Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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* I add the word
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ſetled, as neceſſary
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in making the Ex
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periment.</
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>NIC. </
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>In this
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Propoſition
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it is affirmed that thoſe Solid Magnitules that hap
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pen to be equal in ſpecifical Gravity with the Liquid being lefeat liber
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ty in the ſaid Liquid do ſo ſubmerge in the ſame, as that they lie or ap
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pear not at all above the Surface of the Liquid, nor yet do they go or ſink to the
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Bottom.</
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>For ſuppoſing, on the contrary, that it were poſſible for one of
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thoſe Solids being placed in the Liquid to lie in part without the
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Liquid, that is above its Surface, (alwaies provided that the ſaid
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Liquid be ſetled and undiſturbed,) let us imagine any Plane pro
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duced thorow the Center of the Earth, thorow the Liquid, and
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thorow that Solid Body: and let us imagine that the Section of the
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Liquid is the Superficies A B G D, and the Section of the Solid
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Body that is within it the Superſicies E Z H T, and let us ſuppoſe
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the Center of the Earth to be the Point K: and let the part of the
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ſaid Solid ſubmerged in the Liquid be B G H T, and let that above
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be B E Z G: and let the Solid Body be ſuppoſed to be comprized in
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a Pyramid that hath its Parallelogram Baſe in the upper Surface of
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the Liquid, and its Summity or Vertex in the Center of the Earth:
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which Pyramid let us alſo ſuppoſe to be cut or divided by the ſame
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Plane in which is the Circumference A B G D, and let the Sections
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of the Planes of the ſaid
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Pyramid be K L and
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K M: and in the Liquid
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about the Center K let
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there be deſcribed a Su
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perficies of another
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Sphære below E Z H T,
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which let be X O P;
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and let this be cut by
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the Superficies of the Plane: And let there be another Pyramid ta
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ken or ſuppoſed equal and like to that which compriſeth the ſaid
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Solid Body, and contiguous and conjunct with the ſame; and let
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the Sections of its Superficies be K M and K N: and let us ſuppoſe
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another Solid to be taken or imagined, of Liquor, contained in that
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ſame Pyramid, which let be R S C Y, equal and like to the partial
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Solid B H G T, which is immerged in the ſaid Liquid: But the
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part of the Liquid which in the firſt Pyramid is under the Super
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ficies X O, and that, which in the other Pyramid is under the Su
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perficies O P, are equijacent or equipoſited and contiguous, but
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are not preſſed equally; for that which is under the Superficies
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X O is preſſed by the Solid T H E Z, and by the Liquor that is
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contained between the two Spherical Superficies X O and L M
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and the Planes of the Pyramid, but that which proceeds accord
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ing to F O is preſſed by the Solid R S C Y, and by the Liquid </
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