Galilei, Galileo, Discourse concerning the natation of bodies, 1663

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1Maſs I S. I ſay, that the Solid I S ſhall not
ſinke
, but being never ſo little thicker it ſhall
go
to the bottom: For being that as A I is
11[Figure 11]
to
I O, ſo is the Exceſs of the Gravity of the
Solid
I S, above the Gravity of a Maſs of water
equall
to the Maſs I S, to the Gravity of the
ſaid
Maſs of water: Therefore, compounding, as A O is to O I, ſo
ſhall
the Gravity of the Solid I S, be to the Gravity of a Maſs of water
equall
to the Maſs I S: And, converting, as I O is to O A, ſo ſhall the
Gravity
of a Maſs of water equall to the Maſs I S, be to the Gravity
of
the Solid I S: But as I O is to O A, ſo is a Maſs of water I S, to a
Maſs
of water equall to the Maſs A B S O: and ſo is the Gravity of
a
Maſs of water I S, to the Gravity of a Maſs of water A S: Therefore
as
the Gravity of a Maſs of water, equall to the Maſs I S, is to the
Gravity
of the Solid I S, ſo is the ſame Gravity of a Maſs of water
I
S, to the Gravity of a Maſs of Water A S: Therefore the
vity
of the Solid I S, is equall to the Gravity of a Maſs of water
quall
to the Maſs A S: But the Gravity of the Solid I S, is the ſame
with
the Gravity of the Solid A S, compounded of the Solid I S,
and
of the Air A B C I.
Therefore the whole compounded Solid
A
O S B, weighs as much as the water that would be compriſed in the
place
of the ſaid Compound A O S B: And, therefore, it ſhall make
an
Equilibrium and reſt, and that ſame Solid I O S C ſhall ſinke no
farther
.
But if its thickneſs I O ſhould be increaſed, it would be
ceſſary
alſo to encreaſe the Altitude of the Rampart A I, to
tain
the due proportion: But by what hath been ſuppoſed, the
tude
of the Rampart A I, is the greateſt that the Nature of the
Water
and Air do admit, without the waters repulſing the Air
herent
to the Superficies of the Solid I C, and poſſeſſing the ſpace
A
I C B: Therefore, a Solid of greater thickneſs than I O, and of the
ſame
Matter with the Solid I S, ſhall not reſt without ſubmerging,
but
ſhall deſcend to the bottome: which was to be demonſtrated.
In conſequence of this that hath been demonſtrated, ſundry and
rious
Concluſions may be gathered, by which the truth of my
cipall
Propoſition comes to be more and more confirmed, and the
imperfection
of all former Argumentations touching the preſent
Queſtion
cometh to be diſcovered.

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