The Method of Mechanical Theorems , and the Stomachion. Of these treatises, the last three are of the greatest significance to our understanding of Archimedes. While the other treatises had survived through other manuscripts, there is no other surviving copy of On Floating Bodies in Greek — the language in which Archimedes wrote, and there is no version in any language of The Method of Mechanical Theorems and of the Stomachion. The Archimedes manuscript was used for the majority of the pages of the prayer book. The Archimedes manuscript was written in the second half of the tenth century, almost certainly in Constantinople. It might surprise some people that Abigail is not wearing gloves.

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Play media By placing a metal bar in a container with water on a scale, the bar displaces as much water as its own volume , increasing its mass and weighing down the scale. The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius , a votive crown for a temple had been made for King Hiero II of Syracuse , who had supplied the pure gold to be used, and Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith.

While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, [24] so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained.

This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying " Eureka!

Moreover, the practicality of the method it describes has been called into question, due to the extreme accuracy with which one would have to measure the water displacement. This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. The difference in density between the two samples would cause the scale to tip accordingly.

Galileo considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself. The Greek writer Athenaeus of Naucratis described how King Hiero II commissioned Archimedes to design a huge ship, the Syracusia , which could be used for luxury travel, carrying supplies, and as a naval warship.

The Syracusia is said to have been the largest ship built in classical antiquity. It was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. Also known as "the ship shaker", the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. When the claw was dropped onto an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it. There have been modern experiments to test the feasibility of the claw, and in a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device.

Painting by Giulio Parigi , c. In the modern era, similar devices have been constructed and may be referred to as a heliostat or solar furnace. A test of the Archimedes heat ray was carried out in by the Greek scientist Ioannis Sakkas.

The experiment took place at the Skaramagas naval base outside Athens. On this occasion 70 mirrors were used, each with a copper coating and a size of around five by three feet 1. When the mirrors were focused accurately, the ship burst into flames within a few seconds. The plywood ship had a coating of tar paint, which may have aided combustion. Flames broke out on a patch of the ship, but only after the sky had been cloudless and the ship had remained stationary for around ten minutes.

It was concluded that the device was a feasible weapon under these conditions. The MIT group repeated the experiment for the television show MythBusters , using a wooden fishing boat in San Francisco as the target. Again some charring occurred, along with a small amount of flame.

It was also pointed out that since Syracuse faces the sea towards the east, the Roman fleet would have had to attack during the morning for optimal gathering of light by the mirrors. MythBusters also pointed out that conventional weaponry, such as flaming arrows or bolts from a catapult, would have been a far easier way of setting a ship on fire at short distances.

The show concluded that a more likely effect of the mirrors would have been blinding, dazzling , or distracting the crew of the ship. Earlier descriptions of the lever are found in the Peripatetic school of the followers of Aristotle , and are sometimes attributed to Archytas. The odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled.

After the capture of Syracuse c. Cicero mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus. The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated the other to the Temple of Virtue in Rome.

Pappus of Alexandria stated that Archimedes had written a manuscript now lost on the construction of these mechanisms entitled On Sphere-Making. Modern research in this area has been focused on the Antikythera mechanism , another device built c. While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics. Plutarch wrote: "He placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life.

Through proof by contradiction reductio ad absurdum , he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. In Measurement of a Circle he did this by drawing a larger regular hexagon outside a circle and a smaller regular hexagon inside the circle, and progressively doubling the number of sides of each regular polygon, calculating the length of a side of each polygon at each step.

As the number of sides increases, it becomes a more accurate approximation of a circle. In On the Sphere and Cylinder , Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude.

This is the Archimedean property of real numbers. The actual value is approximately 1. He introduced this result without offering any explanation of how he had obtained it.

This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.

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## The Archimedes Palimpsest Project

Posted The thousand-year-old manuscript contains the earliest surviving writings by Archimedes, the Greek thinker who is regarded as the greatest mathematician of antiquity. Follow the 1,year journey of an ancient document, and watch as modern technology makes the erased text reappear. Chronology of the Archimedes Palimpsest Circa B. Before his death at Syracuse in B. Circa A scribe working in Constantinople handwrites a copy of the Archimedes treatises, including their accompanying diagrams and calculations, onto parchment, which is assembled into a book. Circa A Christian monk handwrites prayers in Greek over the Archimedes text, turning the old mathematical text into a new prayer book.

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## History for Atheists

Early[ edit ] Archimedes lived in the 3rd century BC and wrote his proofs as letters in Doric Greek addressed to contemporaries, including scholars at the Great Library of Alexandria. These letters were first compiled into a comprehensive text by Isidorus of Miletus , the architect of the Hagia Sophia patriarchal church, sometime around AD in the then Byzantine Greek capital city of Constantinople. Their leaves were folded in half, rebound and reused for a Christian liturgical text of later numbered leaves, of which are extant each older folded leaf became two leaves of the liturgical book. The palimpsest remained near Jerusalem through at least the 16th century at the isolated Greek Orthodox monastery of Mar Saba.

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## Inside the Archimedes Palimpsest

Play media By placing a metal bar in a container with water on a scale, the bar displaces as much water as its own volume , increasing its mass and weighing down the scale. The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius , a votive crown for a temple had been made for King Hiero II of Syracuse , who had supplied the pure gold to be used, and Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith. While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, [24] so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained.