# Synagoge 70

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/70

70 λε΄. Δυνατὸν δὲ καὶ παραλληλόγραμμον εὑρεῖν, οὗ ἐπὶ τῆς βάσεως ἐντὸς εὐθεῖαι δύο συνίστανται ταῖς περιεχούσαις τρισὶν ἴσαι καὶ μείζους αὐτῶν προδιδαχθέντος τοῦδε. Ἔστω ἡ ΑΒ τῆς ΒΓ δοθείσῃ μείζων ἢ ἐν λόγῳ ἀγαγεῖν παράλληλον τῇ AΓ τὴν ∠Ε καὶ ποιεῖν ἐν τῷ λόγῳ τὴν Α∠ πρὸς συναμφότερον τὴν ∠Ε ΒΓ. Γεγονέτω. ἐπεὶ ἡ ΑΒ τῆς ΒΓ δοθείσῃ μείζων ἐστὶν ἢ ἐν λόγῳ, ἔστω λόγος τῆς ΑΒ πρὸς τὴν ΒΓ μετὰ δοθείσης· ἔστω τῆς Ζ. ὁ δʼ αὐτός ἐστιν καὶ τῆς Α∠ πρὸς τὰς ∠Ε ΒΓ· καὶ λοιπῆς ἄρα τῆς Β∠ λόγος πρὸς τὴν τῶν Ζ ∠Ε ὑπεροχὴν ὁ αὐτός ἐστίν. καὶ ἔστιν δοθεῖσα ἡ Ζ· δοθεῖσα ἄρα καὶ ἡ ∠Ε *** θέσει ἄρα *** ὥστε καί, ἂν ἡ ΑΒ τῆς ΒΓ μείζων ᾖ ἢ διπλῆ, δυνατὸν ἔσται ἀγαγεῖν παράλληλον τὴν ∠Ε καὶ ποιεῖν τὴν Α∠ διπλῆν συναμφοτέρου τῆς ∠Ε ΒΓ.

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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/.