# Scholia in Euclidis Data Ad prop. LXXXVI.

Scholia in Euclidem, Scholia in Euclidis Data, SCHOLIA.. Ancient Greek.

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

182. Λοιποῦ ἄρα τοῦ ὑπὸ τῶν ∠ΓΒ p. 168, 23] τὸ γὰρ δοθέντι μεῖζον ἢ ἐν λόγῳ ἐστίν, ὅταν ἀφαιρε- θέντος τοῦ δοθέντος τὸ λοιπὸν πρὸς τὸ αὐτὸ λόγον ἔχει δεδομένον, ὡς ἐν τοῖς ὅροις. 183. Ὡς δὲ τὸ ὑπὸ τῶν ΑΒΓ p 170, 4] ἐὰν γὰρ τὴν Β∠ τῇ ΑΒ ἐπʼ εὐθείας ποιήσωμεν, δῆλον· ὡς γὰρ τὰ παραλληλόγραμμα πρὸς ἄλληλα, οὕτως καὶ αἱ βάσεις. 184. Ἐὰν γὰρ εὐθεῖα ὡς ἡ ΒΓ τμηθῇ, ὡς ἔτυχεν, κατὰ τὸ ∠, τὸ ἀπὸ τῆς ὅλης ἴσον ἐστὶ τῷ τε ὑπὸ τῆς ὅλης καὶ ἑκατέρου τῶν τμημάτων περιεχομένῳ ὀρθο- γωνίῳ, ὡς ἐν τῷ β΄ θεωρήματι τοῦ β΄ βιβλίου Εὐκλείδου. 185. Καὶ συνθέντι ἄρα p. 170, 18–19] ἐὰν γὰρ συν- αμφοτέρου τῆς ΒΓ∠ πρὸς τὴν Β∠ λόγος ἐστὶ δοθείς, συνθέντι συναμφοτέρου ἄρα τῆς ΒΓ∠ μετὰ τῆς Β∠ πρὸς τὴν Β∠ λόγος ἐστὶ δοθείς· συναμφότερος δὲ ἡ ΒΓ∠ μετὰ τῆς Β∠ δύο εἰσὶν αἱ ΓΒ. 186. Ὡρ δὲ ἡ ΓΒ πρὸς Β∠ p. 170, 21] ἐὰν γὰρ ποιήσωμεν ἐπʼ εὐθείας τὴν ΓΒ τῇ ΒΑ καὶ ἴσην τὴν Β∠ τῇ ΒΕ, δῆλον, ὡς ἡ ΓΒ πρὸς Β∠, οὕτως τὸ ὑπὸ ΓΒ∠ πρὸς τὸ ἀπὸ Β∠, τουτέστι τὸ ΕΓ πρὸς τὸ ∠Ε· ὡς γὰρ αἱ βάσεις, οὕτως τὰ παραλληλόγραμμα. 187. Καὶ τοῦ ὑπὸ τῶν ΓΒ∠ p. 170, 22] ἐπεὶ γὰρ δέδοται ἑκατέρα τῶν ΓΒ, Β∠, καὶ τὸ ὑπʼ αὐτῶν δεδο- μένην ἔχει γωνίαν· ὀρθογώνιον γάρ· δέδοται τὸ ὑπὸ τῶν ΓΒ∠, ὡς ἐν τοῖς ὅροις. ἔστι δὲ καὶ τὸ ἀπὸ τῆς Β∠ δοθέν· τετράγωνον γάρ· λόγος ἄρα τοῦ ὑπὸ τῶν ΓΒ∠ πρὸς τὸ ἀπὸ τῆς Β∠ ἐστι δοθεὶς διὰ τὸ α΄. 188. Δοθεῖσα ἄρα ἐστὶ καὶ ἡ ΑΒ p. 172, 3] ἐπεὶ γὰρ λόγος ἐστὶ τῆς ΓΒ πρὸς τὴν ΒΑ δοθείς, τῆς Β∠ πρὸς τὴν ΒΑ λόγος ἐστὶ δοθείς. καί ἐστι δοθεῖσα ἡ Β∠· δοθεῖσα ἄρα ἐστὶ καὶ ἡ ΑΒ. ἑκάστη ἄρα τῶν ΑΒ, ΒΓ δοθεῖσα.

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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/.