Commentarii in libros de sphaera et cylindro
Eutocius
Eutocius. ArchimeĢde, Volume 4. Mugler, Charles, editor. Paris: Les Belles Lettres, 1972.
37
Ἀλλὰ τὸ ὑπὸ ΕΘ καὶ τῶν ΕΖ, Γ△, ΚΑ δέδεικται ἴσον τῷ ὑπὸ τῶν ΕΛ, ΚΘ | Ἐν γὰρ τῷ δευτέρῳ καὶ εἰκοστῷ θεωρήματι δέδεικται ὅτι αἱ ΕΖ, Γ△, ΚΑ πρὸς τὴν ΘΚ τὸν αὐτὸν ἔχουσι λόγον, ὃν ἡ ΛΕ πρὸς ΕΘ· ὥστε τὸ ὑπὸ τῶν ἄκρων ἴσον ἐστὶ τῷ ὑπὸ τῶν μέσων.
Τὸ δὲ ὑπὸ ΕΛ, ΚΘ ἔλασσόν ἐστι τοῦ ἀπὸ ΘΑ | Καὶ γὰρ τοῦ ὑπὸ ΛΘ, ΘΚ ἴσου ὄντος τοῦ ἀπὸ ΘA, ὥς ἐστι δῆλον ἐπιζευγνυμένης τῆς ΑΛ καὶ διὰ τοῦτο ὁμοίου γινομένου τοῦ ΘΑΚ τριγώνου τῷ ΘΑΛ· ἔσται γὰρ ὡς ἡ ΛΘ πρὸς ΘΑ, ἡ ΑΘ πρὸς ΟΚ, καὶ τὸ ὑπὸ τῶν ἄκρων ἴσον τῷ ἀπὸ τῆς μέσης.