Galilei, Galileo - Discourse concerning the natation of bodies

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

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though the Concluſions are true, yet are the Cauſes thus aſſigned
deficient, nor is it true, that the Solid in ſubmerging, raiſeth and
repulſeth Maſſes of Water, equall to the parts of it ſelf ſubmerged;
but the Water repulſed, is alwayes leſs than the parts of the Solid

ſubmerged: and ſo much the more by how much the Veſſell in
which the Water is contained is narrower: in ſuch manner that it
hinders not, but that a Solid may ſubmerge all under Water, with
out raiſing ſo much Water in Maſs, as would equall the tenth or
twentieth part of its own Bulk: like as on the contrary, a very

ſmall quantity of Water, may raiſe a very great Solid Maſs, though
ſuch Solid ſhould weigh abſolutely a hundred times as much, or
more, than the ſaid Water, if ſo be that the Matter of that ſame
Solid be in ſpecie leſs grave than the Water. And thus a great
Beam, as ſuppoſe of a 1000 weight, may be raiſed and born afloat
by Water, which weighs not 50: and this happens when the Mo
ment of the Water is compenſated by the Velocity of its Motion.

How the ſub
merſion of So
lids in the Wa
ter, is effected.

What Solids
ſhall float on the
Water.

What Solids
ſhall ſinke to the
botome.

What Solids
ſhall reſt in all
places of the Wa
ter.

The Gravitie of
the Water and
S olid muſt be
compared in all
Problems, of Na
tation of Bodies.

The water re
pulſed is ever leſs
than the parts of
the Sollid ſub
merged.

A ſmall quantity
of water, may
float a very
great Solid Maſs.

But becauſe ſuch things, propounded thus in abſtract, are ſome
what difficult to be comprehended, it would be good to demonſtrate
them by particular examples; and for facility of demonſtration, we
will ſuppoſe the Veſſels in which we are to put the Water, and place
the Solids, to be inviron'd and included with ſides erected perpendi
cular to the Plane of the Horizon, and the Solid that is to be put
into ſuch veſſell to be either a ſtreight Cylinder, or elſe an upright
Priſme

The which propoſed and declared, I proceed to demonstrate the truth
of what hath been hinted, forming the enſuing Theoreme.

THEOREME I.

The Maſs of the Water whichaſcends in the ſub

merging of a Solid, Priſme or Cylinder, or that
abaſeth in taking it out, is leſs than the Maſs of
the ſaid Solid, ſo depreſſed or advanced: and
hath to it the ſame proportion, that the Surface
of the Water circumfuſing the Solid, hath to the
ſame circumfuſed Surface, together with the Baſe
of the Solid.

T he Proportion
of the water rai
ſed to the S olid
ſubmerged.

Let the Veſſell be A B C D, and in it the Water raiſed up to the
Levell E F G, before the Solid Priſme H I K be therein immerged;
but after that it is depreſſed under Water, let the Water be raiſed as
high as the Levell L M, the Solid H I K ſhall then be all under Water,
and the Maſs of the elevated Water ſhall be L G, which is leſs than the

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