King Hiero II of Syracuse made crown for a temple, who supplied the pure gold for this purpose. King asked Archimedes to determine whether the dishonest goldsmith substitute some silver for gold.
Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density.
While taking a bath, he noticed that the level of the water in the tub rose as he got in. He realized that this effect could be used to determine the volume of the crown.
For practical purposes water is incomprehensible, so the submerged crown would displace an amount of water equal to its own volume. He divided the mass of the crown by the volume of water displaced, to obtain the density of the crown.
If jeweler used cheaper and less dense metals than density of crown would be lower than that of gold.
Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying “Eureka!”. He conducted the test successfully, proving that silver had indeed been mixed in.
In the first part of this treatise, Archimedes spells out the law of equilibrium of fluids, and proves that water will adopt a spherical form around a center of gravity.
This may have been an attempt at explaining the theory of contemporary Greek astronomers such as Eratosthenes that the Earth is round.
The fluids described by Archimedes are not self-gravitating, since he assumes the existence of a point towards which all things fall in order to derive the spherical shape.
In the second part, he calculates the equilibrium positions of sections of paraboloids. This was probably an idealization of the shapes of ships’ hulls.
Some of his sections float with the base under water and the summit above water, similar to the way that icebergs float. Archimedes’ principle of buoyancy is given in the work, stated as follows:
Any body wholly or partially immersed in a fluid experiences an upthrust equal to, but opposite in sense to, the weight of the fluid displaced.
Archimedes’ work on levers caused him to remark: “Give me a place to stand on, and I will move the Earth.”
Plutarch describes how Archimedes designed block-and-tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to move.
Historian credited him with improving the power and accuracy of the catapult. He also invented the odometer during the First Punic War. Historian described the odometer as a cart. It contain a gear mechanism that dropped a ball into a container after each mile traveled.
A large ship would leak a considerable amount of water through the hull. He developed a screw in order to remove the water.
Archimedes’ machine was a device with a revolving screw-shaped blade inside a cylinder. It was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals.
The Archimedes’ screw is still in use today for pumping liquids and granulated solids such as coal and grain. Vitruvius described the Archimedes’ screw as improvement version of screw pump. Ancient Engineer used it to irrigate the Hanging Gardens of Babylon.
He was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia, located along the coast of Southern Italy.
Heracleides, friend of Archimedes wrote his biography but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children.
During his youth, Archimedes may have studied in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries.
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Historian regarded him as one of the leading scientists in classical antiquity.
Generally considered the greatest mathematician of antiquity and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola.
Other mathematical achievements include deriving an accurate approximation of pi. He define and investigated the spiral bearing his name. Archimedes created a system using exponentiation for expressing very large numbers.
He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, including an explanation of the principle of the lever.
Historian credited him with designing innovative machines. He also designed screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.
He died c. 212 BC during the Second Punic War. Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two-year-long siege.
According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when Roman captured the city.
A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. The soldier was enraged by this, and killed Archimedes with his sword.
The foremost document containing the work of Archimedes is the Archimedes Palimpsest. The palimpsest holds seven treatises, including the only surviving copy of On Floating Bodies in the original Greek.
The his tomb carried a sculpture illustrating his favorite mathematical proof, consisting of a sphere and a cylinder of the same height and diameter.