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

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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 determina­
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 thick­
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 remo­
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 bot­
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 Ram­
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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