Isaac Newton insist repeatedly that the first two books of the work treated motion in purely mathematical terms, without physical, metaphysical, or ontological commitment. Only in the third book did he expressly draw the links between the mathematical and physical realms. Nature was mathematised in the seventeenth century by means of its extensive mechanisation, which by the end of the century extended, at least programmatically, to the living world of plants and animals. The mathematical models were abstract machines, which in turn were models of the physical world and its components. Examples of mechanical thinking in seventeenth-century mathematics can be found in balances, levers, centres of gravity, velocities, moments, and forces. Francois Viete sought to capture the heuristic power of analysis in a general form common to arithmetic, geometry, and the other branches of mathematics. The practical art of algebra, applied traditionally to numbers, provided the basis.