{"schemaVersion":2,"id":"tlg1799.tlg015.local001","url":"https://thegreeklibrary.org/works/tlg1799.tlg015.local001/","urn":"urn:cts:greekLit:tlg1799.tlg015.local001","title":"Sectio canonis [Sp.]","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/158/mode/2up","sourceLinkType":null,"sourceRights":null,"citation":"Euclid. Sectio canonis [Sp.]. ed. Heinrich Menge. Euclidis Opera Omnia, Teubner, Leipzig, 1916. urn:cts:greekLit:tlg1799.tlg015.local001","excerpt":"Εὐ ἡσυχία εἴη καὶ ἀκινησία, σιωπὴ ἂν εἴη· σιωπῆς δὲ οὔσης καὶ μηδενὸς κινουμένου οὐδὲν ἂν ἀκούοιτο εἰ ἄρα μέλλει τι ἀκουσθήσεσθαι, πληγὴν καὶ κίνησιν πρότερον δεῖ γενέσθαι. ὥστε, ἐπειδὴ πάντες οἱ φθόγγοι γίνονται πληγῆς τινος γινομένης, πληγὴν δὲ ἀμήχανον γενέσθαι μὴ οὐχὶ κινήσεως πρότερον γενομένης, — τῶν δὲ κινήσεων αἱ μὲν πυκνότεραί εἴσιν, αἱ δὲ ἀραιότεραι, καὶ αἱ μὲν πυκνότεραι ὀξυτέρους ποιοῦσι τοὺς φθόγγους, αἱ δὲ ἀραιότεραι βαρυτέρους, — ἀναγκαῖον τοὺς μὲν ὀξυτέρους εἶναι, ἐπείπερ ἐκ πυκνοτέρων καὶ πλειόνων σύγκεινται κινήσεων, τοὺς δὲ βαρυτέρους, ἐπείπερ ἐξ ἀραιοτέρων καὶ ἐλασσόνων σύγκεινταικινήσεων. ὥστε τοὺς μὲν ὀξυτέρους τοῦ δέοντος ἀνιεμένους ἀφαιρέσει κινήσεως τυγχάνειν τοῦ δέοντος, τοὺς δὲ βαρυτέρους ἐπιτεινομένους προσθέσει κινήσεως τυγχάνειν τοῦ δέοντος. διόπερ ἐκ μορίων τοὺς φθόγγους συγκεῖσθαι φατέον, ἐπειδὴ προσθέσει καὶ ἀφαιρέσει τυγχάνουσι τοῦ δέοντος. πάντα δὲ τὰ…","divisions":[{"label":"Chapter pr","url":"https://thegreeklibrary.org/works/tlg1799.tlg015.local001/#tlg1799-tlg015-local001-pr"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg1799.tlg015.local001/","json":"https://thegreeklibrary.org/api/works/tlg1799.tlg015.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg1799/tlg015/local001.json.gz"}}