大成算経前集解題 (数学史の研究)

Abstract

The Taisei Sankei(1711) is a huge monograph of about 1800 pages, in which Seki Takakazu (ca.1642-1708), Takebe Kata akira (1661-1716) and Takebe Katahiro (1664-1739) expounded systematically on all the mathematics known to them. On October 23, 2010, the Nagoya seminar on history of mathematics started a project to read through the Taisei Sankei and translate it into modern Japanese, and then hopefully into English (See [36]). The Chinese book Nine Chapters on Arithmetic was translated into French (See [1]) and Takebe Katahiro s Taisei Sankei into English (See [42]); these are some recent examples of the translation of books on traditional mathematics of East Asia into modern European languages. As the Taisei Sankei was written in classical Chinese, for Japanese scholars it is necessary to translate the original text into modern Japanese to understand its mathematics and its philosophy on mathematics. The Taisei Sankei is composed of an Introduction and 20 volumes, which are divided into three Parts: Part A (volumes 1-3), Part B (volumes 4-15), and Part C (volumes 16-20). To grasp the structure of the book we have to fully understand the Introduction (especially, its first section On Mathematics ) and the first volume of each Part. In this paper we give an overview of the Taisei Sankei and then translate the key points of Part A directly into modern Japanese. We translated Volume 4 into modern Japanese in [36] and will publish the translation of Volume 16 in a forthcoming paper.