Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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Cone weighing equally with the water, the part ſubmerged S B D T,
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becomes indifferent to move downwards or upwards; and the Cone
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A S T,
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being equall in Maſs to the water that would be contained in
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the concave of the Rampart
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E S T O,
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ſhall be alſo equall unto it in
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Gravity: and, therefore, there ſhall be a perfect
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Equilibrium,
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and,
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conſequently, a Reſt. </
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<
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>Now here ariſeth a doubt, whether the
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Cone
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A B D
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may be made heavier, in ſuch ſort, that when it is put
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wholly under water, it goes to the bottom, but yet not in ſuch ſort,
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as to take from the Rampart the vertue of ſuſtaining it that it ſink not,
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and, the reaſon of the doubt is this: that although at ſuch time as
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the Cone
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A B D
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is ſpecifically as grave as the water, the Rampart
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E S T O
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ſuſtaines it, not only when the point
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A S T
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is tripple in
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height to the Altitude of the Rampart
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E S,
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but alſo when a leſſer
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part is above water; [for although in the Deſcent of the Cone the
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Point
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A S T
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by little and little diminiſheth, and ſo likewiſe the
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Rampart
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E S T O,
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yet the Point diminiſheth in
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greater proportion than the Rampart, in that
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it diminiſheth according to all the three
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menſions, but the Rampart according to two
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only, the Altitude ſtill remaining the ſame;
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or, if you will, becauſe the Cone
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S T
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goes
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miniſhing, according to the proportion of the
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cubes of the Lines that do ſucceſſively become
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the Diameters of the Baſes of emergent Cones,
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and the Ramparts diminiſh according to the proportion of the
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Squares of the ſame Lines; whereupon the proportions of the Points
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are alwayes Seſquialter of the proportions of the Cylinders,
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tained within the Rampart; ſo that if, for Example, the height of
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the emergent Point were double, or equall to the height of the
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Rampart, in theſe caſes, the Cylinder contained within the
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part, would be much greater than the ſaid Point, becauſe it would be
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either ſeſquialter or tripple, by reaſon of which it would perhaps
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ſerve over and above to fuſtain the whole Cone, ſince the part
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merged would no longer weigh any thing;] yet, nevertheleſs, when
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any Gravity is added to the whole Maſs of the Cone, ſo that alſo the
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part ſubmerged is not without ſome exceſſe of Gravity above the
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Gravity of the water, it is not manifeſt, whether the Cylinder
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tained within the Rampart, in the deſcent that the Cone ſhall make,
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can be reduced to ſuch a proportion unto the emergent Point, and to
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ſuch an exceſſe of Maſs above the Maſs of it, as to compenſate the
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exceſſe of the Cones Specificall Gravity above the Gravity of the
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ter: and the Scruple ariſeth, becauſe that howbeit in the deſcent
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made by the Cone, the emergent Point
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A S T
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diminiſheth, whereby
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there is alſo a diminution of the exceſs of the Cones Gravity above </
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