This post is dedicated to Archimedes, one of the most brilliant scientific minds of all time. Our reader can find here basic information on this quite influential figure of Ancient Greek Science.
Archimedes lived from 287 to 212 B.C. He was born in Syracuse, on the coast of Sicily, where he spent most of his life. He was the son of Pheidias, an astronomer, who estimated the ratio of the diameters of the Sun and the Moon.
The word “Archimedes” is composed of two parts: arché, which means beginning, dominion or original cause; and mêdos, which means mind, thinking or intellect. Its meaning is then given by The Master of Thought or The Mind of the Beginning.
Archimedes spent some time in Egypt. It is possible that he studied at the city of Alexandria, which was then the center of Greek science, with the successors of the mathematician Euclid, who flourished around 300 B.C. and published the famous book of geometry known as The Elements.3 Many of Archimedes’s works were sent to mathematicians who lived in Alexandria or who had been there.
Archimedes is considered one of the greatest scientists of all time, and the greatest mathematician of antiquity.
By utilizing the method of exhaustion, Archimedes was able to determine the area, volume, and center of gravity of many important geometrical figures, which had never been accomplished before him. He is considered one of the founders of statics and hydrostatics.
Those works of Archimedes that have survived were addressed to the astronomer Conon of Samos (at that time living in Alexandria), to Conon’s disciple Dositheus after the death of Conon, to king Gelon, son of the king Hiero of Syracuse, and to Eratosthenes, librarian of the Library of Alexandria and famous for his precise estimation of the radius of the Earth.
Archimedes would send his works together with some introductory texts. Through these texts we can discover the order of some of his discoveries and a little of his personality.
His habit of sending initially only the enunciations of some theorems, without demonstrations, may have led some mathematicians plagiarize Archimedes, claiming that his results belonged to them.
Archimedes would often spend years trying to find the proof of a difficult theorem.
Although the works that have come down to us are related to mathematics and theoretical physics, the fame of Archimedes in antiquity is due to his work as an engineer and builder of war machines (catapults, burning mirrors, etc.).
One of the inventions attributed to him is a water pumping system known as the cochlias, or Archimedes screw, which is used even to this day. The word cochlias is Greek, meaning snail. It is believed that he invented this hydraulic machine during his stay in Egypt, where it was used for irrigating fields and pumping water.
He built a famous planetarium that had a single hydraulic mechanism which moved several globes simultaneously, reproducing the motions of the stars, the Sun, the Moon, and the planets around the Earth. He also built a hydraulic organ in which the air fed to the pipes was compressed above water in an air chamber. Also attributed to him are the inventions of the compound pulley, machines for discharging showers of missiles, the Roman balance with unequal arms etc.
Several authors quote a famous sentence by Archimedes in connection with his mechanical devices and his ability to move great weights with a small force:
“Give me a place to stand on, and I will move the Earth.” Apparently he uttered this when he accomplished a feat ordered by king Hiero to launch a ship weighing many tons and carrying a full load. He succeeded in this all alone, with his hands and the aid of a few mechanical instruments.
During the second Punic war between Rome and Carthage, the city of Syracuse was allied with Carthage. Syracuse was attacked by the Romans in 214 B.C., under General Marcellus. Many histories about Archimedes have survived in a famous biography of Marcellus written by Plutarch. Marcellus attacked Syracuse by land and sea, heavily armed. According to Plutarch:
[All machines of Marcellus], however, were, it would seem, but trifles for Archimedes and his machines. These machines he had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with King Hiero’s desire and request, some little time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of the people in general.
Elsewhere, Plutarch writes:
When, therefore, the Romans assaulted the walls in two places at once, fear and consternation stupefied the Syracusans, believing that nothing was able to resist that violence and those forces. But when Archimedes began to ply his engines, he at once shot against the land forces all sorts of missile weapons, and immense masses of stone that came down with incredible noise and violence; against which no man could stand; for they knocked down those upon whom they fell in heaps, breaking all their ranks and files. In the meantime huge poles thrust out from the walls over the ships sunk some by the great weights which they let down from on high upon them; others they lifted up into the air by an iron hand or beak like a crane’s beak and, when they had drawn them up by the prow, and set them on end upon the poop, they plunged them to the bottom of the sea; or else the ships, drawn by engines within, and whirled about, were dashed against steep rocks that stood jutting out under the walls, with great destruction of the soldiers that were aboard them. (…) In fine, when such terror had seized upon the Romans, that, if they did but see a little rope or a piece of wood from the wall, instantly crying out, that there it was again, Archimedes was about to let fly some engine at them, they turned their backs and fled, Marcellus desisted from conflicts and assaults, putting all his hope in a long siege.
Also connected with the defence of Syracuse is the famous story about burning the Roman ships with mirrors. Archimedes used a great mirror or a system of small mirrors in order to concentrate the sun’s rays and focus them on the ships. The two most famous accounts are due to Johannes Tzetzes, a Byzantine scholar, and John Zonaras, both of the twelfth century:
When Marcellus withdrew them [his ships] a bow-shot, the old man [Archimedes] constructed a kind of hexagonal mirror, and at an interval proportionate to the size of the mirror he set similar small mirrors with four edges, moved by links and by a form of hinge, and made it the centre of the sun’s beams–its noon-tide beam, whether in summer or in mid-winter. Afterwards, when the beams were reflected in the mirror, a fearful kindling of fire was raised in the ships, and at the distance of a bow-shot he turned them into ashes. In this way did the old man prevail over Marcellus with his weapons.
At last in an incredible manner he [Archimedes] burned up the whole Roman fleet. For by tilting a kind of mirror toward the sun he concentrated the sun’s beam upon it; and owing to the thickness and smoothness of the mirror he ignited the air from this beam and kindled a great flame, the whole of which he directed upon the ships that lay at anchor in the path of the fire, until he consumed them all.
Only after a siege of three years was Marcellus able to conquer Syracuse. Archimedes was killed by a Roman soldier in 212 B.C. during the capture of the city. Marcellus had given express orders that Archimedes’s life should be spared, in recognition of the genius of this enemy who had caused him so many losses. In spite of this, a soldier killed him while he was trying to protect or finish some mathematical discoveries. The last words uttered by Archimedes seem to have been addressed to this soldier: “Fellow, stand away from my diagram.”
Plutarch gives us three different versions of his death:
But nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion
of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus; which he declining to do before he had worked out his problem to a demonstration, the soldier,
enraged, drew his sword and ran him through. Others write that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was then at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate that, as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.
The works of Archimedes
The works of Archimedes known to us are available in the original Greek and in Latin.
Archimedes wrote in the Doric dialect. In the manuscripts still extant his original language was transformed in some books totally, in others only partially, into the Attic dialect common in Greece. In the 9th century some of his works were translated to Arabic. The first Latin translations of the works of Archimedes and of several scientists and philosophers of Greece were made during the 12th and 13th centuries.
• On the Equilibrium of Planes, or The Centers of Gravity of Planes. Book I.
• Quadrature of the Parabola.
• On the Equilibrium of Planes, or The Centers of Gravity of Planes. Book II.
• The Method of Treating Mechanical Problems, to Eratosthenes. This work is usually called simply The Method.
• On the Sphere and Cylinder, Books I and II.
• On Spirals.
• On Conoids and Spheroids.
• On Floating Bodies. Books I and II.
• Measurement of a Circle.
• The Sand-Reckoner.
It is also known that Archimedes wrote other works which exist today only in fragments or in references by other writers:
• The Stomachion.
• The Cattle-Problem.
• Book of Lemmas.
• Semi-Regular Polyhedra.
• Area of the Triangle.
• Construction of a Regular Heptagon.
• Principles, or Naming of Numbers.
• On how to Express Large Numbers.
• On the Centers of Gravity.
• Elements of Mechanics.
• On the Center of Gravity and Law of the Lever.
• Equilibria.
• Book on Columns, or Book of Supports.
• On Balances, or On Levers.
• One work on Optics.
• On Sphere-Making.
• On the Calendar.
• On Circles Touching One Another.
• On Parallel Lines.
• On Triangles.
• On Properties of Right-Angled Triangles.
• On the Assumptions for the Elements of Geometry.
• Book of Data or Definitions
(Source: the book “Archimedes, the Center of Gravity, and the First Law of Mechanics”, by Andre K.T. Assis)
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