In addition, Tianshu also played an important role in the development of ancient mathematics in China. Before the publication of "Round Sea Mirror", although there were unknown words to solve equations and polynomials in China, no systematic records were left. Ye Li systematically and generally summarized the astrology in "Measuring the Round Sea Mirror", which made the word algebra begin to evolve into symbolic algebra.
The so-called Tianyuan method is to set "Tianyuan I" as an unknown number, list two equal polynomials according to the known conditions of the problem, and get a higher-order equation after subtraction, which is called Tianyuan open method, which is the same as setting X as an unknown series equation in modern times. Mathematicians in Europe did not fully realize this until after16th century. There are 170 questions in this book, which basically lists Tianyuan formula (according to "Appraisal Miscellaneous Notes") and finds the solution to the Pythagorean problem.
At the age of 40, Ye Li gave up his reputation and devoted his life to mathematical research. He opposed the mysticism of object number and thought that mathematics came from objective nature. These views are reflected in the preface of his own book "Measuring the Round Sea Mirror", which was very valuable at that time and was one of the main factors for his great achievements in mathematics. In the Qing Dynasty, Ruan Yuan thought the Round Sea Mirror was "China's Mathematical Collection", and Li praised it as "China's Arithmetic Book".
"Sea Mirror for Measuring Circle" not only keeps Cave's nine-capacity formula, that is, nine methods to find the diameter of inscribed circle of right triangle, but also gives some new formulas to find the diameter of circle. The identification miscellanies in Volume 1 illustrate the relationship between the side lengths of each Pythagorean figure in the circular city model and their relationship with the diameter of the circle. There are more than 600 articles, each of which can be regarded as a theorem (or formula). This part is a summary of Pythagoras' inclusion in ancient China. The exercises in the following volumes can be derived by using astronomical techniques on the basis of "recognizing miscellaneous notes" Ye Li summed up a set of concise and practical celestial programs, and gave the method of transforming fractional equation into integral equation. He invented the minus sign and advanced decimal notation, using whole numbers from 0 to 9. Numbers other than o have existed since ancient times, which is a reflection of the plan. However, when there is an o vacancy in the formula, there is no symbol o. Judging from the existing ancient arithmetic books, the Round Sea Mirror and Nine Chapters of Qin are two books that used O earlier, and the time difference between them is only one year. Rounding the Sea Mirror focuses on the equation, but it doesn't involve much in solving the equation. However, many high-order equations (up to six) in the book are derived by astrophysics, and the roots given are accurate, which shows that Ye Li has mastered the numerical solution of high-order equations.
There are three major achievements in the mathematics of the round sea mirror: "Astrology", that is, a "mechanized" program for solving problems with equations, which is equivalent to a modern method of setting X as an unknown equation and is a pioneering work with world significance; The Pythagorean solution pushes the traditional Pythagorean study to a new height; A new starting point of mathematical abstraction: Although this book still adopts the expression of problem set in form, the problems obviously do not come from real life, but are generated for the needs of mathematical research. It is only because of tradition that it is put on the coat of "practicality", which is undoubtedly an important breakthrough and supplement for ancient mathematics of the Han nationality. As far as the content is concerned, some special concepts and formulas (Notes on Miscellaneous Notes) are given, and the method of deductive reasoning is adopted. In China,