This is the acclaimed translation by Stillman Drake of "Discourses and Mathematical Demonstrations Concerning Two New Sciences Pertaining to Mechanics and Local Motions." It is the work written by Galileo in the last years of his life, while under house arrest by the Inquisition for suspected heresy. The two new sciences that comprise the subject of the book are the science of motion on earth and the study of the strength of materials. In presenting his findings, Galileo formulates a methodology for rigorous experimental study of natural phenomena that is the foundation for modern experimental science.History of Free Fall, by Stillman DrakeAppended to Drake's translation and commentaries and bound in with them in the same volume is his monograph History of Free Fall: Aristotle to Galileo on the history of the discovery of the law of falling bodies, from its formulation by Aristotle to its clear statement by Galileo. Drake's painstaking research includes a close examination of Galileo's working papers which record his famous experiments with inclined planes and carefully controlled parabolic projectile paths.