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The battleship group of the Mawei Army entered Europe, and the large and small fleets on the European sea at the beginning thought that this British fleet, after all, the style of these warships was the closest to the British warships, but they did not recognize the color of the battleships and the words on the battleships, and they could only recognize a few of the old sailors who had gone to the East on the sea, as well as a few Western nobles, and their families had classics that recorded each other's words. Anyone who recognized it expressed great surprise that in the far east, that ancient country was still so powerful. As for why, being able to send such a fleet thousands of miles across the ocean does not speak of being powerful?

It is said that until this time, people in European countries still had a very high evaluation of the ancient country in the East, and they also longed for it. Westerners who have traveled to the East will record their sights and hears, the most famous is of course "Marco Polo's Travels", but in addition to "Marco Polo's Travels", there are also some accounts of other people, which are all about the Ming Dynasty as seen by some Westerners. The Qing Dynasty was founded for a short time, and most of Europe did not know about it. However, in those previous accounts, they all compared the Ming Kingdom to heaven.

"In this big country, people are well-fed, well-dressed, and their homes are richly furnished, and above all, they work hard and are big businessmen and traders. All these people, together with the fertility of the aforementioned land, make it rightfully called the richest country in the world."

"They produce a lot of silk and it's of the highest quality. The colors are perfect. Significantly more than Granada Silk. It is one of the largest trades in the country."

"There are many rivers in the country. People grow rice, which is the common food and grain of the whole country, and they harvest so much that when the price of rice is at its highest, you can live in abundance for a month with a pound. ”

"All the countryside is beautiful and smelly, because there are many kinds of fragrant flowers. It is also dotted with green villages planted along the banks of rivers and streams, where there are many rivers. There are orchards and gardens, and there are very cheerful banquet halls. They often go to rest and escape from their emotional worries. The old men, that is, the gentlemen. Large forests and dense forests are often planted, and wild boars are raised in them. sheep, hares, and all sorts of other wild beasts, make fine fur from their skins."

"In the mountains uncultivable, there are plenty of pine trees, bigger and more flavorful nuts than you usually find in Spain. Between these trees, they grow corn, which is the general food of the Mexican and Peruvian Indians. In short, they don't leave a single foot of uncultivated land, and you can hardly see any wasteland or no harvest in the whole country. The people of this country are so hardworking. ”

"Their houses are generally beautiful and are usually neatly planted with trees outside their doors. It looks beautiful and shines on the street. The interior of the house is as white as milk, and looks like smooth paper, and the floor is paved with large and flat ashlar stones, and the ceiling is made of a childish wood, which is well structured and painted, and looks like brocade, and the color is golden, and it looks very good; Each house has three courtyards and a courtyard full of ornamental flowers. All of them had a fish pond, even though it was small. One side of the courtyard is gorgeously furnished. ”

"They are extremely clean, not only in their houses, but also on the streets. They usually have three or four necessary or public resting places in the streets, well arranged, so that those who are busy with official business do not stain the streets, and receive supplies from them, and the law is similar to that which passes all roads throughout the country. Some cities have navigable streets, like Venice in Italy. ”

"Their women were dressed in peculiar fashion, much like the style of the Spaniards, and they wore a lot of gold and precious stones, and their clothes had wide sleeves, and they wore gold and silver and all kinds of silk materials, as mentioned earlier, they had a great quantity of silk, of excellent texture, and very cheap, and the poor wore velvet, untrimmed velvet, and beep. They kept their hair and combed it carefully and diligently, like the Genoese women, who tied it around their heads with wide ribbons and adorned with pearls and precious stones. ”

From these accounts, we can see how yearning the Westerners at this time were for the country, this country where "all the countryside exudes a strange fragrance", but this is completely different from the Chinese people with long braids and dirty bodies in the eyes of Westerners in the late Qing Dynasty.

The naval units of the Mawei Army, especially the fleets that have not returned to their homeland for a long time, have already shaved their hair clean, and since then they have kept their hair short, so that they look more capable, and more importantly, at sea, they have always had long hair, not to mention that it is not easy to take care of, and it is easy to carry bacteria to cause diseases. On the ocean, there is a shortage of medical treatment, which is a very dangerous thing, so the Mawei Army has long been prepared. As for the merchants from Fujian and Guangdong, it is another matter, some of them were improvised patchwork, and their hair was very long, but they were no longer full of money, and they had grown in the past two years, and they continued to keep the hairstyle of the former Ming.

In Lisbon, the Portuguese welcomed the huge fleet of ships from afar, even if they only stayed here for three days. The Kunpeng caravans, along with the accompanying fleets of small ships, brought with them a large number of exquisite goods from the Orient, which were coveted by the European aristocracy. Beautiful silks, fine porcelain, all kinds of handicrafts, and of course the perfumes of the princess shop, in the entire port of Lisbon, Portuguese merchants ate only a small part of the goods, less than a fifth of the fleet. But just this fifth, that is a total of 2,000 tons of small goods, and the other fifth of the goods, has almost made the entire fleet return to its capital, it is conceivable that when all the goods on the merchant ships are emptied, the fleet will get such an amazing profit!

In addition, the Fifth Detachment of the Mawei Army, which accompanied the escort, also greatly shocked the merchants of Portugal and other European countries in Lisbon. Such a fleet, although there were only twenty warships, had six third-class warships, six fourth-class warships, and eight fifth-class warships, and the dense gun ports on both sides and the spirit of the navy on the battleships showed everyone how powerful they were. Compared with the European soldiers, these Westerners suddenly discovered. The soldiers on these ships were more like professional soldiers than their soldiers. On the deck of a battleship. Motionless like a wooden stake. Disembarked. When escorting the goods loaded onto the docks, the pace was neat, and the spirit was far higher than that of the Portuguese soldiers on duty in the port.

If Geng Jingzhong could see this scene, it is estimated that he would really understand why the navies of later generations like to visit other countries in a friendly manner. One is to show other countries their power, and the other is to improve their country's international image. At this moment, the Mawei Navy has done this very well, although the size of the naval soldiers does not seem to be as tall as the Europeans, but these Portuguese do not doubt that they have no combat effectiveness if they really fight.

Responsible for the overall affairs of the fleet. It was Miao Quanchen, who came to Europe a few years ago, and when he came to Europe before, the people he brought came and went in a hurry, and the information collected was not very much, but this time it was different. In the past two years, Fujian has sent personnel to Europe, and there are quite a few of them, and all European countries are distributed, and there are also three people here in the largest port in Portugal. The task of these people is to gather all the valuable information about Europe, of course. What is valuable, Geng Jingzhong has already made a detailed list. On this trip, the Fifth Detachment escorted the Kunpeng caravan and other merchant fleets to Europe. The information they had collected in the previous two years could be handed in at the same time.

Moreover, seeing the arrival of the fleet, they also knew that it would not be long before they could really go home, and no matter how good it was in Europe, it would not be as good as their own home. Fortunately, their task is to stay for five years, and after five years, they can return to Fujian, return to their hometown, and at the same time, they can also be promoted and reused, and it is worth it.

Geng Jingzhong's concern for Europe is not for a reason, and it is true that in many respects, Europe has been ahead of China. Of course, these aspects refer to those aspects of science and technology, as for those cultures in Europe, what kind of art and the like, it is better to leave it to the Europeans to enjoy themselves, the land of China has its own art, and there is no need to learn from the West.

For thousands of years, China did not attach importance to science and technology, dismissed it as a strange and obscene skill, and always thought that reading the books of sages was orthodox, but Geng Jingzhong knew that those things were very good, but they could only stay at the spiritual level, and society should develop, and finally science and technology should be used, and only science and technology can truly liberate the productive forces and make social progress.

Now for Europe, the long Middle Ages have come to an end, the Renaissance has brought spiritual awakening to Europeans, and the dogmatic authority of cumbersome philosophy and theology, which has constrained the free development of European thought, has been gradually destroyed. Feudal society began to disintegrate, and in its place came capitalist society, and the productive forces were greatly liberated. The prosperity of the capitalist factory handicraft industry and the transition to machine production led to the rapid development of technical science and mathematics.

The most typical is that in navigation, in order to determine the position of a ship, more precise astronomical observations are required. In the military aspect, ballistics has become a central topic of research. The manufacture of accurate timepieces, the excavation of canals, the construction of embankments, the theory of the elliptical orbits of the planets, etc., also require a lot of complex calculations. Elementary mathematics since ancient Greece has gradually become inadequate to meet the needs of the time.

In the history of science, this period saw a number of heavy events that raised new questions to mathematics. First of all, Copernicus put forward heliocentrism, which fundamentally shook geocentrism, an important theoretical pillar of theology. His disciple Retticus saw that astronomical observations were becoming more sophisticated and that it was urgent to calculate detailed tables of trigonometric functions, so he began to make sine, tangent, and secant tables every 10'. It was all by hand, and Retticus and his assistants worked diligently for twelve years, only to be completed after his death by his disciple Otto.

In the second half of the 16th century, the Danish astronomer Tycho made a large number of precise astronomical observations, on the basis of which the German astronomer Kepler summarized the three laws of the motion of the stars, which led to Newton's discovery of universal gravity. In addition, Kepler's "New Solid Geometry of the Barrel" sees the barrel as the accumulation of countless round flakes to find its volume, which is the precursor work of integralism.

In addition, the Italian scientist Galileo Galilei advocated that natural science research must be carried out systematically through observation and practice, and that mathematical tools should be used to explore the mysteries of nature. These ideas have had a huge impact on the development of science, especially physics and mathematics. His pupil Cavalieri founded the "Indivisible Principle". Relying on this principle, he solved many of the problems that could have been solved in the seventeenth century with a more rigorous method of integration. The idea of "indivisible" germinated 54 years ago, in 1620, under the influence of Kepler and Galileo, and was the transition from the exhaustion method of the Greek Eudoxus to the calculus of Newton and Leibniz.

A hundred years ago. Or Italy in the sixteenth century. A series of achievements have been made in the theory of algebraic equations. Tartaglia, Cardano, Ferrari, Bomberi and others successively discovered and improved the universal solutions of cubic and quadratic equations. And for the first time, imaginary numbers were used. This is the biggest breakthrough in algebra since the Greek Diophantus. France's Vedic was a great example of algebra by creating a large number of algebraic symbols, using letters to represent unknowns, and improving calculation methods, which greatly improved algebra.

In numerical calculations, Steven systematically elaborated and used decimals, and then Napier created logarithms, which greatly accelerated the computation. Later, Pascal invented the addition machine. Leibniz invented the multiplication machine, which, although not practical, opened up new avenues of mechanical calculation.

At the beginning of the seventeenth century, the main subjects of elementary mathematics (arithmetic, algebra, geometry, trigonometry) were basically formed, but the development of mathematics was in the ascendant, and it entered the next stage of the history of mathematics at an accelerated pace: the period of variable mathematics The difference between this period and the previous period (often called the period of elementary mathematics) is that the previous period mainly used static methods to study individual elements of the objective world, while this period is the process of exploring the change and development of things from the point of view of motion.

The mathematics of variables began with the establishment of analytic geometry as www.biquge.info, followed by the flourishing of calculus. At this time, new fields such as probability theory and projective geometry were already emerging in this part of Europe, and calculus was at its most famous. The other qiē was overshadowed by its powerful brilliance. But even so, analytics is moving forward in a surging way. In the history of later generations, it was not until the eighteenth century that it reached an unprecedented splendid stage, and its richness of content and wide application made people dizzy.

However, the mathematics established during this period is roughly equivalent to what Geng Jingzhong studied in his first and second years of college. In order to distinguish it from elementary mathematics at the secondary level, Europeans sometimes referred to it as classical higher mathematics, and this period was correspondingly called the period of classical higher mathematics in later generations.

At this time, scholars in European schools are not only interested in advanced mathematics, but also in analytic geometry. The emergence of analytic geometry is generally marked by the publication of Descartes' Geometry 37 years ago. The content of this book is not only geometry, but also a lot of algebraic problems. It is very different from the analytic geometry textbooks in Europe at the moment, and there is not even a "Cartesian coordinate system" in it. But what is valuable is that it introduced revolutionary ideas and contributed to the opening of new fields of mathematics, and in recent years, geometry has also become the object of scholars' pursuit.

At the same time as analytic geometry, there has been another important revolution in the field of geometry in recent years, and that is the establishment of projective geometry. The decisive advance was the work of Dezag and Pascal, the former introduced the infinite point and the infinite line, discussed the pole and the polar line, transmission, perspective and other problems, and he discovered the "Dezag theorem" as the basic theorem of all projective geometry. Pascal's Theory of Conic Curves, published thirty years ago, was the greatest advance in the theory of conic curves since Apollonius. However, most mathematicians at this time were devoted to the study of analysis, and projective geometry was not taken seriously, but these were still on Geng Jingzhong's list.

In the seventeenth century, Europe was indeed a period of abundant creativity, and the most brilliant achievement was the invention of calculus. Its emergence is a major event in the entire history of mathematics and the entire history of mankind. It arose from the needs of production technology and theoretical science, and at the same time went back and profoundly influenced the development of production technology and natural science. For later generations of scientific and technological workers, calculus is like a cloth and corn corn, which is inseparable.

Previously, when Geng Jingzhong was compiling his own textbooks, he recorded and sorted out all the things he could remember, and then handed them over to those high-paid Western talents in the scientific research base, and then took them to the school after being transformed again. But Geng Jingzhong can't remember many things clearly, it can be said that he knows it but doesn't know why, and he has to find specialized talents for detailed derivation.

No heavy invention can be flawless from the start. Just as calculus at the moment in Europe still has strict logical difficulties, so that it has been criticized from many quarters. It is based on the theory of limits, and the previous ideas of limits of Newton and Leibniz were also very vague. What exactly is the limit and what is the infinitesimal is a fundamental problem at present. Still, calculus' triumph in practice is convincing enough. Most mathematicians put aside their logical foundation for the time being and went forward to open up this new field, and Geng Jingzhong needed nothing else but to recruit all these scholars to China. Fortunately, at this time, China is still very attractive to these Westerners, and coupled with the absolute high salary, it has indeed attracted a lot of talents.

Not only in mathematics, although Geng Jingzhong knows that the most basic aspects of this qiē are inseparable from mathematics, there are also some equally important things, that is, physics and chemistry. Of course, what biology and so on, Geng Jingzhong recorded in detail on his information sheet, and the tasks of these people he sent to Europe were very detailed, even if there were things that Geng Jingzhong did not expect, the people sent still had the right to arbitrarily decide on the spot.

Although Geng Jingzhong has been hiring European scholars to go to the East, that is, Fujian, to teach all these years. The purpose is very clear, Geng Jingzhong wants to cultivate a large number of his own talents, and also lay the foundation for quickly surpassing Europe. However, it is also required that these personnel sent should not forget their own learning and choose one subject and one direction. (To be continued......)