Galilei, Galileo, The systems of the world, 1661

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1in as much more time as it was in coming by the inclining plane, it
would
paſs double the ſpace of the plane inclined: namely (for
example
) if the ball had paſt the plane D A in an hour,
tinuing
to move uniformly with that degree of velocity which it
is
found to have in its arriving at the term A, it ſhall paſs in an
hour
a ſpace double the length D A; and becauſe (as we have
ſaid
) the degrees of velocity acquired in the points B and A, by
the
moveables that depart from any point taken in the
lar
C B, and that deſcend, the one by the inclined plane, the
ther
by the ſaid perpendicular, are always equal: therefore the
cadent
by the perpendicular may depart from a term ſo near to B,
that
the degree of velocity acquired in B, would not ſuffice (ſtill
maintaining
the ſame) to conduct the moveable by a ſpace
ble
the length of the plane inclined in a year, nor in ten, no nor
in
a hundred.
We may therefore conclude, that if it be true,
that
according to the ordinary courſe of nature a moveable, all
external
and accidental impediments removed, moves upon an
clining
plane with greater and greater tardity, according as the
inclination
ſhall be leſs; ſo that in the end the tardity comes to be
infinite
, which is, when the inclination concludeth in, and joyneth
to
the horizontal plane; and if it be true likewiſe, that the
gree
of velocity acquired in ſome point of the inclined plane, is
equal
to that degree of velocity which is found to be in the
able
that deſcends by the perpendicular, in the point cut by a
parallel
to the Horizon, which paſſeth by that point of the
ning
plane; it muſt of neceſſity be granted, that the cadent
parting
from reſt, paſſeth thorow all the infinite degrees of
dity
, and that conſequently, to acquire a determinate degree of
velocity
, it is neceſſary that it move firſt by right lines,
ing
by a ſhort or long ſpace, according as the velocity to be
red
, ought to be either leſs or greater, and according as the plane
on
which it deſcendeth is more or leſs inclined; ſo that a plane
may
be given with ſo ſmall inclination, that to acquire in it the
aſſigned
degree of velocity, it muſt firſt move in a very great ſpace,
and
take a very long time; whereupon in the horizontal plane, any
how
little ſoever velocity, would never be naturally acquired,
ſince
that the moveable in this caſe will never move: but the

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