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
235[Figure 235]
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
235[Figure 235]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.
* Or, according to
Commandine, ſhall
be equall in Gravi
ty to the Liquid,
neither moving up
wards or down
wards.
Commandine, ſhall
be equall in Gravi
ty to the Liquid,
neither moving up
wards or down
wards.
RIC. This hath been an ingenuous Demonſtration; and in regard I do ſuffici
ently underſtand it, that we may loſe no time, we will proceed to the ſecond Suppo
ſition, which, as I need not tell you, ſpeaks thus.
ently underſtand it, that we may loſe no time, we will proceed to the ſecond Suppo
ſition, which, as I need not tell you, ſpeaks thus.