关于明清之际中国杠杆力学问题的算法

THE SOLUTION FOR PROBLEMS OF LEVEL MECHANICS IN CHINA BETWEEN THE LATE MING DYNASTY AND THE EARLY QING DYNASTY

关于杠杆平衡问题,中国古籍中虽然很早即已论及,但有关此类问题的具体力学计算方法最早见于明末程大位的数学著作《算法统宗》。此后,在明清之际出现的数学著作,如《算法统宗释义》、《算法统宗广法》、《同文算指通编》、《数学钥》、《数度衍》和《九章录要》等书中,都讨论了用算术方法计算杠杆力学问题,不少问题还具有一定的难度,反映了明清之际中算家的力学水平。到康熙中后期梅彀成等编纂的《数理精蕴》一书中,有关此类问题的计算达到了比较成熟的阶段,该书已采用代数方法求解杠杆力学问题,接近于近代静力学所用的解法。本文对明清之际数学著作中的杠杆力学问题的解法作了详细的介绍和论述。

The problems of level equilibrium were dealt with very early in Chineseancient books,but the concrete methods of computation of their mechanicsfirt appeared in Suan Fa Tong Zong(Systematic Treatise on Arithmetic)written by Cheng Dawei in the late Ming Dynasty.Mathematical works oflater times such as Suan Fa Tong Zong Shi Yi(Explanation of Suan FaTong Zong),Suan Fa Tong Zong Guang Fa(Extensive Methods of SuanFa Tong Zong),Tong Wen Suan Zhi Tong Bian,Shu Xue Yao,Shu DuYan and Jiu Zhang Lu Yao solved problems of level mechanics with arith-metic methods,and many of these problems are quite difficult,so this factreflects the level of knowledge of mechanics reached by Chinese mathemati-cians between the late Ming Dynasty and the early Qing Dynasty.In ShuLi Jing Yun,edited by Mei Gucheng and others in the middle and late peri-ods of Kang Xi's reign,problems of level mechanics were already solvedwith algebraic methods that approach the methods of modern statics.Thispaper introduces and discusses the solution of such problems in the mathe-matical works of late Ming and early Qing.