{"schemaVersion":2,"id":"tlg1799.tlg002.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg002.local001/","urn":"urn:cts:greekLit:tlg1799.tlg002.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. 1–3), ed. Stamatis (post Heiberg), op. cit., vol. 1, 2nd edn. (1969) 181–186. Cod: 877: Math.","citationShort":"Elementa (demonstrationes alterae, lib. 1–3), ed. Stamatis (post Heiberg), op. cit., vol. 1, 2nd edn. (1969) 181–186."},"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. 1–3), ed. Stamatis (post Heiberg), op. cit., vol. 1, 2nd edn. (1969) 181–186.. urn:cts:greekLit:tlg1799.tlg002.local001","excerpt":"κέντρον τοῦ κύκλου, τὸ Δ, μεγίστημὲν ἔσται ἡ ΔΗ, μείζων δὲ ἡ μὲνΔΓ τῆς ΔΒ, ἡ δὲ ΔΒ τῆς ΔΑ. ἀλλὰκαὶ ἴση· ὅπερ ἐστὶν ἀδύνατον· οὐκἄρα τὸ Ε κέντρον ἐστὶ τοῦ ΑΒΓκύκλου. ὁμοίως δὴ δείξομεν, ὅτιοὐδ' ἄλλο τι πλὴν τοῦ Δ· τὸ Δ ἄρα σημεῖον κέντρονἐστὶ τοῦ ΑΒΓ κύκλου· ὅπερ ἔδει δεῖξαι. Ad γʹ, prop. ιʹ ΑΛΛΩΣ Κύκλος γὰρ πάλιν ὁ ΑΒΓ κύκλον τὸν ΔΕΖ τεμνέτωκατὰ πλείονα σημεῖα ἢ δύο τὰ Β, Η, Θ, Ζ καὶ εἰλήφθω τὸκέντρον τοῦ ΑΒΓ κύκλου τὸ Κ, καὶἐπεζεύχθωσαν αἱ ΚΒ, ΚΗ, ΚΖ. Ἐπεὶ οὖν κύκλου τοῦ ΔΕΖ εἴλη-πταί τι σημεῖον ἐντὸς τὸ Κ, καὶ ἀπὸτοῦ Κ πρὸς τὸν ΔΕΖ κύκλον προσ-πεπτώκασι πλείους ἢ δύο ἴσαι εὐθεῖαιαἱ ΚΒ, ΚΖ, ΚΗ, τὸ Κ ἄρα σημεῖονκέντρον ἐστὶ τοῦ ΔΕΖ κύκλου. ἔστιδὲ καὶ τοῦ ΑΒΓ κύκλου κέντρον τὸ Κ·δύο ἄρα κύκλων τεμνόντων ἀλλήλους τὸ αὐτὸ κέντρονἐστὶ τὸ Κ· ὅπερ ἐστὶν ἀδύνατον. οὐκ ἄρα κύκλος κύκλοντέμνει κατὰ πλείονα σημεῖα ἢ δύο· ὅπερ ἔδει δεῖξαι. Ad γʹ, prop. ιαʹ Ἀλλὰ δὴ πιπτέτω ὡς ἡ ΗΖΓ, [καὶ]…","divisions":[{"label":"Section 1","url":"https://thegreeklibrary.org/works/tlg1799.tlg002.local001/#tlg1799-tlg002-local001-tlg1799-tlg002"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg002.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg002.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg002/local001.json.gz"}}