5 · Ancient Greece science and technology

Archimedes of Syracuse

about 250 BC Syracuse, Sicily (Italy)

In short

Archimedes of Syracuse was a mathematician, physicist and inventor. He discovered why an object placed in water is pushed upwards, and he studied levers, saying, according to tradition: “Give me a place to stand and I will move the world.” He worked out the value of pi with great accuracy. When the Romans besieged Syracuse he designed machines to defend the city, and he died during its capture, in 212 BC.

Why it matters His discoveries about levers and floating are still studied at school today.

Source: Treccani, entry “Archimede”

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Illustration: Archimedes of Syracuse (Syracuse, Sicily (Italy)) — Illustration created with AI for Storiascopio

Where: Syracuse, Sicily (Italy)

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The story

A genius from Syracuse

Syracuse, in the 3rd century BC, was one of the largest and richest cities in the Mediterranean, a Greek colony in Sicily ruled by King Hieron II. Here, around 287 BC, Archimedes was born. We know little about his life: we know mainly his works and the stories the ancients handed down about him. He was a mathematician, physicist and inventor. That is why our site gives “about 250 BC”: it is not a precise year, but the period of his full activity. He died in 212 BC.

“Eureka!”

The most famous story about Archimedes concerns a crown. It is told by the Roman writer Vitruvius, much later. King Hieron II had had a gold crown made and wanted to know whether the goldsmith had cheated him by mixing some silver with the gold. Archimedes had to find out without damaging it. While taking a bath, he noticed that the water in the tub overflowed in proportion to the part of his body that was immersed, and he understood how to solve the problem. He cried “eureka!”, that is “I have found it!”. Scholars think the method was more probably a comparison in water between the crown and an equal weight of gold. Vitruvius' tale is an anecdote rather than a documented fact.

The real discovery is written in the treatise “On Floating Bodies”, which founds hydrostatics, the study of the equilibrium of liquids. From it comes “Archimedes' principle”: a body immersed in a fluid receives an upward push. This is the reason why a very heavy iron ship floats and a small stone sinks.

The lever and the screw

Archimedes also studied the lever, in the treatise “On the Equilibrium of Planes”: he proved with mathematics why a large weight can be lifted with a small one, if the fulcrum is well chosen. He is also credited with (or studied) the Archimedes screw, which perhaps existed before him: a tube wound in a spiral inside a cylinder that, when turned, lifts water. It was used to irrigate fields and, according to the ancients, to empty the water from the hold of an enormous ship built by Hieron, the Syracusia.

Numbers and figures

He was a very great mathematician. In the “Measurement of a Circle” he calculated the ratio between the circumference and the diameter, what we now call pi, and proved that it lies between 3 + 10/71 (about 3.1408) and 3 + 1/7 (about 3.1429). For that time it was an extraordinary precision. He also proved that the volume of a sphere is two thirds of that of the cylinder that exactly contains it.

In the treatise “The Sand Reckoner” he asked himself a curious question: how many grains of sand would it take to fill the whole universe, as far as the sphere of the fixed stars? To write it he had to invent a new way of expressing large numbers. In another work, the “Method”, written in the form of a letter to his friend Eratosthenes, he explains how he found his results: first with a mechanical argument, imagining figures and weights, and then he proved them rigorously.

The machines of the siege

In 212 BC the Romans, under the consul Marcellus, captured Syracuse after a long siege. According to the ancient historians Polybius, Livy and Plutarch, during the siege the machines designed by Archimedes were very useful for the defence. People speak of an “iron hand”, a hook that grabbed enemy ships. Another legend, told much later, says he had built mirrors to concentrate the Sun's light and set the ships on fire. Scholars regard this story as a legend. In 1973 an experiment with 70 mirrors managed to set fire to a model ship at about 50 metres, but it is not certain that the ancients could have done it.

His death

When the Romans entered the city, Archimedes was killed by a soldier. There are several versions. In the most famous he was drawing geometric figures in the sand and is said to have told the soldier not to spoil his drawing. Livy and Plutarch tell that the consul Marcellus was very sorry about his death and had him buried.

Archimedes had asked for a sphere inscribed in a cylinder to be carved on his tomb, in memory of his best-loved discovery. More than a century later the Roman politician Cicero, when he was quaestor in Sicily, found the tomb, covered in brambles, thanks precisely to that drawing.

Why it happened

Archimedes lived in a Syracuse that loved technology. King Hieron II needed engineers to build ships, war machines and public works, and protected scholars. Archimedes' talent was put at the service of the city.

What made his results possible was Greek mathematics, already advanced: Euclid had written the “Elements” a few decades earlier, and Archimedes used its methods of proof. Alexandria was close, at least by letter: from the “Method” we know that he exchanged ideas with Eratosthenes, one of the most important scholars of the Mouseion. So the discoveries of mathematics and those of mechanics met in his mind.

What changed

Archimedes' discoveries have entered school textbooks. Archimedes' principle explains why ships, balloons and submarines float or rise. The law of the lever is the basis of many simple machines. The idea of the Archimedes screw is the basis of machines still used today.

In mathematics, Archimedes joined intuitive reasoning, with imaginary figures and weights, to rigorous proofs: two ways of working that mathematicians still use today.

The story of his writings is an adventure. The “Method” was believed lost. It was rediscovered in 1906 by the scholar Johan Heiberg in a medieval manuscript in which the original text had been scraped off and covered by a prayer: a “palimpsest”. The codex was then lost, reappeared in the 1990s and was sold at auction in 1998.

Key people and places

People

Archimedes: Mathematician, physicist and inventor from Syracuse (about 287–212 BC).
Hieron II: King of Syracuse, who commissioned the crown and the great ship Syracusia.
Marcellus: Roman consul who captured Syracuse in 212 BC and had Archimedes buried.
Eratosthenes: Scientist of Alexandria, to whom Archimedes addressed the “Method”.
Cicero: Roman writer who, as quaestor, found Archimedes' tomb.

Places

Syracuse: The great Greek city of Sicily where Archimedes was born and died.
Alexandria, Egypt: The city of the Mouseion, with which Archimedes exchanged ideas by letter.

Good to know

Archimedes estimated pi between 3+10/71 and 3+1/7, that is between about 3.1408 and 3.1429.
On his tomb there was a sphere inside a cylinder, because he had proved that the volume of the sphere is two thirds of that of the cylinder.
In the “Sand Reckoner” he calculated how many grains of sand it would take to fill the universe, and to do so he invented a new system for large numbers.
One of Archimedes' works, the “Method”, was found in 1906 in a medieval prayer book written over the original text.
In 1973 an experiment with 70 mirrors managed to set fire to a model ship at about 50 metres, but the story of Archimedes' mirrors remains a legend.