{"schemaVersion":2,"id":"tlg1799.tlg007.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg007.local001/","urn":"urn:cts:greekLit:tlg1799.tlg007.local001","title":"Data","titleGreek":null,"alternateTitles":[],"author":"Euclid","authorityName":"EUCLIDES Geom.","authorUrl":"https://thegreeklibrary.org/authors/tlg1799-euclides-geom/","authorityUrl":"https://thegreeklibrary.org/authors/tlg1799-euclides-geom/","editors":["Johan Ludvig Heiberg","Heinrich Menge"],"publication":{"digitalPublisher":"Harvard College Library","sourceTitle":"Euclidis Opera Omnia","edition":null,"publisher":"Teubner","place":"Leipzig","date":"1896","volume":"6","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":[],"principal":"Gregory Crane","responsibilities":[{"role":"Corrected and encoded the text","names":[]},{"role":"Librarian for Hellenic Studies and Coordinator for the Classics Collection Development","names":[]},{"role":"Project Manager (University of Leipzig)","names":[]},{"role":"Project Assistant (University of Leipzig)","names":[]},{"role":"Lead Developer (University of Leipzig) 2015-2017","names":[]},{"role":"Technical Advisor","names":[]}]},"corpus":{"version":"2.2.0","date":"2026-08-29"},"revisionDate":"2026-08-15","sourceUrl":"https://archive.org/stream/euclidisoperaomn06eucluoft#page/n67/mode/2up","sourceLinkType":null,"sourceRights":null,"citation":"Euclid. Data. ed. Johan Ludvig Heiberg, Heinrich Menge. Euclidis Opera Omnia, Leipzig, Teubner, 1896. urn:cts:greekLit:tlg1799.tlg007.local001","excerpt":"α΄. Δεδομένα τῷ μεγέθει λέγεται χωρία τε καὶ γραμμαὶ καὶ γωνίαι, οἷς δυνάμεθα ἴσα πορίσασθαι. β΄. Λόγος δεδόσθαι λέγεται, ᾧ δυνάμεθα τὸν αὐτὸν πορίσασθαι. γʹ. Εὐθύγραμμα σχήματα τῷ εἴδει δεδόσθαι λέγεται, ὧν αἵ τε γωνίαι δεδομέναι εἰσὶ κατὰ μίαν καὶ οἱ λόγοι τῶν πλευρῶν πρὸς ἀλλήλας δεδομένοι. δʹ. Τῇ θέσει δεδόσθαι λέγονται σημεῖά τε καὶ γραμμαὶ καὶ γωνίαι, ἃ τὸν αὐτὸν ἀεὶ τόπον ἐπέχει. εʹ. Κύκλος τῷ μεγέθει δεδόσθαι λέγεται, οὗ δέδοται ἡ ἐκ τοῦ κέντρου τῷ μεγέθει. ϛʹ. Τῇ θέσει δὲ καὶ τῷ μεγέθει κύκλος δεδό- σθαι λέγεται, οὗ δέδοται τὸ μὲν κέντρον τῇ θέσει, ἡ δὲ ἐκ τοῦ κέντρου τῷ μεγέθει. ζ΄. Τμήματα κύκλων τῷ μεγέθει δεδόσθαι λέ- γεται, ἐν οἷς αἱ γωνίαι δεδομέναι εἰσὶ καὶ αἱ βάσεις τῶν τμημάτων τῷ μεγέθει. η΄. Τῇ θέσει δὲ καὶ τῷ μεγέθει τμήματα δε- δόσθαι λέγεται, ἐν οἷς αἵ τε γωνίαι δεδομέναι εἰσὶ τῷ ΕΥΚΛΕΙΔΟΥ ΔΕΔΟΜΕΝΑ Ρ et atr. rubro Vat.; εὐκλεί- δου δεδομένα v et acc. om. 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