Galilei, Galileo - Discourse concerning the natation of bodies

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

Table of figures

Point downwards, it ſhall not deſcend to the bot
tom: for the Aeriall Cylinder contained betwixt

[Figure 14]

the Ramparts D A C E, is equall in Maſs to the
Cone A B C; ſo that the whole Maſs of the Solid
compounded of the Air D A C E, and of the Cone
A B C, ſhall be double to the Cone A C B: And,
becauſe the Cone A B C is ſuppoſed to be of Matter double in Gra
vity to the water, therefore as much water as the whole Maſſe
D A B C E, placed beneath the Levell of the water, weighs as much
as the Cone A B C: and, therefore, there ſhall be an Equilibrium,
and the Cone A B C ſhall deſcend no lower. Now, I ſay farther,
that the ſame Cone placed with the Baſe downwards, ſhall ſink to
the bottom, without any poſſibility of returning again, by any means
to ſwimme.

Let, therefore, the Cone be A B D, double in Gravity to the
water, and let its height be tripple the height

[Figure 15]

of the Rampart of water L B: It is already
manifeſt, that it ſhall not ſtay wholly out of
the water, becauſe the Cylinder being com
prehended betwixt the Ramparts L B D P,
equall to the Cone A B D, and the Matter of
the Cone, beig double in Gravity to the
water, it is evident that the weight of the ſaid
Cone ſhall be double to the weight of the Maſs of water equall to the
Cylinder L B D P: Therefore it ſhall not reſt in this ſtate, but
ſhall deſcend.

COROLARY I.

I ſay farther; that much leſſe ſhall the ſaid Cone stay afloat, if one

immerge a part thereof.

Much leſs ſhall
the ſaid Cone
ſwim, if one im
merge a part
thereof.

Which you may ſee, comparing with the water as well the part
that ſhall immerge as the other above water. Let us therefore
of the Cone A B D, ſubmergeth part N T O S, and advance the
Point N S F above water. The Altitude of the Cone F N S, ſhall
either be more than half the whole Altitude of the Cone F T O, or
it ſhall not be more: if it ſhall be more than half, the Cone F N S
ſhall be more than half of the Cylinder E N S C: for the Altitude
of the Cone F N S, ſhall be more than Seſquialter of the Altitude
of the Cylinder E N S C: And, becauſe the Matter of the Cone is
ſuppoſed to be double in Specificall Gravity to the water, the water
which would be contained within the Rampart E N S C, would be
leſs grave abſolutely than the Cone F N S; ſo that the whole Cone
F N S cannot be ſuſtained by the Rampart: But the part immerged
N T O S, by being double in Specificall Gravity to the water, ſhall

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