A famous teacher is missing.
Li Rui is from Henan. His grandfather's name is Heng and his father's name is Heng. Li was a scholar in the seventeenth year of Qianlong (1752). He used to be the magistrate of Yiyang (now Ruyang) in Henan Province, and later served as the minister of war. Li Rui was born in1769 65438+1October 15. "Young, sensitive and gifted. I got "Arithmetic Unity" from the book, and I know what it means, so it is a study of nine chapters and eight lines. "
1788, Li Rui was born in Yuanhe County. The following year, Qian Daxin came to preside over Ziyang Academy, and Li Rui was accepted by his family. 179 1 year, Li Rui studied astronomy and mathematics from Qian Daxin. Qian "began to teach the method of triangle, eight lines, small wheel and ellipse, and later introduced it to ancient times." Qian Daxin's "daily work is to turn over the books of the group to correct hatred, and discuss with Sharp if you have any questions". For example, Li Rui was asked to proofread and make a postscript after the book was written, which shows that Qian was quite satisfied with this disciple's knowledge. During this apprenticeship, Li Rui not only learned knowledge, but also became familiar with the research methods of Ganjia school masters. Someone wrote: "Gong Zhan, who was educated by money, was nine figures. Gong Zhan said:' Anyone who is a disciple is not a good disciple. My friend Duan Ruoying (that is, Yu Zhuo) is to Dai Dongyuan (that is, the earthquake). Mr. Wang (that is, Li Rui) then spent five years meditating, trying to understand what others said. "
Thanks to Qian Daxin's introduction, Li Rui began to correspond with Jiao Xun, who is six years older than him. 1790, Jiao Xun sent two copies of Jing Gong Tu to Qian Daxin, and Qian Daxin replied that "a copy has been sent to Li Sheng Shangzhi, and Zunza will be read by him. I also deeply admire it, and I hate that I can't shake hands. " Li Rui also wrote a letter to Jiao Xun, mainly discussing planetary motion.
Mubin's career
1795, Ruan Yuan became a political scholar in Zhejiang, and began to plan and compile his biography. Soon Li Rui was invited to Hangzhou, and actually became the lead author of the first biography of astronomy and mathematicians in China history. During this period, he often traveled between Suzhou and Hangzhou, and he was able to get extensive contact with rare books and cheats collected by famous bibliophiles in the south of the Yangtze River, and perhaps he could also read the manuscripts of the Complete Works of Wen Lan Ge Si Ku. On this basis, Li Rui made a serious study of ancient mathematics in China, and his work was consistent with the extensive collation of ancient classics by the Ganjia School. He compiled China's ancient mathematical masterpieces successively, such as Round Sea Mirror and Ancient Analysis, Wang Xiaotong's Ancient Arithmetic, Qin's Shu Shu Jiu Zhang, Jiu Zhang Arithmetic and so on. In astronomy, Li Rui has worked out the calendars of three wonders, four points, dry elephant, meeting the source, occupying the sky, spring outing, Tian Hui, Daming and Datong. He has successively completed five manuscripts, including Notes on Three Series Techniques and Notes on Four Points Techniques. In the study of Confucian classics, he assisted Ruan Yuan in collating Zhouyi, Gu Liang and Mencius, and his achievements were included in the Notes to Thirteen Classics compiled by Ruan Yuan. He also wrote his own Confucian classics, such as A Brief Example of Yu Family in Zhouyi and A Survey of Hao and Yue Ming.
1798, Li Rui completed the book Sagittarius actuarial science. Reading Song Shu at 1799? When I was in the Journal of Law, I learned about the method of He Chengtian's adjustment to Japan reported by Brown and wrote a book entitled "The Test of Japanese Mana". In the same year, the Biography of Domains was compiled. During this period, Li Rui and Jiao Xun lived together in Ruan Yuan. Get along with each other day and night. "In history, the poor have news." About this time, Li Rui learned about Wang Lai's work through Jiao Xun; Wang and Li first met at 1800.
Wang Lai won Yangzhou in 180 1, and wrote the fifth volume of Hengzhai Arithmetic in the same year, discussing the knowability and unknowability of Qin He's prescription, that is, whether the numerical equation also has a positive root. After the manuscript was completed, Wang distributed it to Zhang Dunren for justice, and presented Wang Lai's manuscript to Li Rui one by one. Read Li Rui's book "Deeply sigh for the essence of goodness, and then write three boxes of prescriptions in two days". This happened on September 5 1862. At that time, Li Rui lost his wife soon, and every time he lost his son, he lived alone near the lonely mountain near the West Lake, and his mood was very bleak. In his postscript to Wang Lai, he said: "This volume is very small, and it is really a masterpiece of my family." The "three examples" given later are the opening works of his research on equation theory.
1805, Li Rui went to the curtain call at the invitation of Yangzhou satrap Zhang Dunren. Now mathematicians are Wang Lai, Ling Tingkan and Shen. By then, the situation will change, especially Li, Wang and Jiao (Li, Ling and Jiao), who are called "three friends of chatting". Zhang Dunren has written many works, such as The Essentials of Ancient Calculations, Calculating Calculations, Prescription Supplement, etc., all of which have been fully helped by Li Rui. After he found Nine Chapters of Arithmetic (the first five chapters), Sun Tzu's Art of War and Zhang Qiu's Calculations in the Southern Song Dynasty, he asked Li Rui to proofread them. At about the same time, Wang Lai completed the seventh book of Hengzhai Arithmetic, which made the study of equation theory take a big step forward.
1806, Li Rui returned to Suzhou. This year, he successively wrote Pythagoras Arithmetic Fine Grass, Pan Zheshuo, Ge Jikao and other works, and re-edited Autumn Arithmetic for Zhang Dunren. In 1808, it was written as "New Techniques of Equation", and a copy was sent to Li Huang in Beijing immediately after the book was completed. At that time, Li Huang was engaged in the research of nine chapters of arithmetic. Later, he wrote back to Li Rui, and spoke highly of this book and Pythagoras Calculation Fine Grass sent by Zhang Dunren two years ago. Li Rui and Li Rui are also called "Nanbei Li".
Although Li Rui participated in the imperial examinations many times in his life, he failed. 180 1 year, Li Rui left Zhang Dunren's mansion in Nanchang to take the last exam in Beijing. Shun Tianfu's rural examination ended in failure again, but he was able to get together with Li Huang, an academic confidant for many years. During their stay in Beijing, they had frequent exchanges, mainly discussing the problems in Nine Chapters of Arithmetic.
Li Rui cherished China's ancient arithmetic books all his life. In addition to the proofreading and explanation of many ancient arithmetic books mentioned above, he also personally purchased 1800, a precious mathematics book recorded by Mei Wending in the Ming and Qing Dynasties, West Mirror Record. After this book, Jiao Xun copied another volume, which has been passed down to this day. During his stay in Beijing, he read many arithmetic books recorded by Ruan Yuan in Yongle Ceremony from Li Huang. 18 14, Li Rui got a messy Yang Hui algorithm, which was rearranged literally. 18 16 He got a copy of "Meeting with Siyuan" that Ruan Yuan visited earlier and presented to Four Treasures of the Study, and began to sort it out. Unfortunately, he failed to graduate due to physical exhaustion. Ruan Yuan sighed: "It's a pity that Li Jun didn't finish his seiko, so he couldn't study."
Accompanied by poverty and disease
Although Li Rui has been running between dignitaries for many years, his family life is very poor. In his diary, you can often see the record of "receiving a certain amount of silver"; One diary also mentioned that Li Huangtuo asked Zhang Dunren to "mind his family's affairs and write a book seriously." Li Rui also often rewards his mentor or protector with mental labor. Qian Daxin, Zhang Dunren, Ruan Yuan, Li Huang and others have all used his research results. No wonder some people say that he is a "man of his own mind" and "has no hidden information". Li Rui is addicted to books. For this reason, we have to tighten our belts. Sometimes I just can't afford it. He gets the information he needs by borrowing and copying books. Sadly, in order to inherit the family business, he married another wife Gong and Aiko after their death, until he died and had a son. Excessive workload and heavy family burden undoubtedly aggravated the poverty of his life and damaged his health.
18 14 years, Li Rui was seriously ill. At this time, he began to teach his disciple Li Yingnan's theory of prescription science and solution equation intermittently for three years, and his lecture became "prescription science". 18 17 summer, Li Rui's condition deteriorated. Before he died, he asked Li Yingnan to write the second volume of Prescription, which has not yet been finalized. 18 17 In August, Li Rui, who was in his prime, died of hemoptysis. At the age of 48.
After Li Rui's death, Li Yingnan "followed Mr. Wang's wishes and deduced according to law". The theory of equations was completed in 18 19.
Li Rui's scientific works are mainly included in Li's suicide note. The book was first published in the Jiaqing period, with a volume of 1 1 8. Its sub-titles are: Zhao Haoyue's Ming Kao, Notes on Three Shu Tong, Notes on Sifen Book, Notes on Ganxiang Book, Notes on Fengyuan Book, Notes on Zhan Shu Tian, and Notes on Sifen Book. In addition, he also wrote "Measuring the Fine Grass in the Round Sea Mirror", "Counting the Fine Grass in the Ancient Classics" and "Six Methods of Supplementing Song and Jin Dynasties". "Hui Hui Times Test" and other books.
Li Rui combines inheritance and creation in academic activities. His contribution to mathematics mainly includes the following four aspects:
Biographies of people in the field of compilation
Biography of the People in the Domain is a biography of a large astronomer and mathematician with the evolution of the calendar as the main line and the characters as the core. * * * Including Chinese and foreign calendar mathematicians from ancient times to early Qing Dynasty 3 16. Each character consists of "biography" and "theory": "biography" is mainly a collection of original documents, and "theory" is the editor's brief comment on biography. Without a comprehensive understanding and extensive reading of ancient astronomy and mathematics in China, it is difficult to be competent for this task. Li Rui is the overall designer and main author of this book.
As the nominal editor-in-chief, Ruan Yuan mentioned that his editing process is characterized by "frequent business, both inside and outside the office", while "Yuanhe student Li Rui and Taizhou student Zhou Zhiping are in the majority". Similar words appear repeatedly in his preface to Luo Shilin's Biography of Continuing Domains and Li Ruizi's Biography written by Ke Jiu. Ruan Yuan, as a local governor, runs a school and engraves books, and has published many classics in his name, such as Collection of Classics, Notes on Thirteen Classics, and Interpretation of the Emperor's Ching Classics. , all written by his screen guest. This situation can be inferred from the biographies of domain people. Ruan claimed to be "ignorant of the plan" and decided that Li Rui was "deeper than the plan." The first person in Jiangnan is also ",so it is very likely that the specific work of" Biography of People in the Domain "will be handed over to Li Ruilai.
Judging from the specific contents of the book, Zhang Shouwang, Liu Hong, Ma Xian, Zhao Su, Zhou Zong, Liu Xiaorong, Wei Pu, Yao Shunfu, Benoit, Wang Xiaotong, Li Deqing, Tan Yu, Yang Ji, Yelulu and Bei Lin are all related to Li Rui's works. The word "Li Shang Zhi Rui" can also be seen in the theory of "Yu Na", so there has long been a saying that "the people in the domain were handed down by Yuan and Li".
sift through ancient books
During the Qianlong period, Sikuquanshu was compiled and a large number of precious ancient books buried for a long time were rediscovered. Dai Zhen, Ruan Yuan, Zhang Dunren and others all devoted themselves to various "Ten Calculations Classics" and mathematical masterpieces of the Song and Yuan Dynasties. However, after being copied or engraved, the terminology used in these ancient books is often different from that at that time, and the task of collation and annotation is quite arduous.
Nine Chapters Arithmetic is the representative work of China's ancient mathematics. It is now recognized that the most important collating work in the early days was Li Yu 1820' s Nine Chapters Arithmetic Brief. As early as before, Li Rui had finished two books, Pythagoras Arithmetic Fine Grass and Fang Xin Shu Cao. After the completion of these books, they all gave Li Huang a look, and Li Huang's letter proved this:
"Reading a volume of" The New Art of Equation "is quite positive and negative. It is a mistake in the prequel and explains the unfinished coverage of the ancients. It is pleasant and pleasant." Gu (Arithmetic) Fine Grass ",the year before last (1807), see Gu Yu Taishou (that is, Zhang Dunren). Benefiting from a book, each section has pictures, which is really a thoughtful and powerful work. Comparing Li Huang's and Li Rui's explanations of Pythagorean Theorem and its application, it is not difficult to find that they use almost the same "section and diagram", especially in Li Huang's book about Liu Wei's explanation of proving Pythagorean Theorem by means of "supplementing and supplementing", which obviously completely copied Li Rui. The explanation of "new technology of equation" in Li Huang's book is basically based on Li Rui's works.
Li Rui also wrote "Calculating Classics on the Island" and "Analysis of Ancient Arithmetic", both of which have been lost. However, there is an ancient arithmetic fine grass handed down from ancient times in Zhang Dunren, and Li Rui once revised it and made a postscript. Some people "suspect that this fine grass has expanded its meaning on the basis of the Blue Book of Ancient Arithmetic." Li Rui assisted Zhang Dunren in completing two books, seeking arithmetic and prescription supplements.
Li Rui also compiled Sun Tzu's Calculations, Round Sea Mirror, An Ancient Analysis, Shu Shu Jiu Zhang, Si Jian, Yang Hui Algorithm and so on.
Sparse demodulation day method and searching technology
The method of adjusting the sun is a mathematical method by which ancient astronomers in China approximate basic astronomical data by fractions, but "since the Yuan and Ming Dynasties, people have not known the ancient meaning, and they are competing with heaven to know what they say." Li Rui is reading Song Shu? When I was studying Fahuazhi, I noticed the significance of "He Chengtian took 26% as the strong rate and 9/ 17 as the weak rate in Song Dynasty, and the strong and weak sought the Japanese method" relayed by Zhou Qiong. He explained that he took 26/49 and 19/ 17 as the upper and lower limits. The odd zero part of Shuowangyue is expressed as (26×15+9×1)/(49×15+17×1) = 399/752, that is, the weighted average of the strength ratio is selected to approximate the observation. The numerator in the above score is called Yu Shuo, and the denominator is called Japanese law.
Taking this opportunity, Li Rui investigated 5 1 ancient calendars, trying to express the binary values of the new moon given by the Japanese method and each calendar as the above-mentioned weighted addition form, and speculated whether they came from the Japanese method. This book has made the Japanese adjustment method, an ancient fractional approximation method, re-valued, and it is called "a masterpiece that will be handed down from generation to generation, not just a wing of Qin Shu."
However, from the point of view of modern mathematics, any score between two reduced scores can be expressed as their weighted addition form, so it is not rigorous to judge that the data of ancient calendars came from Japanese adjustment method. Moreover, due to the limitation of precision and the complexity of operation, it is impossible for ancient calendar makers to determine their own daily method and new balance by this method of product, multiplication and product. Li Rui felt the latter difficulty, and he created a method of "seeking strength (number) by Japanese method". Its purpose is still to express the ratio of Yu Shuo to Japanese method as the weighted sum of 26/49 and 917. If A stands for Japanese method, and X and Y stand for strong numbers and weak numbers respectively, Li Rui's problem is equivalent to solving binary linear indefinite equation: 47x+17y = A. His skill provides a simple algorithm to find one by skill, thus communicating the relationship between binary linear indefinite equation and congruence group for the first time in the history of Chinese mathematics.
Learning algebraic equation theory
Li Rui's interest in algebraic equation theory stems from the arrangement and research of the works of the last mathematicians such as Qin and others, but its direct cause is Wang Lai's discussion on whether all kinds of equations have only one positive root in the fifth volume of Hengzhai Arithmetic. In his postscript to Wang Lai, he summarized the 96 "knowing or not knowing" obtained by Wang Lai into three criteria, in which the first one is equivalent to saying that the equation of coefficient sequence sign change has only one positive root, and the third one is equivalent to saying that the equation of coefficient sequence sign change will not have only one positive root; They are very similar to two propositions put forward by Italian mathematician Cardan in16th century.
In Prescription Science, Li Rui gave a more general statement: "Where negative, positive, can open a number", "negative, positive, negative, can open two numbers", "negative, negative, negative, can open three numbers or one number", "negative, negative, negative, positive. By extension, he means that the number of positive roots of a (real coefficient) numerical equation is equal to or less than the number of changes in its coefficient symbol sequence (the accurate statement should be "one even number less"). This understanding is similar to the symbolic rule of judging the number of positive roots of equations proposed by Descartes, a French mathematician, in 1637.
In addition to judging the number of positive roots of equations, there are many other important achievements in open root theory. For example, Li Rui first introduced the concepts of negative roots and multiple roots; He also called the non-positive solution of the equation "countless", and claimed that "there must be two for every infinite, and there is no infinite", which vaguely contained the idea that the imaginary root * * * appeared. Li Rui also discussed the discriminant conditions of quadratic equations and biquadratic equations without real roots in the integer range, and created a "replacement method" to find the first place first, and then find the rest digits and roots from the deformation equation. Various equation deformation methods included in the final element calculation book, such as double root deformation, root shrinkage deformation, root shrinkage deformation and negative root deformation, are explained and improved one by one.
All these contents indicate that Li Rui's work in the field of equation theory broke through the pattern of China's classical algebra and became a remarkable theoretical achievement in the history of mathematics in Qing Dynasty.