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「さっけりーの四辺形」について : 非ゆーくりっど幾何学の初等的展開(第二部)   :   On The Quadrilateral of Saccheri : An Elementary Development of Non-Euclidean Geometry(PART II) 

作成者 三浦, 午次郎
作成者 (ヨミ) ミウラ, ウマジロウ
作成者の別表記 Miura, Umajiro
キーワード等 非ユークリッド幾何学, サッケリーの四辺形
日本十進分類法 (NDC) 375, 410
内容 To prove the 5th postulate of Euclid's Elements from the others, G. Saccheri established three hypotheses that the angle of so called Saccheri's quadrilateral is right, acute, and obtuse, and worked hard to draw a contradiction from the hypotheses of the acute angle and the obtuse. From the former, he made many interesting deductions that are contents of Non-Euclidean Geometry of Bolyai and Lobatschewsky. But he concluded that the hypothesis of the acute angle was incompatible with the others as he had believed that the hypothesis of the right angle was true. It is an object of this short treatise to develop the Non-Euclidean Geometry through his elementary and historically interesting methode. It is proved that the Euclidean geometry is derived from the hypothesis of the right angle. From the hypothesis of the acute angle, the theorems of parallels, the sum of three interior angles of a triangle and its area, and the equidistant curves are proved, which are contents of the Non-Euclidean Geometry of Bolyai and Lobatschewsky. From the last hypothesis, it is discussed that the 1st and 2nd postulates of Elements must be altered so that the Non-Euclidean Geometry of Riemann and Klein is constructed. Finally the notion of regular region is introduced, in which the theorems of the sum of three interior angles of a triangle and its area, etc, are able to be proved as under the other hypotheses.
公開者 千葉大学教育学部
コンテンツの種類 紀要論文 Departmental Bulletin Paper
DCMI資源タイプ text
ファイル形式 application/pdf
ハンドルURL http://mitizane.ll.chiba-u.jp/meta-bin/mt-pdetail.cgi?cd=00025605
ISSN 0577-6856
NCID AN00142727
掲載誌情報 千葉大学教育学部研究紀要 Vol.10 page.55-73 (19611125)
フルテキストへのリンク http://mitizane.ll.chiba-u.jp/metadb/up/AN00142727/KJ00004239625.pdf
情報源 Bulletin of the Faculty of Education, Chiba University
言語 日本語
著者版フラグ publisher


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非ユークリッド幾何学
サッケリーの四辺形