Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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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

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.
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.