Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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this
Weight
ſhould
deſcend
more
than
that
,
or
that
more
than
this
;
and
therefore
they
make
an
Equilibrium
,
and
their
Moments
continue
of
ſemblable
and
equall Vertue.
The
ſecond
Principle
is
;
That
AXIOME II.
The
Moment
and
Force
of
the
Gravity
,
is
encreaſed
by
the
Velocity
of
the
Motion
.
So
that
Weights
abſolutely
equall,
but
conjoyned
with
Velocity
unequall,
are
of
Force
,
Moment
and
Vertue unequall:
and
the
more
potent
,
the
more
ſwift
,
according
to
the
proportion
of
the
Ve
locity
of
the
one
,
to
the
Velocity
of
the
other
.
Of
this
we
have
a
very
pertinent
example
in
the
Balance
or
Stiliard
of
unequall
Arms
,
at
which
Weights
abſolutely
equall
being
ſuſpended
,
they
do
not
weigh
down
,
and
gravitate
equally
,
but
that
which
is
at
a
greater
diſtance
from
the
Centre
,
about
which
the
Beam
moves
,
deſcends
,
raiſing
the
other
,
and
the
Motion
of
this
which
aſcends
is
ſlow
,
and
the
other
ſwift
:
and
ſuch
is
the
Force
and
Vertue,
which
from
the
Velocity
of
the
Mover
,
is
conferred
on
the
Moveable,
which
receives
it
,
that
it
can
exquiſitely
compenſate
,
as
much
more
Weight
added
to
the
other
ſlower
Moveable:
ſo
that
if
of
the
Arms
of
the
Balance
,
one
were
ten
times
as
long
as
the
other
,
whereupon
in
the
Beames
moving
about
the
Centre
,
the
end
of
that
would
go
ten
times
as
far
as
the
end
of
this
,
a
Weight
ſuſpended
at
the
greater
diſtance
,
may
ſuſtain
and
poyſe
another
ten
times
more
grave
abſolutely
than
it
:
and
that
becauſe
the
Stiliard
moving
,
the
leſſer
Weight
ſhall
move
ten
times
faſter
than
the
bigger
.
It
ought
alwayes
therefore
to
be
underſtood
,
that
Motions
are
according
to
the
ſame
Inclinations,
namely
,
that
if
one
of
the
Moveables
move
perpendicularly
to
the
Horizon
,
then
the
other
makes
its
Motion
by
the
like
Perpendicular
;
and
if
the
Motion
of
one
were
to
be
made
Horizontally
;
that
then
the
other
is
made
along
the
ſame
Horizontall
plain
:
and
in
ſumme,
alwayes
both
in
like
Inclinations.
This
proportion
between
the
Gravity
and
Velocity
is
found
in
all
Mechanicall
Inſtruments
:
and
is
conſidered
by
Ariſtotle,
as
a
Principle
in
his
Mechanicall
Queſtions
;
whereupon
we
alſo
may
take
it
for
a
true
Aſſumption
,
That
AXIOME III.
Weights
abſolutely
unequall,
do
alternately
counterpoyſe
and
become
of
equall
Moments
,
as
oft
as
their
Gravi
ties,
with
contrary
proportion
,
anſwer
to
the
Velocity
of
their
Motions
.
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