A Primary Study On Methods And Principles Of The Determining Mathematical Terminologies In Euclid's Elements Of The Chinese Edition In The Ming Dynasty

The publication of the first Chinese edition of Euclid's Elements (with Chinese title Ji-he Yuan-ben) with 6 books in 1607 which was translated by Italian missionary Mathew Ricci (1552—1610) and Chinese scholar Xu Guangqi (1562—1633) is an important historic event in the history of mathematics in China. The work represents a new mathematical system different from the traditional one in China and introduces new mathematical contents and new thinking way of mathematics into China. The Chinese version of the Elements not only provides great deal of new terminologies, but also establishes the terminological foundation for the translations of western scientific treatises, therefore, becomes an example of subsequent introduction of western science treatises. It is of important academic meanings for the study and understanding of the historical evolution of Chinese mathematics terminology in the past 400 years to study the Chinese terminology displayed in the translation of Euclid's Elements and the methods and principles of determining them.The present dissertation deals with the Chinese mathematics terminology introduced in the translation work Elements by studying the similarities and differences of them with those of traditional Chinese mathematics, and by analyzing the abandoned traditional terminologies and new appearing one, so as to find the methods and principles for the determination of mathematics terminology in the ji-he yuan-ben.The main contents of the dissertation, besides an introduction, consist of five parts:Part one studies the terminologies about mathematics subject itself, the logic reasoning, and mathematical expression. The study shows that the terms ji-he, liang-fa, du-fa, each of which represents a subject of mathematics, are settled by attaching new meanings to old mathematical words, and some terms of logic reasoning and mathematical expression are loaded from the tradition terms and the other are created newly. In addition, the translators make well use of the characteristic of the sequent order of some Chinese characters in corresponding the western letters. Part two studies the geometrical terminologies appearing the first four books of the Element to show the method and principle of reconstructing or abandoning traditional terms. The translators of the Elements make great efforts to avoid using terms of practice meaning and to introduce terms of general and abstract meanings.Part three studies the group of terms about proportion and similitude appearing in the books five and six of the Elements and the idea of determining them. The translators do not engage the traditional words in stead of composing a group of new terms.Part four compares the terminology in the version of 1607 with those of anotherChinese version which is first printed in the shu-li jing-yun (Essential ofMathematics Science) in 1723 to show the evolution and changes of the terminology.Part five is a summary of the principles and methods based on the studies in theabove four parts.