LYCOS RETRIEVER 
Archimedes: King Hiero
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On another occasion Archimedes told Hieron that with a given force he could move any given weight. Archimedes had investigated properties of the lever and pulley, and it is on the basis of these that he is said to have asserted, "Give me a place to stand and I can move the earth." Hieron, amazed at this, asked for some physical demonstration. In the harbor was a new ship which the combined strength of all the Syracusans could not launch. Archimedes used a mechanical device that enabled him, standing some distance away, to move the ship. The device may have been a simple compound pulley or a machine in which a cogwheel with oblique teeth moves on a cylindrical helix turned by a handle.
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There are many stories about how Archimedes made his discoveries. A famous one tells how he uncovered an attempt to cheat King Hieron. The king ordered a golden crown and gave the crown's maker the exact amount of gold needed. The maker delivered a crown of the required weight, but Hieron suspected that some silver had been used instead of gold. He asked Archimedes to think about the matter. One day Archimedes was considering it while he was getting into a bathtub.
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The discoveries Archimedes made in the field of mathematics seems to evolve from his love of the subject and basic curiosity concerning geometry. On the other hand, many of his inventions and physical science discoveries were the result of challenges and problems posed by King Hiero.
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It seems that it was the devotion to Hieron that induced Archimedes to divert his mathematical studies to his engineering skills. There are many "stories" of Archimedes' achievements in this field that are difficult to substantiate but many indicate that the inventions were created at Hieron's request. A well published story by Vitruvius is that of Hieron's desire to know if all the gold he had given to a goldsmith to create a crown was actually used instead of being substituted with an amount of silver.
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Hieron saw that Archimedes had a most inventive mind in such practical matters as constructing mechanical aids. At this time one use for such inventions was in the military field. Hieron persuaded Archimedes to construct machines for possible use in warfare, both defensive and offensive.
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King Hiero