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篇名 鄭玄的數學世界——鄭氏以數學注經的方式、背景與歷史貢獻
卷期 48:11=570
並列篇名 Zheng Xuan’s Mathematical World —The Method, Historical Background and Influence of Zheng’s Using Mathematics
作者 朱一文
頁次 145-161
關鍵字 鄭玄《九章算術》經學經算劉歆三禮Zheng XuanThe Nine Chapters on Mathematical ProceduresConfucianismLiu XinThree Ritual BooksA&HCI
出刊日期 202111

中文摘要

作為兩漢經學的集大成者,鄭玄遍注群經、統一融合古今文說,又精通曆算,善《九章算術》。然而,以往學術界對其數學未有專門之研究。從鄭玄三禮注看,他引鄭眾說注「九數」,暗示《九章算術》來源於《周禮》,並多次提到「粟米法」、使用「勾股術」。他又往往給出算法的大概或者其結果、而不給出計算細節,並以之來消除各經典或版本之間的差異,其注緯書也用到數學,從而為後世學者創造了發展數學的文本語境。王莽之際,劉歆提出數學是音律、度量衡、曆法基礎的思想;光和二年,大司農斛、權銘文確立了這一思想與《九章算術》的權威地位。東漢末年經學章句繁多,與鄭眾、許慎、馬融等人相比,鄭玄更擅長使用數學、曆算,因此鄭氏引《九章算術》注經具有了政治與學術的雙重合法性。然而,在其經學研究的基礎上,後世儒家發展出與以《九章算術》為代表的傳統算學相對獨立的經算傳統,卻偏離了鄭玄以數學注經之初衷。

英文摘要

As a great master of Confucianism in the Han dynasty, Zheng Xuan commented on almost all Confucian classics, and unified and mixed different meanings in different classics. He was also good at calendrical computations, and The Nine Chapters on Mathematical Procedures (Jiuzhang suanshu). However, previous studies paid less attention to his mathematics. Based on the analysis of his commentaries on three ritual books, he quoted Zheng Zhong’s commentary to comment on The Nine Numbers (jiu shu), quoted the method of husked and unhusked grains (su mi fa) and the method of the short side and the long side in a right-angle triangle (gou gu shu), so as to imply that The Nine Chapters on Mathematical Procedures was derived from the Rites of Zhou (Zhouli). Zheng Xuan usually mentioned an outline of a procedure or the result of a procedure, but without giving any computational detail of the procedure. He usually used a procedure to eliminate the difference in Confucian classics. He also carried out mathematical procedures in his commentary on the divination books. As a result, his commentary created a textual context to develop mathematics. In the reign of Wang Mang, Liu Xin put forward his idea that mathematics is the foundation of harmonics, metrology and calendars. In the second year of Guanghe (179 CE), the inscriptions of the copper vessel and the copper weight published by the chamberlain for the national treasury (da si nong) established the official authority of Liu Xin’s idea and The Nine Chapters on Mathematical Procedures. In the late years of the eastern Han dynasty, there were numerous commentaries on Confucian classics. Rather than Zheng Zhong, Xu Shen and Ma Rong, Zheng Xuan was better at using mathematics and calendrical computations. Therefore, Zheng Xuan had the political and scholarly legitimacies to use The Nine Chapters on Mathematical Procedures in his commentarial works. On the basis of Zheng Xuan’s Confucian study, later generation developed the Confucian mathematical methods, which was independent to The Nine Chapters on Mathematical Procedures. However, this development deviated from Zheng Xuan’s intention.

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