In this paper I want to examine in some detail one eighteenth-century attempt to restructure the foundations of mechanics, that of Leonhard Euler. It is now generally recognised that the idea, due to Mach, that all that happened in the eighteenth century was the elaboration of a deductive and mathematical mechanics on the basis of Newton's laws is misleading at best. Newton's Principia needed much more than a reformulation in analytic terms if it was to provide the basis for the comprehensive mechanics that was developed in the eighteenth century. Book II of the Principia, in particular, where the problem of the resistance offered to the motion of a finite body by a fluid medium was raised, was generally (and rightly) thought to be in large part mistaken and confused. There were also a number of ideas crucial to the unification of mechanics which Newton did not deal with at all in the Principia: particularly the dynamics of rigid, flexible and elastic bodies, and the dynamics of several bodies with mutual interactions. Although a start had been made on some of these topics in the seventeenth century (notably by Galileo, Beeckman, Mersenne, Huygens, Pardies, Hooke, and Leibniz), it was only in the eighteenth century that they were subjected to detailed examination, and Euler's contribution to the development of these topics, and hence to the unification of mechanics, was immense. 1