# Synagoge 41

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/pappus-alexandrinus/synagoge/41

41 Ἅμα καὶ διʼ ἀριθμῶν ἐλαχίστων πέντε συνίστασθαι κατά τε τοὺς πολλαπλασίους λεγομένους λύγους καὶ ἐπιμορίους καὶ τοὺς λοιπούς, ἀδιαιρέτου γοῦν τῆς μονάδος ὑποκειμένης. ἐπὶ μὲν γὰρ τοῦ διπλασίου λόγου τῆς ΑΒ πρὸς τὴν Γ ὑποδείγματος ἕνεκεν ἔσονται τὸ προκείμενον ποιοῦντες ἀριθμοὶ ἐλάχιστοι ὅ τε ιβ΄ καὶ ὁ θ΄ καὶ ὁ Ϛ΄ καὶ ὁ δ΄ καὶ ὁ γ΄, ἐπὶ δὲ τῆς τριπλασίονος ἀναλογίας ἀριθμοὶ ἐλάχιστοι γίνονται ὅ τε ιη΄ καὶ ὁ ιβ΄ καὶ ὁ Ϛ΄ καὶ ὁ γ΄ καὶ ὁ β΄. καὶ δῆλον ὡς δεῖ καὶ ἐπὶ τῶν ἄλλων λόγων τοὺς ἐλαχίστους ἀριθμοὺς ἀνευρίσκειν τῶν τριῶν μεσοτήτων.

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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/.