A Study On A Mathematical Works, Zhongxi Suanxue TiJing,by Chen Pingying

Abstract:Chen Pingying was born in Changle City,Fujian Province in April19,1881,and died in unknow.At the age of his17years old,he took part in provincial examination,and he won the75th juren.He. taught mathematics in Guangzhou Zhongxue Tang. His representative works in Mathematics was Zhongxi Suanxue Tijing, which was Chen’s learning experience after he studied Chinese and Western mathematics at that time.This dissertation mainly analyzes and interprets Zhongxi Suanxue Tijing. Chen’s works consisted of four main sections.Firstly, it was Chen’s attainment experience after studying Daishu Shu.He gave some new solutions to indefinite equation and solve Cardano formula.Secondly,the works included some articles,which were Chen’s studies on the calculus introduced into China in the Late Qing, such as the ellipse arc length and differential method for the area of ellipse sector. Thirdly, Chen translated and introduced some materials about modern Euclidean geometry.Finally, and most importantly, Chen attained some achievements on the methods of Duoji and Pingfang,which belonged to Chinese traditional mathematics.A cubic equation was based on Daishu Shu’s methods, how to make a complex equation become a cubic equation without quadratic term and another method of deduction of Cardano formula.On the solution of an indeterminate equation, based on the algebraic method of Daishu Shu. he gave convenient methods of solving the indefinite equation,which combined with the knowledge of Day an Qiuyi Shu and Euclidean algorithm.In aspect of Duoji and Kaifang,Chen used the symbolic algebra methods to explain and generalize the foundations of the traditional mathematics.Chen also gave two new tables of Jijiao and Jijiao Huanyuan.He also gave the new method of Shugen Kaifang.On the study of the conic sections,Chen gave the differential method and the solution of ellipse arc length by the methods in Daiweiji Shiji and Weiji Suyuan.In terms of translation to modern Euclidean geometry, this book involed the Apollonius problem, points, win-lines, unlike the nine-point circle problems and so on. Also, each of them has a simple proof and discusse in details.Chen’s works not only contained the studies on the Chinese traditional mathematics, and contained the comprehension, assimilation and application of Western mathematics, but also reflected the fusion of two kinds of mathematics. The disseration can be regarded as a case study on the dissemination of of western modern mathematics in the Late Qing.