Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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<
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>LEMMA I.</
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The abſolute Gravities of Solids, have a proportion com-
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pounded of the proportions of their ſpecificall Gravities,
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and of their Maſſes.
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The abſolute
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Gravity of
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lids, are in a
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portion
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pounded of their
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Specifick
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ties, and of their
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Maſſes.</
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>Let A and B be two Solids. </
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<
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>I ſay, that the Abſolute Gravity
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of A, hath to the Abſolute Gravity of B, a proportion
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pounded of the proportions of the ſpecificall Gravity of A, to
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the Specificall Gravity of B, and of the Maſs
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A to the Maſs B. </
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<
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>Let the Line D have the
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ſame proportion to E, that the ſpecifick
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Gravity of A, hath to the ſpecifick Gravity
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of B; and let E be to F, as the Maſs A to the
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Maſs B: It is manifeſt, that the proportion
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of D to F, is compounded of the proportions
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D and E; and E and F. </
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<
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>It is requiſite,
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therefore, to demonſtrate, that as D is to F, ſo the abſolute Gravity
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of A, is to the abſolute Gravity of B. </
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<
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>Take the Solid C, equall in
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Maſs to the Solid A, and of the ſame Gravity
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in ſpecie
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with the Solid
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B. Becauſe, therefore, A and C are equall in Maſs, the abſolute
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Gravity of A, ſhall have to the abſolute Gravity of C, the ſame
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portion, as the ſpecificall Gravity of A, hath to the ſpecificall Gravity
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of C, or of B, which is the ſame
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in ſpecie
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; that is, as D is to E. And,
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cauſe, C and B are of the ſame Gravity
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in ſpecie,
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it ſhall be, that as
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the abſolute weight of C, is to the abſolute weight of B, ſo the Maſs
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C, or the Maſs A, is to the Maſs B; that is, as the Line E to the Line
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F. </
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<
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>As therefore, the abſolute Gravity of A, is to the abſolute
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Gravity of C, ſo is the Line D to the Line E: and, as the abſolute
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Gravity of C, is to the abſolute Gravity of B, ſo is the Line E to the
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Line F: Therefore, by Equality of proportion, the abſolute
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vity of A, is to the abſolute Gravity of B, as the Line D to the
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Line F: which was to be demonſtrated. </
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<
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>I proceed now to
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ſtrate, how that,</
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