“益积”和“翻法”研究

The Study of Life of Fanji and Yiji Methods in Process of Extraction

最早见于《九章算术》“少广”章的开方术,后经宋元发展为一种解决一元高次方程的一个正实根的有效方法,即“立成释锁”和“增乘开方”算法。开方算法在中算中内容丰富、地位重要,在开方算法中也有与计算细节相关的各种称谓,“翻法”和“益积”就是这样的例子。从刘益开始,经秦九韶研究易名、李冶推广、朱世杰的心不在焉、周述学的复兴,到焦循完备化和李锐的放弃,“翻法”和“益积”经历了出生、成长、繁荣和终结的过程。这些名称强烈地依赖于开方算法的过程,他们因算法中细节的改变而生,之后历经成长、繁荣和成熟,最后随着算法的完备而消亡。

Extraction method is one of the most advanced and mature content in Chinese traditional mathematical algorithm,first seen in"Nine Chapters".And it was developed into two methods of“Zengchengkaifang”and“Lichengshisuo”,an effectivemethod to solve the equations with one unknown only for one positive solution,sometimes approximate root,after the Song and Yuan dynasties.The square algorithm plays an important role in the Chinese traditional calculation,and there are also various terms related to calculation details,such as"Fanfa"and"Yiji".Starting from Liu Yi,through the deeply study of Qin Jiushao and the promotion of Li Ye,Zhu Shijie′s absent mindedness,Zhou Shuxue′s revival,JIAO Xun′s perfection and Li Rui′s abandonment.These names strongly depend on the process of the algorithm.They are born with the change of the details in the algorithm.After that,they grow prosperous and mature,and finally die with the completion of the algorithm.