Archimedes
,
Natation of bodies
,
1662
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But now that that Solid is lighter in the Liquid than out of it, as
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is affirmed in the ſecond part, ſhall be demonſtrated in this man
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ner. </
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<
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>Take a Solid, as ſuppoſe A, that is more grave than the Li
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quid, and ſuppoſe the Gravity of that ſame Solid A to be BG.
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<
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>And of a Maſs of
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L
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iquor of the ſame bigneſs with the Solid A, ſup
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poſe the Gravity to be B: It is to be demonſtrated that the Solid
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A, immerged in the Liquid, ſhall have a Gravity equal to G. </
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<
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>And
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to demonſtrate this, let us imagine another Solid, as ſuppoſe D,
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more light than the Liquid, but of ſuch a quality as that its Gravi
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ty is equal to B: and let this D be of ſuch a Magnitude, that a
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Maſs of
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L
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iquor equal to it hath its Gravity equal to the Gravity
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B G. </
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<
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>Now theſe two Solids D and A being compounded toge
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ther, all that Solid compounded of theſe two ſhall be equally
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Grave with the Water: becauſe the Gravity of theſe two Solids
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together ſhall be equal to theſe two Gravities, that is, to B G, and
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to B; and the Gravity of a Liquid that hath its
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Maſs equal to theſe two Solids A and D, ſhall be
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equal to theſe two Gravities B G and B.
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L
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et
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theſe two Solids, therefore, be put in the
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L
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iquid,
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and they ſhall ^{*} remain in the Surface of that
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L
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i
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quid, (that is, they ſhall not be drawn or driven
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upwards, nor yet downwards:) For if the Solid
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A be more grave than the Liquid, it ſhall be
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drawn or born by its Gravity downwards to
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wards the Bottom, with as much Force as by the Solid D it is thruſt
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upwards: And becauſe the Solid D is lighter than the
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L
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iquid, it
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ſhall raiſe it upward with a Force as great as the Gravity G: Be
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cauſe it hath been demonſtrated, in the ſixth
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Propoſition,
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That So
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lid Magnitudes that are lighter than the Water, being demitted in
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the ſame, are repulſed or driven upwards with a Force ſo much the
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greater by how much a
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L
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iquid of equal Maſs with the Solid is more
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Grave than the ſaid Solid: But the
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L
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iquid which is equal in Maſs
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with the Solid D, is more grave than the ſaid Solid D, by the Gra
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vity G: Therefore it is manifeſt, that the Solid A is preſſed or
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born downwards towards the Centre of the World, with a Force
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as great as the Gravity G: Which was to be demonſtrated.</
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* Or, according to
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Commandine,
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ſhall
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be equall in Gravi
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ty to the Liquid,
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neither moving up
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wards or down
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wards.</
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<
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>RIC. </
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<
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>This hath been an ingenuous Demonſtration; and in regard I do ſuffici
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ently underſtand it, that we may loſe no time, we will proceed to the ſecond
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Suppo
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ſition,
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which, as I need not tell you, ſpeaks thus.</
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