Yes he did.
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yes he did, and he also run into the streets of siracuse naked shouting this
Archimedes shouted eureka.
Archimedes.
He was wearing nothing when he shouted eureka.
According to legend, Archimedes shouted "Eureka!" (which means "I have found it!") while running down the streets naked. The reason he did this is because he found out that, a body immersed in water has a buoyant force equal to the weight of the water that it displaces. He was able to find out if the kings crown was really made of pure gold this way (and it wasn't).