This is an immediate consequence of the property of inertia, explained
in the last chapter. If we were to suppose that by their mutual impact
A were to give to B either more or less motion than that which it (A)
loses, it would necessarily follow, that either A or B must have a
power of producing or of resisting motion, which would be inconsistent
with the quality of inertia already defined. For if A give to B _more_
motion than it loses, all the overplus or excess must be excited in B
by the _action_ of A; and, therefore, A is not inactive, but is capable
of exciting motion which it does not possess. On the other hand, B
cannot receive from A _less_ motion than A loses, because then B must
be admitted to have the power by its resistance of destroying all the
deficiency; a power essentially active, and inconsistent with the
quality of inertia.
(57.) If we contemplate the effects of impact, which we have now
described, as facts ascertained by experiment (which they may be),
we may take them as further verification of the universality of the
quality of inertia. But, on the other hand, we may view them as
phenomena which may certainly be predicted from the previous knowledge
of that quality; and this is one of many instances of the advantage
which science possesses over knowledge _merely_ practical. Having
obtained by observation or experience a certain number of simple facts,
and thence deduced the general qualities of bodies, we are enabled,
by demonstrative reasoning, to discover _other facts_ which have
never fallen under our observation, or, if so, may have never excited
attention. In this way philosophers have discovered certain small
motions and slight changes which have taken place among the heavenly
bodies, and have directed the attention of astronomical observers to
them, instructing them with the greatest precision as to the exact
moment of time and the point of the firmament to which they should
direct the telescope, in order to witness the predicted event.
(58.) Since by the quality of inertia a body can neither generate
nor destroy motion, it follows that when two bodies act upon each
other in any way whatever, the total quantity of motion in a given
direction, after the action takes place, must be the same as before
it, for otherwise some motion would be produced by the action of the
bodies, which would contradict the principle that they are inert. The
word “action” is here applied, perhaps improperly, but according to the
usage of mechanical writers, to express a certain phenomenon or effect.
It is, therefore, not to be understood as implying any active principle
in the bodies to which it is attributed.
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