{"schemaVersion":2,"id":"tlg5022.tlg007.local001","url":"https://thegreeklibrary.org/works/tlg5022.tlg007.local001/","urn":"urn:cts:greekLit:tlg5022.tlg007.local001","title":"Scholia in Euclidis data et catoptrica (scholia vetera)","titleGreek":null,"alternateTitles":[],"author":"Scholia in Euclidem","authorityName":"SCHOLIA IN EUCLIDEM","authorUrl":"https://thegreeklibrary.org/authors/tlg5022-scholia-in-euclidem/","authorityUrl":"https://thegreeklibrary.org/authors/tlg5022-scholia-in-euclidem/","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/190/mode/2up","sourceLinkType":null,"sourceRights":null,"citation":"Scholia In Euclidem. Scholia in Euclidis data et catoptrica (scholia vetera). ed. Heinrich Menge. Euclidis Opera Omnia, Teubner, Leipzig, 1916. urn:cts:greekLit:tlg5022.tlg007.local001","excerpt":"Scholia codicis Vat. Gr. 1038 fol. 129 sub fine Datorum in mg. inferiore. α α α α α α α α α α α β γ δ ε Ϛ ζ η θ ι δυαδικαὶ συζυγίαι α γ ϛ ι ιε κα κη λϚ με τριαδικαὶ συζυγίαι α δ ι1) κ λε νς πδ ρκ α ε ιε λε ο ρκς σι α Ϛ κα νϚ ρκϚ σνβ α ζ κη πδ σι α η λϚ ρκ α θ με αι α Ὅρων δοθέντων ὁποσαοῦν εὑρεῖν δυαδικὰς συζυγίας. εὑρίσκομεν δὲ αὐτὰς οὕτως· λαμβάνομεν τῶν δοθέντων ὅρων ῑ ἀριθμὸν μονάδι ἐλάττονα καὶ πολυπλασιάζομεν αὐτὸν εἰς τὸν ἐγγὺς αὐτοῦ μονάδι μείζονα καὶ ἐκ τοῦ γενομένου ποσοῦ λαμβάνομεν τὸ ἥμισυ· καὶ ἔχομεν αὐτὴν εὕρεσιν τῶν δοθέντων ὅρων δυαδικὰς συζυγίας. τὰς δὲ τριαδικὰς οὕτως· λαμβάνομεν τὸν δυάδι ἐλάσσονα ἀριθμὸν τοῦ ποσοῦ τῶν ἐξ ἀρχῆς δοθέντων ὅρων καὶ πολλαπλασιάζομεν ἐπὶ τὸ ποσὸν τὸ γεγονὸς ἐκ τῶν δυαδικῶν συζυγιῶν ἐκ τοῦ ποσοῦ τῶν δοθέντων ἐξ ἀρχῆς ὄρων καὶ τοῦ γεγονότος πολλαπλασιασμοῦ λαμβάνομεν τὸ τρίτον μέρος· καὶ ἔχομεν τριαδικὰς συζυγίας. καὶ ἑξῆς ὁμοίως. Μέθοδος…","divisions":[{"label":"Work 1","url":"https://thegreeklibrary.org/works/tlg5022.tlg007.local001/#tlg5022-tlg007-local001-1"}],"formats":{"html":"https://thegreeklibrary.org/works/tlg5022.tlg007.local001/","json":"https://thegreeklibrary.org/api/works/tlg5022.tlg007.local001.json","compressedReadingDocument":"https://thegreeklibrary.org/works/tlg5022/tlg007/local001.json.gz"}}