# Synagoge 3.9

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.9

9 Ϛ΄ Ἔστω κύκλος ὁ ΑΒΓ καὶ ἐφαπτόμεναι αἱ Α∠ ∠Γ, καὶ ἐτεζεύχθω ἡ ΑΓ καὶ διήχθω ἡ ΕΖ, καὶ ἔστω ἴση ἡ ΗΘ τῇ ΗΚ· ὅτι καὶ ἡ ΕΗ τῇ ΗΖ ἐστὶν ἴση. Εἰλήφθω τὸ κέντρον τοῦ κύκλου τὸ Α, καὶ ἐπεζεύχθωσαν αἱ ΕΛ ΛΑ ΛΗ ΛΖ ΜΓ. ἐπεὶ ὀρθή ἐστιν ἑκατέρα τῶν ὑπὸ τῶν ΕΑΛ ΕΗΛ, ἐν κύκλῳ ἐστίν τὰ E A H Λ σημεῖα ἴση ἄρα ἐστὶν ἡ ὑπὸ τῶν ΗΑΛ γωνία τῇ ὑπὸ τῶν ΗΕΛ γωνίᾳ. πάλιν ἐπεὶ ὀρθή ἐστιν ἑκατέρα τῶν ὑπὸ τῶν ΛΗΖ ΜΓΖ, ἐν κύκλῳ ἐστὶν τὰ Μ Η Ζ Γ σημεῖα· ἴση ἄρα ἐστὶν ἡ ὑπὸ τῶν ΗΓΛ γωνία, τουτέστιν ἡ ὑπὸ τῶν ΗΑΛ , τουτέστιν ἡ ὑπὸ τῶν ΗΕΛ, τῇ ὑπὸ τῶν ΗΖΛ· ἴση ἄρα ἐστὶν καὶ ἡ ΕΛ τῇ ΛΖ. καὶ ἔστιν κάθετος ἡ ΛΗ· ἴση ἄρα ἐστὶν ἡ ΕΗ τῇ ΗΖ.

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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/.