# Scholia in opticorum recensionem Theonis (scholia vetera) 20

Scholia in Euclidem, Scholia in opticorum recensionem Theonis (scholia vetera), Section 20. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/scholia-in-euclidem/scholia-in-opticorum-recensionem-theonis-scholia-vetera/20

20. Γεγράφθω γὰρ περὶ τὸ τρίγωνον κύκλος, καὶ ἐκβεβλήσθωσαν αἱ Κ∠, ΚΓ ἐπʼ εὐθείας ἐπὶ τὰ Ν, Ξ. καὶ ἐπεὶ ἀμβλεῖα δείκνυται ἡ ὑπὸ Ζ∠Ν ὡς ἐκτὸς οὖσα, ἡ ἄρα ἀπὸ τοῦ ∠ τῇ Ζ∠ πρὸς ὀρθὰς ἀγομένη ἔσται ὡς ἡ ∠Α. πάλιν ἐπεὶ ἀμβλεῖα δείκνυται ἡ Γ ὡς ἐκτὸς οὖσα, ἡ ἄρα ἀπὸ τοῦ Γ πρὸς ὀρθὰς ἀγομένη ἔσται ὡς ἡ ΓΜ. τούτων δὲ οὕτως ἐχόντων δειχθήσεται ἡ ΖΛΝ περιφέρεια μείζων τῆς ΞΒ περιφερείας ἐκ τοῦ παρακειμένου λήμματος τοῦ ἐν τῷ δʹ θεωρήματι τοῦ γʹ βιβλίου τῶν Σφαιρικῶν· ἴσας γὰρ περιφερείας ἀφαιροῦσιν αἱ κάθετοι. ὥστε καὶ γωνία ἡ Σ μείζων ἐστὶ τῆς Φ. ὥστε καὶ ἡ Ζ∠ μείζων φανήσεται τῆς ΓΒ.

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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/.