# Fragmenta 6.30

Euclid, Fragmenta, Chapter 6. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/euclid/fragmenta/6.30

λ΄. Κύκλος, οὗ διάμετρος ἡ ΑΒ, καὶ ἀπὸ τυχόντος ἐπ᾿ αὐτὴν κάθετος ἡ ∠Ε, διήχθω ἡ ∠Ζ, ἐπεζεύχθω ἡ ΕΖ καὶ ἐκβεβλήσθω, καί, καθ᾿ ὃ συμπίπτει τῇ διαμέτρῳ, ἔστω τὸ Η· ὅτι ἐστίν, ὡς ἡ ΑΗ πρὸς τὴν ΗΒ, οὕτως ἡ ΑΘ πρὸς τὴν ΘΒ. ἐπεζεύχθωσαν αἱ ∠Α, ΑΕ, ΑΖ. ἐπεὶ οὖν ἐπὶ διάμετρον κάθετος ἡ ∠Ε, ἴση ἐστὶν ἡ ὑπὸ ∠ΑΒ τῇ ὑπὸ ΒΑΕ. ἀλλ᾿ ἡ ὑπὸ ∠ΑΒ τῇ ἐν τῷ αὐτῷ τμήματι ἴση ἐστὶν τῇ ὑπὸ ΘΖΒ, ἡ δὲ ὑπὸ ΒΑΕ ἴση ἐστὶν τῇ ἐκτὸς τετραπλεύρου τῇ ὑπὸ ΒΖΗ καὶ ἡ ὑπὸ ΘΖΒ ἄρα γωνία ἴση ἐστὶν τῇ ὑπὸ ΒΖΗ. καί ἐστιν ὀρθὴ ἡ ὑπὸ ΑΖΒ γωνία· διὰ δὴ τὸ λῆμμα γίνεται, ὡς ἡ ΑΗ πρὸς τὴν ΗΒ, οὕτως ἡ Α πρὸς τὴν ΒΘ.

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Euclid, Fragmenta, ed. Heinrich Menge. 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/tlg1799.tlg016.local001/.