Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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241 - 270
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040/01/1103.jpg
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Maſſe of the Solid depreſſed, namely of
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H I K, being equall to the only part E I K,
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which is contained under the firſt Levell
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E F G. </
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>Which is manifeſt, becauſe if
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the Solid H I K be taken out, the Water
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I G ſhall return into the place occupied by
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the Maſs E I K, where it was continuate
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fore the ſubmerſion of the Priſme. </
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<
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>And
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the Maſs L G being equall to the Maſs
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E K: adde thereto the Maſs E N, and it
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ſhall be the whole Maſs E M, compoſed of the parts of the Priſme E N,
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and of the Water N F, equall to the whole Solid H I K: And,
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fore, the Maſs L G ſhall have the ſame proportion to E M, as to the
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Maſs H I K: But the Maſs L G hath the ſame proportion to the Maſs
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E M, as the Surface L M hath to the Surface M H: Therefore it is
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nifeſt, that the Maſs of Water repulſed L G, is in proportion to the Maſs
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of the Solid ſubmerged H I K; as the Surface L M, namely, that of the
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Water ambient about the Sollid, to the whole Surface H M, compounded
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of the ſaid ambient water, and the Baſe of the Priſme H N. </
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<
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>But if we
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ſuppoſe the firſt Levell of the Water the according to the Surface H M,
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and the Priſme allready ſubmerged H I K; and after to be taken out and
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raiſed to E A O, and the Water to be faln from the firſt Levell H L M as
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low as E F G; It is manifeſt, that the Priſme E A O being the ſame with
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H I K, its ſuperiour part H O, ſhall be equall to the inferiour E I K:
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and remove the common part E N, and, conſequently, the Maſs of the
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Water L G is equall to the Maſs H O; and, therefore, leſs than the
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Solid, which is without the Water, namely, the whole Priſme E A O, to
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which likewiſe, the ſaid Maſs of Water abated L G, hath the ſame
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tion, that the Surface of the Waters circumfuſed L M hath to the ſame
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circumfuſed Surface, together with the Baſe of the Priſme A O: which
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hath the ſame demonſtration with the former caſe above.
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And from hence is inferred, that the Maſs of the Water, that riſeth in
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the immerſion of the Solid, or that ebbeth in elevating it, is not equall to
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all the Maſs of the Solid, which is ſubmerged or elevated, but to that
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part only, which in the immerſion is under the firſt Levell of the Water,
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and in the elevation remaines above the firſt Levell: Which is that
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which was to be demonſtrated. </
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<
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>We will now purſue the things that
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remain.
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<
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>And firſt we will demonſtrate that,</
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