# Synagoge 40

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/40

40 Ἔστω οὖν ἡ Ζ μέση τῶν ΑΒ Γ ἔν ἴσῃ ὑπεροχῇ· καὶ ἔσται ἀριθμητικὴ μεσότης τῶν ΑΒ Ζ Γ εὐθειῶν. γεγενήσθω δὲ καὶ ὡς ἡ Ζ πρὸς τὴν Γ, ἡ Γ πρὸς Η· καὶ ἔσται τῶν Ζ Γ Η εὐθειῶν γεωμετρικὴ μεσότης, τουτέστιν ἀναλογία κυρίως. κἂν διὰ τὸ προδειχθὲν δύο εὐθειῶν τῶν Γ Η, ὧν μείζων ἡ Γ, τὴν Θ ποιησόμεθα, ὥστʼ εἶναι ὡς τὴν Γ πρὸς τὴν Θ, οὕτως τὴν τῶν Γ Η ὑπεροχὴν πρὸς τὴν τῶν Η Θ ὑπεροχήν, ἔσται ἄρα καὶ τῶν Γ Η Θ εὐθειῶν ἁρμονικὴ μεσότης. ὁ αὐτὸς δὲ λόγος τῆς ΑΒ πρὸς τὴν Γ, καὶ τῆς Γ πρὸς τὴν Θ, τῶν ἄκρων ὅρων ἐπί τε τῆς ἀριθμητικῆς μεσότητος καὶ τῆς ἁρμονικῆς· ἔσονται οὖν πέντε τὸν ἀριθμὸν ἐλάχισται εὐθεῖαι περιέχουσαι τὰς τρεῖς μεσότητας .

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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/.