Galilei, Galileo - The systems of the world

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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