梅文鼎筹算开带纵平方方法来源研究

Research on the Origin of Mei Wending’s Extraction Method of the Root of Affected Square

摘要: 梅文鼎的《筹算》是清朝初期一部非常重要的算学著作，其对后来的众多历算家都有影响，还一度传入了清朝宫廷，影响到了康熙皇帝。该书中的筹算开带纵平方法一直被认为是梅文鼎发明创造的。然而，经研究发现：1) 梅文鼎的筹算开带纵平方方法是对李之藻《同文算指》中笔算开带纵平方法的继承和改造；2) 梅文鼎的改造方式是在原方法的多个步骤中使用纳皮尔筹，使得中间步骤的运算和书写更加简单；3) 改造后的开带纵平方方法有利有弊。优点是使得试算和大数乘法更加迅捷和方便，无需记录中间数值。缺点是计算步骤增多，需要借助外部工具即纳皮尔筹，整个过程变麻烦了。

Abstract: Mei Wending’s book titled Chou Suan (筹算) was a significant work of mathematics in the early Qing Dynasty in China, which had a profound impact on many later mathematicians. It was even introduced into the Forbidden City of the Qing Dynasty and affected the emperor Kangxi. The ex-traction method of the root of the affected square in this book has always been considered to be invented by Mei Wending. However, after researching, it is found that: 1) Mei Wending’s extraction method of the root of the affected square is the inheritance and transformation of the written cal-culation method of extracting the affected square’s root in mathematician Li Zhizao’s book titled Tong Wen Suan Zhi (同文算指). 2) Mei Wending’s modified method applies Napier’s bones in mul-tiple steps of the calculation process, making the calculation and number record of the intermediate steps easier. 3) The modified extraction method of the root of the affected square has both ad-vantage and disadvantage. The advantage is that it makes trial calculations and multiplication of large numbers faster and convenient, without the need to record intermediate numbers. The dis-advantage is that it has more calculation steps and the whole process becomes more complicated with the help of external tools Napier’s bones.