论文部分内容阅读
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。
As for the issue of lever balance, although the Chinese ancient books have already been mentioned very early, the specific mechanical calculation method for such problems was first seen in the mathematical masterpiece Cheng Duzong of Cheng Da-wei at the end of the Ming dynasty. Since then, mathematics books appeared in the Ming and Qing dynasties such as “Interpretation of UContent”, “Algorithm of Ungazu Wide Law”, “Same Textual Compilation of General Terms”, “Mathematical Key”, “Several Degrees” and “Chapter Nine Recorded ”and other books, all discussed the use of mathematical methods to calculate the mechanics of leverage, many problems also have some difficulty, reflecting the mechanics of the Ming and Qing dynasties in the count. To the mid and late Kangxi compiled by Meijia into “Mathematical Jingyun,” a book, the calculation of such problems reached a more mature stage, the book has used algebraic method to solve the mechanics of leverage, close to the modern statics used solution. This article gives a detailed introduction and discussion of the solution to the problem of leverage mechanics in the mathematical works in the Ming and Qing Dynasties.