# Synagoge 3.6

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.6

6 δ΄ Ἔστω κύκλος ὁ ΑΒΓ, οὗ κέντρον ἔστω τὸ Ε, διάμετρος δὲ ἡ ΒΓ, καὶ ἐφαπτομένη ἡ Α∠ συμπίπτουσα τῇ ΒΓ κατὰ τὸ ∠, καὶ διήχθω ἡ ∠Ζ, καὶ ἐπιζευχθεῖσα ἡ ΑΕ ἐκβεβλήσθω ἐπὶ τὸ Η, καὶ ἐπεζεύχθωσαν αἱ ΖΚΗ ΗΛΘ· ὅτι ἴση ἐστὶν ἡ ΕΚ τῇ ΕΛ. Γεγονέτω καὶ ἤχθω τῇ ΚΛ παράλληλος ἡ ΘΞΜ· ἴση ἄρα καὶ ἡ ΜΞ τῇ ΞΘ. ἤχθω ἀπὸ τοῦ Ε ἐπὶ τὴν ΖΘ κάθετος ἡ ΕΝ· ἴση ἔρα ἐστὶν ἡ ΖΝ τῇ ΝΘ. ἦν δὲ καὶ ἡ ΜΞ τῇ ΞΘ παράλληλος ἄρα ἐστὶν ἡ ΝΞ τῇ ΜΖ· οὕτως ἄρα ἴση ἐστὶν ἡ ὑπὸ τῶν ΘΝΞ. τῇ ὑπὸ τῶν ΝΖΜ, τουτέστιν τῇ ὑπὸ τῶν ΘΑΞ· οὕτως ἄρα ἐν κύκλῳ ἐστὶν τὰ Α Ν Ξ Θ σημεῖα οὕτως ἄρα ἴση ἐστὶν ἡ ὑπὸ τῶν ΑΝΘ γωνία τῇ ὑπὸ τῶν ΑΞΘ, τουτέστιν τῇ ὑπὸ τῶν ΑΕΛ· οὕτως ἄρα ἐν κύκλῳ ἐστὶν τὰ Α Ν Ε ∠ σημεῖα. ἔστιν δέ ὀρθὴ γάρ ἐστιν ἑκατέρα τῶν ὑπὸ τῶν ΕΑ∠ ΕΝ∠.

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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/.