{"title":"《自然要素》第一卷的注释。哈特霍恩和其他地方","authors":"Piotr Błaszczyk, Anna Petiurenko","doi":"10.24917/20809751.13.7","DOIUrl":null,"url":null,"abstract":"(Hartshorne, 2000) interprets Euclid’s Elements provides an interpretation of Euclid’s Elements in the Hilbert system of axioms, specifically propositions I.1-I.27, covering the so-called absolute geometry. We develop an alternative interpretation that explores Euclid’s practice concerning the relation greater-than. Discussing the Postulate 5, we present a model of nonEuclidean plane in which angles in a triangle sum up to π. It is a subspace of the Cartesian plane over the ordered field of hyperreal numbers R*.","PeriodicalId":33912,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","volume":"36 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Commentary to Book I of the Elements. Hartshorne and beyond\",\"authors\":\"Piotr Błaszczyk, Anna Petiurenko\",\"doi\":\"10.24917/20809751.13.7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"(Hartshorne, 2000) interprets Euclid’s Elements provides an interpretation of Euclid’s Elements in the Hilbert system of axioms, specifically propositions I.1-I.27, covering the so-called absolute geometry. We develop an alternative interpretation that explores Euclid’s practice concerning the relation greater-than. Discussing the Postulate 5, we present a model of nonEuclidean plane in which angles in a triangle sum up to π. It is a subspace of the Cartesian plane over the ordered field of hyperreal numbers R*.\",\"PeriodicalId\":33912,\"journal\":{\"name\":\"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae\",\"volume\":\"36 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24917/20809751.13.7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Universitatis Paedagogicae Cracoviensis Studia Naturae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24917/20809751.13.7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Commentary to Book I of the Elements. Hartshorne and beyond
(Hartshorne, 2000) interprets Euclid’s Elements provides an interpretation of Euclid’s Elements in the Hilbert system of axioms, specifically propositions I.1-I.27, covering the so-called absolute geometry. We develop an alternative interpretation that explores Euclid’s practice concerning the relation greater-than. Discussing the Postulate 5, we present a model of nonEuclidean plane in which angles in a triangle sum up to π. It is a subspace of the Cartesian plane over the ordered field of hyperreal numbers R*.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
