Researches On The Geometry Part Of Li Dupei's Illustration Of The Mathematics Of China And West Of The Late Of Ming Dynasty

In the late Ming dynasty,with the arrival of missionaries,western mathematics was introduced into China and had a great influence on Chinese mathematicians,From then on,traditional mathematics walked on the road of combining Chinese with western.Xu Guangqi,an early representative of Chinese and western mathematical association,put forward the idea of‘achieving mastery through association',Most Chinese mathematician had responded positively,Li dupei's Illustration of the mathematics of China and West(????????)is the product of the combination of Chinese and western mathematics in this period.This paper mainly focuses on the study of the geometric part of Illustration of the mathematics of China and West,The research object is the XingJi Xiang Bu(????)of volume 1 and Gou Gu Xiang Qiu(????)and Gou Gu He Jiao(????)of volume 9,Researching the five aspects about the writing style,geometric terms,algorithms,graphics,deductive reasoning.Literature analysis and comparative analysis are used to analyze in detail the contents of Illustration of the mathematics of China and West(????????)?Jiu Zhang Suan Fa Bi Li Da Quan(??????????)?Suan Fa Tong Zong(??????)and Elements of Geometry(??????).At last,summarized the method and achievement of li dupei combining Chinese mathematical with western mathematical.Through the study of the geometrical part in the Illustration of the mathematics of China and West,the conclusion shows that under the influence of Elements of Geometry,Li Dupei tries to integrate the essence of western mathematics into Chinese traditional mathematics,and at the same time makes innovations.For this reason,he retained the characteristics of traditional Chinese mathematics in the compilation style of the whole content.The expression way of geometric terms and algorithm,and western mathematics as a supplement penetrated into them.There are both traditionaland western mathematical expressions in geometric terms;In the algorithm,Using The Pythagorean to connect geometry,with Chinese algorithm interpretation of the western algorithm,The idea of deductive definition,algorithm and drawing method of graphics was completely borrowed from western mathematics and integrated into the argumentation of traditional Chinese mathematics,which made the solution and argumentation of propositions easy to understand.However,Li du Pei also made innovations in many aspects in order to form his own characteristics in the process of combinging Chinese mathematics with western mathematics.Such as,new terms and their expressions were invented;The inner diameter of Regular heptagonal and Regular nine-sided and the relationship between the inner diameter and the diameter of the circle are measured by the graduated‘moment';The problem of drawing regular hexagon and Regular nine-sided is solved by using the method of bisecting circumference and diameter;The principle of ‘Xing Ji Xiang Bu'is put forward,which was a new method for solving the area of regular polygons;The formulas for calculating the inner diameter of regular triangle,regular pentagon,regular hexagon,regular heptagon,regular nine-angle,regular ten-angle and regular twelve-angle are given.Although his innovative terminology was not rigorous enough and did not reflect the uniqueness of representation,but the beauty of representation is far more direct than any other ways;Although his drawing method of regular hexagon and regular nine-Angle did not give a rigorous argument,but his drawing method filled the gap of geometry and become the first person to give the drawing method of regular hexagon and regular hexagon at that time.Looked from the propositional reasoning methods,He had preliminarily formed the mathematical idea of combining numbers and shapes.So Chinese mathematicians did not have deep understanding of the logical deduction system of western mathematics in the late of Ming dynasty,However,the efforts and achievements in the process of understanding Chinese and western mathematics should not be ignored,It can be used forreference to the development of mathematics later.