Great flood era(Polish: Potop) YesPolish-Lithuanian commonwealth A historical era, including a series of battles.Broadly speaking, in this eraKhmelnitskyThe uprising began and ended with the Andrew Sawyer Truce in 1667Russian Polish WarAnd the second Northern WarpolandThe stage is also in this period.In a narrow sense, the era of great flood refers toSwedish EmpireThis stage of invasion and occupation of the Union only includes the Union stage (1655-1660) in the Second Northern War, which is also called“SwedenBig flood era "(Lithuanian:Švedų tvanas,Polish:Potop Szwedzki)。
Poles in the Great Flood Era
The Federation lost about one-third of its population and its status as a great power in the war.
Major events
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In 1601, Matteo Ricci was allowed to enter Beijing and preach. Since then, he has accepted the salary of the imperial court. He, together with Xu Guangqi, Li Zhizao and other senior officials of the Ming Dynasty, stirred up a wave of cultural and technological exchanges between China and foreign countries.
Ming Dynasty in 1616Jianzhou WeiLocal officer Nurhachi defectedDamingCutting soil to stand on its own, it established the Later Jin Dynasty and later renamed it Qing Dynasty.
September: The Qing Dynasty moved its capital to Beijing.
1645 (the second year of Shunzhi in the Qing Dynasty, the first year of Hongguang in the Nanming Dynasty, the Nanming DynastyLongwuFirst year)
January: The Qing army captured Xi'an, and Li Zicheng fled south to Huguang.
April: The Qing army attacked Yangzhou,Historical methodkilled.The Qing soldiers slaughtered Yangzhou, which is known in history“Yangzhou 10th”。Li Zicheng died at Jiugong Mountain.
May: The Qing army captured Nanjing, and soon captured Zhu Yousong.
June: The Qing government successively issued“Shaving order”And“Yifu Order”。King LuZhu Yihai supervised the country in Shaoxing.Tang WangZhu YujianIn Fuzhou, he became the emperor and built the Yuan Dynasty "Longwu".
June August:JiangyinPeople in Jiading, Jiading and other places were massacred by the Qing army during the uprising against the Qing Dynasty“Jiangyin 81st”And“Jiading Three Slaughters”。
1646 (the third year of Shunzhi in the Qing Dynasty, the second year of Longwu in the Southern Ming Dynasty)
December: The Qing army captured Sichuan, the King of the WestZhang XianzhongstayPhoenix MountainKilled.The Qing army captured Guangzhou and killed Emperor ShaowuZhu Yuqi。
1648 (the fifth year of Shunzhi in the Qing Dynasty, the second year of Yongli in the Southern Ming Dynasty)
Hao Huanqi、Li GuoAndHe Tengjiao、Qu ShisiThe Qing army defeated the Qing army in Yuezhou and Quanzhou, and recovered Hengyang, Changsha and other places.At this time, the peasant armies in Guangdong, Sichuan and other places also responded.Ming generals who had surrendered to the Qing Dynasty, such as JiangxiJin ShenghuanAnd GuangdongLi ChengdongThey betrayed the Qing Dynasty.
In the rear of the Qing army, the Yuyuan army, the Luliang mountainInsurgent armyandGuanzhongThe peasant army launched a broad offensive, and the Hui people in Shaanxi and Gansu who had participated in the peasant uprising were also inMira India、Ding GuodongAn anti Qing uprising was held under the leadership of the Communist Party of China.The first anti Qing climax appeared in Nanming.
1649 (the sixth year of Shunzhi in the Qing Dynasty and the third year of Yongli in the Southern Ming Dynasty)
January: He Tengjiao was killed in Xiangtan when the Qing army captured Hunan.
1650 (the seventh year of Shunzhi in the Qing Dynasty and the fourth year of Yongli in the Southern Ming Dynasty)
November: The Qing army once again captured Guangzhou and massacred it.
The Qing army occupied Guilin, and Qu Shisi was killed in Guilin.
1652 (the ninth year of Shunzhi in the Qing Dynasty and the sixth year of Yongli in the Southern Ming Dynasty)
Li DingguoHe led the army east out of Guangxi, down to Guilin, counterattacked Hunan, and south into Guangdong.King Jingjin of the Qing Dynasty was killed. King DingnanKong YoudeSelf immolation.
Liu Wenxiu sent troops to Sichuan, defeated Wu Sangui and defeated himSouthern SichuanIn addition, he has made contact with the thirteen armies of Kuidong.
Activities in the southeast coastal areaZhang Huangyan、Zhang MingzhenAt this time, the anti Qing team led by Wang and others also began to counter attack and accepted the title given by Emperor Yongli, forming the second climax of the anti Qing movement.
1662 (the first year of Kangxi in the Qing Dynasty, the 16th year of Yongli in the Southern Ming Dynasty)
Zhu Youlang, Emperor Yongli of the Southern Ming Dynasty, was killed in Kunming, and Li Dingguo and Zheng Chenggong died one after another.The political power of Nanming in mainland China came to an end.
1664 (the third year of Kangxi in the Qing Dynasty, the 18th year of Yongli in the Southern Ming Dynasty)
"Kuidong Thirteen Schools" were attacked and destroyed by the Qing army.
Qing Army AttacksZhoushanAnd other coastal islands, Zhang Huangyan was killed.
1674 (the 13th year of Kangxi in the Qing Dynasty, the 28th year of Yongli in the Southern Ming Dynasty)
TaiwanZheng JingIt attacked Fujian on a large scale and was later repulsed by the Qing army.
1683 (the 22nd year of Kangxi in the Qing Dynasty, the 37th year of Yongli in the Southern Ming Dynasty)
The Qing army captured Taiwan, and the Nanming forces collapsed.The Qing Dynasty completely establishedChinaThe rule of.
historical background
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16. In Europe in the 17th century, the long Middle Ages have ended, and the Renaissance has brought about people's awakening and bound peopleFreedom of thoughtDevelopmentalTedious philosophyAnd theological dogmas were gradually destroyed.feudal societyStart to disintegrate, and replace it withcapitalist society The productive forces have been greatly liberated.The prosperity of handicraft industry in capitalist workshops and the transition to machine production promotedTechnical scienceAnd mathematics developed rapidly.
For example, in navigation, more preciseAstronomical observation。On the military side,BallisticsIt has become the central topic of research.Manufacture of accurate hour meters,canalThe digging, the construction of dams, the planetaryElliptical orbitTheory and so on also need a lot of complex calculations.ancient GreekSinceElementary mathematics, has gradually failed to meet the needs of the time.
Astronomy
stayHistory of ScienceDuring this period, there were many important events, which raised new topics for mathematics.FirstCopernicusPutting forward the theory of earth movement, which is an important theoretical pillar of theologyGeocentric theoryA fundamental shake has taken place.His discipleReticusThe astronomical observation was becoming more and more precise, and the calculation was detailedtrigonometric functionThe watch has become a matter of urgency, so we began to make sinetangentandSecantTable.At that time, it was all calculated by hand. Reticus and his assistant worked hard for 12 years, until his death, his disciplesOttoDone.
In the second half of the 16th century,DenmarkAstronomer Tycho made a lot of precise astronomical observations. On this basis, German astronomer Kepler summarized the three laws of planetary motion, which led to NewtonUniversal gravitationDiscovery of.
Kepler's The New Solid Geometry of the Wine Bucket regards the wine bucket as the accumulation of countless circular slices, and then calculates its volume.This isIntegral calculusThe precursor work of.
Classical Advanced Mathematics
ItalyGalileo, a scientist, advocated that systematic observation and experiment must be carried out in natural science research to make full use ofMathematical toolsTo explore the mysteries of nature.These views have a great impact on the development of science (especially physics and mathematics).His studentsKavalieriThe principle of indivisibility was founded.Based on this principle, he solved many problems that could be solved in the 17th centuryintegration methodProblems solved.The idea of "indivisibility" sprouted in 1620 and was deeply influenced by Kepler and GalileoOdexsosOfExhaustion methodTo Newton, LeibnizCalculusTransition of.
Italy in the 16th century also made a series of achievements in algebraic equation theory.Tatalia、Caldano、Ferrari、Bombelli People have successively discovered and improved three timesQuartic equationAnd used for the first timeimaginary number。This is from GreeceDifantuThe biggest breakthrough in algebra since then.FrenchWeidaBased on the achievements of our predecessors, we created a large number of algebraic symbols, used letters to represent unknowns, improved the calculation methodAlgebraGreat changes.
In terms of numerical calculation,StevenHe systematically elaborated and used decimals, and then Napier createdlogarithm, which greatly speeds up the calculation speed.in the futurePascalInventedAdderLeibniz invented the multiplication machine. Although it was not practical, it opened up a new way of mechanical calculation.
At the beginning of the 17th century, the main subjects of primary mathematics (arithmetic, algebra, geometry, trigonometry) have basically taken shape, but the development of mathematics is just in the ascendant, and it has stepped intoHistory of mathematicsThe difference between this period and the previous period (often referred to as the primary mathematical period) is that the previous period was mainly staticmethod studyobjective worldThis period is the process of exploring the changes and development of things from the perspective of movement.
Variable mathematicsanalytic geometryThe establishment ofCalculusThe rise of.In this periodprobability theoryandProjective geometryAnd other new fields.But it seems to be covered by the powerful brilliance of calculus.AnalyticsIt developed with a surging trend and reached an unprecedented level in the 18th century. Its rich content and wide application make people dizzy.
The mathematics established in this period is roughly equivalent to the learning content of the first and second year of the university.In order to distinguish from elementary mathematics in middle school, it is sometimes called classical mathematicsAdvanced mathematicsThis period is also called the period of classical higher mathematics.
geometry
The generation of analytic geometry is generally based onDescartesThe publication of Geometry is the symbol.This book is not only about geometry, but also about algebra.There is a big gap between it and the analytic geometry textbooks of the 17th century, which can not even be seen“Cartesian coordinate system”。But what is valuable is that it introduced revolutionary ideas and made contributions to opening up a new field of mathematics.
The main achievements of Geometry can be summed up in three points: unifying the two opposite research objects "shape" and "number" in the past, introducing variables, and usingalgebraic methodTo solve classical geometric problems;Finally, he abandoned the Greek uniformity restrictions;Improved algebraic notation.
French mathematician Fermat also shared the honor of founding analytic geometry. His discovery may be earlier than that of Descartes, but it was published very late.He is aAmateur mathematicianHe has made important contributions to number theory, probability theory and optics.He has got the gist of calculus and has proposed the method of finding the maximum and minimum of functions.He established many number theory theorems, among which“Fermat's big theorem”The most famous one asserts that when the integer n>2, the equation x ^ n+y ^ n=z ^ n has nopositive integerSolution.After being put forward, it went through many people's conjectures and dialectics, and after more than 300 years of history, it was finally recognized by British mathematicians in 1995Andrew Wiles prove.
The interest in probability theory originally came fromInsuranceBut it is the request of gamblers that impels mathematicians to think about some special probability problems.Fermat, Pascal and Huygens were the early founders of probability theory. Later, after the 18th and 19th centuriesLaplace、PoissonWith the research of others, probability theory has become a huge branch of mathematics that is widely used.
At the same time as analytic geometry, another major change took place in the field of geometry in the 17th century, which was the establishment of projective geometry.The decisive progress is the work of Dezag and Pascal.The former introducesInfinity point、Infinity line, discussed pole andPolar lineThe "Dezag theorem" he discovered is the basic theorem of all projective geometry.
Pascal published in 1640《Conic theory》, is fromApolloniusThe greatest progress in conic theory since then.But most mathematicians at that time devoted themselves toAnalyticsThe study of projective geometry did not receive much attention until the end of the 18th century.
The Invention of Calculus
The 17th century was a period of rich creation, and the most brilliant achievement was the invention of calculus.Its appearance is the whole history of mathematics as well as the wholeHuman historyIt's a big event.It comes fromProduction technologyandTheoretical scienceAt the same time, it profoundly affects the development of production technology and natural science.Calculus forscientific and technical workerFor example, it is already like a grain of cloth, which can not be left for a moment.
Calculus came into being after a long period of gestation.The idea of integration dates back toArchimedesThe era has sprouted. At the turn of the 16th and 17th centuries, Kepler, Cavallieri, FermaWallisIn particular, Barrow and others have made many preparations.AsDifferential calculusCentral problemtangentThe discussion of the problem is relatively late, so the starting point of differential calculus falls far behind that of integral calculus.
Famous mathematicians (mainly French) in the 17th century, such asFermatDescartesLobeval、DezagPeople have been involved in the debate of "tangent problem".Descartes and Fermat think that the tangent is when two intersection points coincidesecant。From the point of view of motion, Lobeval regards the tangent line as the direction of the motion that describes the curve at this point, which has practical significance in mechanics.
Newton and Leibniz's greatest contribution is to connect two seemingly unrelated problems, one is the tangent problem (the central problem of differential calculus), the other is the quadrature problem (the central problem of integral calculus), to establish a bridge between themBasic Theorem of CalculusOr "Newton -Leibniz formula”Express it.
On Newton's May 20, 1665(Gregorian calendar31) There was the earliest record of calculus in a handwritten document, but his work was unknown for a long time. It was not until 1687 that he was abstracted in geometric form in his masterpiece《Mathematical Principles of Natural Philosophy》Medium.Newton established calculus mainly fromkinematicsLeibniz considered it from the point of view of geometry.Special and Barrow's“Differential triangle”There is close relationship.
Leibniz's first article on differential calculus was published in Xueyi in 1684, and his first article on integral calculus was published in the same magazine in 1686.The symbols he created were far superior to Newton's, so they were used by later generations.Its theory will soon be knownL'Hopital 、Bernoulli FamilyThe inheritance and development of Euler and others entered a harvest period in the 18th century.
No great invention can be complete from the beginning.Calculus in the 17th century has serious logic difficulties, which has been criticized in many aspects.It is based onLimit theoryHowever, Newton and Leibniz's concept of limit is very vague.What is the limit,InfinitesimalWhat was it? It was a problem of fundamental nature at that time.Nevertheless, the victory of calculus in practice is convincing enough.Most mathematicians put aside their logic foundation for the time being, and went forward bravely to open up this new garden.
Characteristics of mathematical development
The characteristics of the development of mathematics in the 17th century can be summarized as follows.
It has produced several new fields with great influence, such as analytic geometry, calculus, probability theory, projective geometry, etc.Every field dwarfs the achievements of the ancient Greeks.
The main body of Greek mathematics is geometry, and algebraic problems are often demonstrated by geometric methods.Algebra in the 17th century occupied a more important position than geometry. It broke through the Greek frame and further transformed into symbolic algebra. Geometric problems were often solved by algebraic methods in turn.
A large number of new concepts have emerged, such as irrational numbers, imaginary numbersInstantaneous rate of change, derivatives, integrals, etcEmpirical factOfDirect reflectionIt is produced by further abstraction of mathematical theory.
Mathematics is more closely related to other natural sciences,Experimental scienceThe rise (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 astronomers, physicists or philosophers themselves.
Mathematical knowledge was widely exchanged and spread. In the Greek era, only a few people were studying mathematics. Until the 16th century, the situation did not change much.In the 17th century, researchers increased greatly, academic groups (societies or colleges) were established successively, andprinting businessThe mathematical knowledge has been widely popularized and applied.
In general, the 17th century was the initial stage of many new subjects, the 18th century was the stage of enrichment and development, and the 19th century was the stage of review, promotion and reform, and entered the next century with a new attitude.
Anglo Spanish WarAt the end, the London Treaty was signed, which was beneficial to the Western Portuguese Empire as a whole and restored to the pre war situation.
·German astronomer Kepler published New Astronomy, and created the ellipse law and ellipse of planetary motionArea law(that is, the first planet movementSecond law)
·The first one was made by Galileo, ItalyAstronomical telescope, observed the sky with a telescope for the first time
·The first set was created in Santorino, ItalyCurrent meter
·Germany J. Trautmann successfully implemented the first case with accurate recordscaesarean birthoperation
1611
.Zhao ShizhenDeath of illness, written《Divine Instrument Manual》, "Continuation of Divine Weapon Manual", "Divine Weapon Manual or Question", "Preparation of Border Garrison Trucks" and other works, including 24 types of firearm patterns
·China's Nurhachi rebelled against the Ming Dynasty and became independent Khan. His country was called Jin, and was known as Later Jin in history (see Qing Dynasty)
Chen ShigongComplete《Orthodox surgery》(A large number of effective prescriptions have been collected. He pays attention to practice, dares to innovate, and creatively carries out toe amputation (finger amputation), tracheal suture, etcsurgical operationAnd made contributions to our foreign science.Some of the bookstumourIt is also discussed.)
publishMao Yuanyi《Wu Beizhi》This book is composed of five parts, namely, the evaluation of military tactics, the strategic examination, the array training system, the military personnel, and the accounting records. However, in the Qing DynastyQianlongBanned during.
Wang Zheng compiled the first systematic monograph on mechanical engineering in China
one thousand six hundred and twenty-sevenApocalypse EmperorDeath,ChongzhenExecuteWei Zhongxian, Donglin Party's one party dominance completely out of control, collusion between government and business, nationalTax systemComplete collapse
stayMinister of RitesCompilation was completed in the Ming Dynasty under the leadership of Xu Guangqi《Chongzhen almanac》, 46 kinds in total, 137 volumes.In the book, Tycho createdsphere systems And geometry
1636
·Huangtaiji, the emperor of China in Shengjing, changed the country name to Qing (1636-1911)
·First set made in Greeceseeder, the prototype of modern seeder
Song YingxingIn On Qi, Qi Sheng, he made a theory similar to that of modern times on the generation and transmission of sound, believing that sound is generated by rapid movement hitting air or objects vibrating, while sound is transmitted through air, which is very similar to that of modern theory in the same year,Fang YizhiThe concept of space-time that time and space cannot exist independently is put forward.
Song Yingxing Completed《Tiangong Kaiwu》It is a comprehensive scientific and technological masterpiece in ancient China. Some people call it a“encyclopedia”A book of style.In Tiangong Kaiwu, Song Yingxing regards lead, copper, mercury, sulfur and other elements as basic substances, and the substances they produce as derivatives, resulting in the concept of similar modern chemical elements.
Xu HongzuComplete《Xu XiakeTravel Notes, a famous Chinese touristgeographerXu HongzuHis travel diary records the geography and other information he has visited.
·W. Petit's《political arithmetic 》And German Kangling《On national conditions》It was published almost at the same time, becoming the cause and evidence of 200 years' debate between the two major schools of statistics
·J. Woodward of the United Kingdom published "Discussion on the Natural History of the Earth", and put forward the theory of diluvium that floods kill organisms
1698
·UK TSafariMake the first one practical for mine water pumpingsteam engine, using steam as industrial power for the first time