸς τὴν ΕΖ, οὕτως ἡ ΓΗ πρὸς τὴν ΗΖ, ἐναλλάξ ἐστιν, ὡς ἡ ΑΕ πρὸς τὴν ΓΗ οὕτως ἡ ΕΖ πρὸς τὴν ΖΗ. ὡς δὲ ἡ ΑΕ πρὸς τὴν ΓΗ οὕτως ἡ ΕΘ πρὸς τὴν ΗΛ καὶ ὡς ἀρα ἡ Ε πρὸς τὴν ΖΕ, οὕτως ἡ ΕΘ πρὸς τὴν ΗΛ. καί ἔστι παράλληλος ἡ ΕΘ τῇ ΗΛ· εὐθεῖα ἄρα ἐστὶν ἡ διὰ τῶν Θ, Λ, Ζ· ὅπερ ἔδει δεῖξαι.

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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/.