Galilei, Galileo, Mechanics, 1665

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="070/01/012.jpg" pagenum="282"/>
              Axis, ſo that they ſhall conſtantly maintain alike Site and Poſition
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              in reſpect of the Diſtances B A and A C, the Motion ſhall be
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              perpetuated, the Weight I deſcending, and forcing the other G
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              to aſcend. </s>
              <s>Where we are to obſerve the neceſſity of be-laying
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              or winding the Rope about the Wheel, that ſo the Weight I may
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              hang according to the Line that is tangent to the ſaid Wheel: for
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              if one ſhould ſuſpend the ſaid Weight, ſo as that it did hang by the
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              point F, cutting the ſaid Wheel, as is ſeen along the Line F N M,
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              the Motion would ceaſe, the Moment of the Weight M being di­
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              miniſhed; which would weigh no more then if it did hang by the
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              point N: becauſe the Diſtance of its Suſpenſion from the Center
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              A, cometh to be determined by the Line A N, which falleth per­
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              pendicularly upon the Rope F M, and is no longer terminated by
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              the Semidiameter of the Wheel A F, which falleth at unequall
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              Angles upon the ſaid Line F M. </s>
              <s>A violence therefore being offered
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              in the Circumference of the Wheel by a Grave and Exanimate
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              Body that hath no other
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              Impetus
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              then that of Deſcending, it is
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              neceſſary that it be ſuſtained by a Line that is contingent with
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              the Wheel, and not by one that cutteth it. </s>
              <s>But if in the ſame
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              Circumference an Animate Force were employed, that had a Mo­
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              ment or Faculty of making an
                <emph type="italics"/>
              Impulſe
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              on all ſides, the work might
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              be effected in any whatever place of the ſaid Circumference. </s>
              <s>And
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              thus being placed in F, it would draw up the Weight by turning
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              the Wheel about, pulling not according to the Line F M down­
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              wards, but ſide-waies according to the Contingent Line F L, which
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              maketh a Right Angle, with that which is drawn from the Center
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              A unto the point of Contact F: ſo, that if in this manner one do
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              meaſure the Diſtance from the Center A to the Force placed in
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              F, according to the Line A F perpendicular to F L, along which
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              the
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              is made, a man ſhall not in any part have altered the
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              uſe of the ordinary Leaver. </s>
              <s>And we muſt note, that the ſame
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              would be poſſible to be done likewiſe with an Exanimate Force,
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              in caſe that a way were found out to cauſe that its Moment might
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              make Impulſe in the point F, drawing according to the Contingent
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              Line F L: which would be done by adjoyning beneath the Line F L
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              a turning Pulley, making the Rope wound about the Wheel to
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              paſſe along upon it, as it is ſeen to do by the Line F L X, ſuſpending
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              at the end thereof the Weight X equall to the other I, which ex­
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              erciſing its Force according to the Line F L, ſhall alwaies keep a
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              Diſtance from the Center A equall unto the Semidiameter of the
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              Wheel. </s>
              <s>And from what hath been declared we will gather for a
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              Concluſion, That in this Inſtrument the Force hath alwaies the
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              ſame proportion to the Weight, as the Semidiameter of the Axis
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              or Barrell hath to the Semidiameter of the Wheel.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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