Archimedes
,
Natation of bodies
,
1662
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that of the firſt Pyramid is preſſed by the Solid R, and by the Liquid
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which that containeth, that is, that which is in the place of the Py
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ramid according to A B O X: but that part which, in the other Py
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ramid, is preſſed by the Solid H, ſuppoſed to be of the ſame Li
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quid, and by the Liquid which that containeth, that is, that which
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is in the place of the ſaid Pyramid according to P O B G: and the
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Gravity of the Solid R is leſs than the Gravity of the Liquid
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H, for that theſe two Magnitudes were ſuppoſed to be equal in
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Maſs, and the Solid R was ſuppoſed to be lighter than the Liquid:
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and the Maſſes of the two Pyramids of Liquor that containeth theſe
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two Solids R and H are equal ^{*} by what was preſuppoſed: There
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fore the part of the Liquid that is under the Superficies that pro
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ceeds according to the Circumference O P is more preſſed; and,
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therefore, by the
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Suppoſition,
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it ſhall repulſe that part which is leſs
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preſſed, whereby the ſaid Liquid will not be ſetled: But it was be
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fore ſuppoſed that it was ſetled: Therefore that Solid R ſhall not
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totally ſubmerge, but ſome part thereof will remain without the
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Liquid, that is, above its Surface, Which was the
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Propoſition.
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* That is a Maſs of
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the Liquid.</
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* For that the Py
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ramids were ſuppo
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ſed equal.</
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<
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>RIC. </
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>I have very well underſtood you, therefore let us come to the fifth
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Pro
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poſition,
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which, as you know, doth thus ſpeak.</
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>PROP. V. THEOR. V.</
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Solid Magnitudes that are lighter than the Liquid,
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being demitted in the (ſetled) Liquid, will ſo far
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ſubmerge, till that a Maſs of Liquor, equal to the
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Part ſubmerged, doth in Gravity equalize the
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whole Magnitude.
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<
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>NIC. </
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>It having, in the precedent, been demonſtrared that Solids lighter than
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the Liquid, being demitted in the
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L
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iquid, alwaies a part of them remains
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without the
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L
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iquid, that is above its Surface; In this fifth
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Propoſition
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it is
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aſſerted, that ſo much of ſuch a Solid ſhall ſubmerge, as that a Maſs of the
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L
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iquid equal to the part ſubmerged, ſhall have equal Gravity with the whole
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Solid.</
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<
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>And to demonſtrate this, let us aſſume all the ſame Schemes
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as before, in
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Propoſition
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3. and likewiſe let the Liquid be ſet
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led, and let the Solid E Z H T be lighter than the Liquid.
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<
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>Now if the ſaid Liquid be ſetled, the parts of it that are equija
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cent are equally preſſed: Therefore the Liquid that is beneath </
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