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

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Having prefatically explicated theſe things, we may begin to
quire
, what Bodyes thoſe are which totally ſubmerge in Water, and
go
to the Bottom, and which thoſe that by conſtraint float on the
top
, ſo that being thruſt by violence under Water, they return to
ſwim
, with one part of their Maſs viſible above the Surface of the
Water
: and this we will do by conſidering the reſpective
on
of the ſaid Solids, and of Water: Which operation followes
the
Submerſion and ſinking; and this it is, That in the Submerſion

that
the Solid maketh, being depreſſed downwards by its proper
Gravity
, it comes to drive away the water from the place where it
ſucceſſively
ſubenters, and the water repulſed riſeth and aſcends
above
its firſt levell, to which Aſcent on the other ſide it, as being a
grave
Body of its own nature, reſiſts: And becauſe the deſcending
Solid
more and more immerging, greater and greater quantity of
Water
aſcends, till the whole Sollid be ſubmerged; its neceſſary to
compare
the Moments of the Reſiſtance of the water to Aſcenſion,
with
the Moments of the preſſive Gravity of the Solid: And if the
Moments
of the Reſiſtance of the water, ſhall equalize the Moments

of
the Solid, before its totall Immerſion; in this caſe doubtleſs there
ſhall
be made an Equilibrium, nor ſhall the Body ſink any farther.
But if the Moment of the Solid, ſhall alwayes exceed the Moments

wherewith
the repulſed water ſucceſſively makes Reſiſtance, that
Solid
ſhall not only wholly ſubmerge under water, but ſhall deſcend
to
the Bottom.
But if, laſtly, in the inſtant of totall Submerſion,

the
equality ſhall be made between the Moments of the prement
Solid
, and the reſiſting Water; then ſhall reſt enſue, and the ſaid
Solid
ſhall be able to reſt indifferently, in whatſoever part of the
water
.
By this time is manifeſt the neceſſity of comparing the

Gravity
of the water, and of the Solid; and this compariſon might
at
firſt ſight ſeem ſufficient to conclude and determine which are the
Solids
that float a-top, and which thoſe that ſink to the Bottom in the
water
, aſſerting that thoſe ſhall float which are leſſe grave in ſpecie
than
the water, and thoſe ſubmerge, which are in ſpecie more grave.
For it ſeems in appearance, that the Sollid in ſinking continually,
raiſeth
ſo much Water in Maſs, as anſwers to the parts of its own
Bulk
ſubmerged: whereupon it is impoſſible, that a Solid leſs grave
in ſpecie, than water, ſhould wholly ſink, as being unable to raiſe a
weight
greater than its own, and ſuch would a Maſs of water equall
to
its own Maſs be.
And likewiſe it ſeems neceſſary, that the graver
Solids
do go to the Bottom, as being of a Force more than ſufficient
for
the raiſing a Maſſe of water, equall to its own, though inferiour
in
weight.
Nevertheleſs the buſineſs ſucceeds otherwiſe: and

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