The Kujang sulhae 九章術解: Nam Pyoˇng-Gil’s reinterpretation of the mathematical methods of the Jiuzhang suanshu

摘要本文討論並分析十九世紀韓國數學家南秉吉 (1820–1869) 的著作 《九章術解》。此文本為他對中國古算經 《九章算術》 的注解書。南秉吉在本書中摘錄全本 《九章算術》 的問題與術文，但不包含劉徽與李淳風的注解，而僅將他自己的注解置於術文之後。在他的跋文中，南秉吉清楚地表示他不滿先前的注解，理由是劉李注的進路與他當代讀者所使用的進路不吻合。這件事可由南氏注解的特點看出：(1) 他主要使用中西融合的數學知識來解釋 《九章算術》；(2) 他的注解風格為給出簡單明瞭的註解，大量訴諸直覺，這種風格是間接受到巴蒂版 《幾何原本》 的影響；(3) 他迴避了劉、李注中的無窮小與極限方法。基於以上的特點，以及南秉吉的跋文，筆者認為南秉吉將中國古代數學正典 《九章算術》 視為一個重要且無法忽視的歷史文件，而他必須用十九世紀中國與韓國共同認定的數學正典 – 《數理精蘊》 – 來註解之。《九章術解》 可做為一個例證，讓我們看到十九世紀韓國數學家用他們當代的知識重新解讀中國古代數學文本所做的努力。

In this article, a discussion and analysis is presented of the Kujang sulhae by Nam Pyoˇng-Gil (1820–1869), a 19th-century Korean commentary on the Jiuzhang suanshu. Nam copied the problems and procedures from the ancient Chinese classic, but replaced Liu Hui’s and Li Chunfeng’s commentaries with his own. In his postface Nam expressed his dissatisfaction with the earlier commentaries, because the approaches of Liu and Li did not match those of his contemporary readers well. This can be seen from the most important features of Nam’s commentary: the use of a synthesis of European and Chinese mathematical methods, easy explanations appealing to intuition, and disuse of the methods of infinitesimals and limits in Liu’s and Li’s commentaries. Based on his own postface and these features of his commentary, I believe that Nam Pyoˇng-Gil treated the Jiuzhang suanshu as a very important historical document, which he intended to explain according to the new mathematical canon in both Qing China and Chosoˇn Korea, the Shuli jingyun. Thus the Kujang sulhae is an example of the endeavor of 19th-century Korean mathematicians to reinterpret ancient Chinese mathematical texts with their contemporary knowledge.