{"schemaVersion":2,"id":"tlg2039.tlg002.local001","url":"https://thegreeklibrary.org/works/tlg2039.tlg002.local001/","urn":"urn:cts:greekLit:tlg2039.tlg002.local001","title":"De polygonis numeris","titleGreek":null,"alternateTitles":[],"author":"Anonymous","authorityName":"DIOPHANTUS Math.","authorUrl":null,"authorityUrl":"https://thegreeklibrary.org/authors/tlg2039-diophantus-math/","editors":[],"publication":{"digitalPublisher":"Corpus local","sourceTitle":null,"edition":null,"publisher":null,"place":null,"date":null,"volume":null,"series":null,"citation":"De polygonis numeris, ed. Tannery, op. cit., vol. 1, 450–480. Cod: 3,501: Math.","citationShort":"De polygonis numeris, ed. Tannery, op. cit., vol. 1, 450–480."},"rights":{"text":"Document TEI P5 local en UTF-8.","url":null},"provenance":{"authority":null,"sponsors":[],"funders":[],"principal":null,"responsibilities":[]},"corpus":{"version":"2.2.0","date":"2026-08-29"},"revisionDate":"2026-08-29","sourceUrl":"https://maximus.tlg.uci.edu/canon.php","sourceLinkType":"catalogue","sourceRights":null,"citation":"De polygonis numeris. De polygonis numeris, ed. Tannery, op. cit., vol. 1, 450–480.. urn:cts:greekLit:tlg2039.tlg002.local001","excerpt":"Δ, Ε, Ζ, ποιεῖ τινα ἀριθμόν, ὅς ἐστι διπλασίων τοῦ συγκειμένου ἐκ τῶν Α, Β, Γ, Δ, Ε, Ζ. Τὸ γὰρ πλῆθος τῶν Α, Β, Γ, Δ, Ε, Ζ ἤτοι ἄρτιόν ἐστιν ἢ περισσόν. Ἔστω πρότερον ἄρτιον, καὶ ὅσοι εἰσὶν οἱ ἐκτεθέντες, τοσαῦται μονάδες ἔστωσαν ἐν τῷ ΗΘ ἀριθμῷ· ὥστε ἄρτιός ἐστιν ὁ ΗΘ. τετμήσθω δίχα τῷ Κ, καὶ δι- ῃρήσθω ὁ ΗΚ εἰς τὰς ἐν αὐτῷ μονάδας κατὰ τὰ Λ, Μ. Καὶ ἐπεὶ ᾧ ὑπερέχει ὁ Ζ τοῦ Δ, τούτῳ ὑπερέχει καὶ ὁ Γ τοῦ Α, συναμφότερος ἄρα ὁ Ζ. Α συναμφο- τέρῳ τῷ Γ. Δ ἴσος ἐστίν. ἀλλὰ συναμφότερος ὁ Ζ. Α ἴσ. τῷ ὑπὸ συναμφοτέρου τοῦ Ζ. Α καὶ τοῦ ΗΛ· ὥστε καὶ ὁ Γ. Δ ἴσ. τῷ ὑπὸ συναμφοτέρου τοῦ Ζ. Α καὶ τοῦ ΛΜ· διὰ τὰ αὐτὰ δὴ καὶ συναμφότερος ὁ Ε. Β ἴσ. τῷ ὑπὸ συναμφοτέρου τοῦ Ζ. Α καὶ τοῦ ΜΚ· ὥστε καὶ ὁ συγκείμενος ἐκ τῶν Α, Β, Γ, Δ, Ε, Ζ ἴσ. τῷ ὑπὸ συναμφοτέρου τοῦ Ζ. Α καὶ τοῦ ΗΚ· τοῦ δὲ ὑπὸ συναμφοτέρου τοῦ Ζ. Α καὶ τοῦ ΗΚ διπλασίων ἐστὶν ὁ ὑπὸ συναμφοτέρου τοῦ Ζ. Α καὶ τοῦ ΗΘ· ὥστε καὶ τοῦ…","divisions":[{"label":"1","url":"https://thegreeklibrary.org/works/tlg2039.tlg002.local001/#tlg2039-tlg002-local001-1"},{"label":"Section 2","url":"https://thegreeklibrary.org/works/tlg2039.tlg002.local001/#tlg2039-tlg002-local001-segment-1"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg2039.tlg002.local001/","json":"https://thegreeklibrary.org/api/works/tlg2039.tlg002.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg2039/tlg002/local001.json.gz"}}