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

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1
THEOREME II.
Imagine in the Veſſell, as is aforeſaid, the
2[Figure 2]
Priſme
A C D B to be placed, and in the
reſt
of the Space the Water to be
fuſed
as far as the Levell E A: and
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:
fore
, as the Altitude A O is to the Altitude A G, ſo is the
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
cie
than water,
ſtayeth
not
der
water, in
ry
ſmall depthst.

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