Galilei, Galileo - Discourse concerning the natation of bodies

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

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THEOREME III.

A Priſme or regular Cylinder, of a ſubſtance ſpecifically
leſs grave than Water, if it ſhould be totally ſubmerged
in Water, ſtayes not underneath, but riſeth, though the
Water circumfuſed be very little, and in abſolute
Gravity, never ſo much inferiour to the Gravity of the
ſaid Priſme.

Let then the Priſme A E F B, be put into the Veſſell C D F B, the
ſame being leſs grave in ſpecie than the Water: and let the
Water infuſed riſe to the height of the Priſme: I ſay, that the
Priſme left at liberty, it ſhall riſe, being born up
by the Water circumfuſed C D E A. For the

[Figure 3]

Water C E being ſpecifically more grave than
the Solid A F, the abſolute weight of the water
C E, ſhall have greater proportion to the abſo
lute weight of the Priſme A F, than the Maſs
C E hath to the Maſs A F (in regard the Maſs
hath the ſame proportion to the Maſs, that the
weight abſolute hath to the weight abſolute,
in caſe the Maſſes are of the ſame Gravity in ſpecie.) But
the Maſs C E is to the Maſs A F, as the Surface of the water A C, is
to the Superficies, or Baſe of the Priſme A B; which is the ſame pro
portion as the aſcent of the Priſme when it riſeth, hath to the deſcent
of the water circumfuſed C E.

Therefore, the abſolute Gravity of the water C E, hath greater
proportion to the abſolute Gravity of the Priſme A F; than the
Aſcent of the Priſme A F, hath to the deſcent of the ſaid
water C E. The Moment, therefore, compounded of the abſolute
Gravity of the water C E, and of the Velocity of its deſcent, whilſt
it forceably repulſeth and raiſeth the Solid A F, is greater than the
Moment compounded of the abſolute Gravity of the Priſme A F, and
of the Tardity of its aſcent, with which Moment it contraſts and re
fiſts the repulſe and violence done it by the Moment of the water:
Therefore, the Priſme ſhall be raiſed.

The Proportion
according to
which the Sub
merſion & Na
tation of Solids
is made.

It followes, now, that we proceed forward to demonſtrate more
particularly, how much ſuch Solids ſhall be inferiour in Gravity to
the water elevated; namely, what part of them ſhall reſt ſubmerged,
and what ſhall be viſible above the Surface of the water: but firſt
it is neceſſary to demonſtrate the ſubſequent Lemma.

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