Chapter Nine: Galileo Galilei and Hero’s Lost Principles

In his Theoremata circa centrum gravitatis solidorum, Galileo Galilei (1564–1642) demonstrated his mastery of Archimedean mechanical geometry by devising an original method in solid geometry. In his mechanics (Le mecaniche), he devised an original Archimedean proof of the law of equilibrium and followed Guidobaldo’s Archimedean treatment of Hero’s simple machines, but with two crucial additions. He rediscovered independently Hero’s lost principles—the principle of less force and the principle of compensation—and completed Guidobaldo’s mechanics with a definite rule for all machines, that what is lost in speed is gained in power. He detached this rule from the balance and the lever, extended it to impact and hydrostatics, and applied it in his new science of motion. For him the principles of mechanics lay in the very constitution of nature itself, a theme that had been more or less implicit in mechanics since the time of Aristotle.