Archimedes was a Greek scientist, mathematician, and inventor who lived in Syracuse (Sicily) from 287-212 BC.  Archimedes may have discovered his principle of bouyancy while trying to solve a problem given to him by the King of Syracuse.  King Hiero had ordered a local tradesman to design and fabricate a gold crown to be set up in a shrine as an offering to the gods.  The artisan was given a precise amount of gold for the project and returned, sometime later, with a crown of identical weight.  The King appeared to be entirely satisfied until word reached him later that the artist may have replaced some of the gold with silver during the manufacture of the crown.  The King turned to Archimedes for help.  Archimedes probably realized that, because gold has a density (18.9 g/cm³) almost twice that of silver (10.5 g/cm³), a crown made out of gold and silver wouild have a larger volume than a crown made out of pure gold.  Archimedes may also have used his principle of bouyancy to actually measure the density of the crown (a mixture of gold and silver would have a density less than pure gold).  Unfortuately I haven't found out whether the crown turned out to be pure gold or whether the tradesman had tried to cheat the King.