{"schemaVersion":2,"id":"tlg0358.tlg005.local001","url":"https://thegreeklibrary.org/works/tlg0358.tlg005.local001/","urn":"urn:cts:greekLit:tlg0358.tlg005.local001","title":"Problemata arithmetica","titleGreek":null,"alternateTitles":[],"author":"Nicomachus of Gerasa","authorityName":"NICOMACHUS Math.","authorUrl":"https://thegreeklibrary.org/authors/tlg0358-nicomachus-math/","authorityUrl":"https://thegreeklibrary.org/authors/tlg0358-nicomachus-math/","editors":["Richard Hoche"],"publication":{"digitalPublisher":"Harvard College Library","sourceTitle":"Introductio arithmetica","edition":null,"publisher":"Teubner","place":"Leipzig","date":"1866","volume":null,"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":[],"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)","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/autolycidesphaer00autouoft#page/n609/mode/2up","sourceLinkType":null,"sourceRights":null,"citation":"Nicomachus Of Gerasa. Problemata arithmetica. ed. Richard Hoche. Introductio arithmetica, Leipzig, Teubner, 1866. urn:cts:greekLit:tlg0358.tlg005.local001","excerpt":"α. ΤΟΤ ΚΥΝΟΣ. Δοθέντων ἀπὸ μονάδος ὁποσωνοῦν ἀριθμῶν ἐφεξῆς εὑρεῖν, ὅσος ἐστὶν ὁ σύμπας. Ἔστωσαν ἀπὸ μονάδος τῆς α ἐφεξῆς οἱ β, γ, δ, ε, ζ, η, θ, ι· ἢ δὴ ἄρτιόν ἐστι τὸ πλῆθος αὐτῶν ἢ περιττόν· ἔστω πρῶτον περιττόν· φανερὸν δή, ὅτι οἱ μὲν α ι διπλάσιοί εἰσι τοῦ ε, οἱ δὲ β θ τοῦ ε καὶ ἐφεξῆς ὅσον ἄρα ἐστὶ τὸ πλῆθος πάντων, τοσαυταπλασίων ἐστὶν ὁ σύμπας συντεθεὶς τοῦ ε· ἔστιν ἄρα ὡς ὁ ι πρὸς τὴν μονάδα, ὁ σύμπας πρὸς τὸν ε· ὁ ἄρα ὑπὸ τοῦ ι καὶ ε ἴσος ἐστὶ τῷ ὑπὸ τῆς μονάδος καὶ συμπάντων, τουτέστι τῷ σύμπαντι ἀριθμῷ. εἰλήφθω δὴ ὁ ἐφεξῆς τῷ ι, ὁ κ· φανερὸν δὴ ὅτι ὁ κ διπλάσιός ἐστι τοῦ ε, ἴσος γάρ ἐστι τοῖς ι α· ἐπεὶ οὖν ὁ ι τὸν ε πολλαπλασιάσας ποιεῖ τὸν σύμπαντα, ἐὰν ἄρα τὸν κ πολλαπλασιάσας ποιήσῃ τινά, ὁ γενόμενος ἔσται τοῦ σύμπαντος διπλασίων. ὅταν ἄρα ἀπὸ 1. ΠΡΟΒΛ. ΑΡ.] addidi inscript. — 7. hac in serie numeroru ζ ═ 6, η ═ 7, θ 8, ι ═ 9 ponitur; κ (16) ═ 10. μονάδος πλήθους ἀριθμῶν…","divisions":[{"label":"§ 1","url":"https://thegreeklibrary.org/works/tlg0358.tlg005.local001/#tlg0358-tlg005-local001-1"},{"label":"§ 2","url":"https://thegreeklibrary.org/works/tlg0358.tlg005.local001/#tlg0358-tlg005-local001-2"},{"label":"§ 3","url":"https://thegreeklibrary.org/works/tlg0358.tlg005.local001/#tlg0358-tlg005-local001-3"},{"label":"§ 4","url":"https://thegreeklibrary.org/works/tlg0358.tlg005.local001/#tlg0358-tlg005-local001-4"},{"label":"§ 5","url":"https://thegreeklibrary.org/works/tlg0358.tlg005.local001/#tlg0358-tlg005-local001-5"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg0358.tlg005.local001/","json":"https://thegreeklibrary.org/api/works/tlg0358.tlg005.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg0358/tlg005/local001.json.gz"}}