Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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>THE OREME XII.</
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That it is poſſible to fo m Solid Bodies, of what Figure
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and greatneſs ſoever, that of their own Nature goe
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to the Bottome; But by the help of the Air
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tained in the Rampart, reſt without ſubmerging.
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Solids of any
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Figure &
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neſſe, that
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rally ſink, may
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by help of the
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Air in the
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part ſwimme.</
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>The truth of this Propoſition is ſufficiently manifeſt in all thoſe
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Solid Figures, that determine in their uppermoſt part in a plane
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Superficies: for making ſuch Figures of ſome Matter
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cally as grave as the water, putting them into the water, ſo that the
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whole Maſs be covered, it is manifeſt, that they ſhall reſt in all
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places, provided, that ſuch a Matter equall in weight to the water,
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may be exactly adjuſted: and they ſhall by conſequence, reſt or
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lie even with the Levell of the water, without making any Rampart.
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>If, therefore, in reſpect of the Matter, ſuch Figures are apt to reſt
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without ſubmerging, though deprived of the help of the Rampart,
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it is manifeſt, that they may admit ſo much encreaſe of Gravity,
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(without encreaſing their Maſſes) as is the weight of as much water
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as would be contained within the Rampart, that is made about their
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upper plane Surface: by the help of which being ſuſtained, they
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ſhall reſt afloat, but being bathed, they ſhall deſcend, having been
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made graver than the water. </
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>In Figures, therefore, that determine
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above in a plane, we may cleerly comprehend, that the Rampart
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added or removed, may prohibit or permit the deſcent: but in thoſe
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Figures that go leſſening upwards towards the top, ſome Perſons
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may, and that not without much ſeeming Reaſon, doubt whether
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the ſame may be done, and eſpecially by thoſe which terminate in a
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very acute Point, ſuch as are your Cones and ſmall Piramids. </
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ing theſe, therefore, as more dubious than the reſt, I will endeavour
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to demonſtrate, that they alſo lie under the ſame Accident of going,
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or not going to the Bottom, be they of any whatever bigneſs. </
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<
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>Let
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therefore the Cone be A B D, made of a matter
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ſpecifically as grave as the water; it is manifeſt
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that being put all under water, it ſhall reſt in
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all places (alwayes provided, that it ſhall weigh
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exactly as much as the water, which is almoſt
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impoſſible to effect) and that any ſmall weight
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being added to it, it ſhall ſink to the bottom:
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but if it ſhall deſcend downwards gently, I ſay,
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that it ſhall make the Rampart E S T O, and
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that there ſhall ſtay out of the water the point A S T, tripple in
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height to the Rampart E S: which is manifeſt, for the Matter of the </
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