{"schemaVersion":2,"id":"tlg2032.tlg001.local001","url":"https://thegreeklibrary.org/works/tlg2032.tlg001.local001/","urn":"urn:cts:greekLit:tlg2032.tlg001.local001","title":"Synagoge","titleGreek":null,"alternateTitles":[],"author":"Pappus Alexandrinus","authorityName":"PAPPUS Math.","authorUrl":"https://thegreeklibrary.org/authors/tlg2032-pappus-math/","authorityUrl":"https://thegreeklibrary.org/authors/tlg2032-pappus-math/","editors":["Friedrich Hultsch"],"publication":{"digitalPublisher":"Harvard College Library","sourceTitle":"Pappi Alexandrini collectionis quae supersunt","edition":null,"publisher":"Weidmann","place":"Berlin","date":"1876","volume":"1 of 3","series":null,"citation":null,"citationShort":null},"rights":{"text":"Available under a Creative Commons Attribution-ShareAlike 4.0 International License","url":"https://creativecommons.org/licenses/by-sa/4.0/"},"provenance":{"authority":"Harvard College Library","sponsors":["Harvard College Library"],"funders":["Harvard Library Arcadia Fund"],"principal":"Gregory Crane","responsibilities":[{"role":"Corrected and encoded the text","names":[]},{"role":"Editor-in-Chief, Perseus Digital Library","names":[]},{"role":"Project Manager (University of Leipzig)","names":[]},{"role":"Project Assistant (University of Leipzig) 2015 - 2017","names":[]},{"role":"Lead Developer (University of Leipzig)","names":[]},{"role":"Technical Advisor","names":[]}]},"corpus":{"version":"2.2.0","date":"2026-08-29"},"revisionDate":"2026-08-15","sourceUrl":"https://archive.org/stream/pappialexandrin00hultgoog#page/n33/mode/2up","sourceLinkType":null,"sourceRights":null,"citation":"Pappus Alexandrinus. Synagoge. ed. Friedrich Hultsch. Pappi Alexandrini collectionis quae supersunt, Berlin, Weidmann, 1876. urn:cts:greekLit:tlg2032.tlg001.local001","excerpt":"1 γὰρ αὐτοὺς ἐλάσσονας μὲν εἶναι ἑκατοντάδος μετρεῖσθαι δὲ ὑπὸ δεκάδος, καὶ δέον ἔστω τὸν ἐξ αὐτῶν στερεὸν εἰπεῖν μὴ πολλαπλασιάσαντα αὐτούς. Ἔστωσαν οὖν οἱ ἀριθμοὶ ν΄ ν΄ ν΄ μ΄ μ΄ λ΄· ἔσονται ἄρα οἱ πυθμένες ε΄ ε΄ έ δ΄ δ΄ γ΄· ὁ ἄρα ἐξ αὐτῶν στερεὸς γίνεται μονάδων Ϛ. καὶ ἐπεὶ τὸ πλῆθος τῶν δεκάδων ἐστὶν Ϛ΄ καὶ μετρούμενον ὑπὸ τετράδος λείπει δύο, ἔσται ὁ ἐξ αὐτῶν στερεὸς τῶν δεκάδων μυριάδων ἁπλῶν ἑκατόν. καὶ ἐπεὶ ὁ ἐκ τῶν δεκάδων στερεὸς ἐπὶ τὸν ἐκ τῶν πυθμένων στερεὸν ποιεῖ τὸν ἐκ τῶν ἐξ ἀρχῆς στερεόν, αἱ ἄρα μυριάδες ρ΄· ἐπὶ τὰς μονάδας Ϛ γενόμεναι ποιοῦσιν μυριάδας ξ΄ διπλᾶς, ὥστε ὁ ἐκ τῶν ν΄ ν΄ ν΄ μ΄ μ΄ λ΄ στερεός ἐστιν μυριάδων ξ΄ διπλῶν. 2 ιε΄. Ἔστωσαν δὴ πάλιν ὁσοιδηποτοῦν ἀριθμοὶ ἐφʼ ὧν τὰ Β, ὧν ἕκαστος ἐλάσσων μὲν χιλιάδος μετρείσθω δὲ ὑπὸ ἑκατοντάδος, καὶ δέον ἔστω τὸν ἐξ αὐτῶν στερεὸν εἰπεῖν μὴ πολλαπλασιάσαντα τοὺς ἀριθμούς. Γεγονέτω, καὶ ὁ διπλάσιος τοῦ πλήθους αὐτῶν…","divisions":[{"label":"ΠΑΠΠΟΥ ΑΛΕΞΑΝΔΡΕΩΣ ΣΥΝΑΓΩΓΗ","url":"https://thegreeklibrary.org/works/tlg2032.tlg001.local001/#tlg2032-tlg001-local001-1"},{"label":"ΠΑΠΠΟΥ ΑΛΕΞΑΝΔΡΕΩΣ ΣΥΝΑΓΩΓΗΣ Γ.","url":"https://thegreeklibrary.org/works/tlg2032.tlg001.local001/#tlg2032-tlg001-local001-2"},{"label":"Book 3","url":"https://thegreeklibrary.org/works/tlg2032.tlg001.local001/#tlg2032-tlg001-local001-3"},{"label":"ΠΑΠΠΟΥ ΑΛΕΞΑΝΔΡΕΩΣ ΣΥΝΑΓΩΓΗΣ Ε.","url":"https://thegreeklibrary.org/works/tlg2032.tlg001.local001/#tlg2032-tlg001-local001-4"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg2032.tlg001.local001/","json":"https://thegreeklibrary.org/api/works/tlg2032.tlg001.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg2032/tlg001/local001.json.gz"}}