Li Rui, a "poor" Suzhou mathematician - Life History and "The Opening of the Fang"

Li Rui, the word Shangzhi, the number of four incense. A native of Yuanhe (present-day Suzhou), Jiangsu. Born on December 8, 1769 (January 15, 1769) in the 33rd year of the Qianlong Dynasty, and died on June 30, 1817 (August 12, 1817) in Jiaqing, he was an outstanding mathematician in the middle of the Qing Dynasty.

Li Rui "young Kaimin, with superior assets, picked up the "Algorithm Tongzong" from the academy, and his heart understood his righteousness, so he became the study of the nine chapters and eight lines. He became a student of Yuanhe County in the fifty-third year of Qianlong (1788). In the first month of the new year, Qian Daxin came to Suzhou to teach at Ziyang Academy, and Li Rui learned from it. In the fifty-fifth year of Qianlong (1790), Jiao Xun sent money to Daxin in the second part of the "Diagram of the Palace room of the Qunjing", and gave it to Li Rui in one part, and Li Rui wrote a letter of thanks, which was the beginning of Jiao and Li's friendship. The following year, Li Rui "graduated from Ziyang Academy, receiving arithmetic studies from Mr. He began to teach the methods of triangular octagon and small wheel ellipse, and repeatedly introduced them into ancient times. Under Qian Daxin, Li Rui studied the "Great Unified Calendar", "Hijri Calendar", and the "Earth Atlas" of the Westerner Jiang Youren (1715-1774).

In the sixty years of Qianlong (1795), Ruan Yuan was appointed as the scholar of Zhejiang, "because he wanted to write the "Biography of the Domain People", listing the number of people in ancient and modern China and the West and the books that should be collected, such as history, transmission, heaven, and calculation, and instructing Rui to compile it. After Li Rui was invited to Hangzhou by Ruan Yuan, he engaged in the compilation of the "Biography of the Domain People". During this period, he often traveled back and forth between Suzhou and Hangzhou, and was able to extensively contact the rare books collected by various famous scholars in Jiangnan and the manuscripts of the Four Libraries of Wenlan Pavilion, and studied some representative works in ancient Chinese astronomy and mathematics. In mathematics, he successively proofread and sorted out Li Zhi's "Measuring the Round Sea Mirror", "Yigu Yanduan", Wang Xiaotong's "Ji Gu Arithmetic Classic" and Qin Jiushao's "Nine Chapters of the Book of Numbers", and wrote the book "Arc Arrow Arithmetic Fine Grass" in the third year of Jiaqing (1798). In astronomy, he successively dissected the calendars of the Three Unifications, the Four Points, and the Qianxiang Calendar. In the spring of the fourth year of Jiaqing (1799), he read the "Song Shi And Law Chronicles", realized He Chengtian's adjustment of the Japanese law, and wrote a volume of "The Examination of the Strength and Weakness of the Japanese Law Shuo". In terms of scripture, he assisted Ruan Yuan in the proofreading of books such as Zhou Yi and Mencius, and the results were included in the Commentary on the Thirteen Classics edited by Ruan Yuan. He also wrote his own "Examination of the Names of the Summoning Day" and so on.

In October of the fifth year of Jiaqing, Li Rui was in the Hangzhou Ruan Yuan Festival Bureau, and Jiao Xun cohabited with the Zhongcheng Bentang of the Office, "discussing the history of the scriptures and the truth of the news of the poor heavens and people". Around this time, Li Rui learned about Wang Lai's work through Jiao Xun. In November, Li Rui returned to Suzhou. Wang Lai wrote the fifth volume of "Hengzhai Arithmetic" in the sixth year of Jiaqing (1801), discussing the "knowable" and "unknowable" of Qin Jiushao and Li Yefanggen, and sent it to Zhang Dunren and Jiao Xun respectively after the manuscript was completed, and Jiao Xun presented the manuscript of the book to Li Rui half a year later. Li Rui believed that "it is the most difficult and extremely small volume, and the true arithmetic is also the most important", and "more in terms of positive and negative openings, including three examples", and wrote a text on August 9 (September 5, 1802), which Wang Lai later appended to the sixth volume of the Hengzhai Arithmetic. In this year, Li Rui also studied the "Fine Grass of the Ancient Arithmetic Classic" for Zhang Dunren, and wrote a piece of text for it on December 20 (January 13, 83).

In the tenth year of Jiaqing (1805), Li Rui went to Yangzhou to serve as a guest of Zhang Dunren. At that time, Scholars such as Wang Lai, Shen Qinpei, and Chen Jie were also in Yangzhou, and they often discussed issues together. After Zhang Dunren wrote the "Supplement to the Opening Of the Fang", he also asked Li Rui to proofread it for him. After Zhang Dunren found the Song edition of the Nine Chapters of Arithmetic (the first five volumes), the Sun Tzu Arithmetic Classic, the Zhang Qiu Jian Arithmetic Classic, and other classics, Li Rui was also able to read and proofread the ten books of the Arithmetic Classic.

In the eleventh year of Jiaqing (1806), Li Rui returned to Suzhou. In October of that year, he successively finalized the works of "Pythagorean Arithmetic", "TheOry of The Fold of the Pipe" and "Ge Ji Kao", and re-proofread "Qiuyi Arithmetic" for Zhang Dunren. The following year, the book "Pythagorean Arithmetic Grass" was published by Zhang Dunren in Suzhou. In the thirteenth year of Jiaqing (1808), Li Rui wrote the Equation New Technique Grass and sent the manuscript to Beijing to Li Huang. Li Huang replied: "Reading a volume of the masterpiece "Equation New Technique Grass", the positive and negative rates are equal, and one is natural. It is the mistake of the prequel engraving, the interpretation of the ancients' unborn, happy day. "Pythagorean Fine Grass" before the year of the ancient fool too shou see Hui a book, the sections of each map, into the millimeter, really thoughtful and powerful work also. ”

In the fifteenth year of Jiaqing (1810), Li Rui went to Beijing in March to participate in the Shuntianfu Examination, and arrived in Beijing in early June. Although this test was unsuccessful, I had to talk with Li Huang. He also "saw more than a hundred miscellaneous banknotes and arithmetic books in Li Yunmen's residence, and was the one who recorded it from the Yongle Canon when Ruan Yuntai was transferring the Wenying Pavilion, including several of Yang Hui's "Picking Odds", and had to see the synopsis at the beginning." While in Beijing, Li Rui also accepted Li Yingnan and others as disciples. In the nineteenth year of Jiaqing (1814), Li Rui obtained a scattered "Yang Hui Algorithm", "all scattered leaves, and upside down and chaotic", Li Rui then "tested its meaning, arranged neatly, obtained six books, the beginning and end of the sequence are not missing, and urgently ordered the workers to pack a huge book, and hide it". It was also in the autumn of that year that Li Rui began to teach Li Yingnan the main contents of the Kaifang Theory (the manuscript was written in the eighteenth year of Jiaqing). In the twenty-first year of Jiaqing (1816), Li Rui read the manuscript of the "Four Yuan Yu jian" sent by Zhang Dunren and commented on the "Zicao-shaped section" and other issues in it, but unfortunately due to physical illness, he failed to complete the proofreading of the whole book. The following summer, Li Rui's condition worsened and he died of hemoptysis. Before his death, he repeatedly instructed Li Yingnan to write the next volume of his unfinished "Kaifang Theory", so Li Shi "obeyed Mr. Li's last will, deduced according to law, and did not dare to participate in his own opinion", and finally completed this work on equation theory in the twenty-fourth year of Jiaqing (1819).

Li Rui had no fixed financial resources in his life, and mainly relied on his family life and academic activities as a guest of honor, so his life was often in poverty. However, he was able to live in poverty, insisted on astronomical and mathematical research in the face of adversity, and eventually achieved brilliant academic achievements.