March: Li Zicheng invaded the capital, Emperor Chongzhen hanged himself in the Ming Dynasty, and the Ming Dynasty perished.

April: The Qing army, led by Wu Sangui, marched into Shanhaiguan and defeated the peasant army in Li Zicheng.

May: Wang Mingfu Zhu Yousong ascended the throne in Nanking, and was renamed as "Hong Guang". Nanming begins.

September: Qing Dynasty moved the capital.

1645 (the second year of Qing Shunzhi, the first year of Hong Guang in Nanming, and the first year of Longwu in Nanming)

1 month: The Qing army captured Xi 'an, and Li Zicheng fled to Huguang in the south.

May: The Qing army captured Nanjing and soon captured Zhu Yousong.

June: The Qing court successively issued "Shaving Order" and "Dressing Order". The king of Lu, Zhu Yi, and the governor of Shaoxing. Zhu, king of the Tang Dynasty, proclaimed himself emperor in Fuzhou and established the Yuan Dynasty of "Long Wu".

June-August: People in Jiangyin, Jiading and other places held anti-Qing uprisings, all of which were massacred by the Qing army, known in history as "Jiangyin August 1st" and "Jiading Three Slaughters".

1646 (three years of Qing Shunzhi and two years of Nanming Longwu)

June: The Qing army captured Zhejiang and destroyed the king of Lu.

August: The Qing army captured Fujian, and Emperor Zhu of Nanming was killed.

October: Zhu Youlang, Wang Gui, Zhaoqing supervisor, soon proclaimed himself emperor and changed to "Li Yong".

December: The Qing army captured Sichuan, and the queen mother Zhang was killed in Fenghuang Mountain. The Qing army captured Guangzhou and killed Zhu Yuyu, the emperor of Shaowu. 1648 (five years of Qing Shunzhi and two years of Li Yong in Nanming)

Hao, He Tengjiao, Qu Shizhen and others led the troops to defeat the Qing army in Yuezhou and Quanzhou, and recovered Hengyang and Changsha. At this time, the peasant armies in Guangdong and Sichuan also rose to respond. Ming generals who surrendered to the Qing Dynasty, such as Jin Shenghuan in Jiangxi and Li Chengdong in Guangdong, betrayed the Qing Dynasty.

Behind the Qing army, Yuyuan Army, Luliangshan Rebel Army and Guanzhong Peasant Army all launched a large-scale offensive. The Hui people who participated in the peasant uprising also held an anti-Qing uprising under the leadership of Milla and Guodong Ding. The first anti-Qing climax occurred in Nanming. 1649 (six years of Qing Shunzhi and three years of Li Yong in Nanming)

January: The Qing army captured Hunan, and He Tengjiao was killed in Xiangtan.

1650 (seven years of Shunzhi in Qing Dynasty and four years of Li Yong in Nanming Dynasty)

, Hao, and others formed the "Quidditch Thirteen Schools" to fight against the Qing Dynasty.

1 1 month: the Qing army captured Guangzhou again and massacred it.

The Qing army occupied Guilin and Qu Shizhen was killed.

1652 (nine years of Shunzhi in Qing Dynasty and six years of Li Yong in Nanming Dynasty)

Li Dingguo led the army out of Guangxi in the east, down to Guilin, counterattacked Hunan and entered Guangdong in the south. Ni Kan, king of Qing Dynasty, was killed, and Kong Youde, king of South China, set himself on fire. Liu Wenxiu sent troops to Sichuan, defeated Wu Sangui, recovered counties in southern Sichuan, and got in touch with the 13th Army of Kuidong. At this time, the anti-Qing team led by Zhang Huangyan and Zhang Mingzhen, who lived in the southeast coast, also began to fight back and accepted the title of Emperor Li Yong, forming the second anti-Qing climax.

In winter, Emperor Li Yong of Nanming moved his capital to Anlong, Guizhou with the help of Sun Kewang.

1654 (eleven years of Qing Shunzhi and eight years of Li Yong in Nanming)

March: Sun Kewang wrote "The Prison of an Eighteen-year-old", and the relationship between Li Dingguo and Sun Kewang deteriorated.

1656 (thirteen years of Shunzhi in Qing Dynasty and ten years of Li Yong in Nanming Dynasty)

Sun Kewang attacked Li Dingguo on a large scale, and when it failed, it fell.

1659 (sixteen years of Shunzhi in Qing Dynasty and thirteen years of Li Yong in Nanming Dynasty)

1 month: Wu Sangui led the Qing army to capture Yunnan, and Li Yong Emperor Zhu Youlang went into exile in Myanmar.

Li Dingguo was defeated by Wu Sangui at Mopanshan.

July: Zheng Chenggong and Zhang Huangyan's Northern Expedition pushed Nanking and were defeated by the Qing army.

166 1 year (18th year of Qing Shunzhi, 15th year of Li Yong in Nanming)

August: The Qing army invaded Myanmar and Zhu Youlang was captured.

1February: Zheng successfully recovered Taiwan Province province.

1662 (in the first year of Kangxi in Qing dynasty, in the sixteenth year of Li Yong in Nanming dynasty)

Li Yong Zhu Youlang was killed in Kunming, and Li Dingguo and Zheng Chenggong died one after another. Nan Ming's regime in Chinese mainland ended. 1664 (three years of Kangxi in Qing dynasty and eighteen years of Li Yong in Nanming dynasty)

13 "Kuidong School" was conquered by the Qing army.

The Qing army occupied Zhoushan and other coastal islands, and Zhang Huangyan was killed.

1674 (13th year of Kangxi in Qing Dynasty and 28th year of Li Yong in Nanming Dynasty)

Taiwan Province Province and Zheng Jing launched a large-scale attack on Fujian, which was repelled by the Qing army.

1683 (twenty-two years of Kangxi in Qing dynasty and thirty-seven years of Li Yong in Nanming dynasty), the Qing army captured Taiwan province, and Nanming forces fell. The Qing Dynasty completely established its rule in China.

political system

17th century, the biggest thing that changed the world was 1640, when the bourgeois revolution broke out in Britain. The British bourgeois revolution was a social revolution from 1640, when Charles I convened a new parliament, to 1688, when James II abdicated. The feudal rule was overthrown and the British capitalist system was established, represented by the new noble class. Therefore, 1640 was determined as the beginning of modern world history. World history has taken a turning point. Since then, the social system of the whole world has undergone fundamental changes, and capitalism will eventually replace feudalism.

1644 it is a great event to enter the customs in Manchu dynasty. What changed China? It is a change that the Han emperor changed to the Qing emperor, which is a minority regime with Manchu as the main body. Ethnic minorities have played an active role in promoting the development of the Chinese nation. The Chinese nation is a big multi-ethnic family. However, the emperor has changed and the emperor is still the emperor. Contradictions within the feudal society were concealed and alleviated, and the feudal system lasted for more than 200 years in China (capitalism sprouted in China in the late Ming Dynasty). Moreover, the later Manchu regime was more corrupt and humiliated by foreign imperialist powers, which left the Chinese nation in dire straits.

Mathematics and technology

abstract

16 and 17 centuries in Europe, the long middle ages have ended, the Renaissance brought people's awakening, and the complicated philosophical and theological dogmatic authority that bound people's free development of thought was gradually destroyed. Feudal society began to disintegrate, replaced by capitalist society, and the productive forces were greatly liberated. The prosperity of handicraft industry in capitalist workshops and the transition to machine production have promoted the rapid development of technical science and mathematics.

For example, in navigation, in order to determine the position of ships, more accurate astronomical observations are needed. In the military field, ballistics has become the central topic of research. The manufacture of accurate timers, the excavation of canals, the construction of dams, the theory of planetary elliptical orbits, and so on. , also need a lot of complicated calculations. Elementary mathematics since ancient Greece has gradually failed to meet the needs at that time.

astronomy

In the history of science, many important events happened in this period, which put forward new topics for mathematics. First of all, Copernicus put forward the theory of earth motion, which fundamentally shook the geocentric theory, an important theoretical pillar of theology. His disciple Rhaticus saw that the astronomical observation at that time was becoming more and more precise, and it was urgent to calculate the detailed trigonometric function table, so he began to make sine, tangent and secant tables every 10. " At that time, Rhaticus and his assistant worked hard for 65,438+02 years until his disciple Otto died.

/kloc-In the second half of the 6th century, Danish astronomer Tycho made a lot of accurate astronomical observations. On this basis, the German astronomer Kepler summed up the three laws of planetary motion, which led Newton to discover gravity. Kepler's "New Solid Geometry of Wooden Buckets" regards wooden barrels as the accumulation of numerous circular slices, and calculates its volume from it. This is the precursor work of integral calculus.

Classical higher mathematics period

Galileo, an Italian scientist, advocated that natural science research must carry out systematic observation and experiments, and make full use of mathematical tools to explore the mysteries of nature. These viewpoints have great influence on the development of science (especially physics and mathematics). His student cavalieri founded the principle of indivisibility. Relying on this principle, he solved many problems that can only be solved by more rigorous integration methods now. The idea of "inseparability" sprouted in 1620 and was deeply influenced by Kepler and Galileo. This is the transition from the exhaustive method of eudoxus in Greece to Newton and Leibniz calculus. /kloc-Italy in the 6th century also made a series of achievements in the theory of algebraic equations. Tattaglia, cardano, Ferrari and Bombelli discovered and improved the general solutions of cubic and quartic equations successively, and used imaginary numbers for the first time. This is the greatest breakthrough in algebra since Diophantine in Greece. The French Vedas combined the achievements of predecessors, created a large number of algebraic symbols, expressed unknowns with letters, improved the calculation method and greatly changed algebra.

In digital calculation, Steven systematically expounded and used decimals, and then Napier created logarithms, which greatly accelerated the calculation speed. Later Pascal invented the adder and Leibniz invented the multiplier. Although it is not practical, it opens up a new way of mechanical calculation. /kloc-At the beginning of the 7th century, the main subjects of elementary mathematics (arithmetic, algebra, geometry and trigonometry) have basically taken shape, but the development of mathematics is in the ascendant, and it has entered the next stage of the history of mathematics at an accelerated pace. The difference between the variable mathematics period and the previous period (usually called the elementary mathematics period) is that the previous period mainly used static methods to study individual elements of the objective world, while this period explored them from the perspective of movement.

Variable mathematics began with the establishment of analytic geometry, followed by the rise of calculus. During this period, new fields such as probability theory and projective geometry also appeared one after another. But it seems to be overshadowed by the powerful brilliance of calculus. Analytics developed with a surging trend and reached an unprecedented brilliant level in the18th century. Its rich content and wide application make people dizzying.

Mathematics established in this period is roughly equivalent to the learning content of freshmen and sophomores in universities today. In order to distinguish it from elementary mathematics in middle schools, it is sometimes called classical advanced mathematics, and this period is correspondingly called classical advanced mathematics period.

geometry

The appearance of analytic geometry is generally marked by the publication of Descartes' Geometry. The content of this book is not only geometry, but also many algebraic problems. There is a big gap between it and the current analytic geometry textbook, and even the Cartesian coordinate system can't be seen. But what is valuable is that it introduced revolutionary ideas and made contributions to opening up a new garden of mathematics.

The main achievements of geometry can be summarized as three points: unifying the two opposing research objects "shape" and "number" in the past, introducing variables, and solving classical geometric problems by algebraic methods; Finally, the homogeneity restriction of the Greeks was abandoned; Improved algebraic symbols. The French mathematician Fermat also shared the honor of creating analytic geometry. His discovery may have preceded Descartes, but it was published very late. He is an amateur mathematician who has made great contributions to number theory, probability theory and optics. He grasped the essence of calculus and put forward the method of finding the minimum value of function. He established many number theory theorems, among which Fermat's last theorem is the most famous, but this is only a guess and has not been proved.

Interest in probability theory originated from the development of insurance, but it came from the requirements of gamblers, prompting mathematicians to think about some special probability problems. Fermat, Pascal and Huygens were the early founders of probability theory. After the research of Laplace and Poisson in 18 and 19 centuries, probability theory became a huge branch of mathematics with wide application.

While analyzing geometry, another great change has taken place in the field of geometry in17th century, that is, the establishment of projective geometry. The decisive progress is the work of Dezag and Pascal. The former introduces infinite point and infinite line, and discusses poles and lines, transmission and perspective. The "Dezag Theorem" he discovered is the basic theorem of all projective geometry. Pascal's conic curve theory published in 1640 is the greatest progress of conic curve theory since apollonius. However, mathematicians at that time were mostly devoted to analytical research, and projective geometry was not paid attention to, and it did not attract people's attention again until the end of 18.

The invention of calculus

17th century is a rich period of creation, and the most brilliant achievement is the invention of calculus. Its appearance is a great event in the whole history of mathematics and the whole history of mankind. It comes from the needs of production technology and theoretical science, and has a far-reaching impact on the development of production technology and natural science. Calculus for today's scientific and technological workers, has been like a piece of cloth, silk and millet, an instant inseparable.

Calculus is produced after a long period of brewing. The idea of integral has sprouted as early as Archimedes' time. At the turn of 16 and 17 centuries, Kepler, cavalieri, Fermat, Wallis and especially Barrow made a lot of preparations. As the center of differential calculus, the discussion of tangent problem is relatively late, so the starting point of differential calculus lags far behind that of integral calculus.

/kloc-famous mathematicians (mainly French) in the 0/7th century, such as Fermat, Descartes, Roberval, Dezag, etc., all participated in the debate on the tangent problem. Descartes and Fermat think that the tangent is the secant when two intersections coincide. Roberval, on the other hand, regards the tangent as describing the direction of this curve at this point from the point of view of motion, which is of practical significance in mechanics.

The greatest contribution of Newton and Leibniz is to connect two seemingly unrelated problems, one is tangent problem (the central problem of differential calculus) and the other is quadrature problem (the central problem of integral calculus), and build a bridge between them, which is expressed by the basic theorem of calculus or Newton-Leibniz formula. Newton wrote a page on1May 20, 665 (Gregorian calendar 3 1), and there was the earliest record of calculus, but his work was unknown for a long time. It was not until 1687 that it was recorded in the form of geometry in his famous book Mathematical Principles of Natural Philosophy. Newton established calculus mainly from the viewpoint of kinematics, while Leibniz considered it from the perspective of geometry. Especially, it is closely related to Barrow's "differential triangle".

Leibniz's first article on differential calculus was published in Yi Xue in 1684, and the first article on integral calculus was published in the same magazine in 1686. The symbols he created were far superior to Newton, so they were used by later generations. His theory was quickly inherited and carried forward by L'H?pital, Bernoulli family and Euler, and entered the harvest period in the18th century.

No major invention can be perfect from the beginning. /kloc-Calculus in the 0/7th century has serious logical difficulties and has been criticized in many aspects. It is based on limit theory, and the concept of limit of Newton and Leibniz is very vague. What is the limit and what is infinitesimal? This was a fundamental problem at that time. Nevertheless, the victory of calculus in practice is convincing enough. Most mathematicians put aside the logical foundation for a while and went forward to open up this new garden.

Characteristics of mathematical development

/kloc-the characteristics of mathematical development in the 0/7th century can be summarized as follows.

It has produced several new fields with great influence, such as analytic geometry, calculus, probability theory, projective geometry and so on. Every field dwarfs the achievements of the ancient Greeks.

The trend of algebra, the main body of Greek mathematics is geometry, and algebraic problems are often demonstrated by geometric methods. Algebra occupied a more important position than geometry in the17th century. It broke through the Greek box and was further transformed into symbolic algebra. Geometric problems are often solved in turn by algebraic methods.

A large number of new concepts, such as irrational number, imaginary number, instantaneous rate of change, derivative, integral, etc. , is not a direct reflection of empirical facts, but by the further abstraction of mathematical theory.

Mathematics is more closely related to other natural sciences. The rise of experimental science (from Galileo) promoted the development of mathematics, and the achievements of mathematics penetrated into other scientific departments. Many mathematicians, such as Newton, Leibniz, Descartes and Fermat, are themselves astronomers, physicists or philosophers.

Mathematical knowledge has been widely exchanged and disseminated, and only a few people were studying mathematics in Greek times. Until16th century, the situation did not change much. /kloc-in the 0/7th century, researchers increased greatly, academic groups (societies or colleges) were established one after another, the printing industry flourished, and mathematical knowledge was widely popularized and applied.

Generally speaking,17th century is the initial stage of many emerging disciplines,18th century is the stage of rich development, and19th century is the stage of reviewing, upgrading and reforming, entering the next century with a brand-new attitude.