伟烈亚力的中西代数学比较及其史学渊源

Alexander Wylie's Comparisons of Algebra between China and Europe,and Its Historiographical Origins

19世纪来华的英国新教传教士伟烈亚力,除了与中国算学家李善兰合作翻译德摩根《代数学》,正式引入近代西方符号代数并产生重要影响外,还撰写了《中国科学略记·算术及代数学》等著作,对西方和宋元时期的代数学做出比较。文章对比了《略记》、《代数学》中英文序言和其他西文文献,同时考察了伟烈亚力旧藏的中算书籍。受英国实用知识传播学会和学会出版物影响,伟烈亚力从棣么甘(今译德摩根)为《便士百科全书》所撰写的数学词条等中获得了西方代数学和代数学史的知识视角。在宋元代数学方面,清代学者易之瀚、罗士琳的《四元释例》应该是伟烈亚力的重要参考书。《四元释例》对增乘开方法、天元术和四元术等基本规则总结和阐释,在伟烈亚力的著作中有所反映,并成为其中西代数学比较得以深入的关键。伟烈亚力的数学史观也受德摩根等人的影响:其撰写中国数学史的目的着眼于对当下数学知识理解、研究和宗教传播两方面的实用意义,并体现在《略记》发表后伟烈亚力的数学翻译出版当中。

Alexander Wylie（ 1815 - 1887） was a British protestant missionary who arrived in China in 1847. Through his collaboration with Chinese mathematician Li Shanlan（ 1810 - 1882） and their translation of Augustus De Morgan＇s（ 1806 - 1871） Elements of Algebra, Wylie first introduced modern Western symbolic algebra into China. Apart from this important work, he wrote Jottings on the Science of the Chinese and some other works, in which he drew comparisons between the history of algebra in the West and Chinese mathematics of the Song and Yuan dynasties（ 960 - 1368）. This article compares Jottings, the English and Chinese prefaces to the translation of the Elements of Algebra, and other documents in English, and also examines Chinese mathematical books collected by Wylie. Influenced by the Society for the Diffusion of Useful Knowledge and its publications, Wylie gained his perspective on Western algebra and its history from the articles written by De Morgan in Penny Cyclopaedia. As for the mathematics in the Song and the Yuan dynasties, Yi Zhihan and Luo Shilin＇s Interpretations on the Rule of Four Sources ought to be an important reference for him. The explanations for the ＂ method for extracting roots using addition and multiplication＂, ＂ the Heavenly Source procedure ＂ and ＂ the Four Sources procedure ＂ in the Interpretations on the Rule of Four Sources were also reflected in Wylie＇s works, which was the key leading to deeper comparison.Wylie＇s view on the history of mathematics in general was also influenced by De Morgan and other British historians. His historiographical goal was to focus on the practical use of the understanding and study of mathematic knowledge for the transmission of Christianity at that time, which also was embodied in some of Wylie＇s mathematical translations after Jottings.