Metaphysics

Cover Metaphysics
Metaphysics
Bowne, Borden Parker, 1847-1910
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In the second instant, the body is supposed to retain the velocity acquired in the first, and to gain an additional increment ; and so on in successive in- stants. If, now, we suppose the acceleration uniform, the velocity at the end of a given time will be the velocity ac- quired in the unit of time multiplied by the number of units. But it is plain that this could not be the case if the law of inertia did not hold ; for the first increment of ve- locity, dVj in the first instant, dt^ would pe...rish at once ; and hence the next increment of velocity would bagin not with dv, but with plain zero. Hence at the end of any time, ^, the velocity would still be zero, and the body would not MATTER, FORCE, AND MOTION 233 have moved. It may at first appear as if the body should have moved some during the several instants, dt^ but this is seen to be a mistake, when we remember that as long as dt expresses a real duration, we cannot assume that dv remains constant through dt without assuming the law of inertia.

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