{"schemaVersion":2,"id":"tlg1799.tlg005.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/","urn":"urn:cts:greekLit:tlg1799.tlg005.local001","title":"Elementa","titleGreek":null,"alternateTitles":[],"author":"Anonymous","authorityName":"EUCLIDES Geom.","authorUrl":null,"authorityUrl":"https://thegreeklibrary.org/authors/tlg1799-euclides-geom/","editors":[],"publication":{"digitalPublisher":"Corpus local","sourceTitle":null,"edition":null,"publisher":null,"place":null,"date":null,"volume":null,"series":null,"citation":"Elementa (demonstrationes alterae, lib. 11– 13), ed. Stamatis (post Heiberg), op. cit., vol. 4, 2nd edn. (1973) 187–206. Cod: 4,076: Math.","citationShort":"Elementa (demonstrationes alterae, lib. 11– 13), ed. Stamatis (post Heiberg), op. cit., vol. 4, 2nd edn. (1973) 187–206."},"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":"Elementa. Elementa (demonstrationes alterae, lib. 11– 13), ed. Stamatis (post Heiberg), op. cit., vol. 4, 2nd edn. (1973) 187–206.. urn:cts:greekLit:tlg1799.tlg005.local001","excerpt":"ΗΘ, ΘΚ ἴσαι εἰσὶν ἑκατέρα ἑκατέρᾳ, καὶ γωνίας ἴσας περιέχουσιν, βάσις ἄρα ἡ ΑΛ βάσει τῇ ΗΚ ἴση ἐστίν. καὶ ἐπεὶ αἱ πρὸς τοῖς Ε, Θ σημείοις γωνίαι τῆς ὑπὸ ΑΒΓ μείζονές εἰσιν, ὧν ἡ ὑπὸ ΗΘΚ τῇ ὑπὸ ΑΒΛ ἐστιν ἴση, λοι- πὴ ἄρα ἡ πρὸς τῷ Ε γωνία τῆς ὑπὸ ΛΒΓ μείζων ἐστίν. καὶ ἐπεὶ δύο αἱ ΛΒ, ΒΓ δυσὶ ταῖς ΔΕ, ΕΖ ἴσαι εἰσὶν ἑκα- τέρα ἑκατέρᾳ, καὶ γωνία ἡ ὑπὸ ΔΕΖ γωνίας τῆς ὑπὸ ΛΒΓ μείζων, βάσις ἄρα ἡ ΔΖ βάσεως τῆς ΛΓ μείζων ἐστίν. ἴση δὲ ἐδείχθη ἡ ΗΚ τῇ ΑΛ· αἱ ἄρα ΔΖ, ΗΚ τῶν ΑΛ, ΛΓ μείζονές εἰσιν· ἀλλὰ αἱ ΑΛ, ΛΓ τῆς ΑΓ μείζονές εἰσι· πολ- λῷ ἄρα αἱ ΔΖ, ΗΚ τῆς ΑΓ μείζονές εἰσιν. τῶν ΑΓ, ΔΖ, ΗΚ ἄρα εὐθειῶν αἱ δύο τῆς λοιπῆς μείζονές εἰσι πάντῃ μεταλαμβανόμεναι· δυνατὸν ἄρα ἐστὶν ἐκ τῶν ἴσων ταῖς ΑΓ, ΔΖ, ΗΚ τρίγωνον συστήσασθαι· ὅπερ ἔδει δεῖξαι.","divisions":[{"label":"1","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-1"},{"label":"2","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-2"},{"label":"3","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-3"},{"label":"4","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-4"},{"label":"5","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-5"},{"label":"6","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-6"},{"label":"7","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-7"},{"label":"8","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-8"},{"label":"9","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-9"},{"label":"10","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-10"},{"label":"Section 11","url":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/#tlg1799-tlg005-local001-segment-1"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg005.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg005.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg005/local001.json.gz"}}