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

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1
For, if the Cylinder or Priſme M, leſs grave than the water, v.
gra. in Subſequiteriall proportion, ſhall be put into the
ous
Veſſell A B C D, and the water raiſed about it, to three
quarters
of its height, namely, to its Levell A D: it ſhall be ſuſtained
and
exactly poyſed in
librium
. The ſame will
pen
, if the Veſſell E N S F
6[Figure 6]
were
very ſmall, ſo, that
tween
the Veſſell and the
lid
M, there were but a very
narrow
ſpace, and only capable of ſo much water, as the hundredth
part
of the Maſs M, by which it ſhould be likewiſe raiſed and erected,
as
before it had been elevated to three fourths of the height of the
Solid
: which to many at the firſt ſight, may ſeem a notable Paradox,
and
beget a conceit, that the Demonſtration of theſe effects, were
ſophiſticall
and fallacious: but, for thoſe who ſo repute it, the
periment
is a means that may fully ſatisfie them.
But he that ſhall
but
comprehend of what Importance Velocity of Motion is, and how
it
exactly compenſates the defect and want of Gravity, will ceaſe to
wonder
, in conſidering that at the elevation of the Solid M, the great
Maſs
of water A B C D abateth very little, but the little Maſs of
water
E N S F decreaſeth very much, and in an inſtant, as the Solid
M
before did liſe, howbeit for a very ſhort ſpace: Whereupon the
Moment
, compounded of the ſmall Abſolute Gravity of the water
E
N S F, and of its great Velocity in ebbing, equalizeth the Force and
and
Moment, that reſults from the compoſicion of the immenſe
vity
of the water A B C D, with its great ſlowneſſe of ebbing;
ſince
that in the Elevation of the Sollid M, the abaſement of the leſ­

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