Galilei, Galileo
,
Discourse concerning the natation of bodies
,
1663
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the Gravity of the water, yet the caſe ſtands ſo, that the Rampart
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doth alſo contract it ſelf, and the Cylinder contained in it doth
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miniſh. </
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<
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>Nevertheleſs it ſhall be demonſtrated, how that the Cone
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A B D
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being of any ſuppoſed bigneſſe, and made at the firſt of a
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Matter exactly equall in Gravity to the Water, if there may
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be affixed to it ſome Weight, by means of which it may deſcend to
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the bottom, when ſubmerged under water, it may alſo by vertue of
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the Rampart ſtay above without ſinking.</
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<
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>Let, therefore, the Cone
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A B D
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be of any ſuppoſed greatneſſe,
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and alike in ſpecificall Gravity to the water. </
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<
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>It is manifeſt, that
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being put lightly into the water, it ſhall reſt without deſcending;
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and it ſhall advance above water, the Point
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AS T,
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tripple in height to the height of the
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Rampart
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E S
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: Now, ſuppoſe the Cone
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A B D
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more depreſſed, ſo that it advance above
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ter, only the Point
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A I R,
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higher by half than
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the Point
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A S T,
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with the Rampart about it
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C I R N.
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And, becauſe, the Cone
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A B D
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is
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to the Cone
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A I R,
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as the cube of the Line
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S T
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is to the cube of the Line
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I R,
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but the
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der
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E S T O,
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is to the Cylinder
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C I R N,
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as the Square of
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S T
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to
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the Square of
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I R,
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the Cone
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A S T
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ſhall be Octuple to the Cone
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<
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A I R,
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and the Cylinder
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E S T O,
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quadruple to the Cylinder
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C I R N
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:
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But the Cone
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A S T,
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is equall to the Cylinder E
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S T O
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: Therefore,
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the Cylinder
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C I R N,
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ſhall be double to the Cone
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A I R:
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and the
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water which might be contained in the Rampart
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C I R N,
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would be
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double in Maſs and in Weight to the Cone
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A I R,
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and, therefore,
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would be able to ſuſtain the double of the Weight of the Cone
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AIR
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:
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Therefore, if to the whole Cone
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A B D,
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there be added as much
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Weight as the Gravity of the Cone
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A I R,
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that is to ſay, the eighth
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part of the weight of the Cone
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A S T,
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it alſo ſhall be ſuſtained by
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the Rampart
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C I R N,
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but without that it ſhall go to the bottome:
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the Cone
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A B D,
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being, by the addition of the eighth part of the
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weight of the Cone
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A S T,
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made ſpecifically more grave than the
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water. </
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<
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>But if the Altitude of the Cone
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A I R,
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were two thirds
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of the Altitude of the Cone
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A S T,
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the Cone
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A S T
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would be to the
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Cone
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A I R,
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as twenty ſeven to eight; and the Cylinder
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E S T O,
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to
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the Cylinder
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C I R N,
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as nine to four, that is, as twenty ſeven to
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twelve; and, therefore, the Cylinder
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C I R N,
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to the Cone
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A I R,
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as twelve to eight; and the exceſs of the Cylinder
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C I R N,
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above
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the Cone
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A I R,
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to the Cone
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A S T,
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as four to twenty ſeven:
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fore if to the Cone
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A B D
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be added ſo much weight as is the four
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twenty ſevenths of the weight of the Cone
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A S T,
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which is a little
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more then its ſeventh part, it alſo ſhall continue to ſwimme, and </
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