{"schemaVersion":2,"id":"tlg1799.tlg014.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg014.local001/","urn":"urn:cts:greekLit:tlg1799.tlg014.local001","title":"Phaenomena (demonstrationes alterae recensionis b)","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 (demonstrationes alterae recensionis b). ed. Heinrich Menge. Euclidis Opera Omnia, Teubner, Leipzig, 1916. urn:cts:greekLit:tlg1799.tlg014.local001","excerpt":"Ἔστω ὁ ὁρίζων κύκλος ὁ ΑΒΓ∠ καὶ θερινὸς μὲν τροπικὸς ἔστω ὁ Α∠, χειμερινὸς δὲ ὁ ΒΓ, ὁ δὲ τῶν ζῳδίων κύκλος θέσιν ἐχέτω ὡς τὴν ∠ΗΒΖ, καὶ ἔστω ἐπὶ τοῦ ∠ΗΒΖ κατὰ διάμετρον τὰ Ζ, Η σημεῖα· λέγω, ὅτι τοῦ Ζ ἀνατέλλοντος τὸ Η δύνει. εἰ γὰρ δυνατόν, μὴ δυνέτω, ἀλλʼ ἔστω τὸ Θ δῦνον, καὶ διὰ τῶν Ζ, Θ παράλληλοι κύκλοι γεγράφθωσαν οἱ ΝΘ, ΖΚ. ὥστε τοῦ Ζ ἀνατέλλοντος κατὰ τὸ Κ σημεῖον τὸ Θ δύσεται κατὰ τὸ Ν καὶ ὁ τῶν ζῳδίων κύκλος θέσιν ἔξει τὴν ΜΝΛΚ. καὶ ἐπεὶ ἑκάτερος τῶν ΑΒΓ∠, ΜΝΛΚ. κύκλων μέγιστός ἐστιν, κατὰ διάμετρόν ἐστι τὸ Κ τῷ Ν ἀλλὰ τὸ μὲν Κ τῷ Ζ ἔστι τὸ αὐτό, τὸ δὲ Ν τῷ Θ· καὶ τὸ Ζ ἄρα τῷ Θ ἔστι κατὰ διάμετρον· ἀλλὰ καὶ τῷ ὅπερ ἀδύνατον. οὐκ ἄρα τοῦ Ζ ἀνατέλλοντος τὸ Η οὐ δύνει· δύνει ἄρα. 7. ∠ΗΒΖ] Ζ add. m. 2 Vat 10. διά] supra add. m. 2 at. παράλληλοι] comp. m. 1 at., omnibus litteris supra m. 2. 13. καί — ΜΝΛΚ] mg. m. 2 Vat.","divisions":[{"label":"1. Ad prop. VI. Ἁλίως τὸ αὐτό.","url":"https://thegreeklibrary.org/works/tlg1799.tlg014.local001/#tlg1799-tlg014-local001-1"},{"label":"2. Ad prop. XII. Ἄλλως τὸ ιβ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg014.local001/#tlg1799-tlg014-local001-2"},{"label":"3. Ad prop. XIV Ἄλλως τὸ ιδ΄.","url":"https://thegreeklibrary.org/works/tlg1799.tlg014.local001/#tlg1799-tlg014-local001-3"},{"label":"4. Ad prop. 15. Ἄλλως τὸ αὐτό.","url":"https://thegreeklibrary.org/works/tlg1799.tlg014.local001/#tlg1799-tlg014-local001-4"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg014.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg014.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg014/local001.json.gz"}}