# Synagoge 63

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/63

63 κη΄ Ἐφ᾿ ὧν μέντοι τριγώνων αἱ ἐντὸς ἴσαι συνίστανται ταῖς ἐκτός, ἐπʼ ἐκείνων καὶ μείζους τῶν ἐκτὸς ἐντός τινες εἶναι δύνανται συναμφότεραι λαμβανόμεναι. Ἔστωσαν γὰρ β ἐν τῷ ΑΒΓ τριγόνῳ αἱ ∠ΕΖ ἴσαι ταῖς ΑΒΓ, καὶ ἐκβεβλήσθω μία τῶν ἐντὸς ἡ ∠Ε ἐπὶ τὸ Η, καὶ μεταξὺ τῶν Ε Η εἰλήφθω τυχὸν σημεῖον τὸ Κ, καὶ ἐπεζεύχθω ἡ ΚΖ· ἔσονται δὴ αἱ ∠ΚΖ μείζονες τῶν ∠ΕΖ, ὥστε καὶ τῶν ΑΒΓ. δῆλον δʼ ὅτι, κἂν ἐντὸς τοῦ ΑΒΓ τριγώνου τὸ Κ σημεῖον οὕτως ληφθῇ ὥστε τὰς ∠ΕΖ περιέχεσθαι ὑπὸ τῶν ἀπʼ αὐτοῦ ἐπὶ τὰ ∠ Ζ ἐπιζευγνυμένων, ὡς ἔχει ἐπὶ τῆς δευτέρας καταγραφῆς, καὶ οὕτως ἔσται τὸ αὐτό, καὶ ἑκατέρως ἀπειραχῶς ἔσται τὸ προκείμενον.

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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/.