# Synagoge 50-2

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/50-2

50 κή (θ΄ ) Εὐθεῖα ἡ ΑΒ, καὶ ἐπʼ αὐτῆς τυχόντα σημεῖα τὰ Γ ∠ ὅτι τὸ ὑπὸ συναμφοτέρου τῆς ΒΑ Α∠ καὶ τῆς ΓΒ μετὰ τοῦ ἀπὸ ΓΒ ἴσον τῷ δὶς ὑπὸ ΑΒ ΒΓ μετὰ τοῦ ὑπὸ ΒΓ∠. Τῇ Α∠ ἴση ἡ ΑΕ, τῇ δέ ΑΓ ἡ ΑΖ λοιπὴ ἄρα ἡ Γ∠ τῇ ΕΖ ἐστὶν ἴση. ἐπεὶ οὖν τὸ ὑπὸ ΑΒΓ ἴσον ἐστὶν τῷ ὑπὸ ΑΓΒ μετὰ τοῦ ἀπὸ ΓΒ διὰ τὸ γ΄ θεώρημα τοῦ β΄ στοιχείων, τὸ ἄρα δὶς ὑπὸ ΑΒΓ ἴσον ἐστὶν τῷ δὶς ὑπὸ ΑΓΒ μετὰ τοῦ δὶς ἀπὸ ΓΒ. τῷ δέ δὶς ὑπὸ ΑΓΒ ἴσον ἐστὶν τὸ ὑπὸ ΖΓΒ (διπλῆ γάρ ἐστιν ἡ ΖΓ τῆς ΓΑ) καὶ τὸ ὑπὸ ΖΓΒ ἄρα μετὰ τοῦ δὶς ἀπὸ ΓΒ ἴσον ἐστὶν τῷ δὶς ὑπὸ ΑΒΓ. κοινὸν προσκείσθω τὸ ὑπὸ ΓΒ ΕΖ, ὅπερ ἐστὶν τὸ ὑπὸ ΒΓ Γ∠ τὸ ἄρα ὑπὸ ΕΓ ΓΒ μετὰ τοῦ δὶς ἀπὸ ΓΒ ἴσον ἐστὶν τῷ δὶς ὑπὸ ΑΒΓ μετὰ τοῦ ὑπὸ ΒΓ∠ ἀλλὰ τῷ ὑπὸ ΕΓΒ μετὰ τοῦ δὶς ἀπὸ ΓΒ ἴσον ἐστὶ τὸ ὑπὸ ΕΒΓ μετὰ τοῦ ἀπὸ ΓΒ (τὸ γὰρ ὑπὸ ΕΓΒ μετὰ τοῦ ἀπὸ ΓΒ ἴσον ἐστὶν τῷ ὑπὸ ΕΒΓ διὰ τὸ αὐτὸ στοιχείων)· καὶ τὸ ὑπὸ ΕΒΓ ἔρα, ὅπερ ἐστὶν τὸ ὑπὸ συναμφοτέρου τῆς ΒΑ Α∠ καὶ τῆς ΒΓ, μετὰ τοῦ ἀπὸ ΓΒ, ἴσον ἐστὶν τῷ δὶς ὑπὸ ΑΒΓ μετὰ τοῦ ὑπὸ 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/.