{"schemaVersion":2,"id":"tlg0550.tlg001.local001","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/","urn":"urn:cts:greekLit:tlg0550.tlg001.local001","title":"Conica","titleGreek":null,"alternateTitles":[],"author":"Apollonius of Perga","authorityName":"APOLLONIUS Geom.","authorUrl":"https://thegreeklibrary.org/authors/tlg0550-apollonius-geom/","authorityUrl":"https://thegreeklibrary.org/authors/tlg0550-apollonius-geom/","editors":["J. L. Heiberg"],"publication":{"digitalPublisher":"Open Greek and Latin","sourceTitle":"Apollonii Pergaei quae graece exstant","edition":null,"publisher":"Teubner","place":"Leipzig","date":"1893","volume":"2","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":null,"sponsors":[],"funders":["Center for Hellenic Studies"],"principal":null,"responsibilities":[{"role":"Published original versions of the electronic texts","names":[]},{"role":"Digital conversion and editing","names":[]},{"role":"Digital conversion and editing","names":[]},{"role":"Digital conversion and editing","names":[]},{"role":"Digital conversion and editing","names":[]},{"role":"Digital conversion and editing","names":[]},{"role":"Digital conversion and editing","names":[]},{"role":"Digital editor","names":[]}]},"corpus":{"version":"2.2.0","date":"2026-08-29"},"revisionDate":"2026-08-15","sourceUrl":"https://archive.org/details/apolloniipergaei02apoluoft/page/2/mode/1up","sourceLinkType":null,"sourceRights":null,"citation":"Apollonius Of Perga. Conica. ed. J. L. Heiberg. Apollonii Pergaei quae graece exstant, Leipzig, Teubner, 1893. urn:cts:greekLit:tlg0550.tlg001.local001","excerpt":"Ἐὰν κώνου τομῆς ἢ κύκλου περιφερείας ληφθῇ τι σημεῖον ἐκτός, καὶ ἀπ’ αὐτοῦ τῇ τομῇ προσπίπτωσι δύο εὐθεῖαι, ὧν ἡ μὲν ἐφάπτεται, ἡ δὲ τέμνει κατὰ δύο σημεῖα, καὶ ὃν ἔχει λόγον ὅλη ἡ τέμνουσα πρὸς τὴν ἐκτὸς ἀπολαμβανομένην μεταξὺ τοῦ τε σημείου καὶ τῆς γραμμῆς, τοῦτον τμηθῇ ἡ ἐντὸς ἀπολαμβανομένη εὐθεῖα ὥστε τὰς ὁμολόγους εὐθείας πρὸς τῷ αὐτῷ σημείῳ εἶναι, ἡ ἀπὸ τῆς ἁφῆς ἐπὶ τὴν διαίρεσιν ἀγομένη εὐθεῖα συμπεσεῖται τῇ γραμμῇ, καὶ ἡ ἀπὸ τῆς συμπτώσεως ἐπὶ τὸ ἐκτὸς σημεῖον ἀγομένη εὐθεῖα ἐφάπτεται τῆς γραμμῆς. ἔστω γὰρ κώνου τομὴ ἢ κύκλου περιφέρεια ἡ ΑΒΓ, καὶ εἰλήφθω τι σημεῖον ἐκτὸς τὸ Δ, καὶ ἀπ’ αὐτοῦ ἡ μὲν ΔΒ ἐφαπτέσθω κατὰ τὸ Β ἡ δὲ ΔΕΓ τεμνέτω τὴν τομὴν κατὰ τὰ Ε, Γ, καὶ ὃν ἔχει λόγον ἡ ΓΔ πρὸς ΔΕ, τοῦτον ἐχέτω ἡ ΓΖ πρὸς ΖΕ. λέγω, ὅτι ἡ ἀπὸ τοῦ Β ἐπὶ τὸ Ζ ἀγομένη συμπίπτει τῇ τομῇ, καὶ ἡ ἀπὸ τῆς συμπτώσεως ἐπὶ τὸ Δ ἐφάπτεται τῆς τομῆς. [ἐπεὶ οὖν ἡ ΔΓ τέμνει τὴν τομὴν κατὰ δύο σημεῖα,…","divisions":[{"label":"α′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-1"},{"label":"β′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-2"},{"label":"γ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-3"},{"label":"δ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-4"},{"label":"ε′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-5"},{"label":"Ϛ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-6"},{"label":"ζ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-7"},{"label":"η′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-8"},{"label":"θ′","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-9"},{"label":"ι′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-10"},{"label":"ια′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-11"},{"label":"ιβ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-12"},{"label":"ιγ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-13"},{"label":"ιδ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-14"},{"label":"ιε′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-15"},{"label":"ιϛ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-16"},{"label":"ιζ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-17"},{"label":"ιη′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-18"},{"label":"ιθ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-19"},{"label":"κ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-20"},{"label":"κα′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-21"},{"label":"κβ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-22"},{"label":"κγ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-23"},{"label":"κδ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-24"},{"label":"κε′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-25"},{"label":"κϚ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-26"},{"label":"κζ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-27"},{"label":"κη′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-28"},{"label":"κθ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-29"},{"label":"λ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-30"},{"label":"λα′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-31"},{"label":"λβ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-32"},{"label":"λγ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-33"},{"label":"λδ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-34"},{"label":"λε′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-35"},{"label":"λϚ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-36"},{"label":"λζ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-37"},{"label":"λη′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-38"},{"label":"λθ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-39"},{"label":"μ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-40"},{"label":"μα′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-41"},{"label":"μβ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-42"},{"label":"μγ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-43"},{"label":"μδ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-44"},{"label":"με′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-45"},{"label":"μς′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-46"},{"label":"μζ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-47"},{"label":"μη′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-48"},{"label":"μθ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-49"},{"label":"ν′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-50"},{"label":"να′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-51"},{"label":"νβ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-52"},{"label":"νγ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-53"},{"label":"νδ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-54"},{"label":"νε′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-55"},{"label":"νς′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-56"},{"label":"νζ′.","url":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/#tlg0550-tlg001-local001-57"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg0550.tlg001.local001/","json":"https://thegreeklibrary.org/api/works/tlg0550.tlg001.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg0550/tlg001/local001.json.gz"}}