Birth of Archimedes. Archimedes: biography, discoveries, interesting facts and videos

(287 - 212 BC)

Archimedes was born in 287 BC (because of this, many facts of his biography were lost) in the Greek city of Syracuse, where he lived almost his entire life. His father was Phidias, the court astronomer of the ruler of the city of Hieron. Archimedes, like many other ancient Greek scientists, studied in Alexandria, where the rulers of Egypt, the Ptolemies, gathered the best Greek scientists and thinkers, and also founded the famous, largest library in the world.

After studying in Alexandria, Archimedes returned to Syracuse again and inherited his father's position.

In theoretical terms, the work of this great scientist was blindingly multifaceted. The main works of Archimedes concerned various practical applications of mathematics (geometry), physics, hydrostatics and mechanics. In his work “Parabola of Quadrature”, Archimedes substantiated the method for calculating the area of a parabolic segment, and he did this two thousand years before the discovery of integral calculus. In On the Measurement of a Circle, Archimedes first calculated the number "pi" - the ratio of the circumference of a circle to its diameter - and proved that it is the same for any circle. We still use the system of naming integers invented by Archimedes.

The mathematical method of Archimedes, connected with the mathematical works of the Pythagoreans and with the work of Euclid that completed them, as well as with the discoveries of Archimedes' contemporaries, led to the knowledge of the material space that surrounds us, to the knowledge of the theoretical form of objects located in this space, the form of a perfect, geometric form, to which objects more or less approach and whose laws must be known if we want to influence the material world.

But Archimedes also knew that objects have more than just shape and dimension: they move, or can move, or remain stationary under the influence of certain forces that move objects forward or bring them into balance. The great Syracusan studied these forces, inventing a new branch of mathematics in which material bodies, reduced to their geometric form, retain at the same time their heaviness. This geometry of weight is rational mechanics, it is statics, as well as hydrostatics, the first law of which was discovered by Archimedes (the law bearing the name of Archimedes), according to which a force equal to the weight of the liquid displaced by it acts on a body immersed in a liquid.

Once raising his leg in the water, Archimedes noted with surprise that his leg became lighter in the water. "Eureka! Found it,” he exclaimed as he stepped out of his tub. The anecdote is amusing, but, conveyed in this way, it is not accurate. The famous "Eureka!" was uttered not in connection with the discovery of the law of Archimedes, as is often said, but with regard to the law of the specific gravity of metals - a discovery that also belongs to the scientist of Syracuse and the detailed details of which we find in Vitruvius.

It is said that one day Heron, the ruler of Syracuse, turned to Archimedes. He ordered to check whether the weight of the golden crown corresponds to the weight of the gold allotted to it. To do this, Archimedes made two ingots, one of gold, the other of silver, each of the same weight as the crown.

Then he put them in turn in a vessel with water, noted how much its level had risen. Having lowered the crown into the vessel, Archimedes found that its volume exceeds the volume of the ingot. So the dishonesty of the master was proved.

The review of Cicero, the great orator of antiquity, who saw the “Archimedean sphere” - a model showing the movement of heavenly bodies around the Earth, is curious: “This Sicilian possessed a genius that, it would seem, human nature cannot achieve.”

Subsequently, these mechanisms were widely used in different countries of the world. Interestingly, an improved version of the water-lifting machine could be found at the beginning of the 20th century in a monastery located on Valaam, one of the northern Russian islands. Today, the Archimedean screw is used, for example, in an ordinary meat grinder.

The invention of the infinite screw led him to another important invention, even if it had become commonplace, the invention of a bolt constructed from a screw and a nut.

To those of his fellow citizens who would consider such inventions worthless, Archimedes presented decisive evidence to the contrary on the day when, by cunningly fitting a lever, screw and winch, he found a means, to the surprise of onlookers, to launch a heavy galley that had run aground, with everything her crew and cargo.

Even more convincing proof he gave in 212 BC. During the defense of Syracuse from the Romans during the Second Punic War, Archimedes designed several fighting machines that allowed the townspeople to repel the attacks of the outnumbered Romans for almost three years. One of them was a system of mirrors, with which the Egyptians were able to burn the Roman fleet. This feat of his, which Plutarch, Polybius and Titus Livia told about, of course, aroused more sympathy among ordinary people than the calculation of the number "pi" - another feat of Archimedes, very useful in our time for students of mathematics.

Archimedes died during the siege of Syracuse, he was killed by a Roman soldier at the moment when the scientist was absorbed in the search for a solution to the problem set before him.

It is curious that, having conquered Syracuse, the Romans did not become the owners of the works of Archimedes. Only after many centuries they were discovered by European scientists. That is why Plutarch, one of the first to describe the life of Archimedes, mentioned with regret that the scientist did not leave a single work.

Plutarch writes that Archimedes died at a ripe old age. A slab depicting a sphere and a cylinder was placed on his grave. It was seen by Cicero, who visited Sicily 137 years after the scientist's death.

He left numerous disciples. A whole generation of followers, enthusiasts rushed to the new path opened by him, who, like the teacher, were eager to prove their knowledge with concrete conquests.

The first of these students was the Alexandrian Ctesibius, who lived in the 2nd century BC. The inventions of Archimedes in the field of mechanics were in full swing when Ctesibius added to them the invention of the gear wheel.

😉 Greetings to the constant readers and guests of the site! In the article "Archimedes: biography, discoveries, interesting facts" - about the life of the ancient Greek mathematician, physicist and engineer. Years of life 287-212 BC At the end of the article there is an interesting and informative video material about the life of a scientist.

Biography of Archimedes

The famous scientist of antiquity Archimedes was the son of the astronomer Fidius and received a good education in Alexandria, where he became acquainted with the works of Democritus,.

During the siege of Syracuse, Archimedes developed siege engines (flamethrowers), which destroyed a significant part of the enemy army. Archimedes was killed by a Roman soldier despite the orders of General Marcus Marcellus.

Edouard Vimont (1846-1930). Death of Archimedes

A legend spread by the Greeks says that the great mathematician was stabbed to death as he wrote an equation in the sand, thus wishing to counter his superiority with Roman incompetence. It is possible that his death was also revenge for the damage done by his inventions to the Roman fleet.

"Eureka!"

The most famous anecdote about Archimedes tells how he invented a method for determining the volume of an irregularly shaped object. Hieron II ordered that the golden crown be donated to the temple.

Archimedes had to determine if the jeweler had replaced some of the material with silver. He had to complete this task without damaging the crown, so he could not melt it in a simple form to calculate its density.

While bathing, the scientist noticed that the water level in the tub increases when he enters it. He understands that this effect can be used to determine the volume of the crown.

From the point of view of this experiment, water has a practically constant volume. The crown will displace the amount of water with its own volume. Dividing the mass of the corona by the volume of water displaced, its density is obtained. This density would be lower than that of gold if less expensive and lighter metals were added to it.

Archimedes, jumping out of the bath, runs naked down the street. He is so excited by his discovery and forgets to get dressed. He loudly shouts "Eureka!" ("I found"). The experience was successful and proved that silver had indeed been added to the crown.

The story of the golden crown is not present in any of the known works of Archimedes. In addition, the practical applicability of the described method is doubtful due to the need for extreme accuracy in measuring changes in water level.

The sage most likely used the principle known in the hydrostat as the law of Archimedes, and later described in his treatise on floating bodies.

According to him, a body immersed in a fluid is subjected to a force equal to the weight of the fluid displaced by it. Using this principle, the density of a golden crown can be compared with the density of gold.

heat ray

Archimedes may have used a group of mirrors acting together as a parabolic mirror to set fire to ships attacking Syracuse. Lucian, a writer of the 2nd century, writes that Archimedes destroyed the ships with fire.

In the 6th century, Antimius of Thrallus called the weapon of Archimedes "burning glass". The device, also called "Thermim Beam Archimedes", was used to focus sunlight on ships, thus illuminating them.

This alleged weapon during the Renaissance became the subject of controversy over its actual existence. rejected it as impossible. Modern scholars attempt to recreate the described effects using only the tools available at the time of Archimedes.

There are suggestions that a large number of highly polished bronze screens acting as mirrors could be used to focus the sun's rays on a ship using the parabolic mirror principle.

Experiments of Archimedes in the modern world

In 1973, the scientist Ioannis Sakas from Greece conducted an experiment with the Archimedes heat ray at the naval base at Skaramaga. He used 70 copper-coated mirrors measuring 1.5 by 1 m. They were aimed at a plywood model ship at a distance of 50 m.

When the mirrors are focused, the mock ship ignites in a few seconds. Previously, ships were covered with resinous paint, which probably contributed to the ignition.

In October 2005, a group of students at the Massachusetts Institute of Technology conducted an experiment with 127 square mirrors measuring 30 x 30 cm, focusing on a wooden model of a ship at a distance of about 30 meters.

The flame appears on a part of the ship, in clear weather with a cloudless sky and if the ship remains stationary for about 10 minutes.

The same group is replicating the "MythBusters" television experiment using a wooden fishing boat in San Francisco. Again there is some ignition. The Mythbusters define the experience as an unfortunate one due to the long time and ideal weather conditions required for ignition.

If Syracuse is in the east, then the Roman fleet will attack in the morning for optimal focusing of the light. At the same time, conventional weapons such as flaming arrows or catapult-launched projectiles can be used much more easily to sink a ship at such a close range.

Many scientists consider the ancient Greek scientist one of the greatest mathematicians in history, along with Gauss and Euler. Huge contribution to geometry, mechanics, he is considered one of the pioneers of mathematical analysis.

He systematically applies mathematics to the natural sciences, technical discoveries and inventions. His scientific contributions were studied and described by Eratosthenes, Conon and Dosifed.

Works of Archimedes

the mathematician calculated the surface of the parabolic segment and the volumes of various mathematical bodies;
he considered several curves and spirals, one of which bears his name: Archimedes spiral;
gave a definition of semi-regular multistats called Archimedes;
presented a proof of the infinity of an array of natural numbers (also known as Archimedes' axiom).

Archimedes (about 287 BC, Syracuse, Sicily - 212 BC, ibid) - an ancient Greek scientist, mathematician and mechanic, the founder of theoretical mechanics and hydrostatics.

Developed anticipating integral calculus methods for finding areas, surfaces and volumes of various figures and bodies.

Archimedes was born in 287 BC in the Greek city of Syracuse, where he lived almost his entire life. His father was Phidias, the court astronomer of the ruler of the city of Hieron. Archimedes, like many other ancient Greek scientists, studied in Alexandria, where the rulers of Egypt, the Ptolemies, gathered the best Greek scientists and thinkers, and also founded the famous, largest library in the world.

After studying in Alexandria, Archimedes returned to Syracuse again and inherited his father's position.

In theoretical terms, the work of this great scientist was blindingly multifaceted. The main works of Archimedes concerned various practical applications of mathematics (geometry), physics, hydrostatics and mechanics. In his work “Parabola of Quadrature”, Archimedes substantiated the method for calculating the area of a parabolic segment, and he did this two thousand years before the discovery of integral calculus. In the work “On the Measurement of a Circle”, Archimedes first calculated the number “pi” - the ratio of the circumference of a circle to its diameter - and proved that it is the same for any circle. We still use the system of naming integers invented by Archimedes.

Once raising his leg in the water, Archimedes noted with surprise that his leg became lighter in the water. "Eureka! Found it,” he exclaimed as he stepped out of his bath. The anecdote is amusing, but, conveyed in this way, it is not accurate. The famous "Eureka!" was uttered not in connection with the discovery of the law of Archimedes, as is often said, but with regard to the law of the specific gravity of metals - a discovery that also belongs to the Syracusan scientist and the detailed details of which we find in Vitruvius.

It is said that one day Archimedes was approached by Hiero, the ruler of Syracuse. He ordered to check whether the weight of the golden crown corresponds to the weight of the gold allotted to it. To do this, Archimedes made two ingots, one of gold, the other of silver, each of the same weight as the crown. Then he put them in turn in a vessel with water, noted how much its level had risen. Having lowered the crown into the vessel, Archimedes found that its volume exceeds the volume of the ingot. So the dishonesty of the master was proved.

The review of the great orator of antiquity, who saw the "Archimedean sphere" - a model showing the movement of heavenly bodies around the Earth, is curious: "This Sicilian possessed a genius that, it would seem, human nature cannot achieve."

And, finally, Archimedes was not only a great scientist, he was, moreover, a man passionate about mechanics. He tests and creates a theory of five mechanisms known in his time and referred to as "simple mechanisms". This is a lever (“Give me a fulcrum,” said Archimedes, “and I will move the Earth”), a wedge, a block, an endless screw and a winch. It is Archimedes who is often credited with the invention of the infinite screw, but it is possible that he only improved the hydraulic screw, which served the Egyptians in draining swamps. Subsequently, these mechanisms were widely used in different countries of the world. Interestingly, an improved version of the water-lifting machine could be found at the beginning of the 20th century in a monastery located on Valaam, one of the northern Russian islands. Today, the Archimedean screw is used, for example, in an ordinary meat grinder.

The invention of the infinite screw led him to another important invention, even if it had become commonplace, the invention of a bolt constructed from a screw and a nut.

Even more convincing proof he gave in 212 BC. During the defense of Syracuse from the Romans during the Second Punic War, Archimedes designed several fighting machines that allowed the townspeople to repel the attacks of the outnumbered Romans for almost three years. One of them was a system of mirrors, with which the Egyptians were able to burn the Roman fleet. This feat of his, which Plutarch, Polybius and Titus Livy told about, of course, aroused more sympathy among ordinary people than the calculation of the number "pi" - another feat of Archimedes, very useful in our time for students of mathematics.

Archimedes died during the siege of Syracuse - he was killed by a Roman soldier at the moment when the scientist was absorbed in the search for a solution to the problem set before him.

Plutarch writes that Archimedes died at a ripe old age. A plate depicting a sphere and a cylinder was placed on his grave. She was seen by Cicero, who visited Sicily 137 years after the scientist's death. Only in the XVI-XVII centuries, European mathematicians were finally able to realize the significance of what was done by Archimedes two thousand years before them.

Archimedes left numerous disciples. A whole generation of followers, enthusiasts rushed to the new path opened by him, who, like the teacher, were eager to prove their knowledge with concrete conquests.

In the fundamental works on statics and hydrostatics (the law of Archimedes), Archimedes gave examples of the application of mathematics in natural science and technology. Archimedes owns many technical inventions (Archimedean screw, determining the composition of alloys by weighing in water, systems for lifting heavy weights, military throwing machines), which won him extraordinary popularity among his contemporaries.

Archimedes was educated by his father, the astronomer and mathematician Phidias, a relative of the Syracusan tyrant Hieron II, who patronized Archimedes. In his youth, he spent several years in the largest cultural center of that time, Alexandria of Egypt, where he met Erastosthenes. Then he lived in Syracuse until the end of his life.

During the Second Punic War (218-201), when Syracuse was besieged by the army of the Roman commander Marcellus, Archimedes took part in the defense of the city and built throwing weapons. The military inventions of the scientist (Plutarch told about them in the biography of the commander Marcellus) for two years helped to restrain the siege of Syracuse by the Romans. Archimedes is credited with burning the Roman fleet with sun rays directed through a system of concave mirrors, but this is unreliable information. The genius of Archimedes was admired even by the Romans. Marcellus ordered to save the scientist's life, but during the capture of Syracuse, Archimedes was killed.

Archimedes holds the primacy in many discoveries from the field of exact sciences. Thirteen treatises of Archimedes have come down to us. In the most famous of them - "On the ball and the cylinder" (in two books), Archimedes establishes that the surface area of the ball is 4 times the area of \u200b\u200bits largest section; formulates the ratio of the volumes of the ball and the cylinder described next to it as 2:3 - a discovery that he cherished so much that in his will he asked to put a monument on his grave with the image of a cylinder with a ball inscribed in it and an inscription of the calculation (the monument was seen by Cicero a century and a half later). The same treatise formulated the axiom of Archimedes (sometimes called the axiom of Eudoxus), which plays an important role in modern mathematics.

In the treatise "On Conoids and Spheroids" Archimedes considers a sphere, an ellipsoid, a paraboloid and a hyperboloid of revolution and their segments and determines their volumes. In the essay "On Spirals" he explores the properties of the curve that received his name (the Archimedean spiral) and the tangent to it. In the treatise "Measuring the Circle", Archimedes offers a method for determining the number π, which was used until the end of the 17th century, and indicates two surprisingly accurate limits for the number π:

3·10/71 In physics, Archimedes introduced the concept of the center of gravity, established the scientific principles of statics and hydrostatics, and gave examples of the application of mathematical methods in physical research. The main provisions of statics are formulated in the essay "On the equilibrium of plane figures."

Archimedes considers the addition of parallel forces, defines the concept of the center of gravity for various figures, and gives the derivation of the law of the lever. The famous law of hydrostatics, which entered science with his name (Archimedes' law), was formulated in the treatise On Floating Bodies. There is a legend that the idea of this law visited Archimedes when he was taking a bath, with the exclamation "Eureka!" he jumped out of the bath and ran naked to write down the scientific truth that had come to him.

Archimedes' principle: any body immersed in a liquid is subjected to a buoyant force directed upward and equal to the weight of the liquid displaced by it. Archimedes' law is also valid for gases.

F - buoyancy force;
P is the force of gravity acting on the body.

Archimedes built the celestial sphere - a mechanical device on which it was possible to observe the movement of the planets, the Sun and the Moon (described by Cicero, after the death of Archimedes, the planetarium was taken by Marcellus to Rome, where for several centuries it aroused admiration); a hydraulic organ, mentioned by Tertullian as one of the marvels of technology (some attribute the invention of the organ to the Alexandrian engineer Ctesibius).

It is believed that in his youth, during his stay in Alexandria, Archimedes invented a water-lifting mechanism (Archimedes screw), which was used to drain the lands flooded by the Nile. He also built a device for determining the apparent (angular) diameter of the Sun (Archimedes talks about it in the treatise Psammit) and determined the value of this angle.

Archimedes (287 BC - 212 BC) - Greek mathematician, engineer and physicist who laid the foundations of mechanics and hydrostatics. He gained worldwide fame thanks to his discoveries in geometry.

Information about Archimedes was left by Titus Livius, Plutarch, Polybius, Cicero, Vitruvius and other ancient authors. But they all lived after the events described. Archimedes was born in Syracuse (a Greek colony in Sicily). The father of the future scientist was the astronomer and mathematician Phidias, who was closely related to the tyrant of Syracuse. The Greek inventor studied in Alexandria of Egypt - the scientific center of that time. Here he met the astronomer Conon and the philosopher Eratosthenes. Archimedes then returned to Syracuse. Here he was always surrounded by attention and never needed funds. But real events from his life are difficult to distinguish from the legends, the reason for which were his inventions.

legends

They say that the famous law of Archimedes, the scientist discovered when he took a bath. According to legend, he shouted "Eureka!" (“Found it!”) jumped out naked into the street.

According to another legend, Archimedes helped launch a heavy multi-deck ship built using a special block system. At the same time, he said: "Give me a fulcrum, and I can turn the world around."

The engineering genius of the scientist manifested itself during the siege of Syracuse during the 2nd Punic War. According to legend, Archimedes was 75 years old at that time. However, powerful throwing machines designed by an engineer bombarded the Roman troops. Special cranes grabbed Roman ships with iron hooks, lifted them up and threw them down in such a way that the ships sank. In addition, during the siege of Syracuse, the Roman fleet was burned with mirrors and polished shields that focused the sun's rays on the ships. Note that the veracity of the latest stories was confirmed by experiments.

Death of Archimedes

There are several versions of the death of Archimedes. According to the story of John Tsets, in the midst of the battle, the mathematician sat near his house and pondered over the drawings that he had made on the road sand. A Roman soldier who was running past stepped on the drawing, after which the scientist rushed at him with the words: “Do not touch the drawings!”. As a result, the soldier killed the old man in cold blood.

But Plutarch says that a soldier came to Archimedes and said that Marcellus was calling him. But the scientist asked the legionary to wait until he solved the problem. The warrior became angry and pierced the inventor with a sword. According to the third version, Archimedes personally went to Marcellus, intending to bring him instruments for measuring the Sun. But his burden attracted the attention of the Romans. The latter decided that the scientist was carrying gold or jewelry, and killed him.

Diodorus Siculus claims that Archimedes died while sketching the diagram. At this time, a Roman soldier began to drag him, but, absorbed in the diagram, the scientist said: “Get out of my diagram! Someone give me my car!" The Roman got scared and killed the old man. Nevertheless, Marcellus gave the scientist a magnificent funeral, and the killer was beheaded. Plutarch also claims that Marcellus was very angry at the death of the inventor, whom he ordered not to be touched.

Scientific activity

Plutarch notes that Archimedes was obsessed with mathematics. Being engaged in science, he even forgot about food. The Greek scientist owns research on arithmetic, geometry and algebra. In particular, it was Archimedes who found all semiregular polyhedra, developed the theory of conic sections, and discovered a geometric method for solving cubic equations. He found a general method for calculating volumes and areas. The ideas of Archimedes became the basis of integral calculus. But he considered his best achievement to be the determination of the volume and surface of a sphere. Even at his grave, Archimedes asked to knock out a ball inscribed in a cylinder.

The inventor calculated the surface area for the segment of the ball and the coil of the so-called "Archimedes' spiral", determined the volumes of the segments of the ellipsoid, ball and paraboloid. Archimedes calculated the ratio of the circumference of a circle to its diameter. The ideas of Archimedes were significantly ahead of their time. Only in the 17th century scientists continued and developed the works of the great mathematician.

Archimedes was the first to successfully apply the lever in practice. For example, he built a lot of block-lever mechanisms that made it easier to lift and transport heavy loads. The great engineer invented the Archimedean screw (auger), designed to scoop out water. This mechanism is still used in Egypt today. Archimedes became the first theoretician of mechanics.

In addition, the Greek scientist built a planetarium, during the movement of which it was possible to observe some of the planets, the rising of the Sun, the phases and eclipses of the Moon. He believed that the system of the world is heliocentric (the planets revolve around the sun).

The following writings of Archimedes have survived to this day:

"About Spirals";
"Square parabola";
"About floating bodies";
"About the ball and the cylinder";
"Circle measurement";
"Psummit";
"Stomachion";
"The Book of Lemmas".

Archimedes created over 40 inventions. Most of them belong to the field of military technology. For example, throwing machines invented by Archimedes launched stones weighing 250 kg. Some modern researchers even claim that Archimedes invented cannons.

In honor of the brilliant scientist named:

crater Archimedes;
asteroid 3600 Archimedes;
streets in Amsterdam, Dnepropetrovsk, Donetsk, Nizhny Novgorod and a square in Syracuse.

Leibniz once said that if you carefully read the writings of Archimedes, then the discoveries of geometers will no longer surprise. Indeed, some of the calculations of the Greek scientist were repeated only after 1.5 thousand years by the same Leibniz and Newton.

Karel Capek wrote the story "The Death of Archimedes". Non-canonical versions of the death of the scientist are given in the stories of Russian writers A. Bashkuev "Kill Archimedes" and O. Raven "War and Geometer".

In 1972, the cartoon "Kolya, Olya and Archimedes" was filmed about the great scientist.

More than two thousand years ago, the entire western part of the Mediterranean coast was engulfed in the flames of a grandiose war. Military operations 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 mortal blow to the very heart of the enemy, conceived a rather bold plan to fight Rome - in Italy itself. In 218 BC, with a large army and war elephants, he crossed the Pyrenees, southern Gaul, and through the Alps penetrated 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 an independent state, the first Greek maritime power. But in the III 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 inhabitants of Syracuse had to accept Roman hegemony.

In order to punish the rebellious for the uprising, the Roman fleet and army, led by the talented commander Marcus Claudius Marcellus, approached the city in 213. Horror seized the inhabitants. Marcellus had just stormed another Sicilian city, Leontine, and executed two thousand defectors from the Roman camp. The same fate awaited this city.

Over a hundred Roman ships entered Syracuse harbor. Marcellus arrayed them in battle order. Linked in pairs, penthers with wooden towers, lifting machines 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. On the lowered bridges, the Roman soldiers were supposed to break into the city with an indomitable avalanche. The fall of the city seemed inevitable. The assault began from the sea and land. But no sooner had the vehicles on penthers lifted the drawbridges, than the catapults and ballistae had had time to throw their shells, when something unexpected happened.

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

Broken Roman ships moved away from the city wall. Marcellus decided to resume the assault at night. He expected that the machines throwing shells would be powerless at night. Projectiles thrown at random will fly over the heads of the besiegers. But the talented leader of the defense 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 from the side of the land. And here the Roman siege weapons and warriors were met with iron hooks, hooks, "scorpions" that picked up the soldiers and threw them on the stones. The proud Roman had to give up his thoughts of taking the city by storm. He decided to move to a blockade and starve the inhabitants out. But it was difficult for the army to cordon off the entire city, and the inhabitants 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 the greatest physicist and mathematician of antiquity - Archimedes, who applied all his brilliant abilities to organize the defense of his native city.

Archimedes was born in Syracuse in 287 BC. According to the well-known Roman politician and orator Cicero, Archimedes was of low social status and lived in poverty. Plutarch claims that Archimedes was fond of mathematics already in childhood. The journey to Egypt had a great influence on the young man, where he visited the city of Alexandria, the center of Hellenic culture. Returning to his homeland, he devoted himself entirely to science and wrote a number of brilliant mathematical works.

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

Unfortunately, not all the works of the genius survived. At various times, the following writings of his were found:

On the equilibrium of plane figures.
On the quadrature of a parabola.
About floating bodies.
On the measurement of a circle.
About a sphere and a cylinder.
About conoids and spheroids, i.e. about bodies learned from the rotation of various figures.
About spirals.
"Psummit".
Separate theorems (lemmas).
Stamachion - about the permutation of flat figures.

In 1907, a new manuscript of the "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:

About a heptagon in a circle.
About the contact of circles.
About parallel lines.
About triangles.
About definitions and data.
Book "Archai".

In the works “On the Sphere and 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 is the famous problem of dividing a ball by a plane into two parts. Archimedes gave the correct solution to this problem, bringing it to a problem of an algebraic nature. Archimedes attached special importance to this work of his.

In the book on the spiral, the scientist considers the properties of the so-called Archimedean spiral.

In Psammit, he set out to prove that gigantic numbers can be expressed.

In the 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 hid 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, drew attention to the fact that as much water flows out of the bath as his body displaces. 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 4,000 tons, Archimedes supplied this ship with a stone-throwing machine that threw stones weighing 80 kg and spears for a considerable distance. He built a screw, named after him the Archimedean screw. This is a water-lifting machine, in which a helical spiral passes inside a cylindrical pipe. The pipe is open at both ends and placed obliquely. With strong rotation, the pipe captures water at the lower end, the water rises in a spiral and pours out at the upper end. There is evidence to suggest that the Archimedean screw was used to dry swamps in Egypt. In the future, he served as the basis for the construction of the propeller of the ship, and found application in the automotive industry.

The scientist developed the theory of the composite block, lever and screw and applied them in practical life. With the help of blocks, he moved heavy weights. Archimedes owns the famous exclamation: "Give me a fulcrum, and I will turn the Earth."

He built a planetarium or "air globe" that rotated through a system of blocks. The planetarium showed the movement of the planets around the Earth.

Death of Archimedes

But back to the city besieged by the Romans. The siege of the city has been going on for three years. Archimedes mobilized all his knowledge by building new machines. Popular rumor added legendary ones to his skillful structures (some writers, for example, say that Archimedes allegedly built incendiary glasses and with their help collected the sun's rays, pointed 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 betrayal of the nobility. Marcellus allowed his warriors to "plunder treasures and capture slaves." Embittered by the long siege, hungry for prey, the Roman soldiers rushed like bloodthirsty jackals to the defenseless city. They broke into dwellings, robbed jewelry, mercilessly killing residents, including old people and children.

Deep in his thoughts, Archimedes sat over the drawings. He described geometric figures on the floor with a compass, not noticing the bacchanalia of robbery and murder taking place in the city. Suddenly, a Roman soldier with a drawn sword burst into him. Seeing the newcomer, Archimedes shielded his geometric drawings from him and said: "Do not spoil my circles for me." The warrior, intoxicated by the thirst for profit in response to the words of Archimedes, dealt him a mortal blow with a sword.

Thus, in 212 BC, the great luminary of science of the ancient world went out. 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 shrubs. Only in 75 BC. e., the famous Cicero, being the ruler in Sicily, found among the abandoned graves a monument to Archimedes, depicting a cylinder. Cicero exclaims bitterly: “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 mind 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 writings into Arabic.

During the Renaissance, the creations of Archimedes were extracted from obscurity, published and admired by scientists.

Summing up the scientific and scientific-practical activities of Archimedes, it is clear that he is rightfully called the father of physics, physical experience, and physical mechanics. Archimedes founded statics as a mathematical science, gave grounds 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.

Portal for the student. Self-training

Biography of Archimedes

"Eureka!"

heat ray

Experiments of Archimedes in the modern world

Works of Archimedes

legends

Death of Archimedes

Scientific activity

Archimedes - life and scientific works

Death of Archimedes

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