Editing Hiero II of Syracuse (section)

==Connection to the "eureka" story==
According to a story told by [[Vitruvius]],<ref>[[De architectura]] IX, Preface, 9-12.</ref> Hiero suspected he was being cheated by the goldsmith to whom he had supplied the gold to make a [[votive crown]] for a temple. He asked Archimedes to find out if all the gold had been used, as had been agreed. [[Archimedes]], on discovering the principle of [[displacement (fluid)|displacement]] needed to measure the [[density]] of the crown is said to have shouted "[[Eureka (word)|eureka, eureka!"]] while running naked through Syracuse. Supposedly, it was while noticing the rise in water level when getting a bath tub that Archimedes realized he could use water-displacement to measure the crown's irregular shape, and in his excitement about the discovery he dashed outside cheering and forgot to dress himself first. Vitruvius concludes this story by stating that Archimedes' method successfully detected the goldsmith's fraud; the smith had indeed taken some of the gold and substituted silver instead.