# Scholia in Euclidis Data Ad prop. XCI demonstr. alt.

Scholia in Euclidem, Scholia in Euclidis Data, APPENDIX SCHΟLIΟRUM.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/scholia-in-euclidem/scholia-in-euclidis-data/Ad%20prop.%20XCI%20demonstr.%20alt.

41. Δοθὲν ἄρα ἐστὶ τὸ ὑπὸ τῶν Α∠Ζ p. 226, 9] ἐπεὶ γὰρ δεδομέναι εἰσὶν αἱ ΑΖ, Ζ∠, καὶ ὅλη ἡ Α∠ δέδοται διὰ τὸ γ΄ ὥστε ἑκατέρα τῶν Α∠, ΑΖ δέδοται. καὶ δῆλον, ὅτι τὸ ὑπʼ αὐτῶν περιεχόμενον δέδοται, ὡς ἐν τοῖς ὅροις· ὅ τε γὰρ λόγος τῆς Α∠ πρὸς τὴν ∠Ζ δέδοται, ἐπειδήπερ ἑκατέρα τῶν Α∠, ∠Ζ δέδοται διὰ τὸ α΄, καὶ αἱ γωνίαι δεδομέναι εἰσίν· ὀρθαὶ γάρ. 42. P. 226, 10] ἐὰν γὰρ διάμετρον ἀγάγωμεν, τὰ λοιπὰ δῆλα, ὡς ἐν τῷ γ΄ τῶν στοιχείων ἐν τῷ λδ΄ θεωρήματι· ὅλαι γὰρ αἱ τέμνουσαι εὐθεῖαι τὸ ὑπὸ τῶν τμημάτων ἴσον ἔχουσι τῷ ἀπὸ τῆς ἐφαπτομένης. 43. Ἑκάτερον γὰρ αὐτῶν ἴσον ἐστὶ τῷ ἀπὸ τῆς ἐφαπτομένης τοῦ κύκλου.

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Scholia in Euclidem, Scholia in Euclidis Data, ed. Heinrich 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.tlg002.local001/.