# Scholia in Euclidis catoptrica (scholia vetera) 56

Scholia in Euclidem, Scholia in Euclidis catoptrica (scholia vetera), Section 56. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/scholia-in-euclidem/scholia-in-euclidis-catoptrica-scholia-vetera/56

56. Ἡ γὰρ γωνία ἡ πρὸς τῇ p. 34Ο, ἐὰν γὰρ ἐπιζεύξωμεν τὴν ἀπὸ τοῦ Γ ἐπὶ τὸ Θ, ἴση ἐστὶν ἡ ὑπὸ ΗΓΘ τῇ ὑπὸ ΘΓΒ· ἡμικυκλίων γάρ. οὐκοῦν ἡ ὑπὸ ΗΓ∠ ἐλάσσων τῆς ὑπὸ ΘΓΒ· πολλῷ πλέον τῆς ὑπὸ ∠ΠΒ. Διὰ τί δὲ ἡ ἀνακλωμένη μὴ ἐπὶ τὸ κέντρον ἐπιζεύγνυται; ἐπειδὴ αἱ ὄψεις ἐν ἴσαις γωνίαις ἀνακλῶνται, ἐλάττων δὲ ἔμελλεν εἶναι ἡ πρὸς τῷ Π τῆς ὑπὸ ΘΓΒ, ἀνάγκη οὖν τὴν ἴσην τῇ πρὸς τῷ Π ἀπὸ τῆς μείζονος ἀφαιρεθεῖσαν τῆς ὑπὸ ΘΓΒ ἀνωτέρω που ποιῆσαι τὴν ἀνάκλασιν ὡς ἐπὶ τὸ Κ.

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Scholia in Euclidem, Scholia in Euclidis catoptrica (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.tlg005.local001/.