大成算経の諸写本について (数学史の研究)

Abstract

The Taisei Sankei (1710) is an encyclopedic work of mathematics written by Seki Takakazu (?-1708), Takebe Katahiro (1663-1739) and Takebe Kata'akira (1661 - 1716). The authors tried to expound all the mathematics in the Chinese and Japanese tradition and their own discoveries in a systematic way. This work was conceived in 1683 by Takebe Katahiro and, around 1695, reached an interim work (12 volumes) called Sanpō Taisei. The final version (20 volumes) was completed after 10 years editorial endeavor by Takebe Kata'akira. The Taisei Sankei was not published but there have been more than twenty manuscripts of the monograph. Hikosaburo Komatsu listed all the manuscripts known to him (see [2]) and he himselfedited a collated version of the Taisei Sankei [4], [5], [6] and [7]. In [2] the manuscripts enumerated by the numbers which we propose to call the Komatsu numbers. The first aim of this article is to overview the present state and availability of the manuscripts according to the Komatsu numbers. Second, in 2018 we investigated a manuscript of the Taisei Sankei preserved at Tsu City Library, Mie Prefecture. We show pictures of its pages and are happy to say the manuscript are in a good condition. Third we sketch our speculation on the interim edition, the Sanpō Taisei, which left no trace at all but the title. We propose here what 12 volumes out of the 20 volumes of the Taisei Sankei consisted the Sanpō Taisei. Lastly, the proceedings [8] of the Takebe Conference 2014 was published on December 25, 2018. Ogawa's survey article in English [9] will provide the background information on Takebe Katahiro, the initiative author ofthe Taisei Sankei. Volumes 12, 17 and 19 ofthe Taisei Sankei were translated in English in [10], [11] and [12], respectively.