Archimedes
,
Natation of bodies
,
1662
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tions of a Sphære, ſhall have its Axis in the Perpendicular, that is
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drawn through the point K; and its Centre of Gravity, for the ſame
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reaſon, ſhall be in the Line N K: let us ſuppoſe it to be the Point R:
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But the Centre of Gravity of the whole Portion is in the Line F T,
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betwixt the Point R and
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the Point F; let us ſuppoſe
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it to be the Point
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X
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: The re
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mainder, therefore, of that
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Figure elivated above the
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Surface of the Liquid, hath
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its Centre of Gravity in
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the Line R X produced or
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continued right out in the
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Part towards X, taken ſo,
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that the part prolonged may
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have the ſame proportion to
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X R, that the Gravity of
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that Portion that is demer
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ged in the Liquid hath to
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the Gravity of that Figure which is above the Liquid; let us ſuppoſe
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that ^{*} that Centre of the ſaid Figure be the Point S: and thorow that
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ſame Centre S draw the Perpendicular L S. </
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>Now the Gravity of the Fi
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gure that is above the Liquid ſhall preſſe from above downwards ac
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cording to the Perpendicular S L; & the Gravity of the Portion that
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is ſubmerged in the Liquid, ſhall preſſe from below upwards, accor
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ding to the Perpendicular R L. </
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<
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>Therefore that Figure will not conti
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nue according to our Adverſaries Propoſall, but thoſe parts of the
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ſaid Figure which are towards E, ſhall be born or drawn downwards,
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& thoſe which are towards H ſhall be born or driven upwards, and
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this ſhall be ſo long untill that the Axis F T comes to be according
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to the Perpendicular.</
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(a)
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Perpendicular
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is taken kere, as
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in all other places,
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by this Author for
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the Line K L
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drawn thorow the
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Centre and Cir
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cumference of the
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Earth.
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C</
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D</
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E</
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*
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i. </
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>e,
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The Center
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of Gravity.</
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F</
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<
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>And this ſame Demonſtration is in the ſame manner verified in
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the other
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ortions. </
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>As, firſt, in the Hæmiſphere that lieth with its
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whole Baſe above or without the
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L
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iquid, the Centre of the Sphære
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hath been ſuppoſed to be the
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P
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oint T; and therefore, imagining T
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to be in the place, in which, in the other above mentioned, the
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P
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oint R was, arguing in all things elſe as you did in that, you ſhall
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find that the Figure which is above the
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L
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iquid ſhall preſs from
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above downwards according to the
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P
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erpendicular S
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L
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; and the
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P
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ortion that is ſubmerged in the
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L
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iquid ſhall preſs from below up
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wards according to the
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P
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erpendicular R
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L.
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And therefore it ſhall
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follow, as in the other, namely, that the parts of the whole Figure
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which are towards E, ſhall be born or preſſed downwards, and thoſe
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that are towards H, ſhall be born or driven upwards: and this ſhall
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be ſo long untill that the Axis F T come to ſtand ^{*}
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P
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