Galilei, Galileo, Discourse concerning the natation of bodies, 1663

Table of figures

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              <s>
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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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                <emph type="italics"/>
              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. </s>
              <s>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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                <emph type="italics"/>
              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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                <figure id="fig278" number="17"/>
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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 </s>
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