ABSTRACT
Mathematics is the home ground of principles. Since Euclid, mathematics has been the model of a body of knowledge organized as a deductive structure based on self-evident axioms. To appreciate the early modern understanding of mathematical principles, it is essential to put to one side certain more recent philosophical views which make it appear implausible. The Aristotelian-Euclidean background to seventeenth-century mathematics means that mathematics does not fit at all into the old picture of the Scientific Revolution as a revolt against scholastic obfuscation in favour of empiricism and experimentalism. It is something of a mystery why the central part of pure mathematics, number theory, has rarely been seen to need principles or axioms in the way that geometry does. Kinematics, the science of motion in itself without regard to its causes, is somewhat harder than statics to reduce to purely mathematical principles, but it can to some extent be done.
