Galilei, Galileo, The systems of the world, 1661

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Here the movent vertue is the ſame, namely the counterpoiſe,

the
moveables are thoſe ſame Weights of lead, and their
brations
are more frequent when they are neerer to the centre,
that
is, when they move by leſſer circles.
Hanging equal
Weights
at unequal cords, and being removed from their
pendicularity
, letting them go; we ſhall ſee thoſe that are
dent
at the ſhorter cords, to make their vibrations under ſhorter
times
, as thoſe that move by leſſer circles.
Again, let ſuch a
kind
of Weight be faſtened to a cord, which cord let play upon
a
ſtaple faſtened in the Seeling, and do you hold the other end
of
the cord in your hand, and having given the motion to the
pendent
Weight, whilſt it is making its vibrations, pull the
end
of the cord that you hold in your hand, ſo that the Weight
may
riſe higher and higher: In its riſing you ſhall ſee the
quency
of its vibrations encreaſe, in regard that they are made
ſucceſſively
by leſſer and leſſer circies.
And here I deſire you to

take
notice of two particulars worthy to be obſerved.
One is
that
the vibrations of one of thoſe plummets are made with ſuch
a
neceſſity under ſuch determinate times, that it is altogether
impoſſible
to cauſe them to be made under other times, unleſſe
it
be by prolonging, or abreviating the cord; of which you
may
alſo at this very inſtant aſcertain your ſelves by experience,
tying
a ſtone to a pack-threed, and holding the other end in
your
hand, trying whether you can ever by any artifice be able
to
ſwing it this way and that way in other than one determinate
time
, unleſſe by lengthening or ſhortening the ſtring, which
you
will find to be abſolutely impoſſible.
The other particular
truly
admirable is, that the ſelf ſame pendulum makes its
tions
with one and the ſame frequency, or very little, and as it
were
inſenſibly different, whether they be made by very great,
or
very ſmall arches of the ſelf-ſame circumference.
I mean that
whether
we remove the pendulum from perpendicularity one, two,
or
three degrees onely, or whether we remove it 70. 80. nay to
an
entire quadrant, it being let go, will in the one caſe and in
the
other make its vibrations with the ſame frequency, as well
the
former where it is to move by an arch of but four or ſix
grees
, as the ſecond, where it is to paſſe arches of 160. or more

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