# Fragmenta 6.19

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.19

ιθ΄. Εἰς τρεῖς εὐθείας τὰς ΑΒ, ΑΓ, Α∠ ἀπό τινος σημείου τοῦ Ε δύο διήχθωσαν αἱ ΕΖ, ΕΒ, ἔστω δέ, ὡς ἡ ΕΖ πρὸς τὴν ΖΗ, οὕτως ἡ ΘΕ πρὸς τὴν ΘΗ ὅτι γίνεται καί, ὡς ἡ ΒΕ πρὸς τὴν ΒΓ, οὕτως ἡ Ε∠ πρὸς τὴν ∠Γ. ἤχθω διὰ τοῦ Η τῇ ΒΕ παράλληλος ἡ ΛΚ. ἐπεὶ οὖν ἐστιν, ὡς ἡ ΕΖ πρὸς τὴν ΖΗ, οὕτως ἡ ΕΘ πρὸς τὴν ΘΗ, ἀλλ᾿ ὡς μὲν ἡ ΕΖ πρὸς τὴν ΖΗ, οὕτως ἡ ΕΒ πρὸς τὴν ΗΚ, ὡς δὲ ἡ ΕΘ πρὸς τὴν ΘΗ, οὕτως ἐστὶν ἡ ∠Ε πρὸς τὴν ΗΛ, καὶ ὡς ἄρα ἡ ΒΕ πρὸς τὴν ΗΚ, οὕτως ἐστὶν ἡ ∠Ε πρὸς τὴν ΗΛ. ἐναλλάξ ἐστιν, ὡς ἡ ΕΒ πρὸς τὴν Ε∠, οὕτως ἡ Κ πρὸς τὴν ΗΛ. ὡς δὲ ἡ ΚΗ πρὸς τὴν ΗΛ, οὕτως ἐστὶν ἡ ΒΓ πρὸς τὴν Γ∠ καὶ ὡς ἄρα ἡ ΒΕ πρὸς τὴν Ε∠, οὕτως ἡ ΒΓ πρὸς τὴν Γ∠. ἐναλλάξ ἐστιν, ὡς ἡ ΕΒ πρὸς τὴν ΒΓ, οὕτως ἡ Ε∠ πρὸς τὴν ∠Γ. τὰ δὲ πτωτικὰ ὁμοίως.

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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/.