Galilei, Galileo - Discourse concerning the natation of bodies

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

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THEOREME II.

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 ele
vate that Solid perpendicularly, the Water circumfu
ſed 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.

The proportion
of the water aba
ted, to the Solid
raiſed.

Imagine in the Veſſell, as is aforeſaid, the

[Figure 2]

Priſme A C D B to be placed, and in the
reſt of the Space the Water to be dif
fuſed as far as the Levell E A: and rai
ſing 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: There
fore, as the Altitude A O is to the Altitude A G, ſo is the Superfi
cies 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.

Why a Solid
leſs grave in ſpe
cie than water,
ſtayeth not un
der water, in ve
ry ſmall depthst.

This Demonſtrated, it will not be difficult to ſhew the true
cauſe, how it comes to paſs, that,

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