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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Pasch's theorem ： ウィキペディア英語版 Pasch's theorem In geometry, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch,〔''Vorlesungen über neuere Geometrie'' (Leipzig, 1882)〕 is a result of Euclidean geometry which cannot be derived from Euclid's postulates. The statement is as follows. Given points ''a'', ''b'', ''c'', and ''d '' on a line, if it is known that the points are ordered as (''a'', ''b'', ''c'') and (''b'', ''c'', ''d''), then it is also true that (''a'', ''b'', ''d'').〔 states the result in 12.274 but does not refer to it specifically as Pasch's theorem.〕 (for example, (''a'', ''b'', ''c'') means that point ''b'' lies between points ''a'' and ''c''. ) ==See also== * Ordered geometry * Pasch's axiom 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pasch's theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.