1the Superficies that proceed according to the Circumferences X O
and P O are equally preſſed; whereby the Gravity preſſed is equal.
233[Figure 233]
But the Gravity of the
Liquid which is in the
firſt Pyramid ^{*} without
the Solid B H T G, is
equal to the Gravity of
the Liquid which is in
the other Pyramid with
out the Liquid R S C Y:
It is manifeſt, therefore,
that the Gravity of the Solid E Z H T, is equal to the Gravity of
the Liquid R S C Y: Therefore it is manifeſt that a Maſs of Liquor
equal in Maſs to the part of the Solid ſubmerged is equal in Gra
vity to the whole Solid.
and P O are equally preſſed; whereby the Gravity preſſed is equal.
233[Figure 233]But the Gravity of the
Liquid which is in the
firſt Pyramid ^{*} without
the Solid B H T G, is
equal to the Gravity of
the Liquid which is in
the other Pyramid with
out the Liquid R S C Y:
It is manifeſt, therefore,
that the Gravity of the Solid E Z H T, is equal to the Gravity of
the Liquid R S C Y: Therefore it is manifeſt that a Maſs of Liquor
equal in Maſs to the part of the Solid ſubmerged is equal in Gra
vity to the whole Solid.
* Without, i.e. that
being deducted.
being deducted.
RIC. This was a pretty Demonſtration, and becauſe I very well underſtand
it, let us loſe no time, but proceed to the ſixth Propoſition, ſpeaking thus.
it, let us loſe no time, but proceed to the ſixth Propoſition, ſpeaking thus.
PROP. VI. THEOR. VI.
Solid Magnitudes lighter than the Liquid being thruſt
into the Liquid, are repulſed upwards with a Force
as great as is the exceſs of the Gravity of a Maſs
of Liquor equal to the Magnitude above the Gra
vity of the ſaid Magnitude.
into the Liquid, are repulſed upwards with a Force
as great as is the exceſs of the Gravity of a Maſs
of Liquor equal to the Magnitude above the Gra
vity of the ſaid Magnitude.
NIC. This ſixth Propoſition ſaith, that the Solids lighter than the Liquid
demitted, thruſt, or trodden by Force underneath the Liquids Sur
face, are returned or driven upwards with ſo much Force, by
how much a quantity of the Liquid equal to the. Solid ſhall
exceed the ſaid Solid in Gravity.
demitted, thruſt, or trodden by Force underneath the Liquids Sur
face, are returned or driven upwards with ſo much Force, by
how much a quantity of the Liquid equal to the. Solid ſhall
exceed the ſaid Solid in Gravity.
And to delucidate this Propoſition, let the Solid A be lighter
than the Liquid, and let us ſuppoſe that the Gravity of the ſaid
Solid A is B: and let the Gravity of a Liquid, equal in Maſs to A,
be B G. I ſay, that the Solid A depreſſed or demitted with Force
into the ſaid Liquid, ſhall be returned and repulſed upwards with
a Force equal to the Gravity G. And to demonſtrate this Propo
ſition, take the Solid D, equal in Gravity to the ſaid G. Now
the Solid compounded of the two Solids A and D will be lighter
than the Liquid: for the Gravity of the Solid compounded of
them both is BG, and the Gravity of as much Liquor as equal
leth in greatneſs the Solid A, is greater than the ſaid Gravity BG,
than the Liquid, and let us ſuppoſe that the Gravity of the ſaid
Solid A is B: and let the Gravity of a Liquid, equal in Maſs to A,
be B G. I ſay, that the Solid A depreſſed or demitted with Force
into the ſaid Liquid, ſhall be returned and repulſed upwards with
a Force equal to the Gravity G. And to demonſtrate this Propo
ſition, take the Solid D, equal in Gravity to the ſaid G. Now
the Solid compounded of the two Solids A and D will be lighter
than the Liquid: for the Gravity of the Solid compounded of
them both is BG, and the Gravity of as much Liquor as equal
leth in greatneſs the Solid A, is greater than the ſaid Gravity BG,