Study of History of Mathematics, in particular, of Japanese Mathematics in early Edo Period and of Analysis in the Nineteenth Century

数学史研究，特别是江户时代初期的日本数学和19世纪的分析

基本信息

批准号：
16540119
负责人：
KOMATSU Hikosaburo
金额：
$ 2.24万
依托单位：
Tokyo University of Science
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

项目摘要

The first step of the historical study is to read extant documents correctly. When they remain only in manuscripts, one has to collate available texts and reconstruct the original. Its importance is well recognized in the fields of Mathematics in the Edo Period and Science in Manchu in the Qing Dynasty, which are the investigators' main subjects. When the editors of the organ journal Kagakusi Kenkyu of the History of Science Society of Japan rejected the paper [1] by Komatsu et al. in 2002, one of the reasons they gave was that the paper cited "Collected Works of Seki Takakazu" which has no collation notes. Yet we do not think even an article in the "Collected Works" has ever been collated in any publications.The main achievements of Komatsu are : first, to have collated Seki's Trilogy, "Methods of Solving Explicit Problems," "Methods of Solving Implicit Problems" and "Method of Solving Concealed Problems" and thus reconstructed the Text by Yamaji Nusizumi [2],[5] ; secondly, to have collated and interpreted about half of the twenty volumes of "Complete Books of Mathematics" by Seki and Takebe brothers. The collated texts of the eighth, nineth and tenth volumes are printed in the Final Report.Moreover, he has shown that Fourier not only formulated his Expansion Theorem and Integrall Theorem but also proved them in his "Analytic Theory of Heat" [6].Watanabe has studied Manchu manuscripts "suwan fa yuwan ben bithe", which is a part of "Elements," and "ge ti ciowan lu bithe," which is a book of medicine and anatomy, Romanized and translated them into English and Japanese. These may be the first substantial study in the world on these texts [7], [8].

历史研究的第一步是正确阅读现存文献。当它们仅保留在手稿中时，人们必须整理现有文本并重建原始文本。它的重要性在江户时代的数学和清代满文的科学领域中得到了充分的认识，这些领域都是研究者的主要学科。当日本科学史学会的器官杂志Kagakusi Kenkyu的编辑拒绝了小松等人的论文[1]时。 2002年，他们给出的理由之一是该论文引用了没有校勘注释的《关高和文集》。但我们认为连《文集》中的一篇文章都没有在任何刊物上校勘过。小松的主要成就是：第一，校勘了关氏三部曲《显性问题的解决方法》、《隐性问题的解决方法》问题”和“解决隐藏问题的方法”，从而重建了山路努斯住的文本[2]，[5]；其次，对关、武部兄弟所著的二十卷《数学全书》中约一半进行了整理和解释。第八卷、第九卷和第十卷的整理文本印在最终报告中。此外，他还表明，傅里叶不仅阐述了他的展开定理和积分定理，而且还在他的《热的解析理论》中证明了它们[6]。渡边研究了满文手稿《Suwan fa yuwan ben bithe》，这是《Elements》的一部分，还有《ge ti ciowan lu bithe》，这是《Elements》的一部分。医学和解剖学书籍，罗马化并翻译成英语和日语。这可能是世界上第一个关于这些文本的实质性研究 [7], [8]。