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

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1
THEOREME
Let the Veſſell be M L G N of any bigneſs, and let there be
ced
in it the Solid Priſme D F G E, leſs grave in ſpecie than the
water
; and look what proportion the Specificall Gravity of
the
water, hath to that of the Priſme, ſuch let the Altitude D F, have
to
the Altitude F B.
I ſay, that infuſing water to the Altitude F B,
the
Solid D G ſhall not float, but ſhall ſtand in Equilibrium, ſo, that
that
every little quantity of water, that is infuſed, ſhall raiſe it.
Let
the
water, therefore, be infuſed to the Levell A B C, and, becauſe
the
Specifick Gravity of the Solid D G, is to the Specifick Gravity of
the
water, as the altitude B F is to the altitude F D; that is, as the Maſs
B
G to the Maſs G D; as the proportion of the Maſs B G is to the
Maſs
G D, as the proportion of the Maſs G D is to the Maſs A F, they
compoſe
the Proportion of the Maſs B G to the Maſs A F. Therefore,
the
Maſs B G is to the Maſs A F, in a proportion compounded of the
proportions
of the Specifick Gravity of the Solid G D, to the
fick
Gravity of the water, and of the Maſs G D
to
the Maſs A F: But the ſame proportions
5[Figure 5]
of
the Specifick Gravity of G D, to the Specifick
Gravity
of the water, and of the Maſs G D to
the
Maſs A F, do alſo by the precedent Lemma,
compound
the proportion of the abſolute
vity
of the Solid D G, to the abſolute Gravity
of
the Maſs of the water A F: Therefore,
as
the Maſs B G is to the Maſs A F, ſo is the
Abſolute
Gravity of the Solid D G, to the
ſolute
Gravity of the Maſs of the water A F.
But as the Maſs B G
is
to the Maſs A F; ſo is the Baſe of the Priſme D E, to the Surface
of
the water AB; and ſo is the deſcent of the water A B, to the
Elevation
of the Priſme D G; Therefore, the deſcent of the

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