A Study On The Integration Of Jihe Yuanben In Early Qing Dynasty By Chinese Mathematicians

The translation and introduction of the Elements played a significant role in the history of Chinese mathematics and mathematics-transmission between China and the West.During the early Qing Dynasty,Chinese scholars carried out a series of works of simplification and integration of Jihe yuanben????(Chinese translation of Euclid's Elements).These works include Jihe yue???(the Principles of Geometry,1661)of Fang Zhongtong???,Jihe yijianji?????(the Collection of Compendious and Simple Analysis of Geometry,1679)of Li Zijin???,Jihe lunyue????(the Discussion of Principles of Geometry,1700)of Du Zhigeng???and Jihe tongjie????(the General Explanation of Geometry)of Mei Wending???.This essay,based on previous studies,compares the integration work based on The Elements with respect to both the axiomatic system and the proof technique.This reveals the ways in which Jihe yuanben was received by Chinese intellectuals.On the basis of textual analysis,this paper explores the traditional Chinese mathematics origin of these works and discusses the connections and differences between traditional Chinese mathematics and Western mathematics.Fang Zhongtong's Jihe yue refined the Jihe yuanben with key words and tiled the graphics to simplify the proofs.These efforts made the essence and proofs of Jihe yuanben intuitive.In Jihe yijianji,some propositions were selected from Jihe yuanben and their proofs were elaborated by Li Zijin.To expound the most profound meaning of Jihe yuanben he explained it with numbers and Gougu??(right-angle triangle,lit.base-leg),which were rooted in traditional Chinese mathematics.Du Zhigeng drastically reduced the original content in Jihe yuanben in his Jihe lunyue.As he put it,"Disscusions which do not have to be retained have been deleted."Nevertheless,"Based on its original text and sequence",Du completely preserved the axiomatic system of Jihe yuanben.Also,in his book Du carried out more in-depth argument based on the logic of Jihe yuanben,according to his principle of"expanding the meaning of Jihe yuanben".Mei Wending selected some of the propositions from Jihe yuanben into his Jihe tongjie.He solved these propositions on the basis of Gougu.This demonstrated that Chinese learning and Western learning,though in different ways,can be integrated through the“principle”?,which was also the purpose of Mei Wending.The initial entry of The Elements into China did cause some misunderstanding among Chinese intellectuals.This is evident,for example,in the changes in the axiomatic system and in the cyclic proof in Jihe yue of Fang Zhongtong.In his work,however,Du Zhigeng did not only follow the axiomatic system of Jihe yuanben but carried forward the proofs as well.This suggests that Chinese mathematicians had the ability to understand Jihe yuanben.In addition,there were some common features between Gougu and Jihe yuanben,which we can see in the works of Li Zijin and Mei Wending.However,this connection applied only in a finite range of second-order algebraic identity,so Li and Mei's works also had some sort of limits.During the early Qing Dynasty,the proficiency in traditional Chinese mathematics and Jihe yuanben of Chinese mathematicians became more sophisticated.Meanwhile,the attitude of Chinese mathematicians towards western learning was also changing subtly.These works of integration based on Jihe yuanben were the products of the convergence of Chinese and Western learning in the era of a new dynasty.The study of the reception and integration of Jihe yuanben reveals important elements in the story of the encounter between the West and China in the 17 th and early 18 th centuries.