ιε΄.
ἐχέτω δεδομένον, καὶ ἀφῃρήσθω ἀφʼ ἑκατέρου αὐτῶν δεδομένον μέγεθος, ἀπὸ μὲν τοῦ ΑΒ τὸ ΕΑ, ἀπὸ δὲ τοῦ ΓΔ τὸ ΓΖ· λέγω, ὅτι τὰ λοιπὰ τὰ ΕΒ, ΖΔ πρὸς ἄλληλα ἤτοι λόγον ἕξει δεδομένον, ἢ τὸ ἕτερον τοῦ ἑτέρου δοθέντι μεῖζόν ἐστιν ἢ ἐν λόγῳ.
πρὸς ΓΔ, οὕτως τὸ ΑΗ πρὸς τὸ ΓΖ. λόγος δὲ τοῦ 1 2 ΑΒ πρὸς τὸ ΓΔ δοθείς· λόγος ἄρα καὶ τοῦ ΑΗ πρὸς τὸ ΓΖ δοθείς· δοθὲν δὲ τὸ ΓΖ· δοθὲν ἄρα καὶ τὸ ΑΗ. ἔστι δὲ καὶ τὸ ΑΕ δοθέν· καὶ λοιπὸν ἄρα τὸ ΕΗ δοθέν ἐστιν. καὶ ἐπεὶ ὡς τὸ ΑΒ πρὸς τὸ ΓΔ, οὕτως
τὸ ΑΗ πρὸς τὸ ΓΖ, λοιποῦ ἄρα τοῦ ΗΒ πρὸς λοιπὸν τὸ ΖΔ λόγος ἐστὶ δοθείς. καί ἐστι δοθὲν τὸ ΕΗ· τὸ ΕΒ ἄρα τοῦ ΖΔ δοθέντι μεῖζόν ἐστιν ἢ ἐν λόγῳ.
Data. Euclid. ed. Johan Ludvig Heiberg, ed. Heinrich Menge. United States. 2016.
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