China entered the late feudal society from the Ming Dynasty. The feudal rulers practiced totalitarian rule, propagated idealistic philosophy and practiced stereotyped examination system. In this case, in addition to abacus, the development of mathematics gradually declined.
After 16, western elementary mathematics was introduced into China, which led to the integration of Chinese and western mathematics research in China. After the Opium War, modern mathematics began to be introduced into China, and China's mathematics turned into a period of mainly learning western mathematics; It was not until the end of 19 and the beginning of the 20th century that the study of modern mathematics really began.
From the early Ming Dynasty to the middle Ming Dynasty, the development of commodity economy and the popularization of abacus were adapted to this commercial development. In the early Ming Dynasty, the appearance of Kuibn Du Xiang's four-character miscellaneous son and Luban Mu Jing showed that abacus had become very popular. The former is a textbook for children to read pictures, and the latter is to include abacus as a family necessity in the manual of general wooden furniture.
With the popularization of abacus calculation, the abacus calculation algorithm and formula are gradually improving. For example, Wang Wensu and Cheng Dawei increased and improved collisions and made formulas; Xu Xinlu and Cheng Dawei add and subtract formulas and are widely used in division, thus realizing all the formulas of four abacus calculations; Zhu Zaiwen and Cheng Dawei applied the method of calculating square root and square root to abacus calculation, and Cheng Dawei used abacus calculation to solve quadratic and cubic equations. Cheng Dawei's works are widely circulated at home and abroad and have great influence.
1582, Italian missionary Matteo Ricci went to China. 1607, he translated the first six volumes of Geometry Elements and one volume of Measuring the Meaning of Law with Xu Guangqi, and compiled Yi Rong's Pen Meaning with Li Zhizao. 1629, Xu Guangqi was appointed by the Ministry of rites to supervise the revision of the calendar. Under his auspices, he compiled the almanac of Chongzhen (137). The almanac of Chongzhen mainly introduces the geocentric theory of European astronomer Tycho. As the mathematical basis of this theory, it also introduces Greek geometry, some trigonometry of Yushan in Europe, Napier's calculation, Galileo's scale specification and other calculation tools.
Among the introduced mathematics, geometric elements have the greatest influence. The Elements of Geometry is China's first mathematical translation. Most mathematical terms are the first, and many are still in use today. Xu Guangqi thinks there is no need to doubt it and change it, and thinks that "there is no one in the world who can't learn well". The Elements of Geometry is a must-read for mathematicians in Ming and Qing Dynasties, which has a great influence on their research work.
Secondly, trigonometry is the most widely used, and the works introducing western trigonometry include Great Survey, Table of Secant Circle and Eight Lines, and Significance of Measurement. The survey mainly explains the properties, tabulation methods and table usage methods of the eight lines of triangle (sine, cosine, tangent, cotangent, secant, cotangent, orthovector and cotangent). In addition to adding some plane triangles that are missing in the big survey, the more important ones are the product sum and difference formula and spherical triangle. All these were used together with translation in the calendar work at that time.
1646, Polish missionary Monig came to China, and his followers were Xue Fengzuo and Fang Zhongtong. After Mounigo's death, Zuo compiled the General Theory of Calendar Societies based on what he had learned, so as to integrate China, France and western France. The mathematical contents in Sydney Huitong mainly include proportional logarithm table, new proportional four-line table and trigonometric algorithm. The first two books introduced the logarithm invented and modified by British mathematicians Napier and Briggs. In addition to the spherical triangle introduced by Chongzhen almanac, the latter book also includes half-angle formula, half-arc formula, German proportional formula, Nestor proportional formula and so on. Fang Zhongtong's "Several Words" explains the logarithmic theory. The introduction of logarithm is very important and is immediately applied in calendar calculation.
There are many books handed down from generation to generation by beginners in the Qing Dynasty by studying Chinese and Western mathematics. Among them, Wang Xichan's Illustration, Mei's Collected Works (including 13 kinds of mathematical works ***40 volumes) and Visual Research have great influence. Mei Wending is a master of western mathematics. He sorted out and studied the solution of linear equations, Pythagorean solution and the method of finding positive roots of higher powers in traditional mathematics, which brought vitality to the dying mathematics of Ming Dynasty. Xirao Nian's Vision is the first book in China to introduce the western perspective.
Emperor Kangxi of Qing Dynasty attached great importance to western science. Besides studying astronomy and mathematics by himself, he also trained some talents and translated some works. 17 12, Emperor Kangxi appointed Mei Li as the assembler of Ren Meng Yangzhai, and worked with Chen Houyao, He Guozong, Ming Jiatu and Yang Daosheng to compile astronomical algorithm books. 172 1 year, fayuanli was completed in volume 100, and published in the name of Kangxi "Yu Ding" on 1723. Among them, Mei Gaocheng is mainly responsible for the essence of mathematics, which is divided into two parts. The first part includes geometrical features and algorithm elements, which are all translated from French works. The second part includes elementary mathematics such as arithmetic, algebra, plane geometry, plane triangle and solid geometry, including prime number table, logarithm table and trigonometric function table. Because it is a comprehensive encyclopedia of elementary mathematics, and it is known as "King James" by Kangxi, it has certain influence on the mathematical research at that time.
To sum up, we can see that mathematicians in the Qing Dynasty did a lot of work on western mathematics and achieved many original results. These achievements, if compared with traditional mathematics, are progressive, but compared with contemporary western countries, they are obviously backward.
After Yongzheng acceded to the throne, he closed his door to the outside world, which led to the cessation of importing western science into China and the implementation of a high-handed policy at home. As a result, ordinary scholars can't get in touch with western mathematics and dare not ask themselves what they have learned, so they bury themselves in studying ancient books. During the reign of Ganjia, the Ganjia school, which mainly focused on textual research, gradually formed.
With the collection and annotation of Ten Books of Calculating Classics and mathematics works in Song and Yuan Dynasties, there appeared a climax of learning traditional mathematics. Among them, Wang Lai, Li Rui and Li. Can break the old rules and have inventions. Compared with Song and Yuan Algebra, their work is better than Chen Wenzhao's. Compared with western algebra, it is a little late, but these achievements were obtained independently without being influenced by modern western mathematics.
At the same time that the research of traditional mathematics reached its climax, Ruan Yuan and Li Rui compiled The Biography of Astronomical Mathematicians-Biography of People in the Domain, which collected more than 270 astronomers and mathematicians who died from the Yellow Emperor to Jiaqing four years ago (among them, less than 50 were handed down from generation to generation), and 4 1 person of missionaries who introduced western astronomical mathematics since the late Ming Dynasty. This book is composed of "collecting history books, collecting group records and recording them", which is completely first-hand original information and has great influence in academic circles.
1840 after the opium war, modern western mathematics began to be introduced into China. First of all, the British set up the Mohai Library in Shanghai and introduced western mathematics. After the Second Opium War, Zeng Guofan, Li Hongzhang and other bureaucratic groups launched the "Westernization Movement", also advocated the introduction and study of western mathematics, and organized the translation of a number of modern mathematics works.
The most important one is Algebra translated by Li and Li. Algebra, Trace of Differential Product and Suspicious Mathematics translated by John Flair, a Briton; Zou He edited Metaphysics, Algebra and Mathematical Writing; Xie Hongtai and Pan He translated Dai Shen and Eight Acts.
A Generation of Differential Calculus is China's first translation of calculus. Algebra is a translation of Symbolic Algebra written by British mathematician Augustus de Morgan. Doubtful mathematics is the first translation of probability theory. In these translations, many mathematical terms and terms have been created, which are still used today, but the mathematical symbols used have generally been eliminated. After the Reform Movement of 1898, new law schools were established in various places, and these works became the main textbooks.
While translating western mathematics works, Chinese scholars have also done some research and written some works, the most important of which are Li's "The Solution of Sharp Cone Reform" and "The Solution of Several Roots". Xia Wanxiang's Picture Book of Cave, Music Induction Techniques, Music Induction Picture Book, etc. , are the research results that will connect Chinese and western academic thoughts.
Because the imported modern mathematics needs a process of digestion and absorption, and the rulers in the late Qing Dynasty are very corrupt, overwhelmed by the impact of the Taiping Heavenly Kingdom Movement and plundered by imperialist powers, they have no time to take care of mathematical research. It was not until the May 4th Movement of 19 19 that the study of modern mathematics in China really began.