{"schemaVersion":2,"id":"tlg2055.tlg001.local001","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/","urn":"urn:cts:greekLit:tlg2055.tlg001.local001","title":"De sectione cylindri","titleGreek":null,"alternateTitles":[],"author":"Anonymous","authorityName":null,"authorUrl":null,"authorityUrl":null,"editors":[],"publication":{"digitalPublisher":"Corpus local","sourceTitle":null,"edition":null,"publisher":null,"place":null,"date":null,"volume":null,"series":null,"citation":"De sectione cylindri, ed. J. L. Heiberg, Sereni Antinoensis opuscula, Leipzig: Teubner, 1896: 2–116. Cod: 12,648: Math.","citationShort":"De sectione cylindri, ed. J. L. Heiberg, Sereni Antinoensis opuscula, Leipzig: Teubner, 1896: 2–116."},"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 sectione cylindri. De sectione cylindri, ed. J. L. Heiberg, Sereni Antinoensis opuscula, Leipzig: Teubner, 1896: 2–116.. urn:cts:greekLit:tlg2055.tlg001.local001","excerpt":"{ΠΕΡΙ ΚΥΛΙΝΔΡΟΥ ΤΟΜΗΣ.} Πολλοὺς ὁρῶν, ὦ φίλε Κῦρε, τῶν περὶ γεωμετρίαν ἀναστρεφομένων οἰομένους τὴν τοῦ κυλίνδρου πλαγίαν τομὴν ἑτέραν εἶναι τῆς τοῦ κώνου τομῆς τῆς καλου- μένης ἐλλείψεως ἐδικαίωσα μὴ χρῆναι περιορᾶν ἀγνο- οῦντας αὐτούς τε καὶ τοὺς ὑπ' αὐτῶν οὕτω φρονεῖν ἀναπεπεισμένους· καίτοι δόξειεν ἂν παντὶ ἄλογον εἶναι γεωμέτρας γε ὄντας περὶ γεωμετρικοῦ προβλήματος ἄνευ ἀποδείξεως ἀποφαίνεσθαί τι καὶ πιθανολογεῖν ἀτεχνῶς ἀλλότριον γεωμετρίας πρᾶγμα ποιοῦντας. ὅμως δ' οὖν, ἐπείπερ οὕτως ὑπειλήφασιν, ἡμεῖς δὲ οὐ συμφερόμεθα, φέρε γεωμετρικῶς ἀποδείξωμεν, ὅτι μίαν καὶ τὴν αὐτὴν κατ' εἶδος ἀνάγκη γίνεσθαι ἐν ἀμφο- τέροις τοῖς σχήμασι τομήν, τῷ κώνῳ λέγω καὶ τῷ κυλίνδρῳ, τοιῶσδε μέντοι ἀλλ' οὐχ ἁπλῶς τεμνομένοις. ὥσπερ δὲ οἱ τὰ κωνικὰ πραγματευσάμενοι τῶν παλαιῶν οὐκ ἠρκέσθησαν τῇ κοινῇ ἐννοίᾳ τοῦ κώνου, ὅτι τριγώνου περιενεχθέντος ὀρθογωνίου συνίσταιτο, περισσότερον δὲ καὶ…","divisions":[{"label":"2","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-2"},{"label":"4","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-4"},{"label":"6","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-6"},{"label":"8","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-8"},{"label":"10","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-10"},{"label":"12","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-12"},{"label":"14","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-14"},{"label":"16","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-16"},{"label":"18","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-18"},{"label":"20","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-20"},{"label":"22","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-22"},{"label":"24","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-24"},{"label":"26","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-26"},{"label":"28","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-28"},{"label":"30","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-30"},{"label":"32","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-32"},{"label":"34","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-34"},{"label":"36","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-36"},{"label":"38","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-38"},{"label":"40","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-40"},{"label":"42","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-42"},{"label":"44","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-44"},{"label":"46","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-46"},{"label":"48","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-48"},{"label":"50","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-50"},{"label":"52","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-52"},{"label":"54","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-54"},{"label":"56","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-56"},{"label":"58","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-58"},{"label":"60","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-60"},{"label":"62","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-62"},{"label":"64","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-64"},{"label":"66","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-66"},{"label":"68","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-68"},{"label":"70","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-70"},{"label":"72","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-72"},{"label":"74","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-74"},{"label":"76","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-76"},{"label":"78","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-78"},{"label":"80","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-80"},{"label":"82","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-82"},{"label":"84","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-84"},{"label":"86","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-86"},{"label":"88","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-88"},{"label":"90","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-90"},{"label":"92","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-92"},{"label":"94","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-94"},{"label":"96","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-96"},{"label":"98","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-98"},{"label":"100","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-100"},{"label":"102","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-102"},{"label":"104","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-104"},{"label":"106","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-106"},{"label":"108","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-108"},{"label":"110","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-110"},{"label":"112","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-112"},{"label":"114","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-114"},{"label":"116","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-116"},{"label":"Section 59","url":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/#tlg2055-tlg001-local001-segment-1"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg2055.tlg001.local001/","json":"https://thegreeklibrary.org/api/works/tlg2055.tlg001.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg2055/tlg001/local001.json.gz"}}