Archimedes
,
Natation of bodies
,
1662
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the Superficies that proceed according to the Circumferences X O
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and P O are equally preſſed; whereby the Gravity preſſed is equal.
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But the Gravity of the
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Liquid which is in the
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firſt Pyramid ^{*} without
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the Solid B H T G, is
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equal to the Gravity of
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the Liquid which is in
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the other Pyramid with
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out the Liquid R S C Y:
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It is manifeſt, therefore,
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that the Gravity of the Solid E Z H T, is equal to the Gravity of
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the Liquid R S C Y: Therefore it is manifeſt that a Maſs of Liquor
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equal in Maſs to the part of the Solid ſubmerged is equal in Gra
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vity to the whole Solid.</
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*
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Without, i.e.
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that
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being deducted.</
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<
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>RIC. </
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>This was a pretty Demonſtration, and becauſe I very well underſtand
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it, let us loſe no time, but proceed to the ſixth
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Propoſition,
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ſpeaking thus.</
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>PROP. VI. THEOR. VI.</
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Solid Magnitudes lighter than the Liquid being thruſt
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into the Liquid, are repulſed upwards with a Force
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as great as is the exceſs of the Gravity of a Maſs
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of Liquor equal to the Magnitude above the Gra
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vity of the ſaid Magnitude.
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<
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>NIC. </
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>This ſixth
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Propoſition
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ſaith, that the Solids lighter than the Liquid
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demitted, thruſt, or trodden by Force underneath the Liquids Sur
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face, are returned or driven upwards with ſo much Force, by
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how much a quantity of the Liquid equal to the. </
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<
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>Solid ſhall
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exceed the ſaid Solid in Gravity.</
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>And to delucidate this
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Propoſition,
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let the Solid A be lighter
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than the
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L
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iquid, and let us ſuppoſe that the Gravity of the ſaid
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Solid A is B: and let the Gravity of a
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L
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iquid, equal in Maſs to A,
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be B G. </
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<
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>I ſay, that the Solid A depreſſed or demitted with Force
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into the ſaid
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L
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iquid, ſhall be returned and repulſed upwards with
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a Force equal to the Gravity G. </
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<
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>And to demonſtrate this
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Propo
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ſition,
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take the Solid D, equal in Gravity to the ſaid G. </
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<
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>Now
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the Solid compounded of the two Solids A and D will be lighter
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than the
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L
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iquid: for the Gravity of the Solid compounded of
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them both is BG, and the Gravity of as much Liquor as equal
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leth in greatneſs the Solid A, is greater than the ſaid Gravity BG, </
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