[56] 56. Ἡ γὰρ γωνία ἡ πρὸς τῇ p. 34Ο,
9 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.
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.
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.
Scholia in Euclidis catoptrica (scholia vetera). Scholia in Euclidem. ed. Johan Ludvig Heiberg, ed. H. Menge. United States. 2018.
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