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

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1
Now let us ſee on which of theſe three dimenſions of the Solid
depends
the terminating, what and how much the Maſs of that ought
to
be, that ſo the aſſiſtance of the Air contiguous unto it, may ſuffice
to
render it ſpecifically leſs grave than the water, whereupon it may
reſt
without Submerſion.
It ſhall undoubtedly be found, that the
length
and breadth have not any thing to do in the ſaid
tion
, but only the height, or if you will the thickneſs: for, if we take
a
Plate or Board, as for Example, of Ebony, whoſe Altitude hath
unto
the greateſt poſſible Altitude of the Rampart, the proportion
above
declared, for which cauſe it ſwims indeed, but yet not if we
never
ſo little increaſe its thickneſs; I ſay, that retaining its
neſs
, and encreaſing its Superficies to twice, four times, or ten times
its
bigneſs, or dminiſning it by dividing it into four, or ſix, or
twenty
, or a hundred parts, it ſhall ſtill in the ſame manner continue
to
float: but encreaſing its thickneſs only a Hairs breadth, it will
alwaies
ſubmerge, although we ſhould multiply the Superficies a
hundred
and a hundred times.
Now foraſmuch as that this is a
Cauſe
, which being added, we adde alſo the Effect, and being
ved
, it is removed; and by augmenting or leſſening the length or
breadth
in any manner, the effect of going, or not going to the
tom
, is not added or removed: I conclude, that the greatneſs and
ſmalneſs
of the Superficies hath no influence upon the Natation or
Submerſion
.
And that the proportion of the Altitude of the
parts
of Water, to the Altitude of the Solid, being conſtituted in
the
manner aforeſaid, the greatneſs or ſmalneſs of the Superficies,
makes
not any variation, is manifeſt from that which hath been above
demonſtrated
, and from this, that, The Priſms and Cylinders which

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