Three Authors of the Taisei Sankei

  • Received : 2012.09.20
  • Accepted : 2012.10.22
  • Published : 2013.02.28


The Taisei Sankei(大成算経 in Japanese) or the Dacheng Suanjing(in Chinese) is a book of mathematics written by Seki Takakazu 関孝和, Takebe Kataakira 建部賢明 and Takebe Katahiro 建部賢弘. The title can be rendered into English as the Great Accomplishment of Mathematics. This book can be considered as one of the main achievements of the Japanese traditional mathematics, wasan, of the early 18th century. The compilation took 28 years, started in 1683 and completed in 1711. The aim of the book was to expose systematically all the mathematics known to them together with their own mathematics. It is a monumental book of wasan of the Edo Period (1603-1868). The book is of 20 volumes with front matter called Introduction and altogether has about 900 sheets. It was written in classical Chinese, which was a formal and academic language in feudal Japan. In this lecture we would like to introduce the wasan as expressed in the Taisei Sankei and three authors of the book. The plan of the paper is as follows: first, the Japanese mathematics in the Edo Period was stemmed from Chinese mathematics, e.g., the Introduction to Mathematics (1299); second, three eminent mathematicians were named as the authors of the Taisei Sankei according to the Biography of the Takebe Family; third, contents of the book showed the variety of mathematics which they considered important; fourth, the book was not printed but several manuscripts have been made and conserved in Japanese libraries; and finally, we show a tentative translation of parts of the text into English to show the organization of the encyclopedic book.



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  2. Komatsu Hikosaburo, "Report of the present status of a revision of the Taisei Sankei"(in Japanese), RIMS Kokyuroku 1546(2007), pp. 140-156.
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  5. Morimoto Mitsuo and Ogawa Tsukane, "Mathematics Treatise on the Technique of Linkage: An Annotated English Translation of Takebe Katahiro's Tetsujutsu Sankei preserved in the National Archives of Japan," SCIAMVS, Volume 13(2012), pp. 157-286.
  6. Morimoto Mitsuo, The Suanxue Qimeng and its Influence on Japanese Mathematics, To appear in the Proceedings of the International Conference on History of Mathematics in Memory of Seki Takakazu (1642?-1708), 2008.
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