和与较:梅文鼎方程算法的理论基础  

Sum and Difference:Theoretical Foundation of Mei Wending's Fangcheng Algorithm

作　　者：陈思宇 CHEN Siyu(Department of Philosophy,Sun Yat-sen University,Guangzhou 510275,China)

机构地区：[1]中山大学哲学系,广东广州510275

出　　处：《广西民族大学学报(自然科学版)》2024年第4期16-22,共7页Journal of Guangxi Minzu University :Natural Science Edition

摘　　要：在中国传统算学中,和、较这对概念通常是在勾股算术中使用的。李之藻和利玛窦在编译《同文算指》时将它们引入方程算法之中。梅文鼎继承了这种以和、较释方程的做法。在《方程论》中,梅文鼎用和、较准确地区分了方程数量关系,自然地回答了方程正负的起源问题,并在此基础上构建出和较方程体系。基于对和较方程体系逻辑关系的理解,梅文鼎构建了一套连贯的方程算法,其根本目的在于发明传统方程的正负术。可惜囿于古算典籍的失传,这一目标无法彻底达成。但梅文鼎的方程算法在清代广为流传,影响深远。In traditional Chinese mathematics,the concepts of sum(he)and difference(jiao)were commonly used in the Gougu(two sides of a right-angled triangle)procedure.Li Zhizao and Matteo Ricci introduced them into the Fangcheng(measures in square)algorithm when compiling the Instructions for Calculation in Common Script(Tongwen suanzhi).Mei Wending inherited this approach of interpreting the Fangcheng algorithm using sum and difference.In his Discussions on Fangcheng(Fangcheng lun),Mei Wending accurately distinguished the quantitative relationships in Fangcheng using sum and difference,naturally elucidated the origin of positive and negative in Fangcheng,and on this basis,constructed a sum-difference Fangcheng system.Based on his understanding of the logical relationships within the sum-difference Fangcheng system,Mei Wending developed a coherent set of Fangcheng algorithms.The fundamental aim of Mei Wending's Fangcheng algorithms was to innovate on the procedures of positive and negative in the traditional Fangcheng algorithm.Unfortunately,due to the loss of ancient mathematical texts,this goal could not be fully achieved.However,Mei Wending's Fangcheng algorithms were widely circulated during the Qing Dynasty and had a profound impact.

关 键 词：和较 方程算法 正负术 算学统一性 

分 类 号：N09[自然科学总论—科学技术哲学]