{"schemaVersion":2,"id":"tlg0552.tlg011.local001","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/","urn":"urn:cts:greekLit:tlg0552.tlg011.local001","title":"Liber assumptorum","titleGreek":null,"alternateTitles":[],"author":"Archimède","authorityName":"ARCHIMEDES Geom.","authorUrl":"https://thegreeklibrary.org/authors/tlg0552-archimedes-geom/","authorityUrl":"https://thegreeklibrary.org/authors/tlg0552-archimedes-geom/","editors":["Charles Mugler"],"publication":{"digitalPublisher":"Harvard College Library","sourceTitle":"Archimède","edition":null,"publisher":"Belles Lettres","place":"Paris","date":"1971","volume":"3","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":[],"funders":["Harvard Library"],"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) 2015 - 2017","names":[]},{"role":"Technical Advisor (Mount Allison University)","names":[]}]},"corpus":{"version":"2.2.0","date":"2026-08-29"},"revisionDate":"2026-08-15","sourceUrl":"http://digital.slub-dresden.de/werkansicht/dlf/106436/1/0/","sourceLinkType":null,"sourceRights":null,"citation":"Archimède. Liber assumptorum. ed. Charles Mugler. Archimède, Paris, Belles Lettres, 1971. urn:cts:greekLit:tlg0552.tlg011.local001","excerpt":"Εἴ κα ᾗ δύο κύκλοι ἐπιψαύοντες ἀλλάλων ἐντός, διάμετροι δὲ αὐτῶν παράλληλοι, ἐπιζευχθεῖσαι αἱ ἀπὸ τοῦ σαμείου ἁφῆς καὶ τῶν περάτων τῶν διαμέτρων δύο εὐθεῖαι ἐσσοῦνται ἀλλάλαις ἐπʼ εὐθείας. Ἔστωσαν δύο κύκλοι, ὧν κέντρα τὰ Ζ, Η, ἐπιψαύοντες ἀλλάλων κατὰ τὸ Ε σαμεῖον, διάμετρος δὲ ἁ ΑΒ παρὰ διάμετρον τὰν Γ△· φαμὶ δή, ἐπιζευχθεῖσαι αἱ Ε△, △Β εὐθεῖαι ἐσσοῦνται ἀλλάλαις ἐπʼ εὐθείας. Ἐπεζεύχθω γὰρ ἁ ΖΗ καὶ ἐκβεβλήσθω ποτὶ τὸ Ε, ἄχθω δὲ ἁ △Θ παρὰ τὰν ΖΗ. Ἐπεὶ οὖν εὐθεῖαι αἱ ΖΒ, ΖΕ ἴσαι ἐντὶ καὶ ἁ H△ τᾷ ΖΘ, κοινὰ ἀφαιρήσθω ἁ ΖΘ, τουτέστιν ἁ ΗΕ· λοιπαὶ ἄρα εὐθεῖαι αἱ Θ△, ΘΒ ἴσαι ἀλλαλαις ἐντί· γωνία ἄρα ἁ ὑπὸ Θ△Β γωνίᾳ τᾷ ὑπὸ ΘΒ△, τουτέστιν τᾷ ὑπὸ H△Ε, ἐστὶν ἴσα· κοινὰ ποτικείσθω γωνία ἁ ὑπὸ H△Β συναμφότερος ἄρα γωνία ἁ ὑπὸ H△Β, △ΒΖ συναμφοτέρῳ τᾷ ὑπὸ Η△Β. Ε△Η ἐστὶν ἴσα· ἔστι δὲ συναμφότερος ἁ ὑπὸ Η△Β, △ΒΖ δυσὶν ὀρθαῖς ἴσα· συναμφότερος ἄρα γωνία ἁ ὑπὸ Η△Β, Ε△Η δυσὶν ὀρθαῖς ἐστιν ἴσα· ἐπʼ…","divisions":[{"label":"α΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-1"},{"label":"β΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-2"},{"label":"γ΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-3"},{"label":"δ΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-4"},{"label":"ε΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-5"},{"label":"ς΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-6"},{"label":"ζ΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-7"},{"label":"ή.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-8"},{"label":"θ΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-9"},{"label":"ι΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-10"},{"label":"ιά.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-11"},{"label":"ιβ΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-12"},{"label":"ιγ΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-13"},{"label":"ιδ΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-14"},{"label":"ιε΄.","url":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/#tlg0552-tlg011-local001-15"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg0552.tlg011.local001/","json":"https://thegreeklibrary.org/api/works/tlg0552.tlg011.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg0552/tlg011/local001.json.gz"}}