# Synagoge 77-2

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/77-2

77 μη΄ (ε΄.) Ἔστω κύκλος ὁ ΑΒΓ∠ περὶ κέντρον τὸ Ε καὶ διάμετρον τὴν ΑΓ, πενταγώνου δὲ ἔστω ἡ ∠ΗΒ πρὸς ὀρθὰς οὖσα τῇ ΑΓ διαμέτρῳ, καὶ κείσθω τῇ ΓΗ ἴση ἡ ΖΗ· ὅτι ἡ ΕΓ ἄκρον καὶ μέσον λόγον τέτμηται κατὰ τὸ Ζ, καὶ τὸ μεῖζον τμῆμά ἐστιν ἡ ΕΖ. Ἐπεζεύχθωσαν γὰρ αἱ Ε∠ Ζ∠ Γ∠. ἐπεὶ οὖν ἡ Γ∠ δ περιφέρεια δεκαγώνου ἐστίν (πενταγώνου γὰρ ἡ ∠ΓΒ), εἴη ἂν ἡ ὑπὸ ∠ΕΓ γωνία δύο πέμπτων ὀρθῆς· ὤστε ἑκατέρα τῶν ὑπὸ ΕΓ∠ Ε∠Γ τεσσάρων πέμπτων ὀρθῆς ἐστιν. ἀλλʼ ἐπεὶ ἡ ΖΗ τῇ ΗΓ ἴση ἐστίν, κοινὴ δὲ ἡ ∠Η καὶ πρὸς ὀρθὰς τῇ ΖΓ, ἔστιν ἄρα καὶ ἡ ∠Ζ εὐθεῖα τῇ ΛΓ ἴση· ὥστε καὶ ἡ ὑπὸ ∠ΖΓ ἴση οὖσα τῇ ὑπὸ ∠ΓΖ τεσσάρων πέμπτων ἐστὶν ὀρθῆς. δύο δὲ πέμπτων ἐστὶν ἡ ὑπὸ ΖΕ∠· λοιπὴ ἄρα ἡ ὑπὸ Ε∠Ζ δύο πέμπτων ὀρθῆς ἐστιν ἴση ἄρα ἡ ὑπὸ ∠ΕΖ τῇ ὑπὸ Ε∠Ζ ὥστε καὶ πλευρὰ ἡ ΕΖ τῇ Ζ∠ ἴση ἐστίν, τουτέστιν τῇ ∠Γ. ἐπεὶ οὖν ἴση ἐστὶν ἡ ὑπὸ Ε∠Γ τῇ ὑπὸ ΕΓ∠, τουτέστιν τῇ ὑπὸ ∠ΑΓ, καὶ κοινὴ ἡ ὑπὸ ∠ΓΖ, λοιπὴ ἄρα ἡ. ὑπὸ ∠ΕΓ λοιπῇ τῇ ὑπὸ Ζ∠Γ ἐστὶν ἴση ἰσογώνιον ἄρα τὸ ∠ΕΓ τρίγωνον τῷ ∠ΖΓ τριγώνῳ ἔστιν ἄρα ὡς ἡ ΕΓ πρὸς Γ∠, οὕτως ἡ Γ∠ πρὸς ΓΖ· τὸ ἄρα ὑπὸ ΕΓΖ ἴσον ἐστὶν τῷ ἀπὸ Γ∠. ἴση δὲ ἡ Γ∠ τῇ ΕΖ τὸ ἄρα ὑπὸ EΓΖ ἴσον ἐστὶν τῷ ἀπὸ EΖ ἡ ΕΓ ἄρα ἄκρον καὶ μέσον λόγον τέτμηται κατὰ τὸ Ζ, καὶ τὸ μεῖζον τμῆμά ἐστιν ἡ EΖ.

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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/.