For the declaration of this Propoſition, let a Solid Magnitude
that hath the Figure of a portion of a Sphære, as hath been ſaid,
be imagined to be de
10[Figure 10]
mitted into the Liquid; and
alſo, let a Plain be ſuppoſed
to be produced thorow the
Axis of that portion, and
thorow the Center of the
Earth: and let the Section
of the Surface of the Liquid
be the Circumference A B
C D, and of the Figure, the
Circumference E F H, & let
E H be a right line, and F T
the Axis of the Portion. If now
it were poſſible, for ſatisfact
ion of the Adverſary, Let
it be ſuppoſed that the ſaid Axis were not according to the (a) Per
pendicular; we are then to demonſtrate, that the Figure will not
continue as it was conſtituted by the Adverſary, but that it will re
turn, as hath been ſaid, unto its former poſition, that is, that the
Axis F T ſhall be according to the Perpendicular. It is manifeſt, by
the Corollary of the 1. of 3. Euclide, that the Center of the Sphære
is in the Line F T, foraſmuch as that is the Axis of that Figure.
And in regard that the Por
11[Figure 11]
tion of a Sphære, may be
greater or leſſer than an He
miſphære, and may alſo be
an Hemiſphære, let the Cen
tre of the Sphære, in the He
miſphære, be the Point T,
and in the leſſer Portion the
Point P, and in the greater,
the Point K, and let the Cen
tre of the Earth be the Point
L. And ſpeaking, firſt, of
that greater Portion which
hath its Baſe out of, or a
bove, the Liquid, thorew the Points K and L, draw the Line KL
cutting the Circumference E F H in the Point N, Now, becauſe
every Portion of a Sphære, hath its Axis in the Line, that from the
Centre of the Sphære is drawn perpendicular unto its Baſe, and hath
its Centre of Gravity in the Axis; therefore that Portion of the Fi
gure which is within the Liquid, which is compounded of two
that hath the Figure of a portion of a Sphære, as hath been ſaid,
be imagined to be de
10[Figure 10]mitted into the Liquid; and
alſo, let a Plain be ſuppoſed
to be produced thorow the
Axis of that portion, and
thorow the Center of the
Earth: and let the Section
of the Surface of the Liquid
be the Circumference A B
C D, and of the Figure, the
Circumference E F H, & let
E H be a right line, and F T
the Axis of the Portion. If now
it were poſſible, for ſatisfact
ion of the Adverſary, Let
it be ſuppoſed that the ſaid Axis were not according to the (a) Per
pendicular; we are then to demonſtrate, that the Figure will not
continue as it was conſtituted by the Adverſary, but that it will re
turn, as hath been ſaid, unto its former poſition, that is, that the
Axis F T ſhall be according to the Perpendicular. It is manifeſt, by
the Corollary of the 1. of 3. Euclide, that the Center of the Sphære
is in the Line F T, foraſmuch as that is the Axis of that Figure.
And in regard that the Por
11[Figure 11]tion of a Sphære, may be
greater or leſſer than an He
miſphære, and may alſo be
an Hemiſphære, let the Cen
tre of the Sphære, in the He
miſphære, be the Point T,
and in the leſſer Portion the
Point P, and in the greater,
the Point K, and let the Cen
tre of the Earth be the Point
L. And ſpeaking, firſt, of
that greater Portion which
hath its Baſe out of, or a
bove, the Liquid, thorew the Points K and L, draw the Line KL
cutting the Circumference E F H in the Point N, Now, becauſe
every Portion of a Sphære, hath its Axis in the Line, that from the
Centre of the Sphære is drawn perpendicular unto its Baſe, and hath
its Centre of Gravity in the Axis; therefore that Portion of the Fi
gure which is within the Liquid, which is compounded of two