Heron Alexandrinus
,
Mechanica
,
1999
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[4]
On
the
different
circles
.
Now
let
the
circles
be
unequal
;
and
let
their
centers
lie
on
the
two
points
<
a
>
and
<
b
>,
further
let
the
larger
of
the
two
circles
be
the
one
whose
center
lies
on
point
<
a
>,
then
the
order
with
these
circles
will
not
be
perfect
as
with
equal
circles
.
Let
us
now
assume
two
points
that
we
let
rotate
from
point
<
e
>
and
let
us
make
,
to
pose
an
example
,
the
diameter
<ge>
twice
the
size
of
the
diameter
<ed>,
then
the
arc
<ezg>
will
be
twice
the
arc
<ehd>,
for
Archimedes
has
already
proven
this
.
Then
in
the
same
time
that
point
<
e
>
in
its
motion
towards
<
g
>
runs
along
the
arc
<ez>,
point
<
e
>
will
run
in
the
opposite
direction
along
the
arc
<ehd>.
Further
in
the
same
time
that
point
<
e
>,
starting
at
<
z
>,
runs
along
the
arc
<zg>,
point
<
e
>
will
,
starting
at
<
d
>,
run
along
the
arc
<dke>
and
reach
point
<
e
>.
Thus
the
point
that
runs
along
the
arc
<ehdke>
will
one
time
make
the
opposite
motion
to
the
point
that
runs
along
the
arc
<ezg>,
the
other
time
be
equal
to
it
.
Further
,
in
the
same
time
that
point
<
g
>
runs
through
the
arc
<gqe>,
point
<
e
>
runs
through
the
arc
<ehdke>,
partially
in
the
same
,
partially
in
the
opposite
direction
as
<
g
>.
If
now
the
one
arc
is
three
times
as
large
as
the
other
one
,
or
in
any
other
relation
to
it
,
then
we
shall
show
that
the
moving
points
are
moving
partially
in
the
same
,
partially
in
the
opposite
direction
.
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