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Maſs 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

[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 Gra

vity of the Solid I S, is equall to the Gravity of a Maſs of water e

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 ne

ceſſary alſo to encreaſe the Altitude of the Rampart A I, to main

tain the due proportion: But by what hath been ſuppoſed, the Alti

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 ad

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 va

rious Concluſions may be gathered, by which the truth of my prin

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

[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 Gra

vity of the Solid I S, is equall to the Gravity of a Maſs of water e

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 ne

ceſſary alſo to encreaſe the Altitude of the Rampart A I, to main

tain the due proportion: But by what hath been ſuppoſed, the Alti

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 ad

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 va

rious Concluſions may be gathered, by which the truth of my prin

cipall Propoſition comes to be more and more confirmed, and the

imperfection of all former Argumentations touching the preſent

Queſtion cometh to be diſcovered.