{"schemaVersion":2,"id":"tlg1799.tlg003.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg003.local001/","urn":"urn:cts:greekLit:tlg1799.tlg003.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. 5–9), ed. Stamatis (post Heiberg), op. cit., vol. 2, 2nd edn. (1970) 229–237, 239. Cod: 1,674: Math.","citationShort":"Elementa (demonstrationes alterae, lib. 5–9), ed. Stamatis (post Heiberg), op. cit., vol. 2, 2nd edn. (1970) 229–237, 239."},"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. 5–9), ed. Stamatis (post Heiberg), op. cit., vol. 2, 2nd edn. (1970) 229–237, 239.. urn:cts:greekLit:tlg1799.tlg003.local001","excerpt":"ΘΜΝ τομεῖς ἴσοι ἀλλήλοις εἰσίν. ὁσαπλασίων ἄρα ἐστὶν ἡ ΛΒ περιφέρεια τῆς ΒΓ περιφερείας, τοσαυταπλασίων ἐστὶ καὶ ὁ ΗΒΛ τομεὺς τοῦ ΗΒΓ τομέως. διὰ τὰ αὐτὰ δὴ καὶ ὁσαπλασίων ἐστὶν ἡ ΝΕ περιφέρεια τῆς ΕΖ περιφερείας, τοσαυταπλασίων ἐστὶ καὶ ὁ ΘΕΝ τομεὺς τοῦ ΘΕΖ τομέως. εἰ ἄρα ἴση ἐστὶν ἡ ΒΛ περιφέρεια τῇ ΕΝ περιφερείᾳ, ἴσος ἐστὶ καὶ ὁ ΒΗΛ τομεὺς τῷ ΕΘΝ τομεῖ, καὶ εἰ ὑπερέχει ἡ ΒΛ περιφέρεια τῆς ΕΝ περι- φερείας, ὑπερέχει καὶ ὁ ΒΗΛ τομεὺς τοῦ ΘΕΝ τομέως, καὶ εἰ ἐλλείπει, ἐλλείπει. τεσσάρων δὴ ὄντων μεγεθῶν δύο μὲν τῶν ΒΓ, ΕΖ περιφερειῶν, δύο δὲ τῶν ΗΒΓ, ΕΘΖ τομέων εἴληπται ἰσάκις πολλαπλάσια τῆς μὲν ΒΓ περιφερείας καὶ τοῦ ΗΒΓ τομέως ἥ τε ΒΛ περιφέρεια καὶ ὁ ΗΒΛ τομεύς, τῆς δὲ ΕΖ περιφερείας καὶ τοῦ ΘΕΖ τομέως ἰσάκις πολλαπλάσια ἥ τε ΕΝ περιφέρεια καὶ ὁ ΘΕΝ τομεύς· καὶ δέδεικται, ὅτι εἰ ὑπερέχει ἡ ΒΛ περι- φέρεια τῆς ΕΝ περιφερείας, ὑπερέχει καὶ ὁ ΒΗΛ τομεὺς τοῦ ΕΘΝ τομέως, καὶ εἰ ἴση,…","divisions":[{"label":"234","url":"https://thegreeklibrary.org/works/tlg1799.tlg003.local001/#tlg1799-tlg003-local001-234"},{"label":"235","url":"https://thegreeklibrary.org/works/tlg1799.tlg003.local001/#tlg1799-tlg003-local001-235"},{"label":"236","url":"https://thegreeklibrary.org/works/tlg1799.tlg003.local001/#tlg1799-tlg003-local001-236"},{"label":"237","url":"https://thegreeklibrary.org/works/tlg1799.tlg003.local001/#tlg1799-tlg003-local001-237"},{"label":"239","url":"https://thegreeklibrary.org/works/tlg1799.tlg003.local001/#tlg1799-tlg003-local001-239"},{"label":"Section 6","url":"https://thegreeklibrary.org/works/tlg1799.tlg003.local001/#tlg1799-tlg003-local001-segment-1"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg003.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg003.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg003/local001.json.gz"}}