Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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Priſmes and
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Cylinders
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ving the ſame
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Baſe, are to one
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another as their
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heights.</
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>THEOREME.
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All Figures
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of all Matters,
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float by hep of
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the Rampart
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pleniſhed with
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Air, and ſome
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but only touch
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the water.</
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All ſorts of Figures of whatſoever Matter, albeit more
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grave than the Water, do by Benefit of the ſaid
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part, not only float, but ſome Figures, though of the
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graveſt Matter, do ſtay wholly above Water, wetting
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only the inferiour Surface that toucheth the Water.
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>And theſe ſhall be all Figures, which from the inferiour Baſe up
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wards, grow leſſer and leſſer; the which we ſhall exemplifie for
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this time in Piramides or Cones, of which Figures the paſſions sre
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common. </
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<
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>We will demonſtrate therefore, that,</
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It is poſſible to form a Piramide, of any whatſoever Matter propoſed,
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which being put with its Baſe upon the Water, reſts not only
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ſubmerging, but without wetting it more then its Baſe.
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>For the explication of which it is requiſite, that we firſt
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the ſubſequent Lemma, namely, that,</
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>LEMMA II.</
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Solids whoſe Maſſes anſwer in proportion contrarily to
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their Specificall Gravities, are equall in Abſolute
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Gravities.
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Solids whoſe
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Maſſes are in
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contrary
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portion to their
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Specifick
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vities, are equall
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in abſolute Gra
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vity.</
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>Let A C and B be two Solids, and let the Maſs A C be to the
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Maſs B, as the Specificall Gravity of the Solid B, is to the Speci
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ficall Gravity of the Solid A C: I ſay, the Solids A C and B are
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equall in abſolute weight, that is, equally grave. For
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if the Maſs A C be equall to the Maſs B, then, by the
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Aſſumption, the Specificall Gravity of B, ſhall be
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quall to the Specificall Gravity of A C, and being
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quall in Maſs, and of the ſame Specificall Gravity
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ſhall abſolutely weigh one as much as another. </
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<
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>But
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if their Maſſes ſhall be unequall, let the Maſs A C be greater, and in it
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take the part C, equall to the Maſs B. And, becauſe the Maſſes B
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and C are equall; the Abſolute weight of B, ſhall have the ſame
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portion to the Abſolute weight of C, that the Specificall Gravity of
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B, hath to the Specificall Gravity of C; or of C A, which is the
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ſame
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in ſpecie
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: But look what proportion the Specificall Gravity of
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B, hath to the Specificall Gravity of C A, the like proportion, by the
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Aſſumption, hath the Maſs C A, to the Maſs B; that is, to the Maſs C: </
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