Galilei, Galileo, The systems of the world, 1661

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in 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, con­
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 perpendicu­
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 dou­
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 in­
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 de­
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 move­
able that deſcends by the perpendicular, in the point cut by a
parallel to the Horizon, which paſſeth by that point of the incli­
ning plane; it muſt of neceſſity be granted, that the cadent de­
parting from reſt, paſſeth thorow all the infinite degrees of tar­
dity, and that conſequently, to acquire a determinate degree of
velocity, it is neceſſary that it move firſt by right lines, deſcend­
ing by a ſhort or long ſpace, according as the velocity to be acqui­
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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