{"schemaVersion":2,"id":"tlg1799.tlg004.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/","urn":"urn:cts:greekLit:tlg1799.tlg004.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. 10), ed. Stamatis (post Heiberg), op. cit., vol. 3, 2nd edn. (1972) 211–234. Cod: 4,097: Math.","citationShort":"Elementa (demonstrationes alterae, lib. 10), ed. Stamatis (post Heiberg), op. cit., vol. 3, 2nd edn. (1972) 211–234."},"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. 10), ed. Stamatis (post Heiberg), op. cit., vol. 3, 2nd edn. (1972) 211–234.. urn:cts:greekLit:tlg1799.tlg004.local001","excerpt":"Β, οὕτως τὸ ἀπὸ τῆς Α πρὸς τὸ ὑπὸ τῶν Α, Β· ἔστιν ἄρα ὡς τὸ ἀπὸ τῆς Α πρὸς τὸ ὑπὸ τῶν Α, Β, οὕτως ὁ Ε πρὸς τὸν Ζ. πάλιν, ἐπεὶ ὁ Δ ἑαυτὸν πολλαπλασιάσας τὸν Η πεποίηκεν, ὁ δὲ Γ τὸν Δ πολλα- πλασιάσας τὸν Ζ πεποίηκεν, ἔστιν ἄρα ὡς ὁ Γ πρὸς τὸν Δ, τουτέστιν ὡς ἡ Α πρὸς τὴν Β, οὕτως ὁ Ζ πρὸς τὸν Η. ἀλλ' ὡς ἡ Α πρὸς τὴν Β, οὕτως τὸ ὑπὸ τῶν Α, Β πρὸς τὸ ἀπὸ τῆς Β· ἔστιν ἄρα ὡς τὸ ὑπὸ τῶν Α, Β πρὸς τὸ ἀπὸ τῆς Β, οὕτως ὁ Ζ πρὸς τὸν Η. ἀλλ' ὡς τὸ ἀπὸ τῆς Α πρὸς τὸ ὑπὸ τῶν Α, Β, οὕτως ἦν ὁ Ε πρὸς τὸν Ζ· δι' ἴσου ἄρα ὡς τὸ ἀπὸ τῆς Α πρὸς τὸ ἀπὸ τῆς Β, οὕτως ὁ Ε πρὸς τὸν Η. ἔστι δὲ ἑκάτερος τῶν Ε, Η τετράγωνος· ὁ μὲν γὰρ Ε ἀπὸ τοῦ Γ ἐστιν, ὁ δὲ Η ἀπὸ τοῦ Δ· τὸ ἀπὸ τῆς Α ἄρα πρὸς τὸ ἀπὸ τῆς Β λόγον ἔχει, ὃν τετράγωνος ἀριθμὸς πρὸς τετράγωνον ἀριθμόν. ὅπερ ἔδει δεῖξαι. Ἀλλὰ δὴ ἐχέτω τὸ ἀπὸ τῆς Α πρὸς τὸ ἀπὸ τῆς Β λόγον, ὃν τετράγωνος ἀριθμὸς ὁ Ε πρὸς τετράγωνον ἀριθμὸν τὸν Η· λέγω, ὅτι σύμμετρός…","divisions":[{"label":"3","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-3"},{"label":"4","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-4"},{"label":"5","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-5"},{"label":"6","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-6"},{"label":"7","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-7"},{"label":"8","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-8"},{"label":"9","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-9"},{"label":"10","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-10"},{"label":"11","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-11"},{"label":"12","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-12"},{"label":"13","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-13"},{"label":"14","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-14"},{"label":"15","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-15"},{"label":"16","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-16"},{"label":"17","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-17"},{"label":"18","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-18"},{"label":"19","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-19"},{"label":"20","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-20"},{"label":"21","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-21"},{"label":"22","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-22"},{"label":"23","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-23"},{"label":"24","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-24"},{"label":"25","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-25"},{"label":"26","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-26"},{"label":"27","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-27"},{"label":"Section 26","url":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/#tlg1799-tlg004-local001-segment-1"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg004.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg004.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg004/local001.json.gz"}}