[Sidenote: The proportion of the greatest thickness of Solids,
beyond which encreased they sink.]
_When ever the excess of the Gravity of the Solid above the Gravity
of the Water, shall have the same proportion to the Gravity of
the Water, that the Altitude of the Rampart, hath to the
thickness of the Solid, that Solid shall not sink, but being
never so little thicker it shall._
[Illustration]
Let the Solid I S be superior in Gravity to the water, and of such
thickness, that the Altitude of the Rampart A I, be in proportion to
the thickness of the Solid I O, as the excess of the Gravity of the
said Solid I S, above the Gravity of a Mass of water equall to the
Mass I S, is to the Gravity of the Mass of water equall to the 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 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
Gravity of the Solid I S, is equall to the Gravity of a Mass of water
equall 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 necessary also to
encrease the Altitude of the Rampart A I, to maintain the due
proportion: But by what hath been supposed, the Altitude of the
Rampart A I, is the greatest that the Nature of the Water and Air do
admit, without the waters repulsing the Air adherent 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 various
Conclusions may be gathered, by which the truth of my principall
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,_