再析建部贤弘“缀术”之本质——兼论《缀术算经》的数学体系

Another Analysis on the Essence of Takebe Katahiro's Tetsujutsu——And on the Mathematical System of Tetsujutsu Sankei

《缀术算经》(1722)是江户时代的一本重要的和算书,中日学者从不同角度分析了其中的内容,然而对于该书十二道算题中的"解题本术"所蕴涵的数学思想只有一些零星讨论,并没有展开系统研究,至于其"缀术"的本质,一般均认为是今日所谓的归纳法。事实上,其"缀术"的思想集中反映在其十二道算题的"解题本术"之中。本文通过对"解题本术"进行系统分析,认为其"缀术"的本质乃将"算法单元"连缀起来的方法。其中的"法则、术理、员数"是对数学内容的分类,"理"、"术"、"数"是解法系统的组成部分,而"据理探"和"据数探"则是缀术的基本方法,数学内容、解法系统、探索方法共同构成了《缀术算经》的数学体系。

Tetsujutsu Sankei is an important math book written by Takebe Katahiro in the Edo era. Chinese and Japanese scholars analyzed its content from different perspectives, but there is seldom systematically research into the mathematical thoughts in Kaidai Honjutsu （解题本术）. Former scholars considered induction as the essence of Tetsujutsu（缀数）. In fact, the thoughts of Tetsujutsu were concentrated on KaitaiHonjutsu. By interpreting the text of KaitaiHonjutsu, thispaper comes up with the opinion that the essence of Tetsujutsu is the method to connect computing units. In this book, math problems are divided into formulation, solution and the quantitative value of circle. The solution to each problem is made up of theory, method and numerical value. Two exploring methods, exploring by number and exploring by principle, form the basic method of Tetsujutsu. The mathematical system of Tetsujutsu Sankei consists of math content, solution system and exploring method.