《無異解》中的三案初探：一個HPM的觀點

Nam Byung Gil's Comments on the "Tian Yuan Shu" Versus "Jie Gen Fang": An HPM Perspective

洪萬生(Wann-Sheng Horng)

《科學教育學刊》 8卷3期 (2000/09) Pp. 215-224

https://doi.org/10.6173/CJSE.2000.0803.01

摘要

本文採取HPM觀點，針對十九世紀韓國數學著作《無異解》進行初步的探討。在此一數學文本中，作者南秉吉從清代中國出版的《測圓海鏡》與《益古演段》中，摘錄了七題與其解法，並且附上了《四庫全書》的編者之「（館）案』以及李銳的「銳案』，然後，再添加他自己的「愚案」。由於這三案的對比，反映了十九世紀中、韓兩國數學家，面對西方代數「借根方』的所表現的不同調適與認知，儘管他們都「活』在中國傳統代數「天元術」的脈絡之中。因此，本文之作，意在為教、學初等代數的師生，提供一點歷史的參考與借鑑。

關鍵字

數學史 ； HPM ； 天元術 ； 借根方

並列摘要

In this article, I am going to give a preliminary observation on Korean mathematical texts in the second half of the 19th century. I will focus on Nam Byung Gil's (1820-1869) Vu Yi He (A Study of commentaries on ”Tian Yuan Shu”, 1855). It is a text basically devoted to a critical evaluation of Chinese mathematician Li Rui's (1768-1817) restoration of the tradition ”Tian Yuan Shu” in terms of the Western ”Jie Gen Fang”. Apparently based on the adaptation that Li Rui, among others, made of the Cardano's version of Western algebra, Nam Byung Gil, who knew Chinese mathematics well, was able to react in a ”meta-cognitive” manner. Specifically, he commented on commentaries. His experience of studying the discipline is very interesting and illuminating, especially for teaching learners of introductory algebra.

並列關鍵字

History of Mathematics ； HPM ； Tian Yuan Shu ； Jie Geng Fang