{"schemaVersion":2,"id":"tlg0552.tlg006.local001","url":"https://thegreeklibrary.org/works/tlg0552.tlg006.local001/","urn":"urn:cts:greekLit:tlg0552.tlg006.local001","title":"Arenarius","titleGreek":null,"alternateTitles":[],"author":"Archimède","authorityName":"ARCHIMEDES Geom.","authorUrl":"https://thegreeklibrary.org/authors/tlg0552-archimedes-geom/","authorityUrl":"https://thegreeklibrary.org/authors/tlg0552-archimedes-geom/","editors":["Charles Mugler"],"publication":{"digitalPublisher":"Harvard College Library","sourceTitle":"Archimède","edition":null,"publisher":"Belles Lettres","place":"Paris","date":"1971","volume":"2","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"],"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) 2015 - 2017","names":[]},{"role":"Technical Advisor (Mount Allison University)","names":[]}]},"corpus":{"version":"2.2.0","date":"2026-08-29"},"revisionDate":"2026-08-15","sourceUrl":"http://digital.slub-dresden.de/werkansicht/dlf/106431/1/0/","sourceLinkType":null,"sourceRights":null,"citation":"Archimède. Arenarius. ed. Charles Mugler. Archimède, Paris, Belles Lettres, 1971. urn:cts:greekLit:tlg0552.tlg006.local001","excerpt":"Ι. Οἴονταί τινες, βασιλεῦ Γέλων, τοῦ ψάμμου τὸν ἀριθμὸν ἄπειρον εἶμεν τῷ πλήθει· λέγω δὲ οὐ μόνον τοῦ περὶ Συρακούσας τε καὶ τὰν ἄλλαν Σικελίαν ὑπάρχοντος, ἀλλὰ καὶ τοῦ κατὰ πᾶσαν χώραν τάν τε οἰκημέναν καὶ τὰν ἀοίκητον. Ἐντί τινες δέ, οἳ αὐτὸν ἄπειρον μὲν εἶμεν οὐχ ὑπολαμβάνοντι, μηδένα μέντοι ταλικοῦτον κατωνομασμένον ὑπάρχειν ἀριθμόν, ὅστις ὑπερβάλλει τὸ πλῆθος αὐτοῦ. Οἱ δὲ οὕτως δοξάζοντες δῆλον ὡς, εἰ νοήσαιεν ἐκ τοῦ ψάμμου ταλικοῦτον ὄγκον συγκείμενον τὸ μέγεθος, ἁλίκος ὁ τᾶς γᾶς ὄγκος ἀναπεπληρωμένων ἐν αὐτῷ τῶν τε πελάγεων πάντων καὶ τῶν κοιλωμάτων τᾶς γᾶς εἰς ἴσον ὕψος τοῖς ὑψηλοτάτοις τῶν ὀρέων, πολλαπλασίως μὴ γνώσονται μηδένα κα ῥηθῆμεν ἀριθμὸν ὑπερβάλλοντα τὸ πλῆθος αὐτοῦ. Ἐγὼ δὲ πειρασοῦμαί τοι δεικνύειν διʼ ἀποδείξιων γεωμετρικᾶν, αἷς παρακολουθήσεις, ὅτι τῶν ὑφʼ ἁμῶν κατωνομασμένων ἀριθμῶν καὶ ἐκδεδομένων ἐν τοῖς ποτὶ Ζεύξιππον γεγραμμένοις ὑπερβάλλοντί τινες οὐ μόνον…","divisions":[{"label":"Chapter 1","url":"https://thegreeklibrary.org/works/tlg0552.tlg006.local001/#tlg0552-tlg006-local001-1"},{"label":"Chapter 2","url":"https://thegreeklibrary.org/works/tlg0552.tlg006.local001/#tlg0552-tlg006-local001-2"},{"label":"Chapter 3","url":"https://thegreeklibrary.org/works/tlg0552.tlg006.local001/#tlg0552-tlg006-local001-3"},{"label":"Chapter 4","url":"https://thegreeklibrary.org/works/tlg0552.tlg006.local001/#tlg0552-tlg006-local001-4"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg0552.tlg006.local001/","json":"https://thegreeklibrary.org/api/works/tlg0552.tlg006.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg0552/tlg006/local001.json.gz"}}