Galilei, Galileo - The systems of the world

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 o
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

motion by the horizontal line, which is neither declined or incli
ned, is a circular motion about the centre: therefore the circu
lar motion is never acquired naturally, without the right motion
precede it; but being once acquired, it will continue perpetually
with uniform velocity. I could with other diſcourſes evince and
demonſtrate the ſame truth, but I will not by ſo great a digreſ
fion interrupt our principal argument: but rather will return to
it upon ſome other occaſion; eſpecially ſince we now aſſumed the

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