In just a few hundred years, the Greeks actually created an extremely glorious ancient culture. This is undoubtedly a miracle in the history of human culture. Greece's cultural achievements are by no means accidental coincidences, but dynamic creations in line with historical laws, with subjective and objective reasons.
(1) The long brewing of civilization has promoted cultural changes
From the perspective of the history of civilization development, Greece has rich Paleolithic culture and Neolithic culture. The earliest human fossil in Europe, Homo erectus of Pietralona (about 300,000 years ago), was discovered in northern Greece. This undoubtedly shows that Greece is an important cradle of Western civilization. When history entered the Aegean civilization, that is, the Cretan and Mycenaean cultural periods (2000 BC to 1100 BC), Greek culture was already ahead of Western history.
During this period, the most important historical development of the Homeric era was the use of iron. The use of iron promoted the development of agriculture, handicrafts, industry and commerce; at the same time, the Greeks created a geometric style culture in the Homeric era based on the Aegean civilization. In the hundreds of years since the formation of geometric culture, epic stories have been transformed by literary imagination, exaggeration and typical shaping into an all-encompassing treasure trove of folk oral literary creations. Later, through great writers like Homer, The poet's refinement and contemplation has become a treasure of world literature and an important source of classical art. In the 9th century BC, Greece established hundreds of city-states, large and small. The establishment of these city-states adapted to the development of productivity and also mobilized the consciousness of the Greeks in creating culture. While absorbing the nutrients of the Aegean civilization and Homer's poetry, Greek society in the ancient times also underwent Solon's reforms. The politics, economy, and culture of the society continued to develop and grow in harmony, thus accumulating rich resources for the creation of culture in the classical era. cultural heritage and the inner driving force of cultural change.
(2) Democratic politics and national spirit gave birth to cultural consciousness
Ancient Greece was the first to implement slave-owner democracy in human history, which had a great impact on the social development of Greece. provided a huge impetus. Compared with the highly centralized and authoritarian slavery in ancient Eastern countries, Greek city-state slavery, especially in Athens, was relatively democratic (of course, this was only the democracy of slave owners).
The Greek national spirit is an important driving force for the prosperity of Greek culture; without the Greek national spirit, there would be no prosperity of Greek culture. The national spirit of the Greeks is a national spirit full of vitality and vitality.
In addition, the Greeks valued education and the spread of wisdom. The Greeks believed that the purpose of education was to enable the public to pursue a noble life and think about the world. At that time, freedom of speech was implemented, and wise men could be free. Traveling around to give lectures and spread wisdom, it can be seen that this is an era with the concept of democracy and freedom, creating a unique ancient democratic politics.
Chapter 5 Science in the Hellenistic Period
(Excerpted from Chapter 5 of Wu Guosheng's "The Process of Science")
During the Peloponnesian War, The kingdom of Macedon in northern Greece grew and prospered. After King Philip II came to the throne in 356 BC, he paid attention to learning advanced Greek culture. At the same time, he enriched the country and strengthened his army, expanded his army and prepared for war, becoming a major military power in the Greek world.
. In 338 BC, Philip II defeated the anti-Macedonian coalition and held the Panhellenic Congress in Corinth the following year, establishing Macedonia's dominance over the Greek states. In 336 BC, Philip II was assassinated in a palace coup. 20-year-old Prince Alexander ascended the throne and began to launch an aggressive war in the East.
Alexander's Eastern Expedition first targeted the Persian Empire. He defeated the Persian army in 334 BC, and the following year he captured Syria, Phoenicia and Egypt. In 331 BC, Alexander set out from Egypt and fought another decisive battle with the Persian army, completely defeating the Persian Empire. After Alexander designated Babylon as his new capital, he continued his eastward expedition and reached the Indus River Valley. However, because the soldiers were not accustomed to the climate, the army did not advance eastward.
Alexander’s more than ten years of military campaigns in the north and south established a huge empire spanning Europe, Asia and Africa. This empire was centered in the East, but with Greek culture as the dominant culture. Not in vain was he a student of Aristotle. The military wizard Alexander attached great importance to the development of academic careers. Throughout his career, he was always followed by a group of scholars. Everywhere they went, geographers drew maps and naturalists collected specimens - it is said that Aristotle's biological research greatly benefited from these rare specimens
< p>. Like Napoleon in modern times, Alexander also valued the role of science and technology in war. It is said that thanks to the help of engineers, the level of Alexander the Great's siege warfare once reached the height of modern times. In this way, Greek civilization spread to a wider area with Alexander's expedition. From then on, the culture in these areas was also called Hellenist (Hellenist) culture.The most dazzling pearl of Hellenistic culture is Alexandria, the city founded by Alexander in Egypt.
This city named after Alexander the Great produced the most outstanding scientists and scientific achievements in the ancient world. The so-called Hellenistic period in this chapter mainly refers to the science of Alexandria. science.
1. Alexandria
Alexandria is located at the mouth of the Nile River and is a port city. After Alexander the Great died of illness in 323 BC, his empire split into three parts: Macedonia under Antigonus, and Seleucid rule. Syria under Ptolemy, and Egypt under Ptolemy. Ptolemy was a general under Alexander and a Greek. He also studied under Aristotle and attached great importance to the development of Greek academic undertakings. He set up the capital of Egypt in Alexandria, used government power to support academic undertakings, and created the glorious scientific culture of the Alexandrian era.
Alexandria, or the city of Alexandria, began to develop rapidly with the arrival of Alexander the Great. Macedonian military commanders
brought Greek culture here. They built a large number of Greek-style buildings in the city, the most majestic of which was the Royal Palace, which is said to account for a quarter or a third of the entire city. The lighthouse of Alexandria Port is known as one of the seven wonders of the ancient world
.
The greatest contribution of the Ptolemaic Dynasty to the development of science was the establishment of Musion, the largest academy in the world at that time. This is a comprehensive education and research institution, with the purpose of disseminating and developing scholarship. It was built near the palace, and some people say that it is part of the palace. The Ptolemaic dynasty indeed regarded it as a "royal academy". Musaion originally meant the temple dedicated to Musa, the goddess of wisdom. Since Plato's Akademi Academy and Aristotle's Lyceum Academy both had Musaion, so
p>
, Alexandria named its academic institution Musion. The word later evolved into the English word "museum".
As a result, many modern people mistakenly regard Muséan as a museum. In fact, in Alexandria, there are not only museums with collections of cultural relics and specimens, but also zoos, botanical gardens, observatories and laboratories. Of course, the most noteworthy thing
is its library, with a collection of 700,000 volumes, which was the largest library in the world at that time.
Egyptian papyrus is abundant and easier to obtain in Alexandria than in mainland Greece. This is one of the advantages for collecting books.
The so-called collection of books in ancient times also meant copying books. Because there was no printing technology in ancient times, books were copied one by one. The Ptolemaic dynasty spent a lot of money to hire a large number of copyists at Musion College, which was another important condition that made it possible to collect a large number of books. It is said that the government ordered that all ships arriving in Alexandria must hand over the books they carry for inspection. If there are books that are not found in the library, they will be copied immediately, the originals will be kept, and the copies will be sent Dedicated to the original owner. This alone shows how much the Ptolemaic dynasty valued cultural accumulation. The flourishing humanities and developed economy made Alexandria the largest academic center in the world at that time. Scholars from all over the world came here to study, and almost all the most famous scientists at that time stayed in Alexandria.
The Muséan Academy lasted for six hundred years, but only the first two hundred years were an important period in the history of science. During this period, scientific talents emerged in large numbers and academic undertakings prospered. Later, as the Ptolemaic family became more and more Egyptian, their interest in Greek learning became more and more indifferent. It is said that Ptolemy VII (146 BC-117 BC) even persecution of the Greeks. Later, Egypt was conquered by the Romans and became a province of Rome, and Greece's scientific heritage was gradually lost.
2. Euclid's "Elements"
In the history of science, there is no other book that combines the outstanding academic level with Euclid's "Elements". Perfectly combined with broad universality
. It integrates the culmination of Greek classical mathematics, constructs the first magnificent deduction system in the history of world mathematics, and plays an immeasurable role in promoting the development of mathematics in later generations; at the same time, it is an excellent book The textbook has been used without any change for more than two thousand years. In Western history, perhaps only the Bible can be compared in terms of number of copies and printings. It is estimated that since printing was introduced to Europe, "Elements" has been reprinted thousands of times and translated into various languages. Xu Guangqi, an outstanding scientist in my country's Ming Dynasty, collaborated with the missionary Matteo Ricci to translate the first six volumes of "Elements of Geometry" in 1607, which was the first Chinese translation in history. The word "geometry" and the title "Elements of Geometry" were both coined by Xu Guangqi
for the first time.
Euclid's life is unknown.
According to the records of Proclus (about 410-485), he came to Alexandria to study and lecture at Musion College in Alexandria at the invitation of King Ptolemy in about 300 BC. Before that, He was educated in Plato's Academy in Athens and was deeply influenced by Plato. There are only two short stories left in history about Euclid. The first one is recorded by Ploquero. It tells that King Ptolemy asked Euclid to teach him geometry. He taught him geometry for a long time, but King Ptolemy didn't.
Understood, he asked Euclid if there was a more convenient way to learn. Euclid replied: "In geometry, there are no shortcuts just for kings." This sentence later became a scholarly motto that has been passed down through the ages. The second story was recorded by Stobaeus (about
AD 500). It tells the story of a young man who was learning geometry from Euclid. As soon as he learned a proposition, he asked
p>
What use will Euclid have after learning geometry? Euclid was very dissatisfied and said to his servant: "Give this student three coins and let him go." He actually wanted to Gaining practical benefits from geometry." This story shows that Euclid emphasized the non-utilitarian nature of geometry.
It also reflects that he was deeply influenced by Plato.
"Elements of Geometry" ***13 articles. The first part talks about straight sides, including the congruence theorem, the parallel theorem, the Pythagoras theorem
, elementary graphing methods, etc.; the second part talks about using geometric methods to solve algebraic problems, that is, using geometric methods to solve algebraic problems. Methods for addition, subtraction, multiplication and division, including finding
area, volume, etc.; Part 3 talks about circles and discusses some properties of chords, tangents, secants, central angles and circumferential angles; Part 4
p>We still talk about circles, mainly about the inscribed and circumscribed shapes of circles; Part 5 is the theory of proportion; Part 6 uses the established proportion discussion
Discuss similar shapes; Part 7 Chapters 8, 9, and 10 continue to discuss number theory; Chapters 11, 12, and 13 talk about solid geometry, and Chapter 12 mainly discusses the method of exhaustion, which is the early source of modern calculus thinking. All 13 articles cover almost all the content in today's elementary geometry course
.
It is generally believed that the content described in "Elements of Geometry" belongs to the Greek classical era, and almost all theorems were proved at that time
Euclid's main contribution was to bring them together into a perfect system and to give more concise proofs of certain theorems. Today we have no way of knowing which theorems were discovered by which mathematicians and when. It is said that one of Aristotle's students named Eudemus (about the second half of the 4th century BC) wrote a history of geometry, which recorded: The development of Greek mathematics up to the time of his arrival, but this book has long been lost. But it can be inferred that Ionian nature
Philosophers such as Thales, Anaximander, Anaximenes, Anaxagoras, Pius of the South Italian School Corus and his disciples - the most famous of whom are Alquita of Tarentum, Parmenides and Zeno of the Eleatic school, The Sophists, the disciples of Plato's school - the most famous of which are Eudoxus, the disciples of Aristotle's school, etc. All have made contributions.
Euclidean, Apollonius and Archimedes are collectively known as the three major Greek mathematicians. We will discuss the work of Archimedes in detail below, but here we will only mention Apollonius. Apollonius was born in Perga in northwest Asia Minor around 262 BC, a century later than Euclid. It is said that he went to Alexandria to study mathematics with Euclid's students in his youth. He can be regarded as Euclid's disciple. He has been studying mathematics in Alexandria ever since. His main work
is the study of conic sections. His research field seems to be very specialized, not as broad as Euclid's "Elements of Geometry". However, the reason why he is as famous as Euclidean is because of his research on conic sections. The level of research is extremely high and unprecedented. People today can't do it better just by using geometric methods. The so-called conic section is a planar shape cut out of a cone with a plane
As mentioned in the previous chapter, it was discovered by the Plato school. However, they did not know that the hyperbola had two branches, but Apolloni did. It is quite complicated to deal with conic section problems using pure geometric methods. Today's mathematicians are more likely to use analytical geometry methods to turn geometric problems into algebraic problems, which is both simple and convenient. But in any case, Apollonius
's work demonstrated superb geometric thinking ability and was the pinnacle of classical Greek mathematics. Moreover, his research on conic sections
became the reference for later generations. Related research has laid the foundation.
3. Aristarchus: Pioneer of Heliocentric Theory
Almost all middle school students know that it was Copernicus who discovered that the earth revolves around the sun and not the other way around.
Awakened from the dream of centralism.
In fact, as early as the Greek era, there was an astronomer who proposed the theory of heliocentric earthquakes. He was the famous Alexandrian astronomer Aristarchus.
Aristarchus was born in Samos, the hometown of Pythagoras, in the Ionian region around 310 BC. He must have been to Athens in his youth
. It is said that he studied in the Lyceum Academy and was mentored by Stratus, the third generation senior of the academy. Later, he went to Alexandria, where he conducted astronomical observations and published his theory of the universe. However, his theory seemed too radical at the time and was not taken seriously by people. If Archimedes had not mentioned him, we would not know this person at all today
< p> His main claim was that it was not the sun, moon and stars that revolved around the earth, but that the earth and stars revolved around the sun together. Obviouslyhis idea inherited the central fire theory of the Pythagoreans, but placed the sun in the position of the central fire
. He said that the diurnal rotation of stars is actually the result of the rotation of the earth on its axis. This idea was indeed genius, but it was also so radical that people at the time did not believe it.
There are several reasons for rejecting Aristarchus' views. First, it contradicts the widely recognized physical theory of Aristotle and Dodd. In Aristotle's view, if the earth was moving, then everything on the earth would fall behind the earth, but in fact no such thing happened. This reason is very acceptable to people. We all know in common sense that if a bottle falls from a moving train, the train will soon leave the bottle behind. This question will only have a complete answer
after the discovery of the law of inertia. Second, many astronomers have proposed that if the earth is moving, its position relative to the stars should change. However, we have not observed such a change in position. We don't know how Aristarchus answered the first question, but it is said that he answered the second question correctly. He
said that the stars are so far away from us that the earth's orbit is insignificant compared with them, so the changes in the position of the stars are not noticed by us
.
Another important astronomical achievement of Aristarchus was the measurement of the distances and relative sizes of the sun, moon and earth. This work was recorded in his book "On the Dimensions and Distances of the Sun and the Moon", which has been passed down to this day. Aristarchus knew that
moonlight is the reflection of sunlight by the moon. Therefore, when the moon is exactly half bright and half dark when viewed from the earth, the sun, moon
and the earth Forming a right-angled triangle, the moon is at the vertex of the right angle. The angle between the sun and the earth and the moon and the earth can be measured from the earth. If you know the angle, you can know the angle between the sun and the earth and the moon and the earth. relative distance between them. The angle measured by Aristarchus is 87°. Therefore, he estimated that the distance between the sun and the earth is 20 times the distance between the moon and the earth. In fact, the angle should be 89°52′, and the distance between the sun and the earth is 89°52′.
The distance is 346 times the distance between the moon and the earth. But Aristarchus's method was absolutely correct. After getting the relative distance, he calculated the actual sizes of the sun and moon from the sizes of the sun and moon seen on the earth. Similarly, because he did not have sufficiently accurate measurement data, his estimation error was very large, but he at least realized that the sun is a celestial body that is much larger than the earth. Because of this, he does have reason to believe that it is not the sun that revolves around the earth, but the earth that revolves around the sun, because it is not natural for large objects to revolve around small objects. Nearly two thousand years later, Copernicus inherited Aristarchus's cause
and advocated the theory of heliocentric geomotion. The refutations he encountered were almost the same, and the reasons he used to defend himself were also almost the same. We will talk about the details later. ?
4. Ancient scientific giant Archimedes
Archimedes, the greatest scientist in the ancient world, was born in Syracuse, Sicily, southern Italy, around 287 BC< /p>
His father was an astronomer, which enabled Archimedes to learn a lot of astronomical knowledge since he was a child. In his youth, like many other young people seeking education, he came to Alexandria, the academic center of the ancient world. Here, he studied geometry under Conon, a disciple of Euclid. It is said that the Archimedes spiral was actually discovered by Conon. A few years later, Archimedes did not stay in Alexandria, but returned to his hometown of Syracuse. It is said that he was related to King Hiron II of Syracuse, and it was Hiron II who invited him to return to his country.
Archimedes was a scientific giant in the Hellenistic era. During the Hellenistic period, the pure, ideal, and free deductive science of the classical Greeks
effectively integrated with the practical and applied computational science of the Orientals, which actually formed the basis of modern science
p>
--he emphasized both mathematics and deduction as well as operation and effectiveness--he set an example, and Archimedes was an outstanding representative of Hellenistic science
.
He is not only a first-rate genius in mathematical and physical sciences, but also has made many achievements in engineering technology. Archimedes is also the most legendary scientist in Greece. He has many legendary stories, and each story reveals the style of Greek science from one side.
As mentioned before, Archimedes, Euclid and Apollonius are listed as the three major Greek mathematicians. Some people even say that he is the greatest in history.
One of three mathematicians (the other two being Newton and Gauss). His main mathematical contribution was his work on finding
area and volume. Greek mathematics before him did not pay attention to arithmetic calculations. Regarding area and volume, mathematicians could only prove the ratio of two areas or volumes, instead of calculating the actual value of each area or volume. How much is it. When
even the area of ??a circle cannot be calculated, because the more accurate value of π is not yet known. Starting from Archimedes, or starting from the mathematicians of Alexandria represented by Archimedes, arithmetic and algebra began to become an independent mathematical discipline.
A famous theorem discovered by Archimedes is that the area of ??any sphere is two-thirds of the surface area of ??the circumscribed cylinder, and the volume of any
sphere is also the circumscribed cylinder. Cut two-thirds of the volume of the cylinder. This theorem is derived from the theorem that the area of ??a sphere is equal to four times the area of ??a great circle. It is said that this theorem was engraved on Archimedes' tombstone in accordance with his will.
Only the area of ??a right-sided shape and the volume of a straight-sided body can be calculated simply by arithmetic, while the area of ??a curved surface and the volume of a three-dimensional body composed of the motion of the curved surface
Neither can be calculated directly. Eudoxus invented the exhaustive method to solve the surface area problem, and Archimedes further developed the exhaustive method. Most of his theorems about the area of ??a sphere and the volume of a sphere were proved by the exhaustive method
. The so-called exhaustion method is to use inscribed and circumscribed straight sides to continuously approach curved sides. This is the direct precursor of the modern limit concept.
Using the exhaustion method, Archimedes calculated the perimeter starting from a regular 6-sided polygon to a regular 96-sided polygon, and obtained 3 <π
<3. Taking two decimal places, he obtained π=3.14. In addition to the calculation of spherical area and spherical volume, Archimedes also did a lot of outstanding work on the quadrature of paraboloids and rotating paraboloids.
Another famous work of Archimedes in mathematics is the creation of a method for recording large numbers, which is recorded in his
The Number of Sands in the Ganges (The Number of Sands in the Ganges). Originally titled "The Grit Counter"). At that time, the Greeks used letters to record numbers, and it was especially inconvenient to remember large numbers.
Archimedes set himself a task: If the universe is full of sand, how to express this astonishing number? He divided numbers into several levels, from 1 to 108 as level 1, from 108 to 1016 as level 2, from 1016 to 10
24 as level 3, until 10, represented by P. But P is still just the first digit in the notation, P2 is the 2nd digit, P3 is the
3rd digit, until P108 is the 108th digit. Archimedes speculated based on the popular cosmology at the time that the grains of sand in the universe were an 8th level number, using only the first digit.
Archimedes' work in physics mainly includes two aspects. One is the study of balance problems, which is the principle of leverage.
This is the first one. The other is a study on the buoyancy problem. The buoyancy law learned in middle school physics falls into this category. Archimedes's work in these two aspects is recorded in his works "On the Balance of a Tablet" and "On Buoyancy". Fortunately, both of these works have been popular.
Passed down. In "On the Balance of a Flat Plate", Archimedes proposed the principle of the lever in the form of a mathematical axiom, that is, if the lever is balanced, the product of the force (weight) at both ends of the fulcrum and the length of the lever arm is equal . Here, it is important to establish the concept of leverage, which includes concepts such as fulcrum, moment arm, etc. For general flat objects, namely flat plates, in order to apply the lever principle, Aki
Mead also established the concept of "center of gravity". With the center of gravity, the balance problem of any flat plate can be solved by the lever principle.
And finding the center of gravity can be reduced to a purely geometric problem.
The lever principle explains why a person can lift a very large stone with a stick. In this regard, Archimedes has a famous saying:
"Give me a fulcrum and I can move the earth." It is said that King Hieron was suspicious of this statement, and Archimedes did not explain much.
He just invited him to the port to watch a demonstration. Archimedes installed a set of pulleys there in advance. He asked someone to tie one end of the rope to a fully loaded ship in the port, and he sat on a chair and easily used a He dragged the big boat to the shore with one hand
. The king was immediately impressed.
The legend about the law of buoyancy is more familiar. King Xilong asked a goldsmith to make a crown of pure gold. After the crown was completed, the king felt that it did not look like pure gold, but there was no way to confirm this.
He asked Archimedes to do this identification work,
and asked that the crown itself not be damaged, because it was not certain that it was mixed with other metals. p>There is no adulteration, and the price is too high. Archimedes has been thinking about this problem, but has not found a better identification method.
One day, when he was thinking deeply, the servant asked him to take a bath. This time the servant filled the water too full and when he sat down in the tub a lot of water overflowed. He looked at the overflowing water absentmindedly, and suddenly he became enlightened. He
realized that the volume of the overflowing water should be exactly equal to his own volume. If he immersed the crown in water, he could know the volume of the crown based on the
liters on the water surface. Dip a piece of gold of the same weight as the crown in water and you will know whether its volume is the same as the crown. If the crown is larger, it means it is adulterated. Archimedes was very excited when he thought of this. He jumped up from the bathtub and ran out naked, shouting, "Yuri" as he ran.
Ka (Greek: discovered), Eureka (discovered).” Archimedes' "Eureka" shouted out the surprise of mankind when he discovered the secrets of nature. It is to commemorate this event that the most famous invention expo in the modern world is named "< /p>
Eureka" named.
Perhaps in the eyes of today's people, Archimedes' discovery is not surprising and very ordinary, but we must note that the ancient Greeks
had no specific gravity. It is indeed remarkable to arrange such an experiment without the concept, or even the concept of weight. Interestingly
Interestingly, the famous story of Cao Chong weighing an elephant in Chinese history also tells the story of young Cao Chong using the principle of buoyancy to weigh an elephant
Archimedes used the principle of buoyancy to weigh an elephant. Experience further summarizes the principle of buoyancy: the upward buoyancy force exerted on an object immersed in a liquid is equal to the weight of the liquid displaced by the object. This principle quantitatively gives the magnitude of buoyancy and is one of the basic principles of fluid statics.
It is said that Archimedes made many inventions in mechanical engineering. While studying in Alexandria, he invented a spiral water lift, which is still called Archimedes' spiral, and was still used in Egypt in the 20th century
p>
Mechanical. It is also said that he built a planetarium that used water power as power, which could simulate the movement of celestial bodies and demonstrate solar and lunar eclipses.
The death of Archimedes is even more legendary. In Archimedes' later years, at the end of the 3rd century BC, Rome and Carthage were at war, and Syracuse was also involved. Rome was a newly emerging country in northern Italy. At that time, it had conquered the entire Italy and its power had expanded to the Mediterranean. Carthage was located in what is now Tunisia in North Africa. It was also a powerful country that monopolized all commerce in the Western Mediterranean. At first, in order to deal with the colonial rule of the Greeks, Carthage united with Rome. But after Greece's power was weakened, the two sides began to fight for the hegemony of Sicily, and the famous Punic wars broke out in history. Syracuse, located in Sicily, had always surrendered to Rome. However, in 216 BC, Carthage's famous military commander Hannibal defeated the Roman army, prompting the new king of Syracuse, Hiron. His grandson Hieronymus was eager to form an alliance with Carthage. Hieronymus obviously had no foresight and did not realize that although Rome was defeated for a while, its strength would soon recover. Sure enough, after Rome regained its rest, it attacked Syracuse first.
In this battle to defend Syracuse, Archimedes showed his talents and defeated the Roman army, but ultimately sacrificed his life
The Roman army in Marseille General Ras led an attack on Syracuse by sea and land at the same time. It is said that Archimedes used the principle of leverage to build a batch of trebuchets, which effectively prevented the Romans from attacking the city; it is also said that Archimedes invented the big crane
< p>The chariot lifted the Roman warship directly out of the water, making it impossible for the navy to approach the ancient city of Syracuse. On another occasion, Archimedes summoned all the women, old and children in the city to hold mirrors and arrange them in a fan shape to focus the sunlight on the Roman warships and direct the enemy's ships. All burned. These new weapons made the Roman army very afraid, and the ancient city of Syracuse could not be conquered for a long time. There were rumors in the armyTalk about the power of Archimedes, Marcellus also smiled bitterly and admitted that this was a battle between the Roman fleet and Archimedes alone
< p>Fight.After three years of siege, Syracuse was captured due to the appearance of traitors within the city. Before the siege, Marcellus ordered the soldiers to capture Archimedes alive and not to harm him. But before the order was issued, the city had already been captured. When a Roman soldier broke into Archimedes' room, he was concentrating on a geometric problem on the sand.
Because he was too focused on deductive logic, he did not realize that the danger was approaching. The red-eyed soldier shouted loudly and drew his sword when he received no answer
At each other, Archimedes, who was deep in thought, only shouted "Don't step on my circle" before he was stabbed by the Roman soldier. die. Afterwards, Marcellus was very sad because he knew the value of Archimedes. The Greek scientific elite died in this way under the swords of barbaric and martial Roman soldiers. The symbolic significance of this incident was soon revealed.
5. Eratosthenes determined the size of the earth
The Greeks were the first people to believe that the earth was a sphere. Since Pythagoras, the two-sphere universe model of celestial sphere and Earth
has been the basis of Greek cosmology theory. The concept of the Earth provides a basis for explaining many near-Earth astronomical phenomena such as lunar eclipses
p>
The basis for belief, and the concept of the celestial sphere satisfies the Platonic school’s requirement of “saving phenomena” very well. Alexandria
Two famous scholars established these two concepts based on empirical observation and rational judgment. One of them was Erato Senes, who scientifically established the concept of the earth and quantitatively determined its size. The other was Hipparchus, who founded spherical geometry and provided mathematical tools for quantitatively describing the motion of the celestial sphere. Eratosthenes was born in the North African city of Serene (today's Shahhat, Libya) around 276 BC. He studied in Plato's Academy in his youth. He has wide interests and is knowledgeable. He is the most encyclopedic scholar in the ancient world after Aristotle. It is only because all his works have been lost that people today do not know much about him. Such an encyclopedic figure was naturally favored by the Ptolemaic dynasty, which cherished talents. They invited him to Alexandria to serve as librarian of the Library of Alexandria. This position suited him well, so he came to Alexandria, where he remained until his death
at the age of 80. According to historical records, Eratosthenes' scientific work includes mathematics, astronomy, geography and the history of science: he invented the sieve of Eratosthenes to determine prime numbers in mathematics; in astronomy In geography, he measured the angle between the ecliptic and the equator; in geography, he drew the most complete map of the world at that time, stretching from Ceylon to the east, the British Isles to the west, the Caspian Sea to the north, and the Caspian Sea to the south. Ethiopia
Obea; perhaps taking advantage of the librarian, he also compiled a chronicle of Greek science, which unfortunately has been lost
Eratosthenes The most famous achievement is the determination of the size of the Earth, a method that is entirely geometric. Assuming that the earth is really a sphere, then the angle between the sun's rays and the ground plane is different at different places on the earth at the same time. As long as the difference in angle and the distance between the two places are measured, the circumference of the earth can be calculated. He heard someone say that in Aswan, Egypt, the sunlight at noon on the summer solstice could shine directly into the bottom of the well, indicating that the sun was perpendicular to the sea at this time. Well ground.
He measured the distance from Sein to Alexandria, and also measured the time of the summer solstice at noon