摘要
“通儒”焦循的《加减乘除释》是一部重要的算学著作,前人多提及其算理而未展开讨论。文章利用丰富的文献,较全面地梳理了《加减乘除释》的编纂过程,指出焦循编纂思想有一种从“难奥”向“浅近”的颇具重要意义的转变;围绕“加减乘除错综变化”探究了焦循的算理内涵,认为“加减乘除”的重点在辨别盈朒,“错综变化”针对的是运算程序;整理了《九章算术》与“加减乘除”的关系表,并对焦循构建算理的逻辑思路进行了阐释;从乾嘉时期重视算理的学术风气、乘除在算学知识中的核心地位、象数学与算学的关系等方面入手,揭示了焦循算理思想的深厚历史渊源;指出了《加减乘除释》体现在研究方法和研究对象上的积极价值,以及它对易学发展的深刻影响。
Jiao Xun(焦循,1763-1820)was an erudite Confucian scholar,who wrote the important work on mathematics Explanation of Addition,Subtraction,Multiplication and Division(Jiajian Chengchu Shi,加减乘除释)in 1794.Its mathematical principles are often mentioned by scholars but without any discussion.This paper makes use of the abundant literature available to describe the compilation process of the book,and points out that Jiao Xun s thought during compilation goes through a significant change from“difficult”to“simple”.The article explores the connotations of Jiao Xun s mathematical principles around the“complex change of addition,subtraction,multiplication and division”,and believes that the focus of the book is to identify the surpluses and the shortages,and“complex change”is aimed at the operation program.This paper sorts out the relationship table between Jiao s book and Nine Chapters on the Art of Mathematics,and explains the construction of his theory of mathematical principles.It reveals the deep historical origins of his mathematical principles from the aspects of the academic atmosphere of attaching importance to mathematical principles,the core position of multiplication and division in mathematics,and the relationship between image-numerology and mathematics.Finally,the article points out the positive value of Explanation of Addition,Subtraction,Multiplication and Division in terms of research methods and research objects,and its profound influence on the development of I-Ching learning.
作者
魏雪刚
WEI Xuegang(Institute for the History of Science and Technology,Inner Mongolia Normal University,Hohhot 010022,China)
出处
《自然科学史研究》
CSSCI
CSCD
北大核心
2022年第4期415-428,共14页
Studies in The History of Natural Sciences
基金
内蒙古师范大学引进高层次人才科研启动项目(项目编号:2019YJRC040)。
关键词
乾嘉学术
焦循
《加减乘除释》
算理
Qian-Jia(乾嘉)learning
Jiao Xun(焦循)
Explanation of Addition,Subtraction,Multiplication and Division(Jiajian Chengchu Shi,加减乘除释)
mathematical principles
