Heron Alexandrinus
,
Mechanica
,
1999
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We
want
to
move
a
known
load
by
means
of
a
known
force
through
the
mechanism
of
cogwheels
.
For
this
purpose
one
builds
a
frame
,
similar
to
a
box
,
in
the
longest
parallel
sides
of
which
rest
parallel
axles
at
a
space
measured
so
that
the
cogs
of
the
one
mesh
with
the
cogs
of
the
others,
as
we
are
going
to
explain
directly
.
Let
this
frame
be
a
box
,
designated
with
<abgd>,
in
it
let
rest
a
light
mobile
axle
,
designated
<ez>,
on
which
is
attached
a
cogwheel
,
the
wheel
<hq>.
Let
its
diameter
be
,
for
instance
,
five
times
the
diameter
of
the
axle
<ez>.
But
in
order
to
explain
our
construction
with
an
example
let
us
assume
the
load
to
be
pulled
is
one
thousand
talents
and
the
moving
force
is
five
talents
,
that
is
the
man
or
the
boy
who
alone
,
without
a
machine
,
can
move
five
talents
.
If
we
now
insert
the
ropes
fastened
to
the
load
through
a
hole
in
the
side
<
ab
>
so
they
wind
up
on
axle
<ez>,
by
the
rotation
of
cog
<hq>
and
the
winding
up
of
the
ropes
the
load
can
be
moved
.
To
make
the
cogwheel
<hq>
move
,
however
,
one
needs
two
hundred
talents
of
force
,
because
the
diameter
of
the
cogwheel
is
five
times
the
diameter
of
the
axle
,
according
to
our
assumption

this
has
been
shown
in
the
proofs
of
the
five
simple
powers
.
We
do
not
,
however
,
have
a
force
of
200
talents
,
since
the
force
assumed
by
us
is
five
talents
;
thus
the
cogwheel
will
not
be
moved
.
Let
us
now
construct
another
axle
,
parallel
to
axle
<ez>,
namely
the
axle
<kl>,
and
let
a
cogwheel
,
namely
the
cogwheel
<mn>,
be
attached
to
it
;
let
further
the
wheel
<hq>
also
have
cogs
that
mesh
with
the
cogs
of
wheel
<mn>
and
let
another
wheel
be
attached
to
the
axle
<kl>,
namely
<co>,
whose
diameter
is
five
times
the
diameter
of
<mn>,
so
that
one
needs
,
in
order
to
move
the
load
through
the
wheel
<co>, 40
talents
of
force
,
since
a
fifth
of
200
talents
is
40
talents
.
We
further
let
the
wheel
<co>
mesh
with
another
wheel
,
namely
the
wheel
<px>,
which
is
attached
to
another
axle
,
namely
the
axle
<fi>,
further
let
another
cogwheel
be
attached
to
this
axle
,
whose
diameter
is
five
times
the
diameter
of
<px>,
namely
the
wheel
<ss>,
then
the
force
that
moves
the
load
at
the
sign
<ss>
will
be
8
talents
;
the
force
assumed
by
us
is
,
however
,
only
five
talents
.
Let
us
therefore
put
in
another
cogwheel
,
namely
the
cogwheel
<tt'>,
whose
diameter
is
double
the
diameter
of
wheel
<ss>,
and
let
it
be
attached
to
another
axle
,
the
axle
<
h
'
d
'>,
so
that
the
wheel
<tt'>
needs
four
talents
of
force
,
so
there
is
in
this
force
a
surplus
of
one
talent
,
which
one
uses
to
overcome
the
resistance
of
the
wheels
that
may
occur
.
Our
explanation
illuminates
:
When
the
mover
sets
the
wheel
<tt'>
in
motion
,
the
axle
<
h
'
d
'>
rotates
and
through
its
rotation
the
wheel
<ss>
rotates
;
therefore
the
axle
<fi>
rotates
and
the
wheel
<px>
rotates
;
at
the
same
time
the
wheel
<co>
and
the
axle
<kl>
rotate
;
therefore
,
the
wheel
<mn>
rotates
and
the
wheel
<mn>
sets
the
wheel
<hq>
in
rotation
,
because
of
which
also
the
axle
<ez>
rotates
,
the
ropes
wind
up
around
the
axle
and
the
load
is
lifted
.
Thus
we
have
,
through
a
force
of
five
talents
,
lifted
a
load
in
the
amount
of
1000
talents
,
by
means
of
the
mechanism
just
described
.
q
.
e
.
d
.
Note
:
It
is
necessary
that
the
axis
IO
goes
out
to
I
,
and
on
it
,
the
perpendicular
I
,
is
erected
equal
to
the
semidiameter
of
wheel
IP
or
more
than
it
,
and
god
knows
better
. TB (
note
on
the
margin
,
not
translated
by
Nix
/Schmidt)
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