大衍求一术在西方的历程  

A HISTORY OF DA-YAN QIU-YI SHU IN THE WEST

作　　者：汪晓勤[1] 

机构地区：[1]中国科学院自然科学史研究所,北京100010

出　　处：《自然科学史研究》1999年第3期222-233,共12页Studies in The History of Natural Sciences

摘　　要：秦九韶解一次同余组的大衍求一术被西方学者所理解，并不是一件顺利的事。1852年英国汉学家伟烈亚力在《北华捷报》上撰文，介绍别、子“物不知数”题的解法，但未能具体介绍求乘率的求一术；德国学者毕尔那茨基在译伟烈亚力的论文以及法国数学家特凯在转译毕氏的德译文时都误解了该解法。德国数学家马蒂生在只有毕氏译文的情况下，敏锐地发现毕氏的错误，并证明了中国解法与高斯解法的一致性，还对模不两两互素的情形作了解释，从而为“中国剩余定理”这一数论术语在西方的确立奠定了基础。然而，马蒂生仍不知中国解法中关键性的求一术。It is not smooth for Qin Jiushao's Da-Yan Qiu-Yi Shu to be understood in theWest. In 1852, A. Wylie, a British missionary who came to China in 1847, published in North-China Herald the famous Jottings on the Science of the Chinese: Arithmetic, in which he ex-plained the solution of Sun Zi's famous remainder problem and the first problem of Shu-ShuJiu-Zhang by means of Da-Yan Shu, without showing explicitly how to find the multiplicator,i. e., the solution of the congruence of ax=1 (mod b). In translating this paper, the GermanScholar K. L. Biernatzki misunder stood the Da-yan Shu, confusing the multiplicator with theJi, which is the least positive residue of a (mod b). So did the French Mathematician O.Terquem in translating Biernatzki'. L. Matthiessen, a German mathematician, judiciously cor-rected Biernatzki's mistake and pointed out the identity of Da-Yan Shu with C. F. Gauss' rulein Disquisitiones Arithemeticae. L. Matthiessen also offered and explanation of the case inwhich the moduli are not relatively prime in pairs. However, he did not know the Qiu-Yi Shu,which Y. Mikami first explained in modern notations in his Development of Mathematics inChina and Japan. Over a century passed before the Belgian scholar U. Libbrecht exhaustivelystudied the Da-Yan Qiu-Yi Shu in his Chinese Mathematics in the Thirteenth Century.

关 键 词：伟烈亚力 大衍术 乘率 毕尔那茨基 中国剩余定理 

分 类 号：O11[理学—数学]