《算法全能集》与元代社会经济初探  

The Collection of Mathematical Methods for Doing Everything and the Social Economy of the Yuan Dynasty

作　　者：隋敬文 吕变庭[1] SUI Jingwen;LV Bianting(Center for Studies of Song History,Hebei University,Baoding 071002,China)

机构地区：[1]河北大学宋史研究中心,保定071002

出　　处：《自然科学史研究》2024年第3期295-306,共12页Studies in The History of Natural Sciences

基　　金：国家社会科学基金重大招标项目“17—20世纪国外学者研究中国宋元数理科学的历史考察和文献整理”(项目编号:20&ZD228)。

摘　　要：《算法全能集》是一部元代数学专著,其记载的内容从侧面反映了元代社会经济问题,蕴藏着极高的史料价值。本文以《算法全能集》所载应用数学问题为基本史料,辅之以其他传统史料,对元代银钞流通、户等征配、物价波动等社会经济现象进行了考证。文章确认《算法全能集》成书于元代后半期,时间上早于《详明算法》和《丁巨算法》;书中官配实物问题体现了元代户等制“均平”的社会价值观念和“按比分配”、“递减分配”等几种现实执行途径;同时,《算法全能集》所载物价信息与现存史料基本吻合,较为真实地反映了当时社会经济的动态过程及江南平民的生活水平。以上分析,对丰富元代史料并深化元代社会经济研究有重要意义。The Collection of Mathematical Methods for Doing Everything(Suanfa quanneng ji算法全能集)is a mathematical monograph dating from the Yuan Dynasty.Its content provides an oblique view of the socioeconomic problems of Yuan Dynasty which is of extremely high historical value.This article takes the applied mathematical problems contained in the work,supplemented by other traditional historical materials,and examines the circulation of silver banknotes,taxation according to household levels,and the fluctuation of prices and other socioeconomic phenomena in the Yuan Dynasty.The paper confirms that the Collection of Mathematical Methods for Doing Everything was written in the second half of the dynasty,earlier than the Detailed and Clear Methods of Mathematics(Xiangming suanfa详明算法)and the Mathematical Methods of Ding Ju(Dingju suanfa丁巨算法),that the problem of official distribution in the book reflects the social values of“equalization”(junping均平)in the period,and that there were several practical ways of tax enforcement,such as“proportional distribution”(按比分配)and“decreasing distribution”(dijian fenpei递减分配).At the same time,the price information contained in it is basically consistent with existing historical materials,and reflect the dynamic processes of the social economy and the living standards of the common people in the South Yangtze River region(Jiangnan江南)at that time.The above analyses are of great significance in enriching extant historical materials on the Yuan Dynasty and deepening relevant socioeconomic research.

关 键 词：元代 《算法全能集》 社会经济 经济数学 贾亨 

分 类 号：N092[自然科学总论—科学技术哲学]