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Archimedes: Water
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The many stories that are told of Archimedes are the prototype of the absentminded-professor stories. A famous one tells how Archimedes uncovered a fraud attempted on Hieron. The King ordered a golden crown and gave the goldsmith the exact amount of gold needed. The goldsmith delivered a crown of the required weight, but Hieron suspected that some silver had been used instead of gold. He asked Archimedes to consider the matter. Once Archimedes was pondering it while he was getting into a bathtub full of water.
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There are several ways Archimedes may have determined the amount of silver in the crown. One likely method relies on an idea that is now called Archimedes's principle. It states that a body immersed in a fluid is buoyed up (pushed up) by a force that is equal to the weight of fluid that is displaced (pushed out of place) by the body. Using this method, he would have first taken two equal weights of gold and silver and compared their weights when immersed in water. Next he would have compared the weight of the crown and an equal weight of pure silver in water in the same way. The difference between these two comparisons would indicate that the crown was not pure gold.
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During his lifetime, Archimedes made his work known through correspondence with the mathematicians in Alexandria. The writings of Archimedes were collected by the Byzantine architect Isidore of Miletus (c. 530 AD), while commentaries on the works of Archimedes written by Eutocius in the sixth century AD helped to bring his work a wider audience. Archimedes' work was translated into Arabic by Thābit ibn Qurra (836–901 AD), and Latin by Gerard of Cremona (c. 1114–1187 AD). During the Renaissance, the Editio Princeps (First Edition) was published in Basel in 1544 by Johann Herwagen with the works of Archimedes in Greek and Latin.[35] Around the year 1586 Galileo Galilei invented a hydrostatic balance for weighing metals in air and water after apparently being inspired by the work of Archimedes.[36]
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Archimedes' work was not as widely recognized in classical antiquity as that of Euclid, and some of his treatises are believed to have been lost when the Library of Alexandria was damaged at various periods in its history. Some of his writings survived through Latin and Arabic translations made during the Middle Ages, and these documents provided Renaissance scholars with an influential source of ideas. Around the year 1586 Galileo Galilei invented a hydrostatic balance for weighing metals in air and water after apparently being inspired by the work of Archimedes.
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Archimedes is probably ... the first mathematical physicist on record, and the best before Galileo and Newton. He invented the field of statics, enunciated the law of the lever, the law of equilibrium of fluids and the law of buoyancy. (He famously discovered the latter when he was asked to determine whether a crown had been made of pure gold, or gold adulterated with silver; he realized that the rise in the water level when it was immersed would be equal to the volume of the crown, and the decrease in the weight of the crown would be in proportion; he could then compare those with the values of an equal weight of pure gold.) He was the first to identify the concept of center of gravity, and he found the centers of gravity of various geometric figures, assuming uniform density in their interiors, including triangles, paraboloids, and hemispheres. Using only ancient Greek geometry, he also gave the equilibrium positions of floating sections of paraboloids as a function of their height, a feat that would be taxing to a modern physicist using calculus.
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Here is what Archimedes had found. Since an object immersed in a fluid displaces the same volume of fluid as the volume of the object, it was possible to determine the precise volume of the crown by immersing it in water. After determining the volume of water, a piece of pure gold could easily be made to match the volume of the water, and ... the volume of the crown. In theory, if the volume of the crown and the volume of the gold block are the same, they should also have the same mass. The only reason they would not have the same mass is if one of them was not pure gold. When the two objects were placed in a balance they did not have equal mass. Faced with this evidence the craftsman confessed to his crime.
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