Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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pieces, according to the Lines E F, G H,
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&c.
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making ſeven Segments,
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we muſt adde to the twenty ſix Palmes of the circuit of the whole
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Board, ſeventy others; whereupon the eight little pieces ſo cut and
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ſeperated, have to cut ninty ſix Palmes of water. </
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>And, if moreover,
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we cur each of the ſaid pieces into five parts,
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ducing them into Squares, to the circuit of ninty
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ſix Palmes, with four cuts of eight Palmes apiece;
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we ſhall adde alſo ſixty four Palmes, whereupon
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the ſaid Squares to deſcend in the water, muſt
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divide one hundred and ſixty Palmes of water,
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but the Reſiſtance is much greater than that of
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twenty ſix; therefore to the leſſer Superficies,
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we ſhall reduce them, ſo much the more eaſily
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will they float: and the ſame will happen in all
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other Figures, whoſe Superficies are ſimular amongſt themſelves, but
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different in bigneſs: becauſe the ſaid Superficies, being either
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ſhed or encreaſed, always diminiſh or encreaſe their Perimeters in
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ſubduple proportion; to wit, the Reſiſtance that they find in
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trating the water; therefore the little pieces gradually ſwim, with more
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and more facility as their breadth is leſſened.</
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This is manifeſt; for keeping ſtill the ſame height of the Solid, with
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the ſame proportion as the Baſe encreaſeth or deminiſheth, doth the ſaid
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Solid alſo encreaſe or diminiſh; whereupon the Solid more diminiſhing
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than the Circuit, the Cauſe of Submerſion more diminiſheth than the Cauſe
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of Natation: And on the contrary, the Solid more encreaſing than the
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Circuit, the Cauſe of Submerſion encreaſeth more, that of Natation
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leſs.
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>And this may all be dedueed out of the Doctrine of
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Ariſtotle
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gainſt his own Doctrine.</
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<
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>Laſtly, to that which we read in the latter part of the Text, that
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is to ſay, that we muſt compare the Gravity of the Moveable with
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the Reſiſtance of the Medium againſt Diviſion, becauſe if the force of
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the Gravity exceed the Reſiſtance of the
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Medium,
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the Moveable will
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deſcend, if not it will float. </
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>I need not make any other anſwer,
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but that which hath been already delivered; namely, that its not
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the Reſiſtance of abſolute Diviſion, (which neither is in Water nor
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Air) but the Gravity of the
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Medium
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that muſt be compared with the
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Gravity of the Moveables; and if that of the
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Medium
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be greater, the
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Moveable ſhall not deſcend, nor ſo much as make a totall Submerſion,
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but a partiall only: becauſe in the place which it would occupy in
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the water, there muſt not remain a Body that weighs leſs than a like
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quantity of water: but if the Moveable be more grave, it ſhall
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cend to the bottom, and poſſeſs a place where it is more conformable </
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