More than two thousand years ago, the entire western part of the Mediterranean coast was engulfed in the flames of a grandiose war. Military actions took place in Italy and Sicily, North Africa and Spain. This war is known in world history as the Second Punic War, in which Rome and Carthage fought for dominance in the Mediterranean.

The famous commander from Carthage, Hannibal, in order to deliver a fatal blow to the very heart of the enemy, conceived a rather bold plan to fight Rome - in Italy itself. In 218 BC new era With a large army and war elephants, he crossed the Pyrenees Mountains, southern Gaul and penetrated through the Alps into Northern Italy. On the fields of Italy, Hannibal defeated three Roman armies in succession and in 216 dealt a crushing blow to the Romans at Cannae. The entire Roman army was destroyed. A number of Roman allies (Capua and others) went over to the side of Carthage. The freedom-loving citizens of the city of Syracuse also rebelled against Roman rule.

Syracuse, one of the greatest cities of antiquity, the center of Greek science and art in the West, was a Greek colony located on the southeastern coast of Sicily. The circumference of the powerful city wall was 23.5 kilometers. For a long time Syracuse was independent state, the first Greek naval power. But in the 3rd century. BC, Rome advanced on Sicily from the north, and Carthage from the south. During the First Punic War, Sicily was conquered by the Romans, and the people of Syracuse had to accept Roman hegemony.

To punish the disobedient for the uprising, the Roman fleet and army under the leadership of the talented commander Marcus Claudius Marcellus approached the city in 213. Horror took possession of the residents. Marcellus had just stormed another Sicilian city, Leontina, and executed two thousand defectors from the Roman camp. The same fate awaited this city.

More than a hundred Roman ships entered Syracuse harbor. Marcellus formed them in battle order. Penteres tied in pairs with wooden towers, lifting engines and siege weapons came close to the wall. Marcellus signaled for the machines to raise the drawbridges to the level of the walls and lower them onto the walls. Over the lowered bridges, the Roman soldiers were supposed to burst into the city like an indomitable avalanche. The fall of the city seemed inevitable. The assault began from sea and land. But before the vehicles on the penthers had time to raise the drawbridges, before the catapults and ballistae had time to throw their shells, something unexpected happened.

Iron hooks and “paws” suddenly descended from huge levers placed on the battlements of the walls. They clung to the bows of ships, lifted them up, overturned them, smashed them against coastal rocks and cliffs at the foot of the city wall, and drowned them in the depths of the sea. Then Marcellus, according to the Greek historian Plutarch, advanced a ram onto the platform. As he approached the wall, the townspeople threw several stones weighing more than a hundred kilograms at him. They completely destroyed it. The stones were followed by lead balls and huge logs that sank ships in the sea.

The broken Roman ships retreated from the city wall. Marcellus decided to resume the assault at night. He hoped that the vehicles throwing shells would be powerless at night. Shells thrown at random will fly over the heads of the besiegers. But the talented leader of the defense also took this circumstance into account: he positioned his spear-throwing machines so that they constantly threw out short spears that hit the enemy.

The Roman fleet received a well-deserved lesson. The same fate befell the Roman army on the landward side. And here the Roman siege weapons and soldiers were met with iron hooks, hooks, and “scorpions” that picked up the soldiers and threw them onto the stones. The proud Roman had to give up thoughts of taking the city by storm. He decided to go on a blockade and starve the residents to death. But it was difficult for the army to cordon off the entire city, and the residents maintained contact with the outside world.

Archimedes - life and scientific works

Who was this most talented engineer, organizer of defense, builder of ingenious machines, who forced the invincible Roman army to retreat?

It was greatest physicist and the ancient mathematician Archimedes, who applied all his genius abilities to organize the defense of his hometown.

Archimedes was born in Syracuse in 287 BC. According to the famous Roman politician and orator Cicero, Archimedes was of low social status and lived poorly. Plutarch claims that Archimedes was already interested in mathematics as a child. A trip to Egypt, where he visited the city of Alexandria, the center of Hellenic culture, had a great influence on the young man. Returning to his homeland, he devoted himself entirely to science and wrote a number of brilliant mathematical works.

Most Greek scientists of the IV-III centuries. BC. was not only condescending, but also somewhat contemptuous of mathematics if it pursued utilitarian goals. Archimedes did not dissociate himself from the people and did not isolate himself in his office from the everyday needs of his fellow citizens. He tried to apply his knowledge to practical life, make all the achievements of science the property of the people and often demonstrated his discoveries to the citizens of Syracuse.

Unfortunately, not all of the genius’s works have survived. IN different time The following works of his were found:

1. On the equilibrium of plane figures.
2. About the squaring of a parabola.
3. About floating bodies.
4. About measuring a circle.
5. About the ball and cylinder.
6. About conoids and spheroids, i.e. about bodies learned from the rotation of various figures.
7. About spirals.
8. "Psummit."
9. Individual theorems (lemmas).
10. Stamachion - about the rearrangement of plane figures.

In 1907, a new manuscript “Ephodik” (manual) was found, which contains theorems on the volumes of cones, as well as spheroids and conoids.

The following works of the scientist are considered lost:

1. About a heptagon in a circle.
2. About the contact of circles.
3. About parallel lines.
4. About triangles.
5. About definitions and data.
6. Book "Archai".

In his works “On the Ball and the Cylinder” the scientist proves that the ratio of the volumes of a cone, hemisphere and cylinder with the same bases and heights is equal to the ratio 1: 2: 3.

Among other problems proposed in the second book, there is the famous problem of dividing a ball into two parts by a plane. Archimedes gave the correct solution to this problem, leading it to an algebraic problem. Archimedes attached special importance to this work.

In the book about the spiral, the scientist examines the properties of the so-called Archimedean spiral.

In his work “Psammit,” he set out to prove that it was possible to express gigantic numbers.

In his works “On Floating Bodies,” Archimedes establishes the basic principles of hydrostatics and hydrodynamics. This law was found thanks to the following case. The ruler of Syracuse ordered a gold crown from a jeweler. But he was informed that the jeweler had hidden some of the gold and replaced it with silver! The king could not verify the correctness of the report and turned to the scientist with a request to find out how much silver was mixed.

Archimedes, while taking a bath one day, noticed the fact that as much water flowed out of the bath as his body displaced. Delighted by this discovery with the exclamation “Eureka! Eureka!”, he jumped out of the bath and ran undressed to test his theory. Archimedes is credited with up to forty discoveries in the field of mechanics. When the Syracusan king built his famous ship with a displacement of 4000 tons, Archimedes equipped this ship with a stone-throwing machine that threw stones weighing 80 kg and spears over a considerable distance. He built a screw, named after him the Archimedean screw. This is a water-lifting machine in which a helical spiral runs inside a cylindrical pipe. The pipe is open at both ends and placed at an angle. With strong rotation, the pipe captures water at its lower end, the water rises upward in a spiral and pours out at the upper end. There is evidence to suggest that the Archimedes screw was used to drain swamps in Egypt. Later it served as the basis for the construction of a ship propeller and found application in the automotive industry.

The scientist developed the theory of a compound block, lever and screw and applied them in practical life. He used blocks to move large weights. Archimedes famously exclaimed: “Give me a point of support, and I will move the Earth.”

He built a planetarium or “aerial globe” that rotated using a system of blocks. In the planetarium, the movement of the planets around the Earth was visible.

Death of Archimedes

But let's return to the city besieged by the Romans. The siege of the city has been dragging on for three years. Archimedes mobilized all his knowledge by building new machines. To his skillful constructions, popular rumor also added legendary ones (some writers, for example, say that Archimedes allegedly built burning glasses and, with their help, collected the sun's rays, aimed them at Roman ships and burned them).

The class struggle intensified among the besieged. The Syracusan nobility, who supported the side of Rome, entered into negotiations with Marcellus, and the city was taken by the Romans due to the treason of the nobility. Marcellus allowed his soldiers to “loot treasures and capture slaves.” Embittered by the long siege, thirsty for booty, the Roman soldiers rushed like bloodthirsty jackals towards the defenseless city. They broke into homes, robbed jewelry, mercilessly killing residents, including the elderly and children.

Archimedes sat deep in his thoughts over the drawings. He described geometric figures on the floor with a compass, not noticing the orgy of robbery and murder taking place in the city. Suddenly a Roman soldier rushed towards him with a drawn sword. Seeing him enter, Archimedes shielded his geometric drawings from him and said: “Don’t spoil my circles for me.” The warrior, intoxicated by the thirst for profit, in response to the words of Archimedes, dealt him a fatal blow with his sword.

Thus the great luminary of science of the ancient world went out in 212 BC. Out of respect for the brilliant thinker, Marcellus ordered to bury him with great honor. A cylinder with a ball inscribed in it was placed on the grave (this was the desire of Archimedes himself). But the grave was soon overgrown with bushes. Only in 75 BC. e., the famous Cicero, being a ruler in Sicily, found among the abandoned graves a monument to Archimedes, depicting a cylinder. Cicero exclaims with bitterness: “So one of the most glorious states, which once gave birth to so many learned people, did not know where the tombstone of the sharpest intellect of its citizens was.”

After the fall of Greek culture, Archimedes was forgotten. Only the Arabs, who appreciated the mathematical genius of Archimedes, translated some of his works into Arabic.

During the Renaissance, Archimedes' works were brought out of obscurity, published, and aroused the admiration of scientists.

Summing up the scientific and scientific-practical activities of Archimedes, it is clear that he is rightly called the father of physics, physical experience, physical mechanics. Archimedes founded statics as mathematical science, gave the foundation to hydrostatics, solved many geometric problems, developed methods for calculating the volume of bodies and the center of gravity, and established a connection between geometry and mechanics.

The greatest mathematician of antiquity, Archimedes, was a patriot who passionately loved his homeland, its independence and culture.

Archimedes, an outstanding ancient Greek mathematician, inventor and engineer, lived in the 3rd century BC (287 - 212 BC).

Archimedes' friend Heraclides wrote a biography of the great scientist, but it was lost and now very little is known about his life. Little is known about his life also because almost all the authors who conveyed his biography themselves lived much later. As a result, the biography of Archimedes is filled with legends, some of which have become very popular. However, legends about Archimedes were created during his lifetime. Much less is known about the scientist’s personal life than about his science.

From the biography of Archimedes:

Archimedes was born in the city of Syracuse in Sicily. At that time it was one of the first ancient Greek colonies on the island of Sicily and was called Magna Graecia. It included the territory of modern Southern Italy and Sicily. + Archimedes was born in 287 BC. e. The date of birth is known from the words of the Byzantine historian John Tzetz. He lived in Constantinople in the 12th century. That is, almost one and a half thousand years after Archimedes. He also wrote that the famous ancient Greek mathematician lived 75 years. Such accurate information raises certain doubts, but we have to believe the ancient historian. The biography of Archimedes is known from the works of Titus, Cicero, Polybius, Livy, Vitruvius and other authors who lived later than the scientist himself. It is difficult to assess the reliability of these data.

Archimedes probably spent his childhood in Syracuse. Elementary education The scientist probably got it from his father. His father, presumably, was the astronomer and mathematician Phidias. Plutarch also claimed that the scientist was a close relative of the ruler of Syracuse, Hiero II.

Being related to such celebrities, Archimedes was able to receive an excellent education: he studied in Alexandria, which at that time was famous as a center of learning. Alexandria of Egypt for several centuries was the cultural and scientific center of civilized Ancient World. There Archimedes met and became friends with many other great scientific figures of his time.

Bust of Archimedes

It was in Alexandria that a young man striving for knowledge established friendships with the mathematician and astronomer Conon of Samos and the astronomer, mathematician and philologist Erastothenes of Cyrene - these were famous scientists of that time. Archimedes struck up a strong friendship with them. It continued throughout my life, and was expressed in correspondence.

Also within the walls of the Library of Alexandria, Archimedes became acquainted with the works of such famous geometers as Eudoxus and Democritus. He also learned many other useful knowledge. After training, he returned to his homeland and could fully engage in science, since he did not need funds. In his homeland in Syracuse, Archimedes quickly established himself as an intelligent and gifted person, and lived for many years, enjoying the respect of others, and lived there until the end of his life.

Nothing is known about his wife and children, but there is no doubt about his studies in Alexandria, where the famous Library of Alexandria was located.

Archimedes died during the Second Punic War, when Roman troops captured Syracuse after a 2-year siege. The Roman commander was Marcus Claudius Marcellus. According to Plutarch, he ordered that Archimedes be found and brought to him. A Roman soldier came to the house of an outstanding mathematician while he was pondering mathematical formulas. The soldier demanded to immediately go with him and meet with Marcellus. But the mathematician brushed off the obsessive Roman, saying that he must first complete the work. The soldier was indignant and stabbed the smartest resident of Syracuse with a sword.

There is also a version that claims that Archimedes was killed right on the street while he was carrying mathematical instruments in his hands. The Roman soldiers decided that these were valuable objects and stabbed the mathematician to death. But be that as it may, the death of this man outraged Marcellus, since his order was violated. There are other versions of this story, but they agree that the ancient Roman political figure and the military leader Marcellus was extremely upset by the death of the scientist and, uniting with both the citizens of Syracuse and his own subjects, gave Archimedes a magnificent funeral.

140 years after these events, the famous Roman orator Cicero arrived in Sicily. He tried to find the tomb of Archimedes, but none of the local residents knew where it was. Finally, the grave was found in a dilapidated state in the bushes on the outskirts of Syracuse. The gravestone depicted a ball and a cylinder inscribed in it. Poems were engraved underneath them. However this version has no documentary evidence.

In the early 60s of the 20th century, an ancient grave was also discovered in the courtyard of the Panorama Hotel in Syracuse. The hotel owners began to claim that this was the burial place of the great mathematician and inventor of antiquity. But again, they did not provide any convincing evidence. In a word, to this day it is unknown where Archimedes is buried and in what place his grave is located.

Scientific activities and inventions of Archimedes:

The ancient Greek physicist, mathematician and engineer Archimedes made many geometric discoveries, laid the foundations of hydrostatics and mechanics, and created inventions that served as the starting point for the further development of science. +Discoveries in the field of mathematics were the scientist’s real passion. According to Plutarch, Archimedes forgot about food and self-care when he was on the verge of another invention in this area. The main direction of his mathematical research was the problems mathematical analysis.

Even before Archimedes, formulas were invented to calculate the areas of circles and polygons, the volumes of pyramids, cones and prisms. But the scientist’s experience allowed him to develop general techniques for calculating volumes and areas. To this end, he improved the method of exhaustion, invented by Eudoxus of Cnidus, and brought the ability to apply it to a virtuoso level. Archimedes did not become the creator of the theory of integral calculus, but his work subsequently became the basis for this theory.

Also, an outstanding mathematician laid the foundations of differential calculus. From a geometric point of view, he studied the possibility of determining the tangent to a curved line, and from a physical point of view, the speed of a body at any moment in time. The scientist examined a flat curve known as the Archimedean spiral. He found the first generalized way to find tangents to a hyperbola, parabola and ellipse. From here we can safely say that this man was ahead of mathematical science by 2 thousand years. Only in the seventeenth century were scientists able to fully understand and reveal all the ideas of Archimedes, which reached those times in his surviving works. The scientist often refused to describe his inventions in books, which is why not every formula he wrote has survived to this day.

The scientist also actively developed mechanical structures. He developed and presented detailed theory lever and effectively used this theory in practice, although the invention itself was known even before him. Block-lever mechanisms were made in the port of Syracuse. These devices made it easier to lift and move heavy loads, speeding up and optimizing port operations.

He also invented a screw that was used to bail out water. His “Archimedes screw” is still used in Egypt. Archimedes created a theory about the balancing of equal bodies. He proved that a body immersed in a liquid is subject to a buoyant force equal to the weight of the displaced liquid. This idea came to him in the bath. She was so shocked by her simplicity outstanding mathematician and the inventor, that he jumped out of the bathtub and, dressed as Adam, ran through the streets of Syracuse shouting “eureka,” which means “found.” Subsequently, this proof was called Archimedes' law. + Great importance have theoretical research as a scientist in the field of mechanics. Based on the proof of the law of leverage, he began to write the work “On the Equilibrium of Plane Figures.” The proof is based on the axiom that on equal shoulders equal bodies will be balanced if necessary. Archimedes followed the same principle of constructing a book - starting with the proof of his own law - when writing the work “On the Floating of Bodies”. This book begins with a description of Archimedes' well-known law.

The scientist considered the invention of formulas for calculating the surface area and volume of a ball to be a worthy discovery. If in the previous cases described, Archimedes refined and improved other people’s theories, or created quick calculation methods as an alternative to existing formulas, then in the case of determining the volume and surface of a ball, he was the first. Before him, no scientist had coped with this task. Therefore, the mathematician asked to knock out a ball inscribed in a cylinder on his gravestone.

There is a legend associated with Archimedes' law. One day, the scientist was allegedly approached by Hiero II, who doubted that the weight of the crown made for him corresponded to the weight of the gold that was provided for its creation. Archimedes made two ingots of the same weight as the crown: silver and gold. Next, he placed these ingots in turn in a vessel with water and noted how much its level increased. The scientist then placed the crown in the vessel and discovered that the water did not rise to the level to which it rose when each of the ingots was placed in the vessel. Thus, it was discovered that the master had kept some of the gold for himself.

Archimedes became the inventor of the first planetarium. When this device moves, the following is observed: the rising of the Moon and the Sun; the movement of the five planets; disappearance of the Moon and Sun beyond the horizon; phases and eclipses of the moon.

The scientist also tried to create formulas for calculating distances to celestial bodies. Modern researchers suggest that Archimedes considered the Earth to be the center of the world. He believed that Venus, Mars and Mercury revolved around the Sun, and this entire system revolved around the Earth.

His contemporaries also composed numerous legends about the gifted mathematician, physicist and engineer. Legend says that one day Hiero II decided to present Ptolemy, the king of Egypt, with a multi-deck ship as a gift. It was decided to name the watercraft "Syracuse", but it could not be launched. In this situation, the ruler again turned to Archimedes. From several blocks he built a system with the help of which the launch of a heavy vessel was possible with one movement of the hand. According to legend, during this movement Archimedes said: “Give me a point of support, and I will turn the world over.”

The scientist helped his compatriots in naval battles. The cranes he developed grabbed enemy ships with iron hooks, lifted them slightly, and then abruptly threw them back. Because of this, ships turned over and crashed. For a long time, these cranes were considered something of a legend, but in 2005 a group of researchers proved the functionality of such devices by reconstructing them from surviving descriptions.

In 212 BC, during the Second Punic War, the Romans began to storm Syracuse. At this time, Archimedes was already an elderly man, but his mind did not lose its sharpness. Archimedes actively used engineering knowledge to help his people achieve victory. As Plutarch wrote, under his leadership, throwing machines were built, with the help of which the soldiers of Syracuse threw heavy stones at their opponents. When the Romans rushed to the walls of the city, hoping that they would not come under fire, another invention of Archimedes - light throwing devices with close action - helped the Greeks pelt them with cannonballs. Roman galleys scurrying around the port of Syracuse were attacked by special cranes with grappling hooks (Archimedes' claw). With the help of these hooks, the besieged lifted ships into the air and threw them down from a great height. The ships, hitting the water, broke and sank. All these technological advances scared the invaders. So, thanks to the efforts of Archimedes, the Romans’ hope of storming the city failed. They abandoned the assault on the city and moved on to a long siege. In the fall of 212 BC, the colony was taken by the Romans as a result of treason. Archimedes was killed during this incident. According to one version, he was hacked to death by a Roman soldier, whom the scientist attacked for stepping on his drawing.

There is a legend that Archimedes ordered the shields to be polished to a mirror shine, and then arranged them in such a way that, reflecting the color of the sun, they focused it into powerful rays. They were sent to Roman ships, and they burned. Mentions of this weapon are just legends, but in last years Experiments were conducted to determine whether these inventions could actually exist. In 2005, scientists reproduced the cranes, which turned out to be fully functional. And in 1973, Greek scientist Ioannis Sakkas set fire to a plywood model of a Roman ship using a combination of mirrors. He created a cascade of 70 copper mirrors and used it to set fire to a plywood model of a ship, which was located 75 meters from the mirrors. So this legend could well have a practical basis.

However, scientists continue to doubt the existence of “mirror” weapons in Syracuse, since none of the ancient authors mentions it; information about him appeared only in early middle ages- from the 6th century author Anthemius of Trallia. Despite a heroic - and ingenious - defense, Syracuse was eventually conquered.

Legacy of Archimedes:

Archimedes wrote his works in Doric Greek, the dialect spoken in Syracuse. But the originals have not survived. They have come to us in retellings by other authors. All this was systematized and collected into a single collection by the Byzantine architect Isidore of Miletus, who lived in Constantinople in the 6th century. This collection was translated into Arabic in the 9th century, and in the 12th century it was translated into Latin.

During the Renaissance, the works of the Greek thinker were published in Basel in Latin and Greek languages. Based on these works, Galileo Galilei invented hydrostatic balances at the end of the 16th century.

*Archimedes screw, or auger, is used for lifting and transporting loads and scooping out water. This device is still used today (for example, in Egypt).

*Various types of cranes, which were based on blocks and levers.

*"Celestial Sphere" is the world's first planetarium, with the help of which it was possible to observe the movement of the sun, moon and five then known planets.

*The number close to the number P is the so-called “Archimedean number”: 3 1/7; Archimedes himself indicated the accuracy of the approximation of this number. To solve this problem, he built a circle with 96-gons inscribed and circumscribed around it, the sides of which he then measured.

*Discovery of the fundamental law of physics in general and hydrostatics in particular. This law is named after him and consists of the relationship between the buoyant force, volume and weight of a body immersed in a liquid.

*As the first theorist of mechanics, Archimedes introduced thought experiments into it. The first such experiments were his proofs of the law of the lever and Archimedes' law.

*In 1906, Danish professor Johan Ludwig Heiberg discovered a 174-page prayer collection in Constantinople, written in the 13th century. The scientist found out that it was a palimpsest, that is, text written over old text. At that time, this was common practice, since the tanned goatskin from which the pages were made was very expensive. The old text was scraped off and new text was written on top of it. It turned out that the scraped work was a copy of an unknown treatise by Archimedes. The copy was written in the 10th century. Using ultraviolet and x-ray light, this hitherto unknown work was read. These were works on equilibrium, on measuring the circumference of a sphere and a cylinder, and on floating bodies. Currently, this document is kept in the Baltimore City Museum (Maryland, USA).

*Works of Archimedes: Quadrature of the parabola, On the ball and cylinder, On spirals, On conoids and spheroids, On the equilibrium of plane figures, Epistle to Eratosthenes on the method, On floating bodies, Measurement of the circle, Psammit, Stomachion, Archimedes' problem on bulls, Treatise on construction around the ball of a solid figure with fourteen bases, Book of Lemmas, Book on the construction of a circle divided into seven equal parts, A book about touching circles.

Archimedes: Interesting Facts

1.Archimedes did not leave any students after himself, because he did not want to create his own school and train successors.

2. Some of Archimedes’ calculations were repeated only fifteen hundred years later by Newton and Leibniz.

3. Some scientists claim that Archimedes was the inventor of the cannon. Thus, Leonardo da Vinci even drew a sketch of a steam cannon, the invention of which he attributed to the ancient Greek scientist. Plutarch wrote that during the siege of Syracuse, the Romans were fired upon by a device that resembled a long tube and “spitted out” cannonballs.

4. Archimedes’ friend Heraclides wrote a biography of the great scientist, but it was lost and now little is known about his life.

5. Some contemporaries considered Archimedes crazy. To demonstrate his skills, the scientist before Hieron pulled the triremes ashore using a system of pulleys.

6. The Roman commander Marcellus, commander of the siege of Syracuse, said: “We will have to stop the war against the geometer.”

7.Archimedes is considered one of the best mathematicians and inventors of all time.

9. According to some legends, during the capture of Syracuse, a special detachment of Romans was sent in search of the scientist, who were supposed to capture Archimedes and deliver him to the command. The scientist died only by an absurd accident.

10. Archimedes’ throwing machines could launch stones weighing up to 250 kg. At that time it was a unique combat vehicle.

11.Archimedes made the world's first planetarium.

12. Contemporaries considered Archimedes almost a demigod, and his military inventions terrified the Romans, who had never encountered anything like this before.

13.The well-known legend about mirrors that burned Roman ships has been repeatedly refuted. Most likely, the mirrors were used only to aim the ballistas, which fired incendiary shells at the Roman fleet. There is also an opinion that the Romans were forced to agree to a night assault on the city precisely because of the use of mirrors by the defenders of Syracuse.

14. The “Archimedes screw” was invented by the scientist in his youth and was intended for irrigating fields. Today, screws are used in many industries. And in Egypt they still supply water to the fields.

15. Archimedes considered mathematics his best friend.

Monument to Archimedes

photo from the Internet

Biography

Archimedes (Ἀρχιμήδης; 287 BC - 212 BC) - ancient Greek mathematician, physicist and engineer from Syracuse. Made many discoveries in geometry. He laid the foundations of mechanics and hydrostatics, and was the author of a number of important inventions.

Information about the life of Archimedes was left to us Polybius , Titus Livy, Cicero, Plutarch, Vitruvius and others. Almost all of them lived many years later than the events described, and the reliability of this information is difficult to assess.

Archimedes was born in Syracuse, a Greek colony on the island of Sicily. Archimedes' father may have been the mathematician and astronomer Phidias. According to Plutarch, Archimedes was closely related to Hiero II, the tyrant of Syracuse. To study, Archimedes went to Alexandria of Egypt - the scientific and cultural center of that time.

Alexandria

In Alexandria, Archimedes met and became friends with famous scientists: the astronomer Conon, the versatile scientist Eratosthenes, with whom he then corresponded until the end of his life. At that time, Alexandria was famous for its library, which collected more than 700 thousand manuscripts.

Apparently this is where Archimedes got acquainted with the works Democritus, Eudoxus and other remarkable Greek geometers, which he mentioned in his writings.

After completing his studies, Archimedes returned to Sicily. In Syracuse he was surrounded by attention and did not need funds. Because of how long ago the life of Archimedes was, it was closely intertwined with the legends about him.

Legends

Already during the life of Archimedes, legends were created around his name, the reason for which was his amazing inventions, which had a stunning effect on his contemporaries. There is a well-known story about how Archimedes was able to determine whether the crown of King Hiero was made of pure gold, or whether the jeweler mixed a significant amount of silver into it. The specific gravity of gold was known, but the difficulty was to accurately determine the volume of the crown: after all, it had irregular shape! Archimedes pondered this problem all the time. Once he was taking a bath and noticed that the amount of water flowing out of it was the same as the volume of his body immersed in the bath, and then he came up with a brilliant idea: by immersing the crown in water, you can determine its volume by measuring the volume of water displaced by it . According to legend, Archimedes ran naked into the street shouting “Eureka!” (ancient Greek εὕρηκα), that is, “Found!” At this moment, the fundamental law of hydrostatics was discovered - Archimedes' law.

Another legend says that the heavy multi-deck ship Syracuse, built by Hieron as a gift to the Egyptian king Ptolemy, could not be launched. Archimedes built a system of blocks (pulley hoist), with the help of which he was able to do this work with one movement of his hand. According to legend, Archimedes said at the same time: “If I had another Earth at my disposal to stand on, I would move ours” (in another version: “Give me a fulcrum, and I will turn the world upside down”).

Siege of Syracuse

The engineering genius of Archimedes manifested itself with particular force during the siege of Syracuse by the Romans in 212 BC. e. during the Second Punic War. At this moment, Archimedes was already 75 years old. Detailed description the siege of Syracuse by the Roman commander Marcellus and the participation of Archimedes in the defense is contained in the writings of Plutarch and Titus Livy.

Powerful throwing machines built by Archimedes threw heavy stones at the Roman troops. Thinking that they would be safe at the very walls of the city, the Romans rushed there, but at that time light, short-range throwing machines pelted them with a hail of cannonballs. Powerful cranes grabbed ships with iron hooks, lifted them up, and then threw them down, so that the ships turned over and sank. In recent years, several experiments have been carried out to test the veracity of the description of this “superweapon of antiquity.” The constructed structure showed its full functionality.

The Romans were forced to abandon the idea of ​​taking the city by storm and switched to a siege. The famous ancient historian Polybius wrote: “Such is the miraculous power of one person, one talent, skillfully directed towards any task... the Romans could quickly take possession of the city if someone had removed one old man from among the Syracusans.”

According to one legend, during the siege, the Roman fleet was burned by the defenders of the city, who, using mirrors and shields polished to a shine, focused the sun's rays on them on the orders of Archimedes. There is an opinion that the ships were set on fire by well-thrown incendiary shells, and the focused beams served only as an aiming mark for the ballistas. However, in an experiment by the Greek scientist Ioannis Sakkas (1973), it was possible to set fire to a plywood model of a Roman ship from a distance of 50 m using 70 copper mirrors. However, the authenticity of the legend is questionable; neither Plutarch nor other ancient historians mention mirrors when describing the defensive inventions of Archimedes; this episode was first discovered in the treatise of Anthemius of Trallia (VI century), one of the architects of Hagia Sophia in Constantinople (the treatise was dedicated to convex and concave mirrors). In the 12th century, the legend gained popularity after John Zonar published an extensive chronicle of world history.

In the autumn of 212 BC. e. As a result of treason, Syracuse was taken by the Romans. At the same time, Archimedes was killed.

Death of Archimedes

The story of Archimedes' death at the hands of the Romans exists in several versions:

The story of John Tzetz (Chiliad, book II): in the midst of the battle, 75-year-old Archimedes sat on the threshold of his house, pondering in depth over the drawings he made right on the sand of the road. At this time, a Roman soldier running past stepped on the drawing, and the indignant scientist rushed at the Roman shouting: “Don’t touch my drawings!” The soldier stopped and coldly killed the old man with his sword.
Plutarch's story: “A soldier approached Archimedes and announced that Marcellus was calling him. But Archimedes insistently asked him to wait one minute, so that the problem he was working on would not remain unsolved. The soldier, who did not care about his proof, became angry and pierced him with his sword.” Plutarch claims that the consul Marcellus was angry at the death of Archimedes, whom he allegedly ordered not to be touched.
Archimedes himself went to Marcellus to take him his instruments for measuring the magnitude of the Sun. On the way, his burden attracted the attention of Roman soldiers. They decided that the scientist was carrying gold or jewelry in the casket, and, without thinking twice, cut his throat.
The story of Diodorus Siculus: “While sketching a mechanical diagram, he bent over it. And when the Roman soldier came up and began to drag him as a prisoner, he, completely absorbed in his diagram, not seeing who was in front of him, said: “Get away from my diagram!” Then, as the man continued to drag him, he turned and recognized The Roman, looking at him, exclaimed: “Quickly, someone, give me one of my cars!” The Roman, frightened, killed the weak old man, the one whose achievements were a miracle. As soon as Marcellus learned of this, he was greatly distressed and, together with the noble citizens and the Romans, arranged a magnificent funeral among the graves of his ancestors. As for the killer, he appears to have been beheaded.”
“Roman History from the Founding of the City” by Titus Livius (Book XXV, 31): “It is reported that when, in the great turmoil that the panic that had spread throughout the captured city could have caused, the soldiers fled, plundering, many disgusting examples of malice and greed; by the way, one warrior killed Archimedes, who was busy drawing in the sand geometric shapes without knowing who he is. Marcellus, they say, was upset by this, took care of the burial of the murdered man, even found the relatives of Archimedes, and his name and memory of him brought respect and safety to the latter.”

Cicero, who was quaestor in Sicily in 75 BC. e., writes in “Tusculan Conversations” (Book V) that in 75 BC. e., 137 years after these events, it was possible to discover the dilapidated tomb of Archimedes; on it, as Archimedes bequeathed, there was an image of a ball inscribed in a cylinder.

Scientific activity

Mathematics

According to Plutarch, Archimedes was simply obsessed with mathematics. He forgot about food and did not take care of himself at all.

Archimedes' works related to almost all areas of mathematics of that time: he did remarkable research on geometry, arithmetic, and algebra. Thus, he found all the semiregular polyhedra that now bear his name, significantly developed the doctrine of conic sections, and gave a geometric method for solving cubic equations of the form x^2 (a \pm x) = b, the roots of which he found using the intersection of a parabola and a hyperbola . Archimedes also carried out a complete study of these equations, that is, he found under what conditions they would have real positive different roots and under what conditions the roots would coincide.

However, Archimedes' main mathematical achievements concerned problems that are now classified as mathematical analysis. The Greeks before Archimedes were able to determine the area of ​​polygons and a circle, the volume of a prism and cylinder, pyramid and cone. But only Archimedes found much more general method calculations of areas or volumes; For this purpose, he improved and masterfully applied the method of exhaustion of Eudoxus of Cnidus. In his Epistle to Eratosthenes on the Method (sometimes called the Method of Mechanical Theorems), he used infinitesimals to calculate volumes. Archimedes' ideas later formed the basis of integral calculus.

Archimedes was able to establish that the volumes of a cone and a sphere inscribed in a cylinder and the cylinder itself are in a ratio of 1:2:3.

He considered his best achievement to be determining the surface and volume of a sphere - a problem that no one had been able to solve before him. Archimedes asked to knock out a ball inscribed in a cylinder on his grave.

In his essay Quadrature of a Parabola, Archimedes proved that the area of ​​a segment of a parabola cut off from it by a straight line is 4/3 of the area of ​​the triangle inscribed in this segment (see figure). To prove this, Archimedes calculated the sum of an infinite series:

Each term of the series is the total area of ​​the triangles inscribed in the part of the parabola segment not covered by the previous terms of the series.

In addition to the above, Archimedes calculated the surface area for a segment of a ball and a turn of the “Archimedes spiral” he discovered, and determined the volumes of segments of a ball, an ellipsoid, a paraboloid and a two-sheet hyperboloid of revolution.

The next problem concerns the geometry of curves. Let some curved line be given. How to determine a tangent at any point? Or, if we put this problem into the language of physics, let us know the path of a certain body at each moment of time. How to determine its speed at any point? At school they teach how to draw a tangent to a circle. The ancient Greeks were also able to find tangents to an ellipse, hyperbola and parabola. The first general method for solving this problem was found by Archimedes. This method subsequently formed the basis of differential calculus.

The ratio of the circumference of a circle to its diameter, calculated by Archimedes, was of great importance for the development of mathematics.

Mechanics

Archimedes became famous for many mechanical designs. The lever was known before Archimedes, but only Archimedes outlined its complete theory and successfully applied it in practice. Plutarch reports that Archimedes built many block-lever mechanisms in the port of Syracuse to facilitate the lifting and transportation of heavy loads. The Archimedes screw (auger) he invented for scooping up water is still used in Egypt.

Archimedes is also the first theorist of mechanics. He begins his book “On the Equilibrium of Plane Figures” with a proof of the law of leverage. This proof is based on the axiom that equal bodies on equal shoulders must necessarily balance. In the same way, the book “On the Floating of Bodies” begins with a proof of Archimedes’ law. These proofs of Archimedes represent the first thought experiments in the history of mechanics.

Astronomy

Archimedes built a planetarium or " celestial sphere", during the movement of which it was possible to observe the movement of five planets, the rising of the Sun and the Moon, the phases and eclipses of the Moon, the disappearance of both bodies beyond the horizon. He worked on the problem of determining distances to planets; Presumably, his calculations were based on a world system centered on the Earth, but with the planets Mercury, Venus and Mars revolving around the Sun and with it around the Earth. In his essay “Psammit” conveyed information about heliocentric system world of Aristarchus of Samos.

Essays

The following have survived to this day:

Quadrature of a parabola / τετραγωνισμὸς παραβολῆς - the area of ​​a parabola segment is determined.
About the ball and the cylinder / περὶ σφαίρας καὶ κυλίνδρου - it is proved that the volume of the ball is equal to 2/3 of the volume of the cylinder described around it, and the surface area of ​​the ball is equal to the area of ​​the lateral surface of this cylinder.
About spirals / περὶ ἑλίκων - the properties of the Archimedes spiral are derived.
About conoids and spheroids / περὶ κωνοειδέων καὶ σφαιροειδέων - the volumes of segments of paraboloids, hyperboloids and ellipsoids of revolution are determined.
On the equilibrium of plane figures / περὶ ἰσορροπιῶν - the law of lever equilibrium is derived; it is proved that the center of gravity of a plane triangle is at the point of intersection of its medians; the centers of gravity of the parallelogram, trapezoid and parabolic segment are located.
Epistle to Eratosthenes on the method / πρὸς Ἐρατοσθένην ἔφοδος - discovered in 1906, thematically it partially duplicates the work “On the Ball and the Cylinder”, but here the mechanical method of proving mathematical theorems is used.
About floating bodies / περὶ τῶν ὀχουμένων - the law of floating bodies is derived; The problem of equilibrium of the cross section of a paraboloid modeling a ship hull is considered.
Measuring a circle / κύκλου μέτρησις - only an excerpt from this work has reached us. It is in it that Archimedes calculates the approximation for the number \pi.
Psammit / ψαμμίτης - a way to write very large numbers is introduced.
Stomakhion / στομάχιον - a description of the popular game is given.
Archimedes' problem about bulls / πρόβλημα βοικόν - a problem is posed that can be reduced to Pell's equation.
A number of Archimedes' works survive only in Arabic translation:

A treatise on the construction of a corporeal figure with fourteen bases around a ball;
Book of Lemmas;
A book about constructing a circle divided into seven equal parts;
A book about touching circles.

Archimedes is an ancient Greek scientist, physicist, mathematician and engineer from Syracuse (island of Sicily), who lived in 287-212 BC. In addition to many discoveries made in the field of mathematics, especially in geometry, he also became the founder of mechanics, hydrostatics, and the author of a number of other significant inventions. He made many significant discoveries in the fields of mathematics and physics. For example, the ratio of the length and diameter of a circle, the scientific basis for the action of a lever, and others.

The life of a scientist can be judged by his works and essays by other ancient Greek figures. Among them are Titus Livius, Polybius, Cicero, Vitruvius. Archimedes developed a love for exact sciences from childhood, since the scientist’s father was also a mathematician. To get a decent education and as much knowledge as possible, the scientist went to Alexandria - cultural and science Center ancient world. Upon returning to Syracuse, the scientist began to study intensively scientific work. It was during this period that the law of hydrostatics, later called Archimedes' law, appeared. His engineering abilities were on full display during the Roman siege. For defense purposes, he created special throwing machines. Unfortunately, the Romans nevertheless took Syracuse, and the scientist was killed.

Some treatises of Archimedes have survived to the present day, which speak of the scientist’s genius. Among them are “On the Sphere and the Cylinder”, “On Floating Bodies”, “On Spirals”, “On the Equilibrium of Plane Figures” and others. Many discoveries were made in the field of astronomy. For example, Archimedes built the first planetarium, with the help of which it was possible to observe the movement of several planets, the rising of the Sun and Moon, the phases of an eclipse of the Moon, etc. In one of his works, he mentions the heliocentric system of the world. In memory of Archimedes, a crater and an asteroid are named after him.

ARCHIMEDES (Archimedes)

OK. 287 – approx. 212 BC e.

Archimedes was an ancient Greek scientist, mathematician and mechanic from Syracuse. He developed methods for finding surface areas and volumes of various figures and bodies. His mathematical works were far ahead of their time and were correctly assessed only in the era of the creation of differential and integral calculus. Archimedes is a pioneer of mathematical physics, one of the creators of mechanics as a science. Mathematics in his works is systematically applied to the study of problems in natural science and technology. Archimedes owns various technical inventions.

Archimedes was born in Syracuse (Sicily) and lived in this city in the 1st and 2nd eras Punic Wars. It is believed that he was the son of the astronomer Phidias. Scientific activity started as a mechanic and technician. Archimedes traveled to Egypt and became close with Alexandrian scientists, including Conon and Eratosthenes. This was the impetus for the development of his outstanding abilities. Archimedes was close to the Syracusan king Hieron II. During the 2nd Punic War, Archimedes organized the engineering defense of Syracuse against Roman troops. His war machines forced the Romans to abandon their attempts to take the city by storm and force them to resort to a long siege. During the capture of the city by the troops of Marcellus, Archimedes was killed by a Roman soldier, whom, according to legend, he greeted with the words “don’t touch my drawings.” At the grave of Archimedes, a monument was erected with the image of a ball and a cylinder described around it. The epitaph indicated that the volumes of these bodies are related as 2: 3 - a discovery of Archimedes, which he especially appreciated.

The works of Archimedes show that he was well acquainted with the mathematics and astronomy of his time, and amaze with the depth of penetration into the essence of the problems under consideration. A number of works take the form of messages to friends and colleagues. Sometimes Archimedes first informed them of his discoveries without proof, adding with subtle irony a few incorrect sentences.

In the IX-XI centuries. Archimedes' works were translated into Arabic from the 13th century. they appear in Western Europe in Latin translation. From the 16th century Printed editions of Archimedes begin to appear in the 17th-19th centuries. they are translated into new languages. The first edition of individual works of Archimedes in Russian dates back to 1823. Some of Archimedes’ works have not reached us or are known only in fragments, and his “Message to Eratosthenes” was found only in 1906.

The central theme of Archimedes' mathematical works are problems of finding surface areas and volumes. Archimedes initially found the solution to many problems of this type using mechanical considerations, which essentially boiled down to the method of “indivisibles,” and then strictly proved it by the method of exhaustion, which he significantly developed. Archimedes' consideration of two-sided error estimates during integration processes allows us to consider him a predecessor not only of I. Newton and G. Leibniz, but also of G. Riemann. Archimedes calculated the area of ​​an ellipse, a parabolic segment, found the surface area of ​​a cone and a sphere, the volume of a sphere and a spherical segment, as well as various bodies of revolution and their segments. Archimedes investigated the properties of the so-called. Archimedean spiral. He constructed a tangent to this spiral and found the area of ​​its turn. Here he acts as a predecessor of the methods of differential calculus. Archimedes also considered one isoperimetric type problem. In the course of his research, he found the sum of an infinite geometric progression with a denominator of 1/4, which was the first example of the appearance of an infinite series in mathematics. While studying a problem that reduced to a cubic equation, Archimedes discovered the role of the characteristic, which was later called the discriminant. Archimedes had a formula for determining the area of ​​a triangle through its three sides (incorrectly called Heron's formula). Archimedes gave a (not entirely comprehensive) theory of semiregular convex polyhedra ( Archimedean solids). Of particular importance is Archimedes' axiom: Of unequal segments, the smaller one, if repeated a sufficient number of times, will surpass the larger one. This axiom defines the so-called. Archimedean orderliness, which plays important role in modern mathematics. Archimedes built a number system that made it possible to write down and name very big numbers. He calculated the value of the number with great accuracy pi and indicated the limits of error.

Mechanics was constantly in the circle of interests of Archimedes. In one of his first works, he studies the distribution of loads between the supports of a beam. Archimedes owns the definition of the concept of the center of gravity of a body. Using, in particular, integration methods, he found the position of the center of gravity of various figures and bodies. Archimedes gave a mathematical derivation of the laws of leverage. He is credited with the proud phrase: “Give me a place to stand, and I will move the Earth.” Archimedes laid the foundations of hydrostatics. He formulated the main principles of this discipline, including the famous Archimedes' law. Archimedes's last work was devoted to the study of the equilibrium of floating bodies. At the same time, he identifies stable equilibrium positions. Archimedes invented a water-lifting mechanism, the so-called. Archimedes screw, which was the prototype of ship propellers, as well as aircraft propellers. They say that Archimedes found the solution to the problem of determining the amount of gold and silver in Hiero's sacrificial crown when he sat in the bath, and ran home naked shouting “eureka!” ("found!").

Archimedes also studied astronomy. He designed an instrument to determine the apparent (angular) diameter of the Sun and found the value of this angle with amazing accuracy. At the same time, Archimedes introduced a correction for the size of the pupil. He was the first to bring observations to the center of the Earth. Finally, Archimedes built a celestial sphere - a mechanical device on which it was possible to observe the movements of the planets, the phases of the Moon, solar and lunar eclipses.