1But now that that Solid is lighter in the Liquid than out of it, as
is affirmed in the ſecond part, ſhall be demonſtrated in this man
ner. Take a Solid, as ſuppoſe A, that is more grave than the Li
quid, and ſuppoſe the Gravity of that ſame Solid A to be BG.
And of a Maſs of Liquor of the ſame bigneſs with the Solid A, ſup
poſe the Gravity to be B: It is to be demonſtrated that the Solid
A, immerged in the Liquid, ſhall have a Gravity equal to G. And
to demonſtrate this, let us imagine another Solid, as ſuppoſe D,
more light than the Liquid, but of ſuch a quality as that its Gravi
ty is equal to B: and let this D be of ſuch a Magnitude, that a
Maſs of Liquor equal to it hath its Gravity equal to the Gravity
B G. Now theſe two Solids D and A being compounded toge
ther, all that Solid compounded of theſe two ſhall be equally
Grave with the Water: becauſe the Gravity of theſe two Solids
together ſhall be equal to theſe two Gravities, that is, to B G, and
9[Figure 9]
to B; and the Gravity of a Liquid that hath its
Maſs equal to theſe two Solids A and D, ſhall be
equal to theſe two Gravities B G and B. Let
theſe two Solids, therefore, be put in the Liquid,
and they ſhall ^{*} remain in the Surface of that Li
quid, (that is, they ſhall not be drawn or driven
upwards, nor yet downwards:) For if the Solid
A be more grave than the Liquid, it ſhall be
drawn or born by its Gravity downwards to
wards the Bottom, with as much Force as by the Solid D it is thruſt
upwards: And becauſe the Solid D is lighter than the Liquid, it
ſhall raiſe it upward with a Force as great as the Gravity G: Be
cauſe it hath been demonſtrated, in the ſixth Propoſition, That So
lid Magnitudes that are lighter than the Water, being demitted in
the ſame, are repulſed or driven upwards with a Force ſo much the
greater by how much a Liquid of equal Maſs with the Solid is more
Grave than the ſaid Solid: But the Liquid which is equal in Maſs
with the Solid D, is more grave than the ſaid Solid D, by the Gra
vity G: Therefore it is manifeſt, that the Solid A is preſſed or
born downwards towards the Centre of the World, with a Force
as great as the Gravity G: Which was to be demonſtrated.
is affirmed in the ſecond part, ſhall be demonſtrated in this man
ner. Take a Solid, as ſuppoſe A, that is more grave than the Li
quid, and ſuppoſe the Gravity of that ſame Solid A to be BG.
And of a Maſs of Liquor of the ſame bigneſs with the Solid A, ſup
poſe the Gravity to be B: It is to be demonſtrated that the Solid
A, immerged in the Liquid, ſhall have a Gravity equal to G. And
to demonſtrate this, let us imagine another Solid, as ſuppoſe D,
more light than the Liquid, but of ſuch a quality as that its Gravi
ty is equal to B: and let this D be of ſuch a Magnitude, that a
Maſs of Liquor equal to it hath its Gravity equal to the Gravity
B G. Now theſe two Solids D and A being compounded toge
ther, all that Solid compounded of theſe two ſhall be equally
Grave with the Water: becauſe the Gravity of theſe two Solids
together ſhall be equal to theſe two Gravities, that is, to B G, and
9[Figure 9]to B; and the Gravity of a Liquid that hath its
Maſs equal to theſe two Solids A and D, ſhall be
equal to theſe two Gravities B G and B. Let
theſe two Solids, therefore, be put in the Liquid,
and they ſhall ^{*} remain in the Surface of that Li
quid, (that is, they ſhall not be drawn or driven
upwards, nor yet downwards:) For if the Solid
A be more grave than the Liquid, it ſhall be
drawn or born by its Gravity downwards to
wards the Bottom, with as much Force as by the Solid D it is thruſt
upwards: And becauſe the Solid D is lighter than the Liquid, it
ſhall raiſe it upward with a Force as great as the Gravity G: Be
cauſe it hath been demonſtrated, in the ſixth Propoſition, That So
lid Magnitudes that are lighter than the Water, being demitted in
the ſame, are repulſed or driven upwards with a Force ſo much the
greater by how much a Liquid of equal Maſs with the Solid is more
Grave than the ſaid Solid: But the Liquid which is equal in Maſs
with the Solid D, is more grave than the ſaid Solid D, by the Gra
vity G: Therefore it is manifeſt, that the Solid A is preſſed or
born downwards towards the Centre of the World, with a Force
as great as the Gravity G: Which was to be demonſtrated.