# Metrica 9-2

Hero of Alexandria, Metrica, ΗΡΩΝΟΣ ΜΕΤΡΙΚΩΝ Γ. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/hero-of-alexandria/metrica/9-2

θ. Κύκλου δοθέντος, οὗ διάμετρος ἡ ΑΒ, γράψαι ἕτερον περὶ τὸ αὐτὸ κέντρον αὐτῷ, οὗ διάμετρος ἡ Γ∠, διαιροῦντα τὸν ἐξ ἀρχῆς κύκλον ἐν λόγῳ τῷ δοθέντι. ἐπεὶ οὖν λόγος ἐστὶν τῆς ΑΒ Γ∠ ἴτυος πρὸς τὸν περὶ διάμετρον τὴν Γ∠ κύκλον δοθείς, λόγος ἄρα καὶ τοῦ περὶ διάμετρον τὴν ΑΒ Γ∠ κύκλου δοθείς. ὡς δὲ οἱ κύκλοι πρὸς ἀλλήλους, οὕτω τὰ ἀπὸ τῶν δίαμέτρων τετράγωνα· λόγος ἄρα καὶ τοῦ ἀπὸ ΑΒ πρὸς τὸ ἀπὸ Γ∠ δοθείς· καὶ ἔστι δοθὲν τὸ ἀπὸ ΑΒ· δοθὲν ἄρα καὶ τὸ ἀπὸ Γ∠. συντεθήσεται δὴ οὕτως· ἔστω ἡ μὲν ΑΒ διάμετρος μονάδων κ, ὁ δὲ δοθεὶς λόγος, ὃν ἔχει τὰ γ πρὸς τὰ ε. σύνθες τὰ γ καὶ τὰ ε· γίγνεται η· καὶ τὰ κ ἐφ᾿ ἐαυτά· γίγνεται υ· ἐπὶ τὸν ε· γίγνεται β. ταῦτα μέρισον παρὰ τὸν η· γίγνεται σν· τούτων πλευρὰν λαβὲ ὡς ἔγγιστα· γίγνεται ιε ιγ. τοσούτου ἔσται ἡ Γ∠ διάμετρος.

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Hero of Alexandria, Metrica, ed. Hermann Schöne. 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/tlg0559.tlg006.local001/.