Eureka! The story of the Archimedes Principle
Kings don't like to be tricked. I'm sure you know this from all the stories you read when you were small. King Hieron II of Syracuse, was no exception. He worried that the people who made his crown charged him the price of using solid gold but instead they tricked him and used gold mixed with silver which costs less.
It is known that King Hieron II was friends with, and a relative of, the great Greek mathematician Archimedes. Archimedes was the son of an astronomer. He had traveled to Alexandria, Egypt, a place of great learning, where he studied the works of some other mathematicians, like Euclid and Conon.
Archimedes helped his friend King Hieron II by creating machines for the king's army. The pulley was one of these inventions, but Archimedes thought the study of mathematics was the most important thing he could do.
Sometimes Archimedes got so busy thinking about mathematics that he forgot to take a bath and his servants would have to force him to go to the public baths.
Legend has it, although some people doubt this, that one time when Archimedes was at the public bath he noticed that when he climbed in to a soaking bath the water level went up. Have you noticed the same thing when you climb into your own bathtub at home?
Archimedes, as the story goes, realized that a solid which is denser than water; will be lighter when immersed in fluid, by the weight of the water the solid displaced.
Archimedes knew he could use this knowledge to test whether King Hieron's crown was made of solid gold. He was so excited about this new idea, that he wanted to tell the king. He jumped out of the bath and shouted "Eureka!" which, is what you should shout whenever you have a great idea!
Then Archimedes ran naked through the streets of Syracuse to tell the King his new idea. (Some people say he grabbed a towel first and wrapped it around his waist before he ran to the King. We can't be sure which story is true since this all happened about 2200 years ago! No photos have survived.)
Archimedes wrote some books about Mathematics, including On Floating Bodies. This is where he wrote what we call Archmedes' principle - "a body immersed in a liquid or a gas has a buoyant force equal to the weight of the liquid or gas that it displaces."