The Study Of Billingsley's English Euclidean Elements And Its Introduction In Late Qing Dynasty

This dissertation is a research on the English translation of Euclidean Elements by Henry Billingsley(1532-1606),and also on the last nine books of the Chinese translation of Jihe Yuanben(??????).Billingsley's Elements is the first English translation,which was published in 1570.It is really a large book,and collects almost all the Elements which was available to Billingsley.There are 284 comments from 40 commentators and a Mathematical Preface by John Dee(1527-1608)in Billingsley's Elements.This dissertation reveals the history context in which Billingsley and Dee had achieved the translation and editing of Billingsley's Elements.The original text of Billingsley's Elements is confirmed here by analysing its layout.These works on Euclid's Elements of the scholars before the Renaissance are investigated on the base of interpreting the comments in Billingsley's Elements.The question is also answered that how those Renaissance persons looked at Euclid's Elements.Last but not least,the translation of "incommensurable" in the last nine books of Chinese translation of Jihe Yuanben is taken as a case,which shows how Billingsley's Elements is spread and adapted.This dissertation contains 6 chapters.Chapter I is the introduction,which introduces the question and summarizes the research status in such related fields.Chapter II reveals in what history context did Billingsley's Elements had been established.Chapter III confirms the original text of Billingsley's Elements by comparing its layout with other editions of Euclid's Elements.The comments and annotations in Billingsley's Elements are also generally sorted.Chapter IV analyses these comments and annotations in detail,so that the viewpoints of the Renaissance scholars on Euclid's Elements are displayed.Chapter V takes the translation and publishing of Chinese Jihe Yuanben as a case to investigate the introduction and influence of Billingsley's Elements in China.Chapter VI concludes the works of the chapters above,and summarizes the different roles of Billingsley's Elements in different history context.The expectation of further study is also indicated.The main ideas of these six chapters are as the following.In chapter I is the introduction,which includes the introduction,the meaning and the approach of the research.The research status on related fields is also summarized.It is pointed out that the investigation into the text,comments and annotations of Billingsley's Elements is still required.And it is also necessary to analyse the translation of Chinese Jihe Yuanben from its original text,namely Billingsley's Elements.In chapter II is the detailed introduction to Henry Billingsley the translator and John Dee the author of the Mathematical Preface.Billingsley keenly concerned about the development of the Britain.He wanted to improve the influence of English and also hoped to promote mathematics research in the Britain.His responsibility to the common wealth provided him a motivation to translate Euclid's Elements into English.In order to achieve this work,Billingsley had collected many rare ancient books,and supplemented which he thought significant into his translation of Elements.The Mathematical Preface by John Dee is among the highlights of Billingsley's Elements.It introduced all the subjects which is related to mathematics,and put forward important concepts for practical mathematics.John Dee described more than 30 subjects in detail which need mathematics,and pointed out the relations among them.He also drew a "mathematical tree" on the base of arithmetic and geometry,which reflects an overall perspective of the mathematical research and application in Renaissance.In chapter III the layout of Billingsley's Elements is compared with its various reference editions.The series of Zamberti's Elements in Latin are confirmed to be the original text of Billingsley's Elements.There are a lot of manuscript notes of Billingsley in the 1558 Volume of Campanus-Zamberti's Elements.However,the layout,content and style of Billingsley's Elements is more similar to the 1516 Volume of Campanus-Zamberti's Elements.The comments in Billingsley's Elements are from 40 commentators besides the translator of its original text,whose age spans from ancient Greece to Renaissance.The work of ancient Greek natural philosophers on geometry and Euclid's Elements are recovered by analysing the comments of Billingsley's Elements.These comments reflect the evolution of Euclid's Elements in the past thousand years,and also constitute the academic pedigree of Billingsley's Elements.In chapter IV the work on Euclid's Elements of Renaissance European Scholars is investigated by reading their comments and annotations collected in Billingsley's Elements.The age of the commentators who is quoted by Billingsley's Elements spans from ancient Greece to Renaissance,especially in the 100 years before the birth of Billingsley's Elements.In the first six books of Billingsley's Elements quotes large numbers of commentators,for the Euclid's Elements had been studied by successive scholars in one and a half millennium after its birth.These comments and annotations on the section of number theory,namely the Book VII,VIII and IX of Euclid's Elements,shows how these ancient scholars studied the concept of "number" and "quantity",which is originated from ancient Greece.They tried to extend the propositions of quantity in the first six books to "number".Some significant thought rises from the study,such as the thought of infinite descent from Campanus.The annotations on the tenth books of Billingsley's Elements explain the nomenclature of the 13 irrational lines,so they become valuable guides of people to understand the tenth book of Elements.The section of solid geometry of Billingsley's Elements contains most of the comments and annotations.The long annotation of John Dee states the significance of solid geometry in mechanics and engineering.The supplement of Flussates reflects an atmosphere of occultism in European Mathematics in the sixteenth century.In chapter V the Chinese translation of "incommensurable quantity" is taken as a case to analyse the translation of Chinese Jihe Yuanben.Alexander Wylie and Li Shanlan the translators tried to create new terms from traditional Chinese vocabulary.Although there may be some failure,the terms they created are reasonable and accurate in general,especially He Xian(??),Jiao Xian(??),Tong Zong(??)and so on.It is revealed that the role of Bibliophilists School of Songjiang(??????)in the translation and publication of the Chinese Jihe Yuanben(??????),and also in spreading western learning to the east.The Bibliophilists School of Songjiang included Han Yingbi(???),Gu Guanguang(???),Li Shanlan(???),Zhang Wenhu(???),the Qian's of Jinshan(????)etc.After the article "An explanation on the six kinds of He Xian and Jiao Xian in Elements"(??????????????)of Gu Guanguang is analysed,it is showed that Gu's explanation is limited by the tradition of Chinese ancient mathematics,so that he was not able to learn the essence of irrational lines.This analysis reflects the difficulties in the transmission of knowledge from one culture to another.Except Li Shanlan and Hua Hengfang(???),these mathematician in Late Qing Dynasty paid more attention to the section of plane geometry in Euclid's Elements.They also compiled teaching materials and cultivated fresh activists for Chinese mathematics.In chapter VI the work of chapters above is summarized.It is displayed that the different roles of Billingsley's Elements in Renaissance and in spreading western learning to the east.More investigation into Euclid's Elements in different history context are expected to show the great significance to human beings of Euclid's Elements entirely.