# Scholia in opticorum recensionem Theonis (scholia vetera) 15

Scholia in Euclidem, Scholia in opticorum recensionem Theonis (scholia vetera), Section 15. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/scholia-in-euclidem/scholia-in-opticorum-recensionem-theonis-scholia-vetera/15

15. Ἔστω τρίγωνον ὀρθογώνιον τὸ ΚΒΖ ὀρθὴν ἔχον τὴν πρὸς τῷ Β, ἴσαι δὲ ἔστωσαν αἱ ΒΓ, Γ∠, ∠Ζ, καὶ ἐπεζεύχθωσαν αἱ ΓΚ, ∠Κ. φημὶ δή, ὅτι ἡ Μ τῆς Ν μείζων ἐστίν, ἡ δὲ Ν τῆς Ξ. ἤχθω γὰρ ἀπὸ τοῦ Γ τῇ ∠Κ παράλληλος ἡ ΓΛ. ἔστιν ἄρα, ὡς ἡ ∠Γ πρὸς ΓΒ, οὕτως ἡ Κ Λ πρὸς τὴν ΛΒ. ἴση δὲ ἡ ∠Γ τῇ ΓΒ, ἴση ἄρα καὶ ἡ Κ Λ τῇ ΛΒ. καὶ ἐπεὶ ὀρθή ἐστιν ἡ πρὸς τῷ Β, μείζων ἡ ΓΛ τῆς ΛΒ, τουτέστι τῆς ΛΚ ὥστε καὶ γωνία ἡ Μ μείζων ἐστὶ τῆς Ο. ἀλλὰ ἡ Ο ἴση ἐστὶ τῇ Ν ἐναλλὰξ γάρ εἰσιν· καὶ ἡ Ν ἄρα τῆς Μ ἐλάσσων ἐστίν. πάλιν ἀπὸ τοῦ ∠ τῇ ΖΚ παράλληλος ἤχθω ἡ ∠Π φανερὸν δή, ὅτι ἡ Ρ μείζων ἐστὶν ὀρθῆς. ὥστε πάλιν ὁμοίως δείξομεν, ὅτι ἡ Π ∠ μείζων ἐστὶ τῆς ΠΚ ὥστε καὶ γωνία ἡ Ν τῆς Σ. ἀλλʼ ἡ Σ τῇ Ξ ἐστιν ἴση· καὶ ἡ Ν ἄρα τῆς Ξ μείζων ἐστίν.

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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/.