China entered the late feudal society from the Ming Dynasty, and after the end of 16, western elementary mathematics was introduced to China one after another, which made China's mathematical research present a situation of combining Chinese and western; 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". After Manchu invaded the Central Plains, science was once again put into the "cold palace". Not only has the second half of the book been delayed in translation, but even the first half of Xu Guangqi's translation is no longer published. The scientific and technological works brought by western missionaries became the exclusive hobby of Emperor Kangxi, Yongzheng or Qianlong. 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 methods of solving linear equations, pythagorean solutions and finding the positive roots of higher powers in traditional mathematics. Xirao Nian's Vision is the first work in China that introduces the western perspective. Emperor Kangxi of Qing Dynasty attached importance to western learning, but only as his own hobby. 17 12, Kangxi appointed Mei Li as the compiler of Ren Meng Yangzhai, and compiled astronomical algorithm books together with Chen Houyao, He Guozong, Ming Jiatu and Yang Daosheng. 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.