 The final chapter of Galileo’s scientific story came in 1638, with the publication of the Two New Sciences. The second science, discussed in the last two Days, deals with the principles of local motion and has been much commented upon in the Galilean literature. But the first science, discussed in the first two Days, has been misunderstood and infrequently discussed. It has misleadingly been called the science of the strength of materials, and so seems to have found a place in history of engineering, since such a course is still taught today. However, this science is not about the strength of materials per se. It is Galileo’s attempt to provide a mathematical science of his unified matter (see Machamer 1998a; Biener 2004; Machamer and Hepburn 2004). Galileo realizes that, before he can work out a science of the motion of matter, he must have some way of showing that the nature of matter may be mathematically characterized. Both the mathematical nature of matter and the mathematical principles of motion he believes belong to the science of “mechanics,” which is the name he gives for this new way of philosophizing.