试论清代割圆连比例方法

割圆连比例曾是清代无穷级数中所用的主要方法，但对它的研究上前还不够充分。该文试图它的概念和原理，并经过分析指出：它是以连比例的递加法为基础，具有一定约束条件的递归过程；它的结构特征取决于所设递加法是其诱导方程；它的初创阶段由于未能运用递加法，其结果归结为迭代过程。

A TENTATIVE DISCUSSION ON THE CYCLOTOMIC CONTINUED PROPORTIONAL METHOD OF THE QING DYNASTY

Cyclotomic continued proportion was the principal method for studies on infinite series in the Qing Dynasty,which we still have to go into a step further.To get a clearer understanding of its concept and principle,this paper shows that it is a recursive procedure based upon the successive addition method of continued proportion with a certain constraint condition;its structural characteristic depends on the way of designs for successive addition and its induced equation;in its initial stage,as it failed to apply the successive addition method,it ended in iteration instead.