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

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1for that B G is the Gravity of the Liquid equal in Maſs unto it:
Therefore the Solid compounded of thoſe two Solids A and D
being dimerged, it ſhall, by the precedent, ſo much of it ſubmerge,
as that a quantity of the Liquid equal to the ſaid ſubmerged part
ſhall have equal Gravity with the ſaid compounded Solid.
And

for an example of that Propoſition let the Su­
perficies of any Liquid be that which pro­
ceedeth according to the Circumference
A B G D: Becauſe now a Maſs or quantity
of Liquor as big as the Maſs A hath equal
Gravity with the whole compounded Solid
A D: It is manifeſt that the ſubmerged part
thereof ſhall be the Maſs A: and the remain­
der, namely, the part D, ſhall be wholly a­
top, that is, above the Surface of the Liquid.
It is therefore evident, that the part A hath ſo much virtue or
Force to return upwards, that is, to riſe from below above the Li­
quid, as that which is upon it, to wit, the part D, hath to preſs it
downwards, for that neither part is repulſed by the other: But D
preſſeth downwards with a Gravity equal to G, it having been ſup­
poſed that the Gravity of that part D was equal to G: Therefore
that is manifeſt which was to be demonſtrated.
RIC. This was a fine Demonſtration, and from this I perceive that you colle­
cted your Induſtrious Invention; and eſpecially that part of it which you inſert in
the firſt Book for the recovering of a Ship ſunk: and, indeed, I have many Que­
ſtions to ask you about that, but I will not now interrupt the Diſcourſe in hand, but
deſire that we may go on to the ſeventh Propoſition, the purport whereof is this.
PROP. VII. THEOR. VII.
Solid Magnitudes beavier than the Liquid, being de­
mitted into the [ſetled] Liquid, are boren down­
wards as far as they can deſcend: and ſhall be lighter
in the Liquid by the Gravity of a Liquid Maſs of
the ſame bigneſs with the Solid Magnitude.
NIC. This ſeventh Propoſition hath two parts to be demonſtrated.
The firſt is, That all Solids heavier than the Liquid, being demit­
ted into the Liquid, are boren by their Gravities downwards as far
as they can deſcend, that is untill they arrive at the Bottom.
Which
firſt part is manifeſt, becauſe the Parts of the Liquid, which ſtill lie
under that Solid, are more preſſed than the others equijacent,
becauſe that that Solid is ſuppoſed more grave than the Liquid.