Well, yes and no. More no than yes. See: http://en.wikipedia.org/wiki/Buoyancy#Archimedes.27_principle
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Yes, Archimedes is credited with discovering the principle of density. He famously discovered this principle while taking a bath, leading to his exclamation "Eureka!".
not that I know of, if I'm right, it was Archimedes.
Density was discovered by the Greek philosopher Archimedes around 250 BC. He realized that the buoyant force exerted by a fluid on an object could be used to determine the object's volume and, by extension, its density. This led to the development of the concept of density as mass per unit volume.
Archimedes' principle states that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid it displaces. This principle helps explain why objects float or sink in fluids based on their density.
Archimedes came across concept of density - that is MASS divided by VOLUME. For each substance this ratio is different but a CONSTANT for that substance. Thus the mass you are dealing with is irrelevant if the crown had the same ratio as the piece of pure gold then the crown was pure god, if it did not then the crown was not gold.
Archimedes was not a chemist.