1contained between the Sphærical Superficies that proceed accord
ing to P O and M N and the Planes of the Pyramid; and the Gra
vity of the Liquid, which is according to M N O P, ſhall be leſſer
than that which is according to L M X O; becauſe that Solid of
Liquor which proceeds according to R S C Y is leſs than the Solid
E Z H T (having been ſuppoſed to be equal in quantity to only
the part H B G T of that:) And the ſaid Solid E Z H T hath been
ſuppoſed to be equally grave with the Liquid: Therefore the Gra
vity of the Liquid compriſed betwixt the two Sphærical Superfi
cies L M and X O, and betwixt the ſides L X and M O of the
5[Figure 5]
Pyramid, together with
the whole Solid EZHT,
ſhall exceed the Gravity
of the Liquid compri
ſed betwixt the other
two Sphærical Superfi
cies M N and O P, and
the Sides M O and N P
of the Pyramid, toge
ther with the Solid of Liquor R S C Y by the quantity of the Gra
vity of the part E B Z G, ſuppoſed to remain above the Surface of
the Liquid: And therefore it is manifeſt that the part which pro
ceedeth according to the Circumference O P is preſſed, driven, and
repulſed, according to the Suppoſition, by that which proceeds ac
cording to the Circumference X O, by which means the Liquid
would not be ſetled and ſtill: But we did preſuppoſe that it was
ſetled, namely ſo, as to be without motion: It followeth, therefore,
that the ſaid Solid cannot in any part of it exceed or lie above the
Superficies of the Liquid: And alſo that being dimerged in the Li
quid it cannot deſcend to the Bottom, for that all the parts of the
Liquid equijacent, or diſpoſed equally, are equally preſſed, becauſe
the Solid is equally grave with the Liquid, by what we preſuppoſed.
ing to P O and M N and the Planes of the Pyramid; and the Gra
vity of the Liquid, which is according to M N O P, ſhall be leſſer
than that which is according to L M X O; becauſe that Solid of
Liquor which proceeds according to R S C Y is leſs than the Solid
E Z H T (having been ſuppoſed to be equal in quantity to only
the part H B G T of that:) And the ſaid Solid E Z H T hath been
ſuppoſed to be equally grave with the Liquid: Therefore the Gra
vity of the Liquid compriſed betwixt the two Sphærical Superfi
cies L M and X O, and betwixt the ſides L X and M O of the
5[Figure 5]Pyramid, together with
the whole Solid EZHT,
ſhall exceed the Gravity
of the Liquid compri
ſed betwixt the other
two Sphærical Superfi
cies M N and O P, and
the Sides M O and N P
of the Pyramid, toge
ther with the Solid of Liquor R S C Y by the quantity of the Gra
vity of the part E B Z G, ſuppoſed to remain above the Surface of
the Liquid: And therefore it is manifeſt that the part which pro
ceedeth according to the Circumference O P is preſſed, driven, and
repulſed, according to the Suppoſition, by that which proceeds ac
cording to the Circumference X O, by which means the Liquid
would not be ſetled and ſtill: But we did preſuppoſe that it was
ſetled, namely ſo, as to be without motion: It followeth, therefore,
that the ſaid Solid cannot in any part of it exceed or lie above the
Superficies of the Liquid: And alſo that being dimerged in the Li
quid it cannot deſcend to the Bottom, for that all the parts of the
Liquid equijacent, or diſpoſed equally, are equally preſſed, becauſe
the Solid is equally grave with the Liquid, by what we preſuppoſed.
RIC. I do underſtand your Argumentation, but I underſtand not that Phraſe
Solid Magnitudes.
Solid Magnitudes.
NIC. I will declare this Term unto you. Magnitude is a general Word that
reſpecteth all the Species of Continual Quantity; and the Species of Continual
Quantity are three, that is, the Line, the Superficies, and the Body; which Body
is alſo called a Solid, as having in it ſelf Length, Breadth, and Thickneſs, or Depth:
and therefore that none might equivocate or take that Term Magnitudes to be
meant of Lines, or Superficies, but only of Solid Magnitudes, that is, Bodies, he
did ſpecifie it by that manner of expreſſion, as was ſaid. The truth is, that he
might have expreſt that Propoſition in this manner: Solids (or Bodies) which being
of equal Gravity with an equal Maſs of the Liquid, &c. And this Propoſition would have
been more cleer and intelligible, for it is as ſignificant to ſay, a Solid, or, a Body, as
to ſay, a Solid Magnitude: therefore wonder not if for the future I uſe theſe three
kinds of words indifferently.
reſpecteth all the Species of Continual Quantity; and the Species of Continual
Quantity are three, that is, the Line, the Superficies, and the Body; which Body
is alſo called a Solid, as having in it ſelf Length, Breadth, and Thickneſs, or Depth:
and therefore that none might equivocate or take that Term Magnitudes to be
meant of Lines, or Superficies, but only of Solid Magnitudes, that is, Bodies, he
did ſpecifie it by that manner of expreſſion, as was ſaid. The truth is, that he
might have expreſt that Propoſition in this manner: Solids (or Bodies) which being
of equal Gravity with an equal Maſs of the Liquid, &c. And this Propoſition would have
been more cleer and intelligible, for it is as ſignificant to ſay, a Solid, or, a Body, as
to ſay, a Solid Magnitude: therefore wonder not if for the future I uſe theſe three
kinds of words indifferently.