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chiefly converſant in the moving of bodies, it comes to paſs that Geometry is commonly referred to their magnitudes, and Mechanics to their motion. In this ſenſe Rational Mechanics will be the ſcience of motions reſulting from any forces whatſoever and of the forces required to produce any motions, accurately propoſed and demonſtrated. This part of Mechanics was cultivated by the ancients in the Five Powers which relate to manual arts, who conſidered gravity (it not being a manual power) no otherwiſe than as it moved weights by thoſe powers. Our design, not reſpecting arts, but philoſophy, and our ſubject, not manual, but natural powers, we conſider chiefly thoſe things which relate to gravity, levity, elaſtic force, the reſiſtance of fluids, and the like forces, whether attractive or impulſive; and therefore we offer this work as mathematical principles of philoſophy. For all the difficulty of philoſophy seems to conſiſt in this, from the phenomena of motions to inveſtigate the forces of nature, and then from theſe forces to demonſtrate the other phenomena. And to this end the general propoſitions in the firſt and ſecond book are directed. In the third book we give an example of this in the explication of
