Synagoge

Pappus Alexandrinus

Pappus Alexandrinus. Pappi Alexandrini collectionis quae supersunt, Volume 1. Hultsch, Friedrich, editor. Leipzig: Weidmann, 1876.

3 Ὅτι δὲ ἡ ΓΕ δύναται τὸ δὶς ὑπὸ ΓΖ ΗΘ, οὕτως ἔσταιε δῆλον ἐπεζεύχθω ἡ ΕΘ. ἐπεὶ τὸ ἀπὸ ΕΓ ἴσον ἐστὶν τοῖς ἀπὸ τῶν ΕΘ ΘΓ καὶ τῷ δὶς ὑπὸ ΓΘ ΘΗ, ἔστιν δὲ καὶ τὰ ἀπὸ ΕΘ ΘΖ ἴσα τῷ ἀπὸ ΕΖ καὶ τῷ δὶς ὑπὸ ΖΘ ΘΗ ἀνάλογον ἄρα ἐστὶν ὡς τὸ ἀπὸ ΓΕ πρὸς τὰ ἀπὸ ΕΘ ΘΓ μετὰ τοῦ δὶς ὑπὸ ΓΘΗ, οὕτως τὰ ἀπὸ ΕΘ ΘΖ πρὸς τὸ ἀπὸ ΕΖ μετὰ τοῦ δὶς ὑπὸ ΖΘΗ. καὶ ὡς ἓν πρὸς ἕν, πάντα πρὸς πάντα. καὶ ἴσον ἐστὶν τὸ ἀπὸ ΓΕ τοῖς ἀπὸ ΕΘΓ καὶ τῷ δὶς ὑπὸ ΓΘΗ, ἴσα ἄρα καὶ τὰ ἀπὸ ΓΕ ΕΘ ΘΖ τοῖς ἀπὸ ΕΘ ΘΓ ΕΖ καὶ τῷ δὶς ὑπὸ ΓΘΗ μετὰ τοῦ [*](1. ἡ ΕΖ Co Sca pro ἡ ΕΗ 2. ἐπὶ τρίτον utroque loco A, corr. BS 5. τὸ ante ἀπὸ ΕΖ add. S 6. ἔσται δὴ A, ἔσται δὴ ἡ BS, corr. V2 (ἔστω δὴ ἡ Sca, sit Co) 7. διπλασίων S, δ/////ίων A, διπλάσιον B 8. 9. τὴν ΖΘ ον Η πρὸς //// τῆς extremo folio A, τὴν ζθ ὃν ἡ πρὸς . . καὶ τῆς S, corr. B Sca 15. ὅληι ἡ AB, corr. S 17. καὶ διπλῆ αὐτῆς del. Sca, ἡ ante διπλῆ add. Hu δὶς add. Co)

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δὶς ὑπὸ ΖΘΗ, τουτέστιν τῷ δὶς ὑπὸ ΓΖ ΗΘ. κοινὸν ἀφῃρήσθω τὸ ἀπὸ ΕΘ· λοιπὰ ἄρα τὰ ἀπὸ ΕΓ ΖΘ ἴσα ἐστὶν τοῖς ἀπὸ ΕΖ ΘΓ καὶ τῷ δὶς ὑπὸ ΓΖ ΗΘ. ὧν τὸ ἀπὸ ΖΘ ἴσον τοῖς ἀπὸ τῶν ΕΖ ΘΓ (τὸ μὲν γὰρ ἀπὸ τῆς ΖΘ ἐστὶν κε΄, τὸ δὲ ἀπὸ τῆς ΘΓ θʼ, καὶ τὸ ἀπὸ ΕΖ ιϚ΄)· λοιπὸν ἄρα τὸ ἀπὸ ΓΕ ἴσον ἐστὶν τῷ δὶς ὑπὸ ΖΓ ΗΘ.