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Impetus

Leibnitz on impetus (Mach, The Science of Mechanics)

Mach, p. 275 (pdf 300)
Leibniz on quantity of motion
Descartes' view was attacked by Leibnitz (1686) in the Acta Eruditorum, in a little treatise bearing the title: "A short Demonstration of a Remarkable Error of Descartes and Others, Concerning the Natural law by which they think that the Creator always preserves the same Quantity of Motion; by which, however, the Science of Mechanics is totally perverted."
In machines in equilibrium, Leibnitz remarks, the loads are inversely proportional to the velocities of displacement; and in this way the idea arose that the product of a body ("corpus", "moles") into its velocity is the measure of force.
This product Descartes regarded as a constant quantity.
Leibnitz's opinion, however, is, that this measure of force is only accidentally the correct measure, in the case of the machines.
The true measure of force is different, and must be determined by the method which Galileo and Huygens pursued.
Leibnitz on the measure of force
Every body rises by virtue of the velocity acquired in its descent to a height exactly equal to that from which it fell.
If, therefore, we assume, that the same "force" is requisite to raise a body \(m\) a height \(4h\) as to raise a body \(4m\) a height \(h\), we must, since we know that in the first case the velocity acquired in descent is but twice as great as in the second, regard the product of a "body" into the square of its velocity as measure of force.
In a subsequent treatise (1695), Leibnitz reverts to this subject.
He here makes a distinction between simple pressure (vis mortua) and the force of a moving body (vis viva), which latter is made up of the sum of the pressure-impulses.
These impulses produce, indeed, an "impetus" (\(mv\)), but the impetus produced is not the true measure of force; this, since the cause must be equivalent to the effect, is (in conformity with the preceding considerations) determined by \(mv^2\).
Leibnitz remarks further that the possibility of perpetual motion is excluded only by the acceptance of his measure of force.