Published online by Cambridge University Press: 28 July 2014
Recent studies in Sinology have shown that Qing dynasty editors acted as philologists. This paper argues that the identification of their philological methods and editorial choices suggests that their choices were not totally neutral and may have significantly shaped the way modern historians interpreted specific works edited by mathematicians of that dynasty. A case study of the re-edition in 1798 of a Song dynasty treatise, the Yigu yanduan (1259), by a Qing dynasty mathematician will illustrate this point. At the end of the eighteenth century, Li Rui (1773–1817) was asked to prepare an edition of the mathematical works written by Li Ye (1192–1279) for a private collection. Li Rui was a talented mathematician, but he was also a meticulous editor and trained philologist. He adopted his editorial model from the preparation of the imperial encyclopaedia, the Siku quanshu, but Li Rui also made some corrections to the text in an effort to restore an older version of Li Ye's treatises that had been lost. Convinced of the Chinese origin of algebra, Li Rui used philological techniques to recover the lost materials and to restore the roots of “Chinese mathematics.” The Yigu yanduan contains two algebraic procedures to set up quadratic equations, one from the procedure of Celestial Source (tian yuan shu) and the other from the Section of Pieces [of Areas] (tiao duan). Curiously, the second procedure has not yet attracted the attention of scholars so far, although Li Rui's edition is the one typically used by twentieth-century historians of mathematics. Today, the Celestial Source characterizes “Chinese algebra.” However, the specific concerns of Li Rui about the procedure of Celestial Source, combined with his editorial methods, contributed to this perspective.
Ye, Li. 1248. 測圓海鏡 (Ceyuan haijing [Sea Mirror of Circle Measurements>]).
Ye, Li. 1259. 益古演段 (Yigu yanduan [The Development of Pieces of Areas according to the Collection Augmenting the Ancient Knowledge]).
Both edited in:
(1) Edition of 1789, 文淵閣四庫全書, (Wen yuan ge Siku quanshu [Complete Library of the Four Treasuries, Wenyuan pavilion]). Original edition, National Palace Museum, Taiwan.
(2) Edition of 1789, 文津閣四庫全書, (Wen jin ge Siku quanshu [Complete Library of the Four Treasuries, Wenjin Pavilion]). Vol. 799. Reprint. 2005.
(3) Edition of 1798, 知不足齋叢書 (Zhibuzu zhai congshu [Collected Works of the Private Library of Knowing Our Own Insufficiencies]). Reprint in 中國科學技術典籍通彙: 數學篇 (Zhongguo kexue jishu dianji tong hui: Shuxue pian [Source Materials of Ancient Chinese Science and Technology: Mathematics Section>]). 郭书春, Guo Shuchun (ed). 河南教育出版社 (Henan jiaoyu chubanshe [Henan Education Press]), Vol 1. 1993.