{"schemaVersion":2,"id":"tlg0559.tlg015.local001","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/","urn":"urn:cts:greekLit:tlg0559.tlg015.local001","title":"Geodaesia [Sp.]","titleGreek":null,"alternateTitles":[],"author":"Hero of Alexandria","authorityName":"HERON Mech.","authorUrl":"https://thegreeklibrary.org/authors/tlg0559-heron-mech/","authorityUrl":"https://thegreeklibrary.org/authors/tlg0559-heron-mech/","editors":["Johan Ludvig Heiberg"],"publication":{"digitalPublisher":"Harvard College Library","sourceTitle":"Heronis quae feruntur sterometrica et de mensuris","edition":null,"publisher":"Teubner","place":"Leipzig","date":"1914","volume":"5","series":"Heronis Alexandrini opera quae supersunt omnia","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","names":[]}]},"corpus":{"version":"2.2.0","date":"2026-08-29"},"revisionDate":"2026-08-15","sourceUrl":"https://hdl.handle.net/2027/mdp.39015017390389?urlappend=%3Bseq=74","sourceLinkType":null,"sourceRights":null,"citation":"Hero Of Alexandria. Geodaesia [Sp.]. ed. Johan Ludvig Heiberg. Heronis quae feruntur sterometrica et de mensuris, Leipzig, Teubner, 1914. urn:cts:greekLit:tlg0559.tlg015.local001","excerpt":"Σημεῖόν ἐστιν, οὗ μέρος οὐδέν. Γραμμὴ δὲ μῆκος ἀπλατές. γραμμῆς δὲ πέρατα σημεῖα. Εὐθεῖα γραμμή ἐστιν, ἥτις ἐξ ἴσου τοῖς ἐφʼ ἑαυτῆς σημείοις κεῖται. Ἐπιφάνεια δέ ἐστιν, ὃ μῆκος καὶ πλάτος μόνον ἔχει. ἐπιφανείας δὲ πέρατα γραμμαί. Ἐπίπεδος ἐπιφάνειά ἐστιν, ἥτις ἐξ ἴσου ταῖς ἐφʼ ἑαυτῆς εὐθείαις κεῖται. Ἐπίπεδος γωνία ἐστὶν ἡ ἐν ἐπιπέδῳ δύο γραμμῶν ἁπτομένων ἀλλήλων καὶ μὴ ἐπʼ εὐθείας κειμένων πρὸς ἀλλήλας τῶν γραμμῶν κλίσις. ὅταν δὲ αἱ περιέχουσαι τὴν γωνίαν γραμμαὶ εὐθεῖαι ὦσιν, εὐθύγραμμος καλεῖται ἡ γωνία. ὅταν δὲ εὐθεῖα ἐπʼ εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ, ὀρθή ἐστιν ἑκατέρα τῶν ἴσων γωνιῶν, καὶ ἡ ἐφεστηκυῖα εὐθεῖα κάθετος καλεῖται, ἐφʼ ἣν ἐφέστηκεν. Ἀμβλεῖα γωνία ἐστὶν ἡ μείζων ὀρθῆς, ὀξεῖα δὲ ἡ ἐλάσσων ὀρθῆς. 1 γεωμετρία Α. τοῦ] om. C. 2 τὸν τῶν σχημάτων] ἤγουν μέθοδος διʼ ἧς μετρεῖται ἡ γῆ Α. 3 μοδισμὸν] τόν τε μοδισμὸν Α. 4 πάντα] om. Α. αὐτοῦ] om. Α. deinde…","divisions":[{"label":"Chapter 1","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-1"},{"label":"Chapter 2","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-2"},{"label":"Chapter 3","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-3"},{"label":"Chapter 4","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-4"},{"label":"Chapter 5","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-5"},{"label":"Chapter 6","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-6"},{"label":"Chapter 7","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-7"},{"label":"Chapter 8","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-8"},{"label":"Chapter 9","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-9"},{"label":"Chapter 10","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-10"},{"label":"Chapter 11","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-11"},{"label":"Chapter 12","url":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/#tlg0559-tlg015-local001-12"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg0559.tlg015.local001/","json":"https://thegreeklibrary.org/api/works/tlg0559.tlg015.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg0559/tlg015/local001.json.gz"}}