The Study Of On Triangles Of Every Kind By Regiomontanus

Before the 15 th century,trigonometry was widely used in astrology,navigation and astronomical fields,especially the development of spherical triangle had the most far-reaching effects on astronomy.This has enabled people always consider that trigonometry to be attached to astronomy,and has not been studied as an independent discipline.At the end of15 th century,the German mathematician Regiomontanus completed the book "On Triangles of Every Kind",for the first time,which systematically studied trigonometry from the perspective of mathematics,making it independent from astronomy and becoming an important branch of mathematics,and also making trigonometry a Renaissance in Europe.Many mathematicians and astronomers have described the life of Regiomontanus,but few scholars have made a thorough study of the book on "On Triangles of Every Kind",in order to cover the shorting,this paper will explain the book of "On Triangles of Every Kind" in detail.First,the life and main contributions of Regiomontanus will still be introduced in this thesis.Its significance is to understand the academic environment and cultural background of the times by analyzing the background of Regiomontanus and further clarify the development of trigonometry at that time and the development of the context.Second,this paper systematically discusses the main ideas of the book from the content itself.It is undeniable that Regiomontanus' s astronomical attainments have made the main contents of the "On Triangles of Every Kind" largely derived from their studies of astronomy.The related explanations of plane triangles and spherical triangle are largely dependent on the use of trigonometry in astronomy.But,analyzing the contents of "On Triangles of Every Kind",it is can be found that in the process of the book writing a number of examples and algebraic form are used to explain the axiom,which explains the book's idea is to separate trigonometry and astronomy,and as a mathematical discipline was studied.Last,the book "On Triangles of Every Kind" has used a significant portion of the book to demonstrate the various properties and theoretical basis of plane triangles and spherical triangle,so that the original emphasis on practical trigonometry knowledge can be presented in the form of theory.It lays a solid foundation for the study of trigonometry in the future.In the 16 th century,"On Triangles of Every Kind" were translated into different languages and spread everywhere.According to the writing background of the book,this thesis makes comparative study of this book and other medieval works of geometry.It is found that there is a close relationship between the book and Arab mathematician Nas.irad-D?n of "Transverse Line Principle" through the study.The elaboration of the related concepts and properties of plane triangles and spherical triangle in the book is largely inherited from the axiom system of "Euclid's Elements".However,the book "On Triangles of Every Kind" also records many of Regiomontanus' s original ideas,such as: using algebraic method to prove the nature and principle of the triangle.In addition,the influence of the triangle on the development of the trigonometry in the Ming and Qing dynasties is also very profound.In the early years,the introduction of many of the western works is related to the book during development of Chinese trigonometry.At that time,due to the influence of the book our country trigonometry research and education is increasingly perfect.So "On Triangles of Every Kind" is a rare masterpiece of trigonometry,which also makes it possible for him to become a mathematics person by virtue of his book "On Triangles of Every Kind".