{"schemaVersion":2,"id":"tlg1799.tlg006.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg006.local001/","urn":"urn:cts:greekLit:tlg1799.tlg006.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 (recensio altera, lib. 11.36–12.17), ed. Stamatis (post Heiberg), op. cit., vol. 4, 2nd edn., 207–238. Cod: 10,153: Math.","citationShort":"Elementa (recensio altera, lib. 11.36–12.17), ed. Stamatis (post Heiberg), op. cit., vol. 4, 2nd edn., 207–238."},"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 (recensio altera, lib. 11.36–12.17), ed. Stamatis (post Heiberg), op. cit., vol. 4, 2nd edn., 207–238.. urn:cts:greekLit:tlg1799.tlg006.local001","excerpt":"ΣΑ, τῆς δὲ ΒΗ ἡμίσεια ἡ ΒΤ. αἱ ΣΑ, ΒΤ ἄρα ἴσαι τε καὶ παράλληλοί εἰσι· καὶ ἐπεζευγμέναι εἰσὶν αἱ ΣΤ, ΑΒ. ἴση ἄρα ἐστὶν ἡ μὲν ΣΥ τῇ ΥΤ, ἡ δὲ ΑΥ τῇ ΥΒ· ὅπερ ἔδει δεῖξαι. Ἐὰν ᾖ δύο πρίσματα ἰσοϋψῆ, καὶ τὸ μὲν ἔχει βάσιν τρίγωνον, τὸ δὲ παραλληλόγραμμον, διπλάσιον δὲ ᾖ τὸ παραλληλόγραμμον τοῦ τριγώνου, ἴσα ἔσται τὰ πρίσματα. Ἔστω δύο πρίσματα ἰσοϋψῆ τὰ ΑΒΓΔΕΖ, ΗΘΚ ΛΜΝ, καὶ τὸ μὲν ἐχέτω τρίγωνον βάσιν τὸ ΚΛΝ, τὸ δὲ παραλληλόγραμμον τὸ ΒΓΔΕ, καὶ ἔστω τὸ ΒΓΔΕ τοῦ ΝΚΛ τριγώνου διπλάσιον. λέγω, ὅτι ἴσα ἐστὶ τὰ πρίσ- ματα. πεπληρώσθω γὰρ τὰ παράλληλα ἐπίπεδα τὰ ΑΔ, ΗΛ. ἐπεὶ οὖν τὸ ΒΔ παραλληλόγραμμον τοῦ ΝΚΛ τρι- γώνου ἐστὶ διπλάσιον, ἔστι δὲ τοῦ ΝΚΛ τριγώνου διπλά- σιον τὸ ΝΛ παραλληλόγραμμον, ἴσον ἄρα ἐστὶ τὸ ΒΔ τῷ ΝΛ. ἐπὶ ἴσων οὖν βάσεων τῶν ΒΔ, ΝΛ ἰσοϋψῆ ἐστι στε- ρεὰ παραλληλεπίπεδα τὰ ΑΔ, ΗΛ. ἴσα ἐστὶν ἀλλήλοις. ἀλλὰ τοῦ μὲν ΑΔ ἥμισύ ἐστι τὸ ΑΒΓΔΕΖ πρίσμα, τοῦ δὲ ΗΛ ἥμισυ τὸ ΗΘΚΛΜ πρίσμα.…","divisions":[{"label":"11","url":"https://thegreeklibrary.org/works/tlg1799.tlg006.local001/#tlg1799-tlg006-local001-11"},{"label":"12","url":"https://thegreeklibrary.org/works/tlg1799.tlg006.local001/#tlg1799-tlg006-local001-12"},{"label":"Section 3","url":"https://thegreeklibrary.org/works/tlg1799.tlg006.local001/#tlg1799-tlg006-local001-segment-1"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg006.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg006.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg006/local001.json.gz"}}