# Synagoge 82-2

Pappus Alexandrinus, Synagoge, ΠΑΠΠΟΥ ΑΛΕΞΑΝΔΡΕΩΣ ΣΥΝΑΓΩΓΗΣ Ε.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/82-2

82 Κείσθω τῇ ΚΓ ἴση ἡ ΚΞ· διὰ μὲν οὖν τὸ ε΄ θεώρημα τῶν προγραφομένων ἡ ΕΓ ἄκρον καὶ μέσον λόγον τέτμηται κατὰ τὸ Ξ, καὶ τὸ μεῖζον αὐτῆς τμῆμά ἐστιν ἡ ΕΞ, διὰ δὲ τὸ Ϛ΄ τὸ ἀπὸ τῆς ΕΓ τοῦ πεντάκις ἀπὸ τῆς ἐλάσσονος τῆς ΞΓ μεῖζον τὸ ἄρα ἀπὸ τῆς ΕΓ τοῦ μὲν ἀπὸ τῆς ΞΓ μεῖζόν ἐστιν ἢ πενταπλάσιον, τοῦ δὲ ἀπὸ τῆς ΚΓ μεῖζον ἢ εἰκοσαπλάσιον. καὶ ἔστιν ὡς τὸ ἀπὸ ΕΓ πρὸς τὸ ἀπὸ ΚΓ, τὸ ἀπὸ ΓΛ πρὸς τὸ ἀπὸ ΓΚ, τουτέστιν τὸ ἀπὸ ΟΝ πρὸς τὸ ἀπὸ ΝΙ (ἰσογώνια γὰρ τὰ ΟΝΙ ΛΙΜ ΛΚΓ τρίγωνα)· τὸ ἄρα ἀπὸ ΟΝ εἴκοσι τῶν ἀπὸ ΝΙ μεῖζόν ἐστιν. καὶ λϚ΄ ἄρα τὰ ἀπὸ ΟΝ ψκ΄ τῶν ἀπὸ ΝΙ μείζονά ἐστιν. ψκ΄ δὲ τὰ ἀπὸ ΝΙ ὀγδοήκοντά ἐστιν τὼ ἀπὸ ΛΙ ἐδείχθη γὰρ τριπλῆ ἡ ΛΙ τῆς ΙΝ). ὀγδοήκοντα δέ τὰ ἀπὸ ΙΛ εἴκοσί ἐστιν τὰ ἀπὸ ΛΚ (διπλῆ γάρ ἡ ΛΚ τῆς ΛΙ). εἴκοσι δὲ τὰ ἀπὸ ΚΛ ιε΄ ἑστὶν τὰ ἀπὸ Β∠ (ἰσόπλευρον γάρ ἐστιν τὸ ∠ΒΛ τρίγωνον, καὶ κάθετος ἡ ΛΚ, καὶ ἐπίτριτος δυνάμει ἡ Β∠ τῆς ΚΛ)· ὥστε λς΄ τὰ ἀπὸ ΟΝ δεκαπέντε τῶν ἀπὸ Β∠, καὶ δώδεκα ἄρα τὰ ἀπὸ OΝ μείζονα πέντε τῶν ἀπὸ Β∠, ὅπερ ἔδει δεῖξαι.

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Pappus Alexandrinus, Synagoge, ed. Friedrich Hultsch. Text: The Greek Library, from the Perseus Digital Library and other open sources, CC BY-SA 4.0. Changes: apostrophes normalised and the text divided into reading sections by Interlinea.
License: CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/). Source: https://thegreeklibrary.pages.lisn.upsaclay.fr/works/tlg2032.tlg001.local001/.