Proof.- Bodies are individual things ([D.i] ), which ([L.I] )
are distinguished one from the other in respect to motion and
rest; thus (I:[xxviii] ) each must necessarily be determined
to motion or rest by another individual thing, namely ([vi] ),
by another body, which other body is also ([A.i] ) in motion
or at rest. And this body again can only have been set in
motion or caused to rest by being determined by a third body
to motion or rest. This third body again by a fourth, and so
on to infinity. Q.E.D.
Corollary.- (13:16) Hence it follows, that a body in motion keeps in
motion, until it is determined to a state of rest by some other body;
and a body at rest remains so, until it is determined to a state of
motion by some other body. (17) This is indeed self-evident. (18) For
when I suppose, for instance, that a given body, A, is at rest, and do
not take into consideration other bodies in motion, I cannot affirm
anything concerning the body A, except that it is at rest. (13:19) If
it afterwards comes to pass that A is in motion, this cannot have
resulted from its having been at rest, for no other consequence could
have been involved than its remaining at rest. (20) If, on the other
hand, A be given in motion, we shall, so long as we only consider A,
be unable to affirm anything concerning it, except that it is in motion.
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