Ancient Greek · ~2 min
12. Ad prop. LV. Ἄλλως.
Euclid, Data (demonstrationes alterae) 12. Ad prop. LV. Ἄλλως.
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Ἔστω χωρίον τὸ ΚΛΜΝΞ δεδομένον τῷ εἴδει καὶ τῷ μεγέθει· λέγω, ὅτι καὶ αἱ πλευραὶ αὐτοῦ δεδομέναι εἰσὶ τῷ μεγέθει. ἀναγεγράφθω γὰρ ἀπὸ τῆς ΜΝ τετράγωνον τὸ ΜΟ· δέδοται ἄρα τῷ εἴδει. ἀλλὰ καὶ τὸ ΛΝ· λόγος ἄρα ἐστὶ τοῦ ΛΝ πρὸς τὸ ΜΟ δοθείς. δοθὲν δὲ τὸ ΛΝ τῷ μεγέθει· δοθὲν ἄρα καὶ τὸ ΜΟ τῷ μεγέθει. καί ἐστι τετράγωνον τὸ ἀπὸ τῆς ΜΝ· δοθὲν ἄρα ἐστὶ τὸ ἀπὸ τῆς ΜΝ· δοθεῖσα ἄρα ἐστὶν ἡ ΜΝ τῷ μεγέθει. διά τὰ αὐτὰ δὴ καὶ ἑκάστη τῶν ΜΛ, ΛΚ, KΞ, ΞΝ δοθεῖσά ἐστι τῷ μεγέθει.