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.
ſinke, but being never ſo little thicker it ſhall
go to the bottom: For being that as A I is
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.
And firſt we gather from the things demonstrated, that,