Galilei, Galileo
,
Mechanics
,
1665
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we
will
ſet
before
you
the
preſent
Contemplation
.
Suppoſe
,
there-
fore
,
that
A
B
,
C
D
,
and
E
F
are
three
Leavers;
and
that
on
the
middle
points
of
them
G
,
H
,
and
I
the
Weight
K
doth
hang
in
common
,
ſo
that
every
one
of
them
ſhall
ſuſtain
the
third
part
of
[Figure 16]
it
:
And
becauſe
the
Power
in
B
,
ſuſtaining
with
the
Leaver
B
A
thependent
Weight
in
G
,
hapneth
to
be
the
half
of
the
ſaid
Weight
,
and
it
hath
been
already
ſaid
,
that
it
ſuſtaineth
the
third
part
of
the
Weight
K
:
Therefore
the
Moment
of
the
Force
B
is
equal
to
half
of
the
third
part
of
the
Weight
K
;
that
is
,
to
the
ſixth
part
of
it
:
And
the
ſame
ſhall
be
demonſtrated
of
the
other
Forces
D
and
F
:
From
whence
we
may
eaſily
gather
,
that
putting
three
Gyrils
or
Rundles
into
the
inferiour
Pulley
,
and
two
or
three
into
the
upper-
[Figure 17]
moſt
,
we
may
multiply
the
Force
accor-
ding
to
our
^{*}
Senarius.
And
if
we
would
encreaſe
it
according
to
any
other
even
Number
,
the
Gyrils
of
the
Pulley
below
muſt
be
multiplyed
according
to
the
half
of
that
Number
,
according
to
which
the
Force
is
to
be
multiplyed, circumpoſing
the
Rope
about
the
Pulleys
,
ſo
as
that
one
of
the
ends
be
faſtned
to
the
upper
Pul-
ley
,
and
let
the
Force
be
in
the
other
;
as
in
this
Figure
adjoyning
may
manifeſtly
be
gathered
.
*
Or
in
Sexcuple
proportion
.
Now
paſſing
to
the
Declaration
of
the
manner
how
to
multiply
the
Force
ac-
cording
to
the
odd
Numbers
,
and
begin-
[Figure 18]
ning
at
the
triple
proportion
:
firſt
,
let
us
propoſe
the
preſent
Contemplation
,
as
that
,
on
the
underſtanding
of
which
the
knowledge
of
all
the
Work
in
hand
doth
depend
.
Let
therefore
the
Leaver
be
A
B
,
its
Fulciment
A
,
and
from
the
middle
of
it
,
that
is
,
at
the
point
C
let
the
Grave
D
be
hanged
;
and
let
it
be
ſu-
ſtained
by
two
equal
Forces
;
and
let
one
of
them
be
applied
to
the
point
C
,
and
the
other
to
the
term
B
.
I
ſay
,
that
each
of
thoſe
Powers
have
Moment
equal
to
the
third
part
of
the
Weight
D
.
For
the
Force
in
C
ſuſtaineth
a
Weight
equal
to
it
ſelf
,
being
placed
in
the
ſame
Line
in
which
the
Weight
D
doth
hang
&
Gravitate
:
But
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