1tions of a Sphære, ſhall have its Axis in the Perpendicular, that is

drawn through the point K; and its Centre of Gravity, for the ſame

reaſon, ſhall be in the Line N K: let us ſuppoſe it to be the Point R:

But the Centre of Gravity of the whole Portion is in the Line F T,

betwixt the Point R and

238[Figure 238]

the Point F; let us ſuppoſe

it to be the Point X: The re

mainder, therefore, of that

Figure elivated above the

Surface of the Liquid, hath

its Centre of Gravity in

the Line R X produced or

continued right out in the

Part towards X, taken ſo,

that the part prolonged may

have the ſame proportion to

X R, that the Gravity of

that Portion that is demer

ged in the Liquid hath to

the Gravity of that Figure which is above the Liquid; let us ſuppoſe

that ^{*} that Centre of the ſaid Figure be the Point S: and thorow that

ſame Centre S draw the Perpendicular L S. Now the Gravity of the Fi

gure that is above the Liquid ſhall preſſe from above downwards ac

cording to the Perpendicular S L; & the Gravity of the Portion that

is ſubmerged in the Liquid, ſhall preſſe from below upwards, accor

ding to the Perpendicular R L. Therefore that Figure will not conti

nue according to our Adverſaries Propoſall, but thoſe parts of the

ſaid Figure which are towards E, ſhall be born or drawn downwards,

& thoſe which are towards H ſhall be born or driven upwards, and

this ſhall be ſo long untill that the Axis F T comes to be according

to the Perpendicular.

drawn through the point K; and its Centre of Gravity, for the ſame

reaſon, ſhall be in the Line N K: let us ſuppoſe it to be the Point R:

But the Centre of Gravity of the whole Portion is in the Line F T,

betwixt the Point R and

238[Figure 238]

the Point F; let us ſuppoſe

it to be the Point X: The re

mainder, therefore, of that

Figure elivated above the

Surface of the Liquid, hath

its Centre of Gravity in

the Line R X produced or

continued right out in the

Part towards X, taken ſo,

that the part prolonged may

have the ſame proportion to

X R, that the Gravity of

that Portion that is demer

ged in the Liquid hath to

the Gravity of that Figure which is above the Liquid; let us ſuppoſe

that ^{*} that Centre of the ſaid Figure be the Point S: and thorow that

ſame Centre S draw the Perpendicular L S. Now the Gravity of the Fi

gure that is above the Liquid ſhall preſſe from above downwards ac

cording to the Perpendicular S L; & the Gravity of the Portion that

is ſubmerged in the Liquid, ſhall preſſe from below upwards, accor

ding to the Perpendicular R L. Therefore that Figure will not conti

nue according to our Adverſaries Propoſall, but thoſe parts of the

ſaid Figure which are towards E, ſhall be born or drawn downwards,

& thoſe which are towards H ſhall be born or driven upwards, and

this ſhall be ſo long untill that the Axis F T comes to be according

to the Perpendicular.

(a) Perpendicular

is taken kere, as

in all other places,

by this Author for

the Line K L

drawn thorow the

Centre and Cir

cumference of the

Earth.

is taken kere, as

in all other places,

by this Author for

the Line K L

drawn thorow the

Centre and Cir

cumference of the

Earth.

C

D

E

* i. e, The Center

of Gravity.

of Gravity.

F

And this ſame Demonſtration is in the ſame manner verified in

the other Portions. As, firſt, in the Hæmiſphere that lieth with its

whole Baſe above or without the Liquid, the Centre of the Sphære

hath been ſuppoſed to be the Point T; and therefore, imagining T

to be in the place, in which, in the other above mentioned, the

Point R was, arguing in all things elſe as you did in that, you ſhall

find that the Figure which is above the Liquid ſhall preſs from

above downwards according to the Perpendicular S L; and the

Portion that is ſubmerged in the Liquid ſhall preſs from below up

wards according to the Perpendicular R L. And therefore it ſhall

follow, as in the other, namely, that the parts of the whole Figure

which are towards E, ſhall be born or preſſed downwards, and thoſe

that are towards H, ſhall be born or driven upwards: and this ſhall

be ſo long untill that the Axis F T come to ſtand ^{*} P

the other Portions. As, firſt, in the Hæmiſphere that lieth with its

whole Baſe above or without the Liquid, the Centre of the Sphære

hath been ſuppoſed to be the Point T; and therefore, imagining T

to be in the place, in which, in the other above mentioned, the

Point R was, arguing in all things elſe as you did in that, you ſhall

find that the Figure which is above the Liquid ſhall preſs from

above downwards according to the Perpendicular S L; and the

Portion that is ſubmerged in the Liquid ſhall preſs from below up

wards according to the Perpendicular R L. And therefore it ſhall

follow, as in the other, namely, that the parts of the whole Figure

which are towards E, ſhall be born or preſſed downwards, and thoſe

that are towards H, ſhall be born or driven upwards: and this ſhall

be ſo long untill that the Axis F T come to ſtand ^{*} P