Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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Priſme, or Cylinder, to wit, that hath its two flat Superficies,
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our and inferiour, alike and equall, and at Right Angles with the
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ther laterall Superficies, and let its thickneſs I O be equall to the
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greateſt Altitude of the Banks of water: I ſay, that if it be put upon
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the water, it will not ſubmerge: for the Altitude
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A I being equall to the Altitude I O, the
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of the Air A B C I ſhall be equall to the Maſs
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the Solid C I O S: and the whole Maſs A O S
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double to the Maſs I S; And ſince the
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of the Air A C, neither encreaſeth nor
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niſheth the Gravity of the Maſs I S, and the Solid I S was
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double in Gravity to the water; Therefore as much water as
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Maſs ſubmerged A O S B, compounded of the Air A I C B, and of
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the Solid I O S C, weighs juſt as much as the ſame ſubmerged Maſs
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A O S B: but when ſuch a Maſs of water, as is the ſubmerged part
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the Solid, weighs as much as the ſaid Solid, it deſcends not farther,
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but reſteth, as by
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(a) Archimedes,
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and above by us, hath been de>
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monſtrated: Therefore, I S ſhall deſcend no farther, but ſhall reſt.
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And if the Solid I S ſhall be Seſquialter in Gravity to the water, it
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ſhall float, as long as its thickneſs be not above twice as much as the
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greateſt Altitude of the Ramparts of water, that is, of A I. </
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<
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>For I S
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being Seſquialter in Gravity to the water, and the Altitude O I
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being double to I A, the Solid ſubmerged A O S B, ſhall be alſo
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Seſquialter in Maſs to the Solid I S. </
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>And becauſe the Air A C,
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neither increaſeth nor diminiſheth the ponderoſity of the Solid I S:
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Therefore, as much water in quantity as the ſubmerged Maſs AOSB,
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weighs as much as the ſaid Maſs ſubmerged: And, therefore, that
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Maſs ſhall reſt. </
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>And briefly in generall.</
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Of Natation
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Lib. 1. Prop. </
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>THEOREME. VI.</
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When ever the exceſs of the Gravity of the Solid above
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the Gravity of the Water, ſhall have the ſame
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portion to the Gravity of the Water, that the
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tude of the Rampart, hath to the thickneſs of the
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Solid, that Solid ſhall not ſink, but being never ſo
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tle thicker it ſhall.
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The
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on of the
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eſt thickneſs of
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Solids, beyond
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which
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ſed they ſink.</
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<
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>Let the Solid I S be ſuperior in Gravity to the water, and of ſuch
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thickneſs, that the Altitude of the Rampart A I, be in
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on to the thickneſs of the Solid I O, as the exceſs of the
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ty of the ſaid Solid I S, above the Gravity of a Maſs of water equall
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to the Maſs I S, is to the Gravity of the Maſs of water equall to the </
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