Archimedes
,
Natation of bodies
,
1662
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the Right Line R Y in Y. </
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<
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ſhall demonſtrate G H to be double
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to H I, as it hathbeen demonſtra
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ted, that O G is double to G X.
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</
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<
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>Then draw G
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touching the Section
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A G Q L in G; and G C perpen di
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cular to B D; and drawing a Line
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from A to I, prolong it to
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Now
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A I ſhall be equall to I
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and
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A Q parallel to G
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It is to be
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demonſtrated, that the Portion being
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demitted into the Liquid, and inclined, ſo, as that its Baſe touch
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the Liquid, it ſhall ſtand ſo incli
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ned, as that its Axis ſhall make
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an Angle with the Surface of the
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Liquid leſſe than the Angle
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and its Baſe ſhall not in the leaſt
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touch the Liquids Surface. </
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<
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>For
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let it be demitted into the Liquid,
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and let it ſtand, ſo, as that its Baſe
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do touch the Surface of the Liquid
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in one Point only: and the Portion
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being cut thorow the Axis by a
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Plane erect unto the Surface of the Liquid, let the Section of
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the Portion be A N Z L, the Section
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of a Rightangled Cone; that of
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the Surface of the Liquid A Z; and
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the Axis of the Portion and Dia
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meter of the Section B D; and let
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B D be cut in the Points K and R
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as hath been ſaid above; and draw
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N F parallel to A Z, and touching
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the Section of the Cone in the Point
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N; and N T parallel to B D; and
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N S perpendicular to the ſame. </
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<
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>Be
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cauſe, now, that the Portion is in Gravity to the Liquid, as
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the Square made of
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is to the Square B D; and ſince that as the
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Portion is to the Liquid in Gravity, ſo is the Square N T to the
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Square B D, by the things that have been ſaid; it is plain, that
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N T is equall to the Line
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: And, therefore, alſo, the Portions
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A N Z and A G Q are equall. </
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<
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>And, ſeeing that in the Equall and
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Like Portions A G Q L and A N Z L; there are drawn from the
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Extremities of their Baſes, A Q and A Z which cut off equall Porti
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ons: It is obvious, that with the Diameters of the Portions they </
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