# Synagoge 85

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/85

85 Ἔστωσαν ἐν ὑποκειμένω ἐπιπέδῳ αἱ ΑΒ ΒΓ εὐθεῖαι ἴσας περιέχουσαι γωνίας μετὰ τῆς ∠ΒΕ ἐν τῷ αὐτῷ κειμένης ἐπιπέδῳ, καὶ ἐφεστάτω ἡ ΒΖ μεθʼ ἑκατέρας τῶν ΑΒ ΒΓ ἴσας περιέχουσα γωνίας· ὅτι ὀρθή ἐστιν τῇ ∠Ε. Ἤχθω ἐπὶ τὸ ὑποκείμενον ἐπίπεδον κάθετος ἡ ΖΗ, καὶ ἐπὶ τὰς ΑΒ ΒΓ αἱ ΗΓ ΗΑ, καὶ ἐπεζεύχθωσαν αἱ ΑΖ ΖΓ ΗΒ· αἱ ΑΖ ΖΓ ἄρα ὀρθαὶ ἔσονται ἐπὶ τὰς ΑΒ ΒΓ. καὶ διὰ τὸ ἴσας εἶναι τὰς ὑπὸ τῶν ΑΒΖ ΓΒΖ γωνίας ἴσαι ἔσονται καὶ αἱ ΑΒ ΒΓ, καὶ ΖΑ ΖΓ, καὶ ΗΑ ΗΓ, καὶ γωνία ἡ ὑπὸ ΑΒΗ τῇ ὑπὸ ΓΒΗ. ἀλλὰ καὶ ἡ ὑπὸ ∠ΒΑ τῇ ὑπὸ ΕΒΓ ὑπόκειται ἴση καὶ ὅλη ἄρα ὅλη· κάθετος ἄρα ἡ ΗΕ ἐπὶ τὴν ∠Ε. ἔστιν δὲ καὶ ἡ ΖΗ ἐπὶ τὸ ἐπίπεδον· καὶ ἡ ΖΒ ἄρα κάθετος ἐπὶ τὴν ∠Ε.

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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/.