{"schemaVersion":2,"id":"tlg1799.tlg012.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/","urn":"urn:cts:greekLit:tlg1799.tlg012.local001","title":"Phaenomena","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. Phaenomena. ed. Heinrich Menge. Euclidis Opera Omnia, Teubner, Leipzig, 1916. urn:cts:greekLit:tlg1799.tlg012.local001","excerpt":"Ἐπειδὴ ὁρᾶται τὰ ἀπλανῆ ἄστρα ἀεὶ ἐκ τοῦ αὐτοῦ τόπου ἀνατέλλοντα καὶ εἰς τὸν αὐτὸν τόπον δυόμενα καὶ τὰ ἅμα ἀνατέλλοντα ἀεὶ ἅμα ἀνατέλλοντα καὶ τὰ ἅμα δυόμενα ἀεὶ ἅμα δυόμενα καὶ ἐν τῇ ἀπ᾿ ἀνατολῆς ἐπὶ δύσιν φορᾷ τὰ πρὸς ἄλληλα διαστήματα τὰ αὐτὰ ἔχοντα, τοῦτο δὲ γίνεται ἐπὶ τῶν ἐγκύκλιον φορὰν φερομένων μόνον, ἐπὰν ἡ ὄψις πάντῃ τῆς περιφερείας ἴσον ἀπέχῃ, ὡς ἐν τοῖς ὀπτικοῖς δείκνυται, θετέον, τὰ ἄστρα ἐγκυκλίως φέρεσθαι καὶ ἐνδεδέσθαι ἐν ἑνὶ σώματι καὶ τὴν ὄψιν ἴσον ἀπέχειν τῶν περιφερειῶν. ὁρᾶται δέ τις ἀστὴρ μεταξὺ τῶν ἄρκτων οὐ μεταλλάσσων τόπον ἐκ τόπου, ἀλλ᾿ ἐν ᾗ ἐστι χώρᾳ, ἐν ταύτῃ στρεφόμενος. ἐπεὶ δὲ οὗτος πρὸς τὰς περιφερείας τῶν κύκλων, καθ᾿ ὧν οἱ λοιποὶ ἀστέρες φέρονται, ἴσον ἀπέχων πάντῃ φαίνεται, θετέον, τοὺς κύκλους πάντας παραλλήλους εἶναι, ὥστε πάντα τὰ ἀπλανῆ ἄστρα κατὰ παραλλήλων φέρεσθαι πόλον ἐχόντων τὸν προειρημένον ἀστέρα. τούτων δὲ ἔνια οὔτε ἀνατέλλοντα οὔτε…","divisions":[{"label":"Chapter pr","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-pr"},{"label":"α΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-1"},{"label":"β΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-2"},{"label":"γ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-3"},{"label":"δ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-4"},{"label":"ε΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-5"},{"label":"Ϛ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-6"},{"label":"ζ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-7"},{"label":"η΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-8"},{"label":"θ΄.1)","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-9"},{"label":"ι΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-10"},{"label":"ια΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-11"},{"label":"ιβ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-12"},{"label":"ιγ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-13a"},{"label":"Λημμα.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-13b"},{"label":"ιδ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-14"},{"label":"ιε΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-15"},{"label":"ιϚ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/#tlg1799-tlg012-local001-16"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg012.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg012.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg012/local001.json.gz"}}