王文素《算学宝鉴》筹算开方新法——传统筹算开方到珠算开方的过渡形态

The New Method for Extracting Root in Wang Wensu's Suanxue Baojian:the Transitional Form Between the Traditional Method for Extracting Root with Counting Rods and the Method for Extracting Root with Abacus

王文素《算学宝鉴》载有非常丰富的开方内容,前人关于王氏开方法所用算具有一些不同意见。文中经过仔细考察王文素《算学宝鉴》中的开方用语及图式,认为其运算图式侧重于对求每位商数作解释,与珠算开方的数据不能很好对应,因而不能说明王文素的开方法属于珠算开方;书中关于开方的说明文字则说明王文素采用的是筹算开方法。王氏开方法是有异于传统筹算开方的筹算开方新法,但其中有些复杂的运算,可能借助于算盘、数码和文字共同完成。与现存其他算书中的筹算开方新法相比,王文素的方法最接近珠算商除开方法,属于传统筹算开方通向在一横行内排列各项之珠算开方的最直接的过渡形态。

The content of extraction of root in Wang Wensu＂ s Suanxue Baojian is extraordinarily rich. Scholars have different opinions on what tools Wang used for calculation. Based on careful exami- nations of terms and diagrams that Wang used, this paper concludes that the operation diagrams focus on the explanations of seeking every digit number of the root, and they cannot be accurately in corre- spondence with the data placed on the abacus for extracting root, which fails to demonstrate that Wang＇ method belongs to the method for extracting root with abacus. The descriptive text of extraction of root in this book shows that what Wang used was the method for extracting root with counting rods. Wang＇ s is a new method for extracting root with the counting rods, which is very different from the traditional one. But some difficult operations of the new method might be operated with the aid of abacus, Chinese numerical symbols and Chinese characters. Compared with other new methods for extracting root with counting rods that are different from the traditional one, Wang＇ s method is the closest one to shangchu method for extracting root with abacus, and it is the most direct transitional form from the traditional method for extracting root with counting rods to the method for extracting root with abacus on which all the terms are placed in a horizontal line.