To provide entertainment at a dinner held by the Grand Duke of Tuscany, Galileo debated the Aristotelian physicist Lodovico delle Columbe on the topic of floating bodies. Galileo employed Archimedes’ mathematical analysis. Columbe, untrained in mathematics, relied upon Aristotle’s qualitative principles. Cardinal Maffeo Barberini awarded the debate in favor of Galileo, and the Grand Duke printed a treatise expressing Galileo’s views. In this treatise, Galileo also reports his ongoing telescopic observations, including sunspots, the phases of Venus, the peculiar shape of Saturn, and his calculated periods for Jupiter’s satellites.