# Synagoge 2-2

Pappus Alexandrinus, Synagoge, ΠΑΠΠΟΥ ΑΛΕΞΑΝΔΡΕΩΣ ΣΥΝΑΓΩΓΗΣ Γ.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/2-2

2 α΄. Ἔστωσαν δύο εὐθεῖαι αἱ ΑΒ ΑΓ πρὸς ὀρθὰς ἀλλήλαις, καὶ ἤχθω ἀπὸ τοῦ Β τῇ ΑΓ παράλληλος ἡ Β∠, καὶ κείσθω τῇ ΑΒ· ἴδη ἡ Β∠, καὶ ἐπεζεύχθω ἡ ∠Γ, καὶ συμπιπτέτω τῇ ΒΑ κατὰ τὸ Ε, καὶ ἀπὸ τοῦ Ε τῇ ΑΓ παράλληλος ἡ ΕΘ, καὶ ἐκβεβλήσθω ἡ Β∠, καὶ ἤχθω ἀπὸ τοῦ ∠ τῇ ΒΕ παράλληλος ἡ ∠Η, καὶ κείσθωσαν τῇ Β∠ ἴσαι αἱ ∠Ν ΝΛ ΛΞ ΞΚ καὶ διὰ τῶν Ν Λ Ξ Κ σημείων τῇ ΒΕ παράλληλοι αἱ ΝΟ ΛΜ ΞΠ ΚΘ καὶ κείσθω τῇ ΒΑ ἴση ἡ ΚΡ, καὶ τετμήσθω δίχα ἡ ΚP κατὰ τὸ Σ, καὶ ὡς ἡ ΚΘ πρὸς ΘΣ, οὕτως ἡ ΣΘ πρὸς ΘΤ, ὡς δέ ἡ ΣΘ πρὸς ΘΤ, οὕτως ἡ ΘΤ πρὸς ΘΦ, καὶ ἀφῃρήσθω ἀπὸ τῆς ΞΠ τῇ ΑΒ ἴση ἡ ΧΞ, καὶ ἐπεζεύχθω ἡ ΧΚ καὶ ἡ ΚΦ καὶ ἀπὸ τοῦ Σ τῇ XΦ παράλληλος ἡ ΣΨ, ὑπὸ δὲ τοῦ Ψ τῇ ΚΞ παράλληλος ἡ ΨΩ, καὶ ἔστω ὡς ΛΜ πρὸς ΜΩ, οὕτως ἡ ΩΜ πρὸς ΜΑ. ὡς δὲ ἡ ΩΜ πρὸς ΜΑ, οὕτως ἡ ΑΜ πρὸς ΜΒ, καὶ ἀφῃρήσθω ἀπὸ τῆς ΟΝ τῇ ΑΒ ἴση ἡ ΝΓ, καὶ ἐπεζεύχθω ἡ ΓΛ καὶ ἡ ΓΒ, καὶ ἤχθω ἀπὸ τοῦ Ω τῇ ΒΓ παράλληλος ἡ Ω∠, ἀπὸ δέ τοῦ ∠ τῇ ΛΝ παράλληλος ἡ ΛΕ, καὶ ἔστω ὡς ἡ ∠Η πρὸς ΗΕ, οὕτως ΗΕ πρὸς ΗΖ, ὡς δὲ ἡ ΕΗ πρὸς ΗΖ, οὕτως ἡ ΖΗ πρὸς ΗΘ, καὶ ἐπεζεύχθω ἡ ΘΓ, καὶ ἤχθωσαν τῇ ΘΓ παράλληλοι αἱ ΖΚ ΕΛ, καὶ ἀπὸ τῶν Κ Λ ταῖς ΑΓ B∠ παράλληλοι αἱ ΚΜ ΛΝ δεῖξαι ὅτι τῶν ΑΓ Β∠ υέσαι ἀνάλογόν εἰσιν αἱ ΜΚ ΝΛ.

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Pappus Alexandrinus, Synagoge, ed. Friedrich Hultsch. 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/tlg2032.tlg001.local001/.