ια.
ἄρα τοῦ ΔΒ πρὸς τὸ ΒΓ λόγος ἐστὶ δοθείς. ἀνάπαλιν καὶ συνθέντι λόγος ἐστὶ τοῦ ΓΔ πρὸς τὸ ΔΒ δοθείς· ὁ αὐτὸς αὐτῷ γεγονέτω ὁ τοῦ ΑΔ πρὸς τὸ ΔΕ· λόγος ἄρα καὶ τοῦ ΑΔ πρὸς τὸ ΔΕ δοθείς· δοθὲν δὲ τὸ ΑΔ· δοθὲν ἄρα καὶ τὸ ΔΕ· ὥστε καὶ λοιπὸν τὸ ΕΑ δοθέν
ἐστιν. ἔστι δὲ καὶ ὅλου τοῦ ΑΓ πρὸς ὄλον τὸ ΕΒ λόγος δοθείς· ὥστε καὶ τοῦ ΕΒ πρὸς ΑΓ λόγος ἐστὶ δοθείς. καί ἐστι δοθὲν τὸ ΑΕ· τὸ ΒΑ ἄρα τοῦ ΑΓ δοθέντι μεῖζόν ἐστιν ἢ ἐν λόγῳ.
ἄρα τοῦ ΕΒ πρὸς τὸ ΑΓ λόγος ἐστὶ δοθείς· ὥστε καὶ τοῦ ΑΓ πρὸς τὸ ΕΒ λόγος ἐστὶ δοθείς· ὁ αὐτὸς αὐτῷ γεγονέτω ὁ τοῦ ΑΔ πρὸς ΕΔ· καὶ τοῦ ΔΑ ἄρα πρὸς ΕΔ λόγος ἐστὶ δοθείς· καὶ ἀναστρέψαντι τοῦ ΔΑ πρὸς ΑΕ λόγος δοθείς· καὶ ἀνάπαλιν τοῦ ΕΑ πρὸς
τὸ ΑΔ λόγος ἐστὶ δοθείς. καὶ δοθὲν τὸ ΑΕ· δοθὲν ἄρα καὶ ὅλον τὸ ΑΔ. καὶ ἐπεὶ ὅλου τοῦ ΑΓ πρὸς ὅλον τὸ ΕΒ λόγος ἐστὶ δοθείς, ὧν τοῦ ΑΔ πρὸς τὸ ΔΕ λόγος ἐστὶ δοθείς, ἔσται καὶ λοιποῦ τοῦ ΓΔ πρὸς λοιπὸν τὸ ΔΒ λόγος δοθείς· καὶ διελόντι τοῦ ΓΒ
πρὸς τὸ ΔΒ λόγος ἐστὶ δοθείς· ὥστε καὶ τοῦ ΔΒ πρὸς τὸ ΒΓ λόγος ἐστὶ δοθείς. καί ἐστι δοθὲν τὸ ΔΑ· τὸ ΑΒ ἄρα τοῦ ΒΓ δοθέντι μεῖζόν ἐστιν ἢ ἐν λόγῳ.
Data. Euclid. ed. Johan Ludvig Heiberg, ed. Heinrich Menge. United States. 2016.
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