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

历史研究的第一步是正确阅读现存文献。当它们只留在手稿中时，人们必须整理现有的文本并重建原文。它的重要性在江户时期的数学和清代满语的科学领域是公认的，这两个领域是研究者的主要课题。当日本科学史学会的风琴杂志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，该报引用了没有校勘说明的《高津世纪文集》。小松的主要成就是：第一，整理了关城的三部曲《解决显性问题的方法》、《解决隐含问题的方法》和《解决隐藏问题的方法》，从而重建了山次努西津[2]、[5]的文本；第二，整理和解释了关城和武部兄弟的20卷《数学全书》中的大约一半。第八卷、第九卷和第十卷的校勘正文刊载在《最后报告》中。此外，他还证明了傅立叶不仅阐述了他的展开定理和积分定理，而且在他的《热的分析理论》[6]中对它们进行了证明。渡边捷昭研究了满文手稿《元素》和医学解剖学书籍《格外乔万卢比》，并将其罗马化并翻译成英语和日语。这可能是世界上第一次对这些文本[7]、[8]进行实质性研究。

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].