We argue that Isaac Newton really is best understood as being in the tradition of the Mechanical Philosophy and, further, that Newton saw himself as being in this tradition. But the tradition as Newton understands it is not that of Robert Boyle and many others, for whom the Mechanical Philosophy was defined by contact action and a corpuscularean theory of matter. Instead, as we argue in this paper, Newton interpreted and extended the Mechanical Philosophy's slogan “matter and motion” in reference to the long and distinguished tradition of mixed mathematics and the study of simple machines.