{"schemaVersion":2,"id":"tlg1799.tlg016.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/","urn":"urn:cts:greekLit:tlg1799.tlg016.local001","title":"Fragmenta","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":["Heinrich Menge"],"publication":{"digitalPublisher":"Harvard College Library","sourceTitle":"Euclidis Opera Omnia","edition":null,"publisher":"Leipzig","place":"Teubner","date":"1916","volume":"8","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":["Harvard Library Arcadia Fund"],"principal":"Gregory Crane","responsibilities":[{"role":"Corrected and encoded the text","names":[]},{"role":"Editor-in-Chief, Perseus Digital Library","names":[]},{"role":"Project Manager (University of Leipzig)","names":[]},{"role":"Project Assistant (University of Leipzig)","names":[]},{"role":"Lead Developer (University of Leipzig)","names":[]},{"role":"Technical Advisor","names":[]}]},"corpus":{"version":"2.2.0","date":"2026-08-29"},"revisionDate":"2026-08-15","sourceUrl":"https://archive.org/stream/euclidisoperaomn08eucluoft#page/n3/mode/2up","sourceLinkType":null,"sourceRights":null,"citation":"Euclid. Fragmenta. ed. Heinrich Menge. Euclidis Opera Omnia, Teubner, Leipzig, 1916. urn:cts:greekLit:tlg1799.tlg016.local001","excerpt":"1. Proclus Comm. in Eucl. p. 68,23sqq. (ed. Friedlein): Πολλὰ μὲν οὖν καὶ ἄλλα τοῦ ἀνδρὸς τούτου Euclidis μαθηματικὰ συγγράμματα θαυμαστῆς ἀκριβείας καὶ ἐπιστημονικῆς θεωρίας μεστά· τοιαῦτα γὰρ καὶ τὰ Ὀπτικὰ καὶ τὰ Κατοπτρικά, τοιαῦται δὲ καὶ αἰ κατὰ μουσικὴν στοιχειώσεις, ἔτι δὲ τὸ Περὶ διαιρέσεων βιβλίον. ldem ibid. p. 144,18sqq. δεύτερον δὲ ἀπὸ τῆς ὁλότητος τελειοῦται sc. ὁ τοῦ σχήματος λόγος τῆς εἰς τὰ ἀνόμοια μέρη διακρινομένης, ὅθεν δὴ καὶ αὐτὸς ἑκάστῳ τῶν εἰδῶν ἐπιφέρει τὸ ὅλον, καὶ τῶν σχημάτων ἕκαστον εἰς διάφορα αὐτῶν εἴδη τέμνεται. καὶ γὰρ ὁ κύκλος εἰς ἀνόμοια τῷ λόγῳ καὶ ἕκαστον τῶν εὐθυγράμμων διαιρετόν ἐστιν, ὃ καὶ αὐτὸς ὁ Στοιχειωτὴς ἐν ταῖς Διαιρέσεσι πραγματεύεται τὸ μὲν εἰς ὅμοια τὰ δοθέντα σχήματα διαιρῶν, τὸ δὲ εἰς ἀνόμοια. Cfr. Studien über Euklid p. 36 sqq. sine dubio cum hoc opere Euclidis adfinitate quadam coniunctus est liber III Metricorum Heronis, sed non…","divisions":[{"label":"Περὶ διαιρέσεων.","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-1"},{"label":"Chapter 2","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-2"},{"label":"Ψευδάρια.","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-3"},{"label":"Πορίσματα.","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-4"},{"label":"Chapter 5","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-5"},{"label":"Chapter 6","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-6"},{"label":"Τόποι πρὸς ἐπιφανείᾳ.","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-7"},{"label":"Chapter 8","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-8"},{"label":"Κωνικά.","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-9"},{"label":"Chapter 10","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-10"},{"label":"Chapter 11","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-11"},{"label":"Chapter 12","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-12"},{"label":"Chapter 13","url":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/#tlg1799-tlg016-local001-13"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg016.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg016.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg016/local001.json.gz"}}