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

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Priſme, or Cylinder, to wit, that hath its two flat Superficies, ſuperi­
our and inferiour, alike and equall, and at Right Angles with the
ther laterall Superficies, and let its thickneſs I O be equall to the
greateſt Altitude of the Banks of water: I ſay, that if it be put upon
the water, it will not ſubmerge: for the Altitude
A I being equall to the Altitude I O, the Maſs
of the Air A B C I ſhall be equall to the Maſs of

Figure: /permanent/archimedes/galil_natat_074_en_1663/figures not scanned
[Figure 10]

the Solid C I O S: and the whole Maſs A O S B
double to the Maſs I S; And ſince the Maſs
of the Air A C, neither encreaſeth nor dimi­
niſheth the Gravity of the Maſs I S, and the Solid I S was ſuppoſed
double in Gravity to the water; Therefore as much water as the
Maſs ſubmerged A O S B, compounded of the Air A I C B, and of
the Solid I O S C, weighs juſt as much as the ſame ſubmerged Maſs
A O S B: but when ſuch a Maſs of water, as is the ſubmerged part of
the Solid, weighs as much as the ſaid Solid, it deſcends not farther,

but reſteth, as by (a) Archimedes, and above by us, hath been de­>
monſtrated: Therefore, I S ſhall deſcend no farther, but ſhall reſt.
And if the Solid I S ſhall be Seſquialter in Gravity to the water, it
ſhall float, as long as its thickneſs be not above twice as much as the
greateſt Altitude of the Ramparts of water, that is, of A I.
For I S
being Seſquialter in Gravity to the water, and the Altitude O I
being double to I A, the Solid ſubmerged A O S B, ſhall be alſo
Seſquialter in Maſs to the Solid I S.
And becauſe the Air A C,
neither increaſeth nor diminiſheth the ponderoſity of the Solid I S:
Therefore, as much water in quantity as the ſubmerged Maſs AOSB,
weighs as much as the ſaid Maſs ſubmerged: And, therefore, that
Maſs ſhall reſt.
And briefly in generall.
The proporti­
on of the great­
eſt thickneſs of
Solids, beyond
which encrea­
ſed they ſink.

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