{"schemaVersion":2,"id":"tlg1799.tlg001.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/","urn":"urn:cts:greekLit:tlg1799.tlg001.local001","title":"Στοιχεῖα","titleGreek":"Στοιχεῖα","alternateTitles":["Elements","Éléments","Elements of Euclid","Στοιχεῖα"],"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"],"publication":{"digitalPublisher":"Trustees of Tufts University","sourceTitle":"Euclidis Opera Omnia","edition":null,"publisher":"Teubner","place":"Leipzig","date":"1883-1888","volume":"1-5","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":"Perseus Digital Library Project","sponsors":["Perseus Project, Tufts University"],"funders":["The National Science Foundation"],"principal":"Gregory Crane","responsibilities":[{"role":"Prepared under the supervision of","names":["Lisa Cerrato","David Smith"]}]},"corpus":{"version":"2.2.0","date":"2026-08-29"},"revisionDate":"2026-08-15","sourceUrl":"http://www.archive.org/stream/euclidisoperaomn01eucluoft","sourceLinkType":null,"sourceRights":null,"citation":"Euclid. Στοιχεῖα. ed. Johan Ludvig Heiberg. Euclidis Opera Omnia, Leipzig, Teubner, 1883-1888. urn:cts:greekLit:tlg1799.tlg001.local001","excerpt":"σημεῖόν ἐστιν, οὗ μέρος οὐθέν. γραμμὴ δὲ μῆκος ἀπλατές. γραμμῆς δὲ πέρατα σημεῖα. εὐθεῖα γραμμή ἐστιν, ἥτις ἐξ ἴσου τοῖς ἐφʼ ἑαυτῆς σημείοις κεῖται. ἐπιφάνεια δέ ἐστιν, ὃ μῆκος καὶ πλάτος μόνον ἔχει. ἐπιφανείας δὲ πέρατα γραμμαί. ἐπίπεδος ἐπιφάνειά ἐστιν, ἥτις ἐξ ἴσου ταῖς ἐφʼ ἑαυτῆς εὐθείαις κεῖται. ἐπίπεδος δὲ γωνία ἐστὶν ἡ ἐν ἐπιπέδῳ δύο γραμμῶν ἁπτομένων ἀλλήλων καὶ μὴ ἐπʼ εὐθείας κειμένων πρὸς ἀλλήλας τῶν γραμμῶν κλίσις. ὅταν δὲ αἱ περιέχουσαι τὴν γωνίαν γραμμαὶ εὐθεῖαι ὦσιν, εὐθύγραμμος καλεῖται ἡ γωνία. ὅταν δὲ εὐθεῖα ἐπʼ εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ, ὀρθὴ ἑκατέρα τῶν ἴσων γωνιῶν ἐστι, καὶ ἡ ἐφεστηκυῖα εὐθεῖα κάθετος καλεῖται, ἐφʼ ἣν ἐφέστηκεν. ἀμβλεῖα γωνία ἐστὶν ἡ μείζων ὀρθῆς. ὀξεῖα δὲ ἡ ἐλάσσων ὀρθῆς. ὅρος ἐστίν, ὅ τινός ἐστι πέρας. σχῆμά ἐστι τὸ ὑπό τινος ἤ τινων ὅρων περιεχόμενον. κύκλος ἐστὶ σχῆμα ἐπίπεδον ὑπὸ μιᾶς γραμμῆς περιεχόμενον ἣ καλεῖται…","divisions":[{"label":"Book 1","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/1-book-1/"},{"label":"Book 2","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/2-book-2/"},{"label":"Book 3","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/3-book-3/"},{"label":"Book 4","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/4-book-4/"},{"label":"Book 5","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/5-book-5/"},{"label":"Book 6","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/6-book-6/"},{"label":"Book 7","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/7-book-7/"},{"label":"Book 8","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/8-book-8/"},{"label":"Book 9","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/9-book-9/"},{"label":"Book 10","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/10-book-10/"},{"label":"Book 11","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/11-book-11/"},{"label":"Book 12","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/12-book-12/"},{"label":"Book 13","url":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/13-book-13/"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg001.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg001.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg001/local001.json.gz"}}