Ancient Greek · ~2 min
2. Ad prop. XXIV. Ἄλλως τὸ αὐτό.
Euclid, Data (demonstrationes alterae) 2. Ad prop. XXIV. Ἄλλως τὸ αὐτό.
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Ἐπεὶ λόγος ἐστὶ τῆς Α πρὸς τὴν Γ δοθείς, ὡς δὲ ἡ Α πρὸς τὴν Γ, οὕτως τὸ ἀπὸ τῆς Α πρὸς τὸ ὑπὸ τῶν Α, Γ, λόγος ἄρα καὶ τοῦ ἀπὸ τῆς Α πρὸς τὸ ὑπὸ τῶν Α, Γ δοθείς. τῷῦ δὲ ὑπὸ τῶν Α, Γ ἴσον ἐστὶ τὸ ἀπὸ τῆς Β· λόγος ἄρα τοῦ ἀπὸ τῆς Α πρὸς τὸ ἀπὸ ὸ τῆς Β δοθείς· ὥστε καὶ τῆς Α πρὸς τὴν Β λόγος ἐστὶ δοθείς.