Published after Galileo's death, this work of his youth sought to demonstrate that Archimedes had resolved the famous deceit of the crown not according to the overly simple version handed down by Vitruvius but on the basis of a more refined procedure. Galileo proposed the use of the "bilancetta," a balance that allowed bodies to be weighed directly in the water - thus applying Archimedes' concept of specific weight: masses of gold and silver, like the crown, weighed in the air balance each other but any differences appear when they are weighed in water. They are lighter than in the air in proportion to the ratio between their specific weight and that of water.