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Leibniz sought to confute his opponents by taking another o f Descartes’ rules and expressing it in a new form with the aid o f Galilei’s law o f falling bodies. Descartes had assumed that a force could be measured by . 62 HISTORY OF SCIENCE, TECHNOLOGY, AND PHILOSOPHY the product o f the weight which it would raise, into the height through which it would raise it. Leibniz argued that since, by the law o f falling bodies, the height to which a body rises is proportional to the square o f the initial velocity, the effect o f a force upon a body must be proportional to the product o f the weight into the square of the velocity imparted, not into the simple velocity.

D ’Alembert assumed that, for the whole body, the internal reactions cancel one another, and therefore contribute nothing to the motion, while the other set o f forces do in fact communicate motion to the system, so that the effective forces are statically equivalent to the external or impressedforces. D ’Alembert treated as a typical case for the application o f his principle a beam fastened at one end and variously loaded at the other, forming a system which could similarly be regarded as a compound pendulum or a moving lever.

Leibniz, as we have seen, shared the same opinion: the total amount o f force in the universe suffers no diminution, since no body ever loses force without communicating an equal amount to other bodies; and it likewise shows no increase, since no machine can ever generate force unless it receives an equivalent impulse from without, and therefore the world as a whole cannot do so. Among the mathematical physicists o f the eighteenth century, Johann and Daniel Bernoulli devoted especial attention to the MECHANICS 63 principle o f the conservation o f force.

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A History of Science, Technology, and Philosophy in the Eighteenth Century by A Wolf


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