# Scholia in opticorum recensionem Theonis (scholia vetera) 86

Scholia in Euclidem, Scholia in opticorum recensionem Theonis (scholia vetera), Section 86. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/scholia-in-euclidem/scholia-in-opticorum-recensionem-theonis-scholia-vetera/86

86. Ὅτι δὲ δυνατὸν τέμνεσθαι τὸ ἡμικύκλιον ὑπὸ τοῦ μείζονος τμήματος καὶ ποῦ, οὕτως ἔσται δῆλον· ἔστωσαν ἴσαι αἱ ΑΒ, ΒΓ, καὶ περιγεγράφθω ἡμικύκλιον περὶ τὸ ΑΒ τὸ ΑΘΒ, καὶ συνεστάτω πρὸς τῇ ΒΓ καὶ τῷ Β σημείῳ γωνία ὀξεῖα ἡ ὑπὸ ΓΒ∠, πρὸς δὲ τῷ Γ ἴση τῇ Β ἡ Γ. καὶ συμπιπτέτω κατὰ τὸ ∠, καὶ ἀπὸ τοῦ ∠ ἐπὶ τὸ κέντρον τοῦ ΑΘΒ, ὅ ἐστι τὸ Ε, ἐπεζεύχθω ἡ ∠Ε, καὶ κείσθω τῇ ΒΖ περιφερείᾳ ἴση ἡ ΖΘ, καὶ ἐπεζεύχθωσαν αἱ ∠Θ, ΘΕ. ἐπεὶ οὖν ἡ ΘΕ τῇ ΕΒ ἴση, κοινὴ δὲ ἡ Ε∠, καὶ γωνίας ἴσας περιέχουσιν, ἐπεὶ καὶ ἡ ΘΖ περιφέρεια τῇ ΖΒ ἐστιν ἴση, ἴση ἄρα ἡ Θ∠ τῇ ∠Β. ἡ δὲ ∠Β τῇ ∠Γ· ὥστε ὁ κέντρῳ τῷ ∠, διαστήματι δὲ τῷ ∠Θ γραφόμενος κύκλος τεμεῖ τὸ ἡμικύκλιον καὶ διὰ τοῦ Β ἐλεύσεται. Ad prop. XLIX.

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Scholia in Euclidem, Scholia in opticorum recensionem Theonis (scholia vetera), ed. Johan Ludvig Heiberg, H. 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/tlg5022.tlg004.local001/.