The tradition of Song and Yuan Mathematics Research was interrupted in the Ming Dynasty，But after Qianjia in the Qing Dynasty, it became a research hotspot in the academic community，Its achievements have。This process also reflects from Western missionaries in the late Ming Dynasty to come to China to descend，Under the historical context of the direct collision of the east -west civilization，The important side of Chinese and Western mathematics and cultural exchanges and mutual learning。

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On the occasion of the Ming and Qing Dynasties，Western astronomy、Mathematics passed the "Chongzhen Calendar" (and its subsequent reorganized "Western New Law Books" and "New Law Calculation Book"、Kangxi's "Yuding" "Mathematical Essence" and "Cultivation Elephant Test" and other large -scale works compiled，Get the orthodox status of the court。At that time, it coincided with European Renaissance，Research on the related research of classical humanities and scientific works is full of wind。Western missionaries Yinli，Except the introduction of Ptolemy、The geometric universe models such as the Valley are used to calculate beyond the astronomical calendar，It also translated the first six volumes of ancient Greek mathematics such as "Geometry Original" in Chinese。Therefore, Western mathematics introduced by the missionary is based on geometry，This mathematical branch is characterized by axiom，Start from a few "unbelievable" axioms，Derivation of a series of propositions，Form a complete knowledge system。

Compared with the long history of geometry，The algebra is learned by Europeans from Arabs，Time is not long，Introduced to China during the Kangxi period，Income "Mathematical Essence"，Known as "Borrowing the Root"。that is, the number of fakes、Symptoms，equivalent to the unknown X and X multiplication。Bet365 lotto review According to Han Qi's research，Emperor Kangxi no longer fully trust the missionaries，Promote the spirit of "independence"，Efforts to get rid of the latter's control of the calendar。Mei Yancheng，"The first school of the Qing Dynasty" Mei Wending's grandson，First explain the western name "Alzada" (that is, the transliteration of Algebra) of "Borrowing Fang" from the source of the word source as "Donglai"，It was the "Litian Yuanyi" method of the Song and Yuan Dynasties that spread to the Western Regions again.。

　　Qianjia Scholars' excavation of Song and Yuan Mathematics Classics

Now we know，Algebra originated from Arabic al-jabr，Meaning to restore，is the unknown number in the restore equation。Therefore, Mei Yicheng's word source explanation is a misunderstanding，He is just based on the "Litian Yuanyi" based on the Ming people occasionally mentioned，It is speculated from the overall nature that this is a algebraic method similar to "borrowing the root"。"Borrowing the Root Fang" is affected by "Litian Yuanyi"，Must be widely inspected、Compared with related Chinese and foreign language mathematics historical materials，It can still be proved to be clear.，But whether it is proved or fake，At that time, scholars must first solve the basic problem of obtaining readable and credible Chinese mathematics historical materials。Because of the silence of the Ming Dynasty，The learning of Tianfu has become "unique learning"，"Litian Yuanyi" method is specifically as an algorithm，No one knows at the time。The turning point of solving the problem lies in the compilation of "Siku Quanshu"，Four Kuka Museums edited Li Ye's "Testing Round Sea Mirror" and "Yigu Performance Section" from the "Yongle Ceremony"，confirmed that "Litian Yuanyi" is indeed a algorithm to build a one -dollar high -oriented equation -Tianyuan Square。Four Kuka Museums also edited Qin Jiushao's "Nine Chapter Nine" (also known as "Mathematics Nine Chapter"，The following referred to as "Qin Shu")，and "the mistake of the mistake，Different from those who sparse，Order of the Turner，bet365 live casino games Each additional case is below "，Preliminary collation。

other，Qianjia scholar far away from Jiangnan，You can also copy Li from Siku Pavilion、Qin Cuju and compare it for research，Get a deeper conclusion。Former examiner Qian Daxin keenly pointed out in "The Nine Chapters of Qin Jiu Shao Mathematics",，It is not the same as Li Ye's "Testing the Sea Mirror".。Later, there are famous classical surveyers、Catalogist Gu Guangzheng for the reciprocating calculation of Yangzhou book writer Qin En、Correct the "Nine Chapter" of Zhao Qimei's copy of Zhao Qimei，Prepare publishing and publish。Gu's found "The question is not corresponding to the grass"，And thinks that Qin Jiushao "Dross -Derrying Non -Tianyuan One Method，Unable to have a word of Litian Yuan，Then Guo Shoujing and Li Ye's so -called Tianyuan One "，Correctly pointed out that although Qin Shu's Da Dan is also "Litian Yuanyi"，but not the Tianyuan technique in Li Ye's book。

Although Gu Guangzheng corrected Qin Shu，But I don’t know how to publish it in the end。but but，"Nine Chapters of Digital Books" published the only engraved copy in 1842 (see Figure 1) to date (see Figure 1)，Its publishing process shows the efforts made by Qianjia's scholars, apprentices, friends, friends and friends。Shanghai Giant Fu Yu Songnian once made a preface after publishing two types of "Yijiantang Series"，"The Secret of the Song and Yuan people in Yisi"，I heard "" Nine Books Nine Chapter "Thinking of Practical Expo，Dan Yanqiu、Positive and negative Kai Fang two techniques，Especially the secrets that have not been spread since ancient times "，But the publishing and publishing still have to face the old problem that corrects the wrong leak。Fortunately, Li Rui has surveyed the four libraries before，Shen Qinpei has surveyed Zhao Qimei of Zhang Dunren's family，Therefore, Disciple Shen Qin Pei Song Jingchang was able to be in Shen、For further collation。Now we see the Book of Books "Nine Chapters of Digital Books" attached with Song Jingchang's "Notes"，It is an indispensable and important part of the book，In fact, Shen bet365 Play online games Qinpei、Li Rui and Song Jingchang and other calculators' collation results。

Except Qin Shu，"Yi Jiatang Series" also included six types of books by Yang Hui, another mathematician of the Southern Song Dynasty，Also with notes。Yang Huishu's four storage is not collected，Ruan Yuan has been invited for 30 years without getting it，Only by chance, I can see in the "Yongle Ceremony".，Records about a hundred books; Later, Tibetan book writer Huang Yilie got Yang Shu San Ye，After being neatly compared with Li Rui，Only the book is six volumes。Zhu Shijie's "Four Yuan Jade Jian" was also visited when Ruan Yuan was visited in Zhejiang; "The Enlightenment of Calculation" is the Korean engraved book from the book of his disciple Luo Billin's book.。

Qin Jiu Shao、Li Ye、Mathematics books written by Yang Hui, Zhu Shijie and others，See the day after hundreds of years of silence，Should be attributed to the excavation of Qianjia scholars、Sorting and research。In addition to the tradition of the Qianjia School attaches importance to classical literature,，Han Qi thinks，Western mathematics, especially the introduction of "borrowing root"，Both Qianjia scholars provide knowledge preparation，At the same time, it also stimulated the revival of Song and Yuan Mathematics due to the advocacy of the spirit of "independence"。Indeed，Qianjia scholars' research results of these Song and Yuan mathematics books，shows a unique and ahead of the contemporary modern algebra science knowledge system。These mathematics (history) knowledge，It has also become an important material for the next stage of Western and Western mathematics in the West。

　　The exchange and mutual learning of mathematics culture in the 19th century

In the Kangxi era of "By Dedicated" to China，Western European mathematics has been made through revolutionary breakthroughs。The geometric tradition originated from ancient Greece and the algebra science tradition from Eastern India and Arabs collisted in Europe，Analysis geometry of the length of the two、Mathematical branches and other mathematical branches have been developed one after another，Become one of the important foundations of the modern scientific bet365 Play online games revolution。Because of this series of mathematics achievements，Europeans in the 19th century are quite arrogant，Even India -Arabic Digital and Dontoral Number Method has become a sign of "modern"。John F. Davis, who was once the Governor of Hong Kong, criticized "the number of Chinese is written for a long time，Unlike the Arab digital system，The secondary power of the number increases or decreases according to the digital ten times ten times "。This is because he only read the ordinary Chinese ancient book，without seeing traditional arithmetic books，I don't know how to digital digital from the calculation of digital evolution -Suzhou code -like in the same way as India -Arabic digital。

Five ex -business business with the Opium War，Alexander Wylie, a British sinologist who came to China in the 1950s, learned from Chinese scholars and cooperated with them to translate foreign mathematics works，I realize that predecessors have deep misunderstandings about Chinese mathematics。So he wrote a long paper "Chinese Science A Brief Recruitment" in English，Correct。This article was divided into 9 stages in the "The North-China HERALD" in 1852: (1) Introduction、Mathematics's fate in China、Anti -book 7th century; (2) the abbot from the 7th century to the 14th century; (3) digital and basic arithmetic operations、"Chapter Nine Arccibles" (Part 1); (4) "Chapter Nine Equalization" (below); (5) Qin Jiu Shao Dermia (Part 1);、Kai Fangshu; (8) Four Yuan Shu、Borrowing the root square、Ancient calculations in the early 19th century; (9) Chinese mathematics research at that time、Conclusion。Where，(5) to (8) Phase II is the Song and Yuan Mathematics part，The full text of nearly half of the text。Through Chinese and Western comparison，Weilie Yali discovered Qin Jiushao's Kai Fangshu (see Figure 2)，Weilie Yali discovered Qin Jiushao's Kai Fangshu (see Figure 2)，Think that "Qin is the first person we found to develop a complex equation"。This insight，Together with the important mathematics classics in ancient China、Mathematicians and their Bet365 lotto review contributions，and the development of mathematics at that time，Introduction to the Western World together。This article has a great response，It is soon translated into method、Devinia and other words are widely spread in the European academic community。

Weilie Yali is interested in the topic of comparative learning of Chinese and Western mathematics，Except for Chinese scholars at that time, they took the Song and Yuan Mathematics as an atmosphere，It is also influenced by the British "Cambridge Bridge Big Mathematics School"。The school appeared in the first half of the 19th century，It aims to introduce Leibniz’s calculus symbols into Cambridge University，Create a new counters independent of geometry。Representative characters are the first generation of Charles Babbage、George Peacock and the second generation of Augustus de Morgan。The history of writing mathematics is one of the unique academic practice of this school，Especially the two people in Piccuck and Demonmo。French scholar Duranda Richard (Marie-José Durand-Richard) had in-depth research on Piccock，It is pointed out that the latter wrote the "ArithMetic" in the "Encyclopopaedia Metropolitana" (Encyclopaedia Metropolitana "，Detailed description of the arithmetic of various ethnic groups in the world，and use this as the claim of its school -generation mathematics is a more universal and fundamental science，instead of being a ingenious method of dealing with the problem -the main argument。Demorgan is the "Penny Cyclopaedia" edited by the Society for the Diffusion of Useful Knowledge，I wrote about 850 astronomy and mathematics entries，Many of them also involve the history of mathematics，Weilie Yali mostly quotes in "Strategy"。

other，Weilie Yali believes that ancient Chinese arithmetic and its genetic mathematics derived from it is a science，Demonstrate Chinese traditional mathematics, especially arithmetic — the wisdom and achievements in the counters，can guide the Chinese to learn further。So，He later translated Element of Algebra with Li Shanlan.。Since then，bet365 Play online games Algebra, derived from Arabic, was translated as "algebra"。From this，We can see an interesting mathematical knowledge circulation: the western generation mathematics "borrowing the root" in the Ming and Qing Dynasties stimulated Qianjia scholars' excavation of the Song and Yuan Mathematics books，Then compares Western scholars such as Weilie Yali、Exchange and mutual learning provides possible，At the same time, it promoted deeper algenery、Introduction to the latest mathematical branches such as calculus。

　　(Author is an associate professor at the Institute of Science and Technology History, Inner Mongolia Normal University)