{"schemaVersion":2,"id":"tlg1799.tlg011.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/","urn":"urn:cts:greekLit:tlg1799.tlg011.local001","title":"Catoptrica (recensio Theonis?)","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":"Euclidis Opera Omnia","edition":null,"publisher":"Teubner","place":"Leipzig","date":"1895","volume":"7","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) 2015 - 2017","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/details/euclidisoperaomn07eucluoft/page/284/mode/2up?","sourceLinkType":null,"sourceRights":null,"citation":"Euclid. Catoptrica (recensio Theonis?). ed. Johan Ludvig Heiberg, Heinrich Menge. Euclidis Opera Omnia, Leipzig, Teubner, 1895. urn:cts:greekLit:tlg1799.tlg011.local001","excerpt":"Όψιν εἶναι εὐθεῖαν, ἧς τὰ μέσα πάντα τοῖς ἄκροις ἐπιπροσθεῖ. Τὰ ὁρώμενα ἅπαντα καθʼ εὐθείας ὁρᾶσθαι. Ἐνόπτρου τεθέντος ἐν ἐπιπέδῳ καὶ θεωρουμένου τινὸς ὕψους, ὃ πρὸς ὀρθάς ἐστι τῷ ἐπιπέδῳ, γίγνονται ἀνάλογον, ὡς ἡ μεταξὺ τοῦ ἐνόπτρου καὶ τοῦ θεωροῦντος εὐθεῖα πρὸς τὴν μεταξὺ τοῦ ἐνόπτρου καὶ τοῦ πρὸς ὀρθὰς ὕψους, οὕτω τὸ τοῦ θεωροῦντος ὕψος πρὸς τὸ πρὸς ὀρθὰς τῷ ἐπιπέδῳ ὕψος. Ἐν τοῖς ἐπιπέδοις ἐνόπτροις τοῦ τόπου καταληφθέντος, ἐφʼ ὃν ἡ κάθετος πίπτει ἀπὸ τοῦ ὁρωμένου, οὐκέτι ὁρᾶται τὸ ὁρώμενον. Καὶ ἐν τοῖς κυρτοῖς ἐνόπτροις καταληφθέντος τοῦ τόπου, διʼ οὗ ἀπὸ τοῦ ὁρωμένου εἰς τὸ κέντρον ἄγεται τῆς σφαίρας, οὐκέτι ὁρᾶται τὸ ὁρώμενον. τὸ δʼ αὐτὸ καὶ ἐν τοῖς κοίλοις συμβαίνει. Ἐὰν εἰς ἀγγεῖον ἐμβληθῇ τι καὶ λάβῃ ἀπόστημα ὡς μηκέτι ὁρᾶσθαι, τοῦ αὐτοῦ ἀποστήματος ὄντος ἐὰν ὕδωρ ἐγχυθῇ, ὀφθήσεται τὸ ἐμβληθέν.","divisions":[{"label":"Chapter pr","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-pr"},{"label":"α΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-1"},{"label":"β΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-2"},{"label":"γ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-3"},{"label":"δ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-4"},{"label":"ε΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-5"},{"label":"Ϛ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-6"},{"label":"ζ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-7"},{"label":"η΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-8"},{"label":"θ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-9"},{"label":"ι΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-10"},{"label":"ια΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-11"},{"label":"ιβ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-12"},{"label":"ιγ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-13"},{"label":"ιδ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-14"},{"label":"ιε΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-15"},{"label":"ις΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-16"},{"label":"ιζ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-17"},{"label":"ιη΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-18"},{"label":"ιθ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-19"},{"label":"κ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-20"},{"label":"κα΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-21"},{"label":"κβ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-22"},{"label":"κγ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-23"},{"label":"κδ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-24"},{"label":"κε΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-25"},{"label":"κϚ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-26"},{"label":"κζ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-27"},{"label":"κη΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-28"},{"label":"κθ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-29"},{"label":"λ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/#tlg1799-tlg011-local001-30"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg011.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg011.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg011/local001.json.gz"}}