Euclid (330 ~ 275 BC) lived in Alexandria and was the most famous mathematician in ancient Greece.

He is famous for his Elements of Geometry. The Elements of Geometry is the earliest western masterpiece translated in China's history.

Growing experience

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Little is known about his life now. I probably studied in Athens in my early years and I know Plato's theory very well. Around 300 BC, he came to Alexandria at the invitation of Ptolemy (364-283 BC) and worked there for a long time. He is a gentle and honest educator. He always persuades people who are interested in mathematics. However, we are opposed to the style of refusing to study hard and being opportunistic, and we are also opposed to narrow and practical views. According to Proclus (about 4 10 ~ 485), King Ptolemy once asked Euclid if there were any other shortcuts to learn geometry besides his Elements. Euclid replied, "Geometry has no king's road." It means that in geometry, there is no road paved for kings. This sentence later became an eternal learning motto. Stobeus (about 500) told another story, saying that a student had just started to learn the first proposition and asked Euclid what he would get after learning geometry. Euclid said: Give him three coins because he wants to get real benefits from his study.

Born in Athens, Euclid was a student of Plato. His scientific activities were mainly carried out in Alexandria, where he established a school of mathematics headed by him.

Euclid is famous for his main work "Elements of Geometry". He systematically sorted out and summarized the mathematical achievements of predecessors, and formed a strict system with strict deductive logic based on some axioms, which is of great significance.

The geometric system established by Euclid was so rigorous and complete that even Einstein, the most outstanding great scientist in the 20th century, could not help but look at him with new eyes.

Einstein said: "When he first came into contact with Euclidean geometry, if he was not moved by its clarity and reliability, then he would not have become a scientist."

Perhaps he didn't create much mathematical content in the Elements of Geometry, but he undoubtedly made contributions to the selection of axioms, the arrangement of theorems and some rigorous proofs. In this respect, his work is excellent.

Euclid's Elements of Geometry consists of 13 articles, the first of which is definitions and axioms. For example, he first defined the concepts of point, line and surface.

He compiled five axioms, including:

1. It is possible to make a straight line from one point to another arbitrary point;

2. All right angles are equal;

3. if a = b and b=c, then a = c；;

4. if a=b, A+C = B+C and so on.

Another axiom put forward by Euclid himself is that the whole is greater than the parts.

Although this axiom is not as easy to be recognized and accepted as other axioms, it is necessary and indispensable in Euclidean geometry. It just shows his genius that he can bring it up.

Chapter 1 ~ 4 of Elements of Geometry mainly talks about the basic properties of polygons and circles, such as congruent polygon theorem, parallel line theorem, pythagorean chord theorem and so on.

The second article talks about geometric algebra, which replaces numbers with geometric line segments, and solves the contradiction that the Greeks do not recognize irrational numbers, because some irrational numbers can be expressed as graphic methods.

The third chapter discusses the properties of a circle, such as chord, tangent, secant and central angle.

Chapter four discusses the inscribed circle and circumscribed circle of a circle.

The fifth part is the theory of proportion. This article is of great significance to the future history of mathematics development.

The sixth article is about similarity. One of the propositions is that the area of a rectangle on the hypotenuse of a right triangle is equal to the sum of the areas of two similar rectangles on two right angles. Readers may wish to have a try.

Chapters 7, 8 and 9 are number theory, which describes the nature of the ratio of integers to integers.

Article 10 is to classify irrational numbers.

The article 1 1 ~ 13 is about solid geometry.

All 13 articles contain 467 propositions. The appearance of geometric elements shows that human beings have reached a scientific state in geometry and established a scientific logic theory on the basis of experience and intuition.

Euclid, a professor of mathematics at the University of Alexandria, transformed the earth and heaven into a huge pattern composed of intricate graphics.

He also used his amazing clever fingers to disassemble the pattern into simple components: points, lines, angles, surfaces and solids-translating an endless picture into the limited language of elementary mathematics.

Although Euclid simplified his geometry, he insisted on studying the principle of geometry thoroughly so that his students could fully understand it.

It is said that Dorothy, king of Alexandria, learned geometry from Euclid and was impatient with Euclid's explanation of his principles over and over again.

The king asked, "Is there a simpler way to learn geometry than yours?"

Euclid replied, "Your Majesty, there are two roads in the country, one is the hard road for ordinary people, and the other is the royal road. But geometrically, everyone can only go the same way. Learning to be excellent is an official, please understand. "

Euclid's sentence was later popularized as "there is no shortcut to knowledge" and became an eternal proverb.

Due to lack of information, we know little about the details of Euclid's life. There is a story about Euclid's quarrel with his wife, who was very angry.

The wife said, "put away your messy photos." Does it bring you bread and beef? "

Euclid was born with a foolish temper. He just smiled and said, "Do you know what women think? What I write now will be of great value to future generations! "

The wife sneered: "Can we reunite in the afterlife? You bookworm. "

Euclid was about to argue when his wife picked up a part of his Elements and threw it into the stove. Euclid rushed to catch it, but it was too late.

It is said that his wife burned the last and most wonderful chapter of Geometry. But this regret is irreversible. She burned not only some useful books, but also the crystallization of Euclid's sweat and wisdom.

If the above story is true, then Euclid may not have caused his wife's anger. Because ancient writers told us that he was a "gentle and kind old man."

Because of Euclid's profound knowledge, his students almost worshipped him. When Euclid was teaching students, he guided them and cared for them like a real father.

However, sometimes he whips arrogant students with bitter satire to tame them. After learning the first theorem, a student asked, "What are the benefits of learning geometry?"

So Euclid turned to the servant and said, "Grumma, give this gentleman three coins because he wants to get real benefits from his study."

Euclid advocated that learning must be gradual and diligent, not in favor of opportunism and against narrow practical concepts. Papos, a latecomer, especially appreciated his modesty.

Like most scholars in ancient Greece, Euclid did not care much about the "practical" value of his scientific research. He likes studying for the sake of research.

He is shy and humble, aloof from the world and lives quietly in his own home. In that world full of intrigue, people are allowed to perform noisy and vulgar performances.

He said: "these fleeting things will eventually pass, but the patterns of stars are eternal."

In addition to writing an important geometric masterpiece "The Elements of Geometry", Euclid also wrote works such as data, graphic segmentation, wrong conclusions about mathematics, optics and the book "Reflective Optics".

Major achievements

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Euclid was one of the most famous and influential mathematicians in ancient Greece. He is a member of the Alexandria school. Euclid wrote a book called The Elements, with a volume of 13. This work has a great influence on the future development of geometry, mathematics and science, and on the whole thinking method of westerners. The main object of Geometry Elements is geometry, but it also involves other topics such as number theory and irrational number theory. Euclid used the axiomatic method. Axioms are some basic propositions that do not need to be proved, and all theorems are derived from them. In this deductive reasoning, every proof must be based on axioms or theorems that have been proved. This method later became a model of establishing any knowledge system, and for almost 2000 years, it was regarded as a model of rigorous thinking that must be followed. The Elements of Geometry is the pinnacle of the development of ancient Greek mathematics.

Outstanding contribution

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Euclid arranged the rich achievements accumulated in Greek geometry since the 7th century BC in a strict logical system, making geometry an independent and deductive science. Besides the Elements of Geometry, he has many other works, but most of them have been lost. Known Numbers is the only Greek work except the original among his pure geometry works. Its style is similar to the first six volumes of the original work, and it contains 94 propositions. It has been pointed out that if some elements in a graph are known, others can be determined. Graphics are divided into existing Latin texts and Arabic texts. This paper discusses dividing known figures into equal parts or equal parts by straight lines. Optics is one of the early works of geometric optics. It studies perspective, stating that the incident angle of light is equal to the reflection angle, and that vision is the result of light reaching the object from the eyes. There are still some works that are not sure whether they belong to Euclid or not, and have been lost.

Euclid's Elements of Geometry contains 23 definitions, 5 axioms and 5 postulates, from which 48 propositions are derived (Volume I).

Historical position

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Euclid also wrote several other books, some of which have survived to this day. However, it was the great geometry textbook Geometry Elements that established his historical position. The importance of The Elements of Geometry does not lie in which theorem is put forward in the book. Almost all the theorems put forward in the book were known before Euclid, as were many proofs used. Euclid's great contribution is that he sorted out these materials and made a comprehensive and systematic exposition in his book. This includes making an appropriate choice between axiom and postulate for the first time (this is a very difficult job and requires extraordinary judgment and insight). Then, he carefully sorted out these theorems, making each theorem logically consistent with the previous theorems. Where necessary, he added missing steps and proof of wooden feet. It is worth mentioning that Geometry Elements is basically the development of plane geometry and solid geometry, and also includes a lot of algebra and number theory.

The Elements of Geometry has been used as a textbook for more than two thousand years. It is undoubtedly the most successful textbook in word formation. Euclid's outstanding work eclipsed similar things before. After the book came out, it quickly replaced the previous geometry textbook, which soon disappeared from people's memory. The Elements of Geometry was written in Greek and later translated into many languages. It was first published in 1482, more than 30 years after Gutenberg invented movable type printing. Since then, the Elements of Geometry has been published in thousands of different editions.

In terms of training people's logical reasoning thinking, The Elements of Geometry has a much greater influence than any book on logic written by Beatrice Dodd. As far as the complete deductive reasoning structure is concerned, this is an excellent model. Because of this, thinkers have been fascinated by this book since its publication. To be fair, Euclid's book is a major factor in the emergence of modern science. Science is more than just collecting what has been carefully observed and what has been carefully summarized. The great achievements in science, as far as its origin is concerned, on the one hand, are the combination of experience and experiment; On the other hand, it needs careful analysis and deductive reasoning. We don't know why science was born in Europe and wood was born in China or Japan. But what is certain is that this is no accident. There is no doubt that the role played by outstanding figures like Newton, Flail Lilo, Baini and Képler is extremely important. Perhaps some basic reasons can explain why these outstanding figures appear in Europe, not in the East. Perhaps an obvious historical factor that makes it easy for Europeans to understand science is the Greek rationalism and mathematical knowledge handed down by the Greeks. For Europeans, as long as there are a few basic physical principles, it seems natural to deduce other ideas from them. Because there was Eurydice as a model before them (generally speaking, Europeans do not regard Euclid's geometry as an abstract system; They believe that Euclid's postulate and the theorems derived from it are based on objective reality.

All the characters mentioned above have accepted Euclid's tradition. They really studied Euclid's Elements of Geometry seriously and used it as the basis of their mathematical knowledge. Euclid's influence on Newton was particularly obvious. Newton's Principles of Mathematics was written in the form of "geometry" similar to "Elements of Geometry". Since then, many western scientists have followed Euclid's example and explained how their conclusions were logically derived from the original assumptions. So do many mathematicians, such as Bertrand Russell and alfred whitehead, and some philosophers, such as Spinoza. Compared with China, this situation is particularly prominent.

China has been ahead of Europe in technology for centuries. But there has never been a mathematician in China who can correspond to Euclid. Therefore, China has never had a mathematical theoretical system like that of Europeans (China people have a good understanding of the actual geometric knowledge, but their geometric knowledge has never risen to the level of deductive system). It was not until 1600 that Euclid was introduced into China. After that, it took several centuries for his deductive geometry system to be widely known among the educated people in China. Before that, China people did not engage in substantive scientific work. In Japan, the same is true. It was not until the18th century that the Japanese knew about Euclid's works, and it took many years to understand the main idea of the book. Although there are many famous scientists in Japan today, there were none before Euclid. People can't help but ask, if there is no Euclid's basic work, will science be born in Europe? Now, mathematicians have realized that Euclid's geometry is not the only internal unified geometric system that can be designed. In the past 150 years, many non-Euclidean geometric systems have been created. Since Einstein's general theory of relativity was accepted, people really realized that Euclid's geometry is not always correct in the real universe. For example, around black holes and neutron stars, the gravitational field is extremely strong. In this case, Euclid's geometry cannot accurately describe the situation of the universe. However, these situations are special. In most cases, Euclid's geometry can give a very close conclusion to the real world.

In fact, some scientists in China in the late Ming Dynasty have turned their attention to western science. Xu Guangqi has realized that geometry must be a subject that everyone will learn in the future; At that time, Tongcheng Fangjia, a aristocratic family, had in-depth research on European science for three generations. Zhong Fang systematically introduced the theory and application of logarithm under the guidance of Polish Munigo, whose mathematical monograph Several Degrees. It can be said that without the interruption of the Qing Dynasty's entry into the GATT, modern science would be produced under the combination of the East and the West, and the so-called false proposition "Why can't the Confucian cultural circle produce modern science" would not exist. In the face of historical facts, we can only lament. It can be said that geometry is the common property of mankind, but before Newton and Boyle were born, China people had seen and had the opportunity to read geometry, and the dawn of modern science lit a lamp in the late Ming Dynasty. At the end of the Ming Dynasty, most scientists finally joined the anti-Qing struggle, and their academic tradition and tradition of communicating with western missionaries and scientists were also interrupted. It was not until 300 years later that Wei Yuan began to "open his eyes to see the world".

In any case, these latest advances in human knowledge will not weaken the light of European academic achievements. Nor will it belittle his historical importance in the development of mathematics and the establishment of an indispensable logical framework for the growth of modern science.