16. Ad prop LXVIII. Ἄλλως.

Ἐκκείσθω δεδομένη εὐθεῖα ἡ Κ. καὶ ἐπεὶ λόγος ἐστὶ τοῦ Α πρὸς τὸ Β δοθείς, ὁ αὐτὸς αὐτῷ γεγονέτω ὁ τῆς Κ πρὸς τὴν Λ. λόγος δὲ τοῦ Α πρὸς τὸ Β δοθείς· λόγος ἄρα καὶ τῆς Κ πρὸς τὴν Λ δοθείς. δοθεῖσα δὲ ἡ Κ· δοθεῖσα ἄρα καὶ ἡ Λ. πάλιν ἐπεὶ λόγος ἐστὶ δοθεὶς τῆς ΓΔ πρὸς τὴν ΕΖ, ὁ αὐτὸς αὐτῷ γεγονέτω ὁ τῆς Κ πρὸς τὴν Μ· λόγος ἄρα καὶ τῆς Κ πρὸς τὴν Μ δοθείς· δοθεῖσα δὲ ἡ Κ· δοθεῖσα ἄρα καὶ ἡ Μ. ἔστι δὲ καὶ ἡ Λ δοθεῖσα· λόγος ἄρα τῆς Λ πρὸς τὴν Μ δοθείς. καὶ ἐπεὶ ἰσο- γώνιόν ἐστι τὸ Α τῷ Β, τὸ Α ἄρα πρὸς τὸ Β λόγον ἔχει τὸν συγκείμενον ἐκ τῶν πλευρῶν, τουτέστιν ἐξ οὗ ὅν ἔχει λόγον ἡ ΓΔ πρὸς τὴν ΕΖ, καὶ ἡ ΘΓ πρὸς τὴν ΗΕ. ἀλλὰ μὴν καὶ ἡ Κ πρὸς τὴν Λ λόγον ἔχει τὸν συγκείμενον ἐκ τοῦ ὃν ἔχει ἡ Κ πρὸς τὴν Μ καὶ ἡ M πρὸς τὴν Λ· ὁ ἄρα συγκείμενος λόγος ἐκ τοῦ ὃν ἔχει ἡ ΓΔ πρὸς τὴν ΕΖ καὶ ἡ ΘΓ πρὸς τὴν ΗΕ ὁ αὐτός ἐστι τῷ συγκειμένῳ ἐξ οὗ ὃν ἔχει ἡ Κ πρὸς τὴν Μ καὶ ἡ M πρὸς τὴν Λ, ὧν ὁ τῆς ΓΔ πρὸς τὴν ΕΖ λόγος ὁ αὐτός ἐστι τῷ τῆς Κ πρὸς τὴν Μ λόγῳ· λοιπὸς ἄρα ὁ τῆς ΘΓ πρὸς τὴν ΗΕ λόγος ὁ αὐτός ἐστι τῷ τῆς Μ πρὸς τὴν Λ. τῆς δὲ Μ πρὸς τὴν Λ λόγος δοθείς· λόγος ἄρα καὶ τῆς ΘΓ πρὸς τὴν ΕΗ δοθείς.