Mechanics as a science of motion , as distinguished from a science of machines such as the lever and windlass, started early in the 17th century. By the middle of the next century it had become clear that Isaac Newton’s three laws suffice for the motions of “point masses,” but it was not yet clear how—and indeed whether—those laws could be extended to handle the motions of fluids or rigid bodies. Thus the 18th century saw new laws such as the principle of least action proposed and disputed. The most celebrated of those disputes, concerning the conservation of vis viva (Latin for “living force” and akin to what we now call kinetic energy), was already under way by 1686, the year before Newton published his laws of motion in the Principia. 1  

The vis viva controversy started as a dispute between Gottfried Wilhelm Leibniz (1646–1716) and followers of René...

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