[Sidenote: The proportion of the water abated, to the Solid
raised.]
_When in one of the above said Vessels, of what ever breadth,
whether wide or narrow, there is placed such a Prisme or
Cylinder, inviron'd with Water, if we elevate that Solid
perpendicularly, the Water circumfused shall abate, and the
Abatement of the Water, shall have the same proportion to the
Elevation of the Prisme, as one of the Bases of the Prisme, hath
to the Surface of the Water Circumfused._
[Illustration]
Imagine in the Vessell, as is aforesaid, the Prisme A C D B to be
placed, and in the rest of the Space the Water to be diffused as far
as the Levell E A: and raising the Solid, let it be transferred to G
M, and let the Water be abased from E A to N O: I say, that the
descent of the Water, measured by the Line A O, hath the same
proportion to the rise of the Prisme, measured by the Line G A, as the
Base of the Solid G H hath to the Surface of the Water N O. The which
is manifest: because the Mass of the Solid G A B H, raised above the
first Levell E A B, is equall to the Mass of Water that is abased E N
O A. Therefore, E N O A and G A B H are two equall Prismes; for of
equall Prismes, the Bases answer contrarily to their heights:
Therefore, as the Altitude A O is to the Altitude A G, so is the
Superficies or Base G H to the Surface of the Water N O. If therefore,
for example, a Pillar were erected in a waste Pond full of Water, or
else in a Well, capable of little more then the Mass of the said
Pillar, in elevating the said Pillar, and taking it out of the Water,
according as it riseth, the Water that invirons it will gradually
abate, and the abasement of the Water at the instant of lifting out
the Pillar, shall have the same proportion, that the thickness of the
Pillar hath to the excess of the breadth of the said Pond or Well,
above the thickness of the said Pillar: so that if the breadth of the
Well were an eighth part larger than the thickness of the Pillar, and
the breadth of the Pond twenty five times as great as the said
thickness, in the Pillars ascending one foot, the water in the Well
shall descend seven foot, and that in the Pond only 1/25 of a foot.
[Sidenote: Why a Solid less grave _in specie_ than water, stayeth
not under water, in very small depths:]
This Demonstrated, it will not be difficult to show the true cause,
how it comes to pass, that,