Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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>COROLARY
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Amongſt Cones
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of the ſame Baſe,
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thoſe of leaſt
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titude ſhall ſink
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the leaſt.</
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That making upon the ſame Baſis, a Cone of a leſs Altitude, it ſhall be
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alſo leſs grave, and ſhall ſo much the more reſt without Submerſion.
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>COROLARY II.</
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It is manifeſt, alſo, that one may make Cones and Piramids of any Matter
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whatſoever, more grave than the water, which being put into the
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water, with the Apix or Point downwards, reſt without Submerſion.
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There may be
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Cones and
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mides of any
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Matter, which
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demitted with
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the Point
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wards do float
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top.</
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>Becauſe if we reaſſume what hath been above demonſtrated,
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Priſms and Cylinders, and that on Baſes equall to thoſe of the
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ſaid Cylinders, we make Cones of the ſame Matter, and
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times as high as the Cylinders, they ſhall reſt afloat, for that in Maſs
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and Gravity they ſhall be equall to thoſe Cylinders, and by having
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their Baſes equall to thoſe of the Cylinders, they ſhall leave equall
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Maſſes of Air included within the Ramparts. </
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>This, which for
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ple ſake hath been demonſtrated, in Priſms, Cylinders, Cones and
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Piramids, might be proved in all other Solid Figures, but it would
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require a whole Volume (ſuch is the multitude and variety of their
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Symptoms and Accidents) to comprehend the particuler demonſtration
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of them all, and of their ſeverall Segments: but I will to avoid prolixity
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in the preſent Diſcourſe, content my ſelf, that by what I have declared
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every one of ordinary Capacity may comprehend, that there is not
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any Matter ſo grave, no not Gold it ſelf, of which one may not form
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all ſorts of Figures, which by vertue of the ſuperiour Air adherent to
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them, and not by the Waters Reſiſtance of Penetration, do remain
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afloat, ſo that they ſink not. </
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>Nay, farther, I will ſhew, for removing
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that Error, that,</
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>THEOREME
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A Piramide or
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Cone, demitted
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with the Point
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downwards ſhal
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ſwim, with its
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Baſe downward
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ſhall ſink.</
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A Piramide or Cone put into the Water, with the Point
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downward ſhall ſwimme, and the ſame put with the
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Baſe downwards ſhall ſinke, and it ſhall be impoſſible
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to make it float.
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>Now the quite contrary would happen, if the difficulty of Pene
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trating the water, were that which had hindred the deſcent, for
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that the ſaid Cone is far apter to pierce and penetrate with its ſharp
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Point, than with its broad and ſpacious Baſe.</
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>And, to demonſtrate this, let the Cone be
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A B C,
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twice as grave
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as the water, and let its height be tripple to the height of the Rampart
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D A E C
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: I ſay, firſt, that being put lightly into the water with the </
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