Abstract: In the translation of Books VII-XV of Jihe Yuanben (Euclid’s Elements), Li Shanlan (1811-1882) and Alexander Wylie (1815-1887) carried forward the translation style and format of Xu Guangqi (1562-1633) and Matteo Ricci (1552-1610) in Books I-VI. The Chinese translation of “incommensurable quantity” is taken as a case to analyse the Chinese Jihe Yuanben. The translators, Alexander Wylie and Li Shanlan, attempted to create new terms based on traditional Chinese vocabulary in Book X. Although there may have been some shortcomings, the terms they created are reasonable and accurate in general, especially He Xian (和线), Jiao Xian (较线), Tong Zong (同宗) and so on. This highlights the continuity and adaptability of scholarly creativity, as well as how translators, through the creation of terminology, transmitted mathematical ideas across different historical contexts, constructing an edifice of knowledge.

Key Words: Book X of Jihe Yuanben; Incommensurable quantity; Translation of terms; Translation of propositions