# Synagoge 76-2

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/76-2

76 μζ΄ (δ΄). Ἔστω τρίγωνον ἰσόπλευρον τὸ ΑΒΓ ἐγγεγραμμένον εἰς σφαῖραν, κέντρον δὲ τῆς σφαίρας τὸ ∠, καὶ ἤχθω ἀπʼ αὐτοῦ ἐπὶ τὸ τοῦ τριγώνου ἐπίπεδον κάθετος ἡ ∠Ε (τὸ Ε ἄρα κέντρον ἐστὶν τοῦ περὶ τὸ ΑΒΓ τρίγωνον γραφομένου κύκλου, ὡς ἔστιν ἐν σφαιρικοῖς), καὶ ἐπιζευχθεῖσα ἡ ΑΕ ἐκβεβλήσθω· ὅτι ἡ ΑΕ τῆς ΕΖ διπλῆ ἐστιν. Ἐπεζεύχθωσαν γὰρ αἱ ΒΕ ΕΓ· ἴσαι ἄρα ἀλλήλαις εἰσίν. καὶ ἐπεὶ τρίτου μὲν ὀρθῆς ἐστιν ἑκατέρα τῶν ὑπὸ ΒΑΕ ΕΒΖ, διμοίρου δὲ ὁρθῆς ἑκατέρα τῶν ὑπὸ ΒΕΖ ΑΒΓ, ἰσογώνιόν ἐστιν τὸ ΑΒΖ τρίγωνον τῷ ΒΕΖ τριγώνῳ· ἔστιν ἄρα ὡς ἡ ΑΒ πρὸς ΒΖ, ἡ ΒΕ, τουτέστιν ἡ ΑΕ, πρὸς ΕΖ. δοπλῆ δὲ ἡ ΑΒ τῆς ΒΖ διπλῆ ἄρα καὶ ἡ ΑΕ τῆς ΕΖ.

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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/.