Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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<
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>COROLLARY
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A
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Rule to
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librate
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S
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olids in
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the water.</
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It followes, moreover, that a Solid leſs grave than the water, being put
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into a Veſſell of any imaginable greatneſs, and water being circumfuſed
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about it to ſuch a height, that as much water in Maſs, as is the part of
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the Solid ſubmerged, doth/> weigh abſolutely as much as the whole Solid;
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it ſhall by that water be juſtly ſuſtained, be the circumfuſed Water in
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quantity greater or leſſer.
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>For, if the Cylinder or Priſme M, leſs grave than the water,
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v.
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<
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>gra.
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in Subſequiteriall proportion, ſhall be put into the
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ous Veſſell A B C D, and the water raiſed about it, to three
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quarters of its height, namely, to its Levell A D: it ſhall be ſuſtained
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and exactly poyſed in
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librium.
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The ſame will
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pen, if the Veſſell E N S F
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were very ſmall, ſo, that
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tween the Veſſell and the
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lid M, there were but a very
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narrow ſpace, and only capable of ſo much water, as the hundredth
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part of the Maſs M, by which it ſhould be likewiſe raiſed and erected,
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as before it had been elevated to three fourths of the height of the
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Solid: which to many at the firſt ſight, may ſeem a notable Paradox,
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and beget a conceit, that the Demonſtration of theſe effects, were
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ſophiſticall and fallacious: but, for thoſe who ſo repute it, the
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periment is a means that may fully ſatisfie them. </
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<
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>But he that ſhall
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but comprehend of what Importance Velocity of Motion is, and how
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it exactly compenſates the defect and want of Gravity, will ceaſe to
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wonder, in conſidering that at the elevation of the Solid M, the great
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Maſs of water A B C D abateth very little, but the little Maſs of
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water E N S F decreaſeth very much, and in an inſtant, as the Solid
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M before did liſe, howbeit for a very ſhort ſpace: Whereupon the
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Moment, compounded of the ſmall Abſolute Gravity of the water
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E N S F, and of its great Velocity in ebbing, equalizeth the Force and
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and Moment, that reſults from the compoſicion of the immenſe
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vity of the water A B C D, with its great ſlowneſſe of ebbing;
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ſince that in the Elevation of the Sollid M, the abaſement of the leſ</
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ſer water E S, is performed juſt ſo much more ſwiftly than the great
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Maſs of water A C, as this is more in Maſs than that which we thus
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demonſtrate.</
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T
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he proportion
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according to
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which water
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ſeth and falls in
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different Veſſels
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at the
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on and
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on of
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s
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olids.</
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>In the riſing of the Solid M, its elevation hath the ſame proportion
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to the circumfuſed water E N S F, that the Surface of the ſaid water,
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hath to the Superficies or Baſe of the ſaid Solid M; which Baſe hath
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the ſame proportion to the Surface of the water A D, that the </
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