Galilei, Galileo, Mechanics, 1665

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1and in the Velocity: which peradventure, might not have ſeemed
to
ſome ſo true and manifeſt in the preſent Contemplation; nay,
rather
it ſeems, that in this caſe the Force is multiplied without the
Movers
moving a longer way than the Moveable: In regard, that
if
we ſhall in the Triangle A B C ſuppoſe the Line A B to be the
Plane
of the Horizon, A C the elevated Plane, whoſe Altitude is
meaſured
by the Perpendicular C B, a Moveable placed upon the
Plane
A C, and the Cord E D F tyed to it, and a Force or Weight
applyed
in F that hath to the
Gravity
of the Weight E the
25[Figure 25]
ſame
proportion that the Line
B
C hath to C A; by what
hath
been demonſtrated, the
Weight
F ſhall deſcend
downwards
, drawing the
Moveable
E along the eleva­
ted
Plane; nor ſhall the Move­
able
E meaſure a greater Space
when
it ſhall have paſſed the
whole
Line A C, than that which the ſaid Grave F meaſureth in its
deſcent
downwards.
But here yet it muſt be advertiſed, that al­
though
the Moveable E ſhall have paſſed the whole Line A C, in
the
ſame Time that the other Grave F ſhall have been abaſed the
like
Space, nevertheleſs the Grave E ſhall not have retired from the
common
Center of things Grave more than the Space of the Per­
pendicular
C B. but yet the Grave F deſcending Perpendicularly ſhall
be
abaſed a Space equal to the whole Line A C. And becauſe Grave
Bodies
make no Reſiſtance to Tranſverſal Motions, but only ſo
far
as they happen to recede from the Center of the Earth; There­
fore
the Moveable E in all the Motion A C being raiſed no more
than
the length of the Line CB, but the other F being abaſed per­
pendicularly
the quantity of all the Line A C: Therefore we may
deſervedly
affirm that Way of the Force E maintaineth the ſame
proportion
to the Force F that the Line A C hath to C B; that is,
the
Weight E to the Weight F. It very much importeth, therefore,
to
conſider by [or along] what Lines the Motions are made, eſpe­
cially
in exanimate Grave Bodies, the Moments of which have their
total
Vigour, and entire Reſiſtance in the Line Perpendicular to
the
Horizon; and in the others tranſverſally Elevated and Inclined
they
feel the more or leſs Vigour, Impetus, or Reſiſtance, the more
or
leſs thoſe Inclinations approach unto the Perpendicular Inclina­
tion
.

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