Book 3

24 Συνθεωρεῖται δʼ ὅτι καὶ τὸ ὑπὸ τῶν ΒΚ ΑΓ ἴσον ἐστὶν τῷ ἀπὸ τῆς ΑM. διὰ γὰρ τὴν ὁμοιότητα τῶν ΒΘΚ ΖΛΓ τριγώνων ἐστὶν ὡς ἡ ΒΚ πρὸς ΚΘ, οὕτως ἡ ΖΛ πρὸς τὴν ΛΓ, καὶ τὸ ὑπὸ ΒΚ ΛΓ ἴσον τῷ ὑπὸ ΘΚ ΖΛ, τουτέστιν τῷ ἀπὸ τῆς ΑΜ. Γίνεται δὲ καὶ διὰ μὲν τὸ εἶναι ὡς τὴν BΓ πρὸς τὴν Γ ∠,οὕτως τὴν ΒΛ πρὸς ΚΛ, τὸ ὑπὸ ΒΓ καὶ τῆς ΚΛ, τουτέστιν τῆς τοῦ κύκλου διαμέτρου, ἴσον τῷ ὑπὸ ΒΛ ∠Γ, διὰ δὲ τὸ εἶναι ὡς τὴν Β ∠πρὸς τὴν Γ ∠,οὕτως τὴν BΚ πρὸς ΚΛ, τὸ ὑπὸ τῆς B ∠καὶ τῆς ΚΛ, τουτέστιν τῆς τοῦ κύκλου διαμέτρου, ἴσον τῷ ὑπὸ ΒΚ ∠Γ.