# Metrica 28

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/hero-of-alexandria/metrica/28

κη. Ἔστω τμῆμα κύκλου τὸ ΑΒΓ καὶ ἀπὸ μέσης τῆς ΑΓ πρὸς ὀρθὰς ἡ ∠Β, ἀπὸ δὲ μέσης τῆς Α∠ πρὸς ὀρθὰς ἡ ΕΖ. ὅτι ἡ Β∠ τῆς ΕΖ ἐλάσσων ἐστὶν ἢ ἐπίτριτος. προσαναπεπληρώσθω ὁ κύκλος καὶ ἐκβεβλήσθωσαν αἱ Β∠, ΖΕ ἐπὶ τὰ Η, Θ, καὶ κάθετος ἡ ΖΚ. ἐπεὶ διπλῆ ἐστιν ἡ Α∠ τῆς ∠Ε, τετραπλάσιον ἄρα τὸ ἀπὸ Α∠ τοῦ ἀπὸ ∠Ε, τουτέστι τοῦ ἀπὸ ΖΚ. ὥστε | καὶ τὸ ὑπὸ Η∠Ε τετραπλάσιόν ἐστι τοῦ ὑπὸ ΗΚΒ· ἀλλὰ τὸ ὑπὸ Η∠Β πρὸς τὸ ὑπὸ ΗΚΒ ἐλάσσονα λόγον ἔχει ἤπερ τὸ ὑπὸ Η∠Β πρὸς τὸ ὑπὸ Η∠, ΚΒ, τουτέστιν ἢ ∠Β πρὸς ΒΚ. ἡ ἄρα ∠Β τῆς ΒΚ μείζων ἐστὶν ἢ τετραπλῆ· ἀναστρέψαντι ἄρα ἡ ∠Β τῆς ∠Κ, τουτέστι τῆς ΕΖ, ἐλάττων ἐστὶν ἢ ἐπίτριτος.

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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/.