{"schemaVersion":2,"id":"tlg1799.tlg008.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/","urn":"urn:cts:greekLit:tlg1799.tlg008.local001","title":"Data (demonstrationes alterae)","titleGreek":null,"alternateTitles":[],"author":"Euclid","authorityName":"EUCLIDES Geom.","authorUrl":"https://thegreeklibrary.org/authors/tlg1799-euclides-geom/","authorityUrl":"https://thegreeklibrary.org/authors/tlg1799-euclides-geom/","editors":["Johan Ludvig Heiberg","Heinrich Menge"],"publication":{"digitalPublisher":"Harvard College Library","sourceTitle":"Euclidiis Opera Omnia","edition":null,"publisher":"Teubner","place":"Lepizig","date":"1896","volume":"6","series":null,"citation":null,"citationShort":null},"rights":{"text":"Available under a Creative Commons Attribution-ShareAlike 4.0 International License","url":"https://creativecommons.org/licenses/by-sa/4.0/"},"provenance":{"authority":"Harvard College Library","sponsors":["Harvard College Library"],"funders":[],"principal":"Gregory Crane","responsibilities":[{"role":"Corrected and encoded the text","names":[]},{"role":"Librarian for Hellenic Studies and Coordinator for the Classics Collection Development","names":[]},{"role":"Project Manager (University of Leipzig)","names":[]},{"role":"Project Assistant (University of Leipzig)","names":[]},{"role":"Lead Developer (University of Leipzig) 2015-2017","names":[]},{"role":"Technical Advisor","names":[]}]},"corpus":{"version":"2.2.0","date":"2026-08-29"},"revisionDate":"2026-08-15","sourceUrl":"http://www.archive.org/stream/euclidisoperaomn06eucluoft#page/190/mode/2up","sourceLinkType":null,"sourceRights":null,"citation":"Euclid. Data (demonstrationes alterae). ed. Johan Ludvig Heiberg, Heinrich Menge. Euclidiis Opera Omnia, Lepizig, Teubner, 1896. urn:cts:greekLit:tlg1799.tlg008.local001","excerpt":"Δυνατὸν δέ ἐστί καὶ οὕτως. ἔστω τρία μεγέθη τὰ ΑΒ, Γ, Δ, καὶ τὸ μὲν ΑΒ τοῦ δοθέντι μεῖζον ἔστω- ἢ ἐν λόγῳ, τὸ δὲ Γ τοῦ Δ δοθέντι μεῖζον ἢ ἐν λόγῳ· λέγω, ὅτι καὶ τὸ ΑΒ τοῦ Δ δοθέντι μεῖζόν ἐστιν ἢ ἐν λόγῳ. ἐπεὶ γὰρ τὸ ΑΒ τοῦ Γ δοθέντι μεῖζόν ἐστιν ἢ ἐν λόγῳ, ἀφῃρήσθω τὸ δοθὲν μέγεθος τὸ ΑΕ· λοιποῦ ἄρα τοῦ ΕΒ πρὸς τὸ Γ λόγος ἐστὶ δοθέίς· τὸ δὲ Γ τοῦ Δ δοθέντι μεῖζόν ἐστιν ἢ ἐν λόγῳ· καὶ τὸ ΕΒ ἄρα τοῦ Δ δοθέντι μεῖζόν ἐστιν ἢ ἐν λόγῳ. ἀφῃρήσθω οὖν τὸ δοθὲν μέγεθος τὸ ΕΖ λοιποῦ ἄρα τοῦ ΖΒ πρὸς τὸ Δ λόγος ἐστὶ δοθείς. καί ἐστι δοθὲν τὸ ΑΖ τὸ ΑΒ ἄρα τοῦ Δ δοθέντι μεῖζόν ἐστιν ἢ ἐν λόγῳ. 1. 0m. a. 4. ἄλλὲς τὸ ιθʹ] mg. m. 1 Vat, τὸ ιθ om. v. 5. δυνα- τόν — οὕτως] om. Vat. v. ἔστω] ἔστιν P. 7. μεῖζόν ἐστιν P. 13. καὶ — 14. λόγῳ] mg. m. 2 v. 16. ἐστί] ἐοτῖν v. ἐστι] ἐστιν v, sed. ν eras. 17. ἐστιν] om. Vat., comp. add. m. 2.","divisions":[{"label":"1. Ad prop. XIX. Ἄλλως τὸ ιθ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-1"},{"label":"2. Ad prop. XXIV. Ἄλλως τὸ αὐτό.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-2"},{"label":"3. Ad prop. XXVII. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-3"},{"label":"4. Ad prop. XXX. Ἄλλως τὸ αὐτό.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-4"},{"label":"5. Ad prop. XXX. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-5"},{"label":"6. Ad prop. XXX. Ἅλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-6"},{"label":"7. Ad prop. XXXIII. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-7"},{"label":"8. Ad prop. XXXIV. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-8"},{"label":"9. Ad prop. XLV. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-9"},{"label":"10. Αd prop. XLVI. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-10"},{"label":"11. Ad prop. LIV. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-11"},{"label":"12. Ad prop. LV. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-12"},{"label":"13. Ad prop. LXVII. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-13"},{"label":"14. Αd prop LXVII. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-14"},{"label":"15. A prop. LXVII. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-15"},{"label":"16. Ad prop LXVIII. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-16"},{"label":"17. Ad pro LXXX. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-17"},{"label":"§ 18","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-18"},{"label":"19. Ad prop. XCΙ. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-19"},{"label":"20. Ad prop XCIII. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-20"},{"label":"21. Ad prop. XCIII. Ἄλλως.","url":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/#tlg1799-tlg008-local001-21"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg008.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg008.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg008/local001.json.gz"}}