Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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[11. Figure]
Page: 48
[12. Figure]
Page: 51
[13. Figure]
Page: 52
[14. Figure]
Page: 54
[15. Figure]
Page: 54
[16. Figure]
Page: 56
[17. Figure]
Page: 57
[18. Figure]
Page: 58
[19. Figure]
Page: 76
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LEMMA
I
.
The
abſolute
Gravities
of
Solids
,
have
a
proportion
com-
pounded
of
the
proportions
of
their
ſpecificall
Gravities
,
and
of
their
Maſſes
.
The
abſolute
Gravity
of
So
lids,
are
in
a
pro
portion com
pounded
of
their
Specifick Gravi
ties,
and
of
their
Maſſes
.
Let
A
and
B
be
two
Solids
.
I
ſay
,
that
the
Abſolute
Gravity
of
A
,
hath
to
the
Abſolute
Gravity
of
B
,
a
proportion
com
pounded
of
the
proportions
of
the
ſpecificall
Gravity
of
A
,
to
the
Specificall
Gravity
of
B
,
and
of
the
Maſs
A
to
the
Maſs
B
.
Let
the
Line
D
have
the
[Figure 4]
ſame
proportion
to
E
,
that
the
ſpecifick
Gravity
of
A
,
hath
to
the
ſpecifick
Gravity
of
B
;
and
let
E
be
to
F
,
as
the
Maſs
A
to
the
Maſs
B
:
It
is
manifeſt
,
that
the
proportion
of
D
to
F
,
is
compounded
of
the
proportions
D
and
E
;
and
E
and
F
.
It
is
requiſite
,
therefore
,
to
demonſtrate
,
that
as
D
is
to
F
,
ſo
the
abſolute
Gravity
of
A
,
is
to
the
abſolute
Gravity
of
B
.
Take
the
Solid
C
, equall
in
Maſs
to
the
Solid
A
,
and
of
the
ſame
Gravity
in
ſpecie
with
the
Solid
B
.
Becauſe
,
therefore
,
A
and
C
are
equall
in
Maſs
,
the
abſolute
Gravity
of
A
,
ſhall
have
to
the
abſolute
Gravity
of
C
,
the
ſame
pro
portion,
as
the
ſpecificall
Gravity
of
A
,
hath
to
the
ſpecificall
Gravity
of
C
,
or
of
B
,
which
is
the
ſame
in
ſpecie
;
that
is
,
as
D
is
to
E
.
And
, be
cauſe,
C
and
B
are
of
the
ſame
Gravity
in
ſpecie
,
it
ſhall
be
,
that
as
the
abſolute
weight
of
C
,
is
to
the
abſolute
weight
of
B
,
ſo
the
Maſs
C
,
or
the
Maſs
A
,
is
to
the
Maſs
B
;
that
is
,
as
the
Line
E
to
the
Line
F
.
As
therefore
,
the
abſolute
Gravity
of
A
,
is
to
the
abſolute
Gravity
of
C
,
ſo
is
the
Line
D
to
the
Line
E
:
and
,
as
the
abſolute
Gravity
of
C
,
is
to
the
abſolute
Gravity
of
B
,
ſo
is
the
Line
E
to
the
Line
F
:
Therefore
,
by
Equality
of
proportion
,
the
abſolute
Gra
vity
of
A
,
is
to
the
abſolute
Gravity
of
B
,
as
the
Line
D
to
the
Line
F
:
which
was
to
be
demonſtrated
.
I
proceed
now
to
demon
ſtrate,
how
that
,
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