Galilei, Galileo, The systems of the world, 1661

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1your incredulity; but for the knowledge of this, expect it at
ſome
other time, namely, when you ſhall ſee the matters
ning
local motion demonſtrated by our Academick; at which
time
you ſhall find it proved, that in the time that the one
ble
falls all the ſpace C B, the other deſcendeth by C A as far
as
the point T, in which falls the perpendicular drawn from the
point
B: and to find where the ſame Cadent by the
cular
would be when the other arriveth at the point A, draw from
A
the perpendicular unto C A, continuing it, and C B unto the
interfection
, and that ſhall be the point ſought.
Whereby you
ſee
how it is true, that the motion by C B is ſwifter than by the
inclination
C A (ſuppoſing the term C for the beginning of the
motions
compared) becauſe the line C B is greater than C T,
and
the other from C unto the interſection of the perpendicular
drawn
from A, unto the line C A, is greater than C A, and
therefore
the motion by it is ſwifter than by C A But when we
compare
the motion made by all C A, not with all the motion
made
in the ſame time by the perpendicular continued, but with
that
made in part of the time, by the ſole part C B, it hinders
not
, that the motion by C A, continuing to deſcend beyond, may
arrive
to A in ſuch a time as is in proportion to the other time,
as
the line C A is to the line C B.
Now returning to our firſt
purpoſe
; which was to ſhew, that the grave moveable leaving
its
quieſcence, paſſeth defcending by all the degrees of tardity,
precedent
to any whatſoever degree of velocity that it aequireth,
re-aſſuming
the ſame Figure which we uſed before, let us
ber
that we did agree, that the Deſcendent by the inclination C
A
, and the Cadent by the perpendicular C B, were found to have
acquired
equal degrees of velocity in the terms B and A: now to
proceed
, I ſuppoſe you will not ſcruple to grant, that upon
ther
plane leſs ſteep than A C; as for example, A D [in Fig. 5.]
the
motion of the deſcendent would be yet more ſlow than in the
plane
A C.
So that it is not any whit dubitable, but that there
may
be planes ſo little elevated above the Horizon A B, that the
moveable
, namely the ſame ball, in any the longeſt time may
reach
the point A, which being to move by the plane A B, an
nite
time would not ſuffice: and the motion is made always more
ſlowly
, by how much the declination is leſs.
It muſt be therefore
confeſt
, that there may be a point taken upon the term B, ſo near
to
the ſaid B, that drawing from thence to the point A a plane,
the
ball would not paſs it in a whole year.
It is requiſite next
for
you to know, that the impetus, namely the degree of
city
the ball is found to have acquired when it arriveth at the
point
A, is ſuch, that ſhould it continue to move with this ſelf-ſame
degree
uniformly, that is to ſay, without accelerating or retarding;

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