# Synagoge 79-2

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/79-2

79 κείσθω δὴ τῇ ΑΔ ἴση ἡ ∠Ε· φανερὸν γὰρ ὅτι ἐλάσσων ἐστὶν ἡ ∠Α τῆς Γ∠, ἐπειδήπερ καὶ ἡ ΓΑ ἄκρον καὶ μέσον λόγον τέτμηται, καὶ τὸ μεῖζον αὐτῆς τμῆμά ἐστιν τὸ ∠Γ. καθόλου γάρ, ἐὰν ἄκρον καὶ μέσον λόγον εὐθεῖα γραμμὴ τμηθῇ, ὡς ἡ ΑΒ, καὶ τὸ ἔλασσον τμῆμα οἷον τὸ ΓΒ, καὶ τῇ ΓΒ ἴση τεθῇ ἡ Γ∠, καὶ ἡ ΑΓ ἄκρον καὶ μέσον λόγον τέτμηται, καὶ τὸ μεῖζον αὑτῆς τμῆμά ἐστιν τὸ ∠Γ, διὰ τὰ αὐτὰ καὶ ἡ ∠Γ ἄκρον καὶ μέσον λόγον τέτμηται τῷ Ε, καὶ τὸ μεῖζον αὐτῆς τμῆμά ἐστιν ἡ ∠Ε · τὸ ἄρα τετράκις ὑπὸ ∠ΕΓ μεῖζόν ἐστιν τοῦ ὑπὸ ∠ΓΕ. κοινὸν προσκείσθω τὸ τετράκις ὑπὸ ∠ΓΕ· τὸ ἄρα τετράκις ὑπὸ ∠ΕΓ7 καὶ τὸ τετράκις ὑπὸ ∠ΓΕ, τουτέστιν τὸ τετράκις ἀπὸ ∠Ε, μεῖζον τοῦ πεντάκις ὑπὸ ζονΓΕ. ἀλλὰ τὸ τετράκις ὑπὸ ∠Γ· καὶ τὸ τετράκις ἀπὸ ∠Ε ἴσον ἐστὶν τῷ τετράκις ὑπὸ Γ∠Ε· τὸ ἄρα τετράκις ὑπὸ Γ∠Ε μεῖζον τοῦ πεντάκις ὑπὸ ∠ΓΕ. κοινὸν προσκείσθω τὸ πεντάκις ὑπὸ Γ∠Ε τὸ ἄρα ἐννάκις ὑπὸ Γ∠Ε μεῖζόν ἐστιν τοῦ πεντάκις ὑπὸ Γ∠Ε καὶ τοῦ πεντάκις ὑπὸ ∠ΓΕ, τουτέστιν τοῦ πεντάκις ἀπὸ ∠Γ· τὸ ἄρα τρὶς ὑπὸ Α∠Γ πρὸς τὸ πεντάκις ἀπὸ ∠Γ μείζονα λόγον ἔχει ἤπερ πρὸς τὸ ἐννάκις ὑπὸ Α∠Γ. λόγος δὲ τοῦ τρὶς ὑπὸ Α∠Γ πρὸς τὸ ἐννάκις ὑπὸ Α∠Γ, ὃν α’ πρὸς γ΄ τὸ ἄρα τρὶς ὑπὸ Α∠Γ πρὸς τὸ πεντάκις ἀπὸ ∠Γ μείζονα λόγον ἔχει ἥπερ α’ πρὸς γ΄ συνθέντι τὸ ἄρα τρὶς ὑπὸ Α∠Γ καὶ πεντάκις ἀπὸ ∠Γ, τουτέστιν τὸ πεντάκις ἀπὸ ΓΒ, πρὸς τὸ πεντάκις ἀπὸ ΓΒ μείζονα λόγον ἔχει ἤπερ δ΄ πρὸς γ΄ ἐδείχθη δὲ τὸ τρὶς ὑπὸ Α∠Γ καὶ τὸ πεντάκις ἀπὸ ΓΒ ἴσον τῷ ἀπὸ ΑΒ τετραγώνῳ· τὸ ἄρα ἀπὸ ΑΒ τετράγωνον πρὸς τὸ πεντάκις ἀπὸ ΓΒ μείζονα λόγον ἔχει ἤπερ δ΄ πρὸς γ΄.

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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/.