# Synagoge 3.8

Pappus Alexandrinus, Synagoge, Book 3. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/3.8

8 ε΄. Ἔστω κύκλος ὁ ΑΒΓ, καὶ ἐφαπτόμεναι αἱ Α.∠ ∠Γ, καὶ ἐπεζεύχθω ἡ ΑΓ, καὶ διήχθω ἡ ΕΖ, ἔστω δέ ἡ ΕΗ ἴση τῇ ΗΖ· ὅτι καὶ ἡ ΘΗ τῇ ΗΚ ἐστὶν ἴση. Ἤχθω τῇ ΑΓ παράλληλος ἡ ΕΜ, καὶ εἰλήφθω τὸ κέντρον τοῖ κύκλου τὸ Λ, καὶ ἐπεζεύχθωσαν αἱ ΛΑ ΛΖ ΛΓ ΛΜ ΛΕ ΛΗ. ἐπεὶ ἴση ἐστὶν ἡ ΕΗ τῇ ΗΖ, ἴση ἐστὶν καὶ ἡ ΜΓ τῇ ΓΖ. καὶ ἔστιν ἡ ΜΓʼ πρὸς βρθὰς τῇ ΓΛ· ἴση ἔρα ἐστὶν ἡ τῇ ΛΜ. καὶ ἐπεὶ ἴση ἐστὶν ἡ Α∠ τῇ ΜΓ, ἴση ἐστὶν ἡ ΑΕ τῇ ΜΓ. ἐστιν δὲ καὶ ἡ ΑΛ τῇ ΛΓ ἴση, καὶ ὀρθὴ ἡ ὑπὸ τῶν ΕΑΛ ὀρθῇ τῇ ὑπὸ τῶν ΜΓΛ ἐστὶν ἴση· ἴση ἄρα ἐστὶν καὶ ἡ ΕΛ τῇ ΛΜ, τουτἐστιν τῇ ΛΖ. ἀλλὰ καὶ ἡ ΕΗ τῇ ΗΖ ἐστὶν ἴση ἡ ἄρα κάθετός ἐστιν ἐπὶ τὴν ΕΖ· ἴση ἄρα ἐστὶν ἡ ΘΗ τῇ ΗΚ.

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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/.