1that of the firſt Pyramid is preſſed by the Solid R, and by the Liquid
which that containeth, that is, that which is in the place of the Py
ramid according to A B O X: but that part which, in the other Py
ramid, is preſſed by the Solid H, ſuppoſed to be of the ſame Li
quid, and by the Liquid which that containeth, that is, that which
is in the place of the ſaid Pyramid according to P O B G: and the
Gravity of the Solid R is leſs than the Gravity of the Liquid
H, for that theſe two Magnitudes were ſuppoſed to be equal in
Maſs, and the Solid R was ſuppoſed to be lighter than the Liquid:
and the Maſſes of the two Pyramids of Liquor that containeth theſe
two Solids R and H are equal ^{*} by what was preſuppoſed: There
fore the part of the Liquid that is under the Superficies that pro
ceeds according to the Circumference O P is more preſſed; and,
therefore, by the Suppoſition, it ſhall repulſe that part which is leſs
preſſed, whereby the ſaid Liquid will not be ſetled: But it was be
fore ſuppoſed that it was ſetled: Therefore that Solid R ſhall not
totally ſubmerge, but ſome part thereof will remain without the
Liquid, that is, above its Surface, Which was the Propoſition.
which that containeth, that is, that which is in the place of the Py
ramid according to A B O X: but that part which, in the other Py
ramid, is preſſed by the Solid H, ſuppoſed to be of the ſame Li
quid, and by the Liquid which that containeth, that is, that which
is in the place of the ſaid Pyramid according to P O B G: and the
Gravity of the Solid R is leſs than the Gravity of the Liquid
H, for that theſe two Magnitudes were ſuppoſed to be equal in
Maſs, and the Solid R was ſuppoſed to be lighter than the Liquid:
and the Maſſes of the two Pyramids of Liquor that containeth theſe
two Solids R and H are equal ^{*} by what was preſuppoſed: There
fore the part of the Liquid that is under the Superficies that pro
ceeds according to the Circumference O P is more preſſed; and,
therefore, by the Suppoſition, it ſhall repulſe that part which is leſs
preſſed, whereby the ſaid Liquid will not be ſetled: But it was be
fore ſuppoſed that it was ſetled: Therefore that Solid R ſhall not
totally ſubmerge, but ſome part thereof will remain without the
Liquid, that is, above its Surface, Which was the Propoſition.
* That is a Maſs of
the Liquid.
the Liquid.
* For that the Py
ramids were ſuppo
ſed equal.
ramids were ſuppo
ſed equal.
RIC. I have very well underſtood you, therefore let us come to the fifth Pro
poſition, which, as you know, doth thus ſpeak.
poſition, which, as you know, doth thus ſpeak.
PROP. V. THEOR. V.
Solid Magnitudes that are lighter than the Liquid,
being demitted in the (ſetled) Liquid, will ſo far
ſubmerge, till that a Maſs of Liquor, equal to the
Part ſubmerged, doth in Gravity equalize the
whole Magnitude.
being demitted in the (ſetled) Liquid, will ſo far
ſubmerge, till that a Maſs of Liquor, equal to the
Part ſubmerged, doth in Gravity equalize the
whole Magnitude.
NIC. It having, in the precedent, been demonſtrared that Solids lighter than
the Liquid, being demitted in the Liquid, alwaies a part of them remains
without the Liquid, that is above its Surface; In this fifth Propoſition it is
aſſerted, that ſo much of ſuch a Solid ſhall ſubmerge, as that a Maſs of the
Liquid equal to the part ſubmerged, ſhall have equal Gravity with the whole
Solid.
the Liquid, being demitted in the Liquid, alwaies a part of them remains
without the Liquid, that is above its Surface; In this fifth Propoſition it is
aſſerted, that ſo much of ſuch a Solid ſhall ſubmerge, as that a Maſs of the
Liquid equal to the part ſubmerged, ſhall have equal Gravity with the whole
Solid.
And to demonſtrate this, let us aſſume all the ſame Schemes
as before, in Propoſition 3. and likewiſe let the Liquid be ſet
led, and let the Solid E Z H T be lighter than the Liquid.
Now if the ſaid Liquid be ſetled, the parts of it that are equija
cent are equally preſſed: Therefore the Liquid that is beneath
as before, in Propoſition 3. and likewiſe let the Liquid be ſet
led, and let the Solid E Z H T be lighter than the Liquid.
Now if the ſaid Liquid be ſetled, the parts of it that are equija
cent are equally preſſed: Therefore the Liquid that is beneath