B

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

236[Figure 236]

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

237[Figure 237]

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

236[Figure 236]

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

237[Figure 237]

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