Research of the History of Mathematics

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We investigated the important works of gigantic mathematician Seki Takakazu and Takebe Katahiro of Edo period, namely about Hatsubi-Sampo (Mathematical Methods for Exploring Subtle Points) of Seki, and Kenki-Sampo (Mathematical Methods for Clarifying Slight Signs) of Takebe. These works may be regarded as the opening of the real study of mathematics in this period.Hatsubi-Sampo (1673) was written to give answers to the 15 problems proposed by Sawaguchi Kazuyuki in his Kokon-Sampoki. For the aim to give answers to these problems, he exploited a new method called Tengenjutsu-Boshoho, though it was explicitly given only ten years later. The same problems were also treated by Tanaka Yoshizane in his Sampo-meikai (1678).Kenki-Sampo was the first work of Takebe. It was written to give the solutions of 49 problems given by Ikeda-Masaoki in his Sugaku-Jojo-Orai (1674). Here again, main tools to give solutions were the Tengenjutsu-Boshoho.Both in Hatsubi-Sampo and in Kenki-Sampo, the descriptio … More ns were too short, and perhaps no one could arrive at the understanding of what was given in these books. So, later in 1687, Takebe wrote Hatsubi-Sampo Endan-Genkai (The Colloquial Commentary on the Series of Operations in Hatsubi-Sampo) to give precise procedures to get the final answers. While Takebe gave this Colloquial Commentary for the Hatsubi-Sampo, for the Kenki-Sampo, there still were left the difficulties to know how to do. For this, again the Colloquial Commentary exists, but by whom and when was this done is not known yet.In our present research, we investigate these two books and their Colloquial Commentaries deeply. As the manuals explaining the contents of the books do not exist yet, we publish books to give concrete interpretations of these books.We also consider that it is our important task to present the mathematics studied in the Edo period while the Japan was shut to other world. And we have published "Selected Mathematical Works of Takebe Katahiro" to let know the works of Takebe. worldwide. Less