# Fragmenta 6.13

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.13

ιγ΄. Ἀλλὰ δὴ μὴ ἔστωσαν αἱ ΑΒ, Γ∠ παράλληλοι, ἀλλὰ συμπιπτέτωσαν κατὰ τὸ Ν· ὅτι πάλιν εὐθεῖά ἐστιν ἡ διὰ τῶν Η, Μ, Κ. ἐπεὶ εἰς τρεῖς εὐθείας τὰς ΑΝ, ΑΖ, Α∠ ἀπὸ τοῦ αὐτοῦ σημείου τοῦ Γ δύο διηγμέναι εἰσὶν αἱ ΓΕ Γ∠, γίνεται, ὡς τὸ ὑπὸ ΓΕ, ΗΘ πρὸς τὸ ὑπὸ ΓΗ, ΘΕ, οὕτως τὸ ὑπὸ τῶν ΓΝ, Ζ∠ πρὸς τὸ ὑπὸ τῶν Ν∠, Γ Ζ. πάλιν ἐπεὶ ἀπὸ τοῦ αὐτοῦ σημείου τοῦ ∠ εἰς τρεῖς εὐθείας τὰς ΒΝ, ΒΓ, ΒΖ δύο εἰσὶν διηγμέναι αἱ ∠Ε, ∠Ν, ἔστιν, ὡς τὸ ὑπὸ ΝΓ, Ζ∠ πρὸς τὸ ὑπὸ Ν∠, ΖΓ οὕτως τὸ ὑπὸ ∠Κ, ΕΛ πρὸς τὸ ὑπὸ ∠Ε, ΚΛ. ἀλλʼ ὡς τὸ ὑπὸ ΝΓ, Ζ∠ πρὸς τὸ ὑπὸ Ν∠, Γ Ζ, οὕτως ἐδείχθη τὸ ὑπὸ ΓΕ, πρὸς τὸ ὑπὸ ΓΗ, ΘΕ καὶ ὡς ἄρα τὸ ὑπὸ ΓΕ ΘΗ πρὸς τὸ ὑπὸ ΓΗ, ΘΕ, οὕτως ἐστὶν τὸ ὑπὸ ∠Κ, ΕΛ πρὸς τὸ ὑπὸ ∠Ε, ΚΛ. διὰ δὴ τὸ προγεγραμμένον εὐθεῖά ἐστιν ἡ διὰ τῶν Η, Μ, Κ.

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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/.