Galilei, Galileo, The systems of the world, 1661

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your incredulity; but for the knowledge of this, expect it at
ſome other time, namely, when you ſhall ſee the matters concer­
ning local motion demonſtrated by our Academick; at which
time you ſhall find it proved, that in the time that the one movea­
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 perpendi­
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 remem­
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 ano­
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 infi­
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 velo­
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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