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