Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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<
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>PROP. IV. THEOR. IV.</
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Solid Magnitudes that are lighter than the Liquid,
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being demitted into the ſetled Liquid, will not total
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ly ſubmerge in the ſame, but ſome part thereof will
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lie or ſtay above the Surface of the Liquid.
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<
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>NIC. </
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<
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>In this fourth
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Propoſition
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it is concluded, that every Body or Solid that is
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lighter (as to Specifical Gravity) than the
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L
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iquid, being put into the
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L
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iquid, will not totally ſubmerge in the ſame, but that ſome part of it
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will ſtay and appear without the
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L
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iquid, that is above its Surface.</
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<
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>For ſuppoſing, on the contrary, that it were poſſible for a Solid
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more light than the Liquid, being demitted in the Liquid to ſub
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merge totally in the ſame, that is, ſo as that no part thereof re
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maineth above, or without the ſaid Liquid, (evermore ſuppoſing
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that the Liquid be ſo conſtituted as that it be not moved,) let us
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imagine any Plane produced thorow the Center of the Earth, tho
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row the Liquid, and thorow that Solid Body: and that the Surface
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of the Liquid is cut by this Plane according to the Circumference
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A
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B
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G, and the Solid
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B
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ody according to the Figure R; and let the
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Center of the Earth be K. </
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<
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>And let there be imagined a Pyramid
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that compriſeth the Figure
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R, as was done in the pre.
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</
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<
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>cedent, that hath its Ver
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tex in the Point K, and let
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the Superficies of that
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Pyramid be cut by the
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Superficies of the Plane
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A
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B
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G, according to A K
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and K
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B
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. </
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<
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>And let us ima
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gine another Pyramid equal and like to this, and let its Superficies
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be cut by the Superficies A
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B
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G according to K
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B
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and K
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G
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; and let
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the Superficies of another Sphære be deſcribed in the Liquid, upon
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the Center K, and beneath the Solid R; and let that be cut by the
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ſame Plane according to
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X
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O P. And, laſtly, let us ſuppoſe ano
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ther Solid taken ^{*} from the Liquid, in this ſecond Pyramid, which
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let be H, equal to the Solid R. </
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<
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>Now the parts of the Liquid, name
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ly, that which is under the Spherical Superficies that proceeds ac
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cording to the Superficies or Circumference
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X
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O, in the firſt Py
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ramid, and that which is under the Spherical Superficies that pro
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ceeds according to the Circumference O P, in the ſecond Pyramid,
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are equijacent, and contiguous, but are not preſſed equally; for </
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