Galilei, Galileo, Mechanics, 1665

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="070/01/017.jpg" pagenum="287"/>
              of the Members and Muſcles, and as we uſe to ſay, by Force of
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              Armes, beſides the extern Weight, we are to lift up the Weight of
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              our own Armes, in which greater pains is required. </s>
              <s>Conclude we,
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              therefore, that this upper Pulley doth not bring any Facility to the
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              Force ſimply conſidered, but onely to the manner of applying it:
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              but if we ſhall make uſe of the like Machine
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                <figure id="id.070.01.017.1.jpg" xlink:href="070/01/017/1.jpg" number="12"/>
                <lb/>
              in another manner, as we are now about to
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              declare; we may raiſe the Weight with di­
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              minution of Forces: For let the Pulley
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              B D C be voluble about the Center E placed
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              in it's Frame B L C, at which hang the
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              Grave G; and let the Rope A B D C F
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              paſſe about the Pulley; of which let the end
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              A be faſtned to ſome fixed ſtay, and in the
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              other F let the Force be placed; which
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              moving to wards H ſhall raiſe the Machine
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              B L C, and conſequently the Weight G:
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              and in this operation I ſay, that the Force in
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              F is the half of the Weight ſuſtained by it.
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              </s>
              <s>For the ſaid Weight being kept to Rights by the two ^{*} Ropes A B
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                <arrow.to.target n="marg1110"/>
                <lb/>
              and F C, it is manifeſt, that the Labour is equally ſhared betwixt
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              the Force F and the Fulciment A: and more ſubtilly examining the
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              nature of this Inſtrument, if we but continue forth the Diameter
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              B E C, we ſhall ſee a Leaver to be made, at the midſt of which, that
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              is at the point E, the Grave doth hang, and the Fulciment cometh
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              to be at the end B, and the Force in the Term C: whereupon, by
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              what hath been above demonſtrated, the Force ſhall have the ſame
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              proportion to the Weight, that the Diſtance E B hath to the Di­
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              ſtance; Therefore it ſhall be the half of the ſaid Weight: And
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              becauſe the Force riſing towards A, the Pulley turneth round,
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              therefore that Reſpect or Conſtitution which the Fulciment B and
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              Center E, on which the Weight and Term C, in which the Force
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              is employed do depend, ſhall not change all the while; but yet in
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              the Circuinduction the Terms B and C happen to vary in number,
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              but not in vertue, others and others continually ſucceeding in their
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              place, whereby the Leaver B C cometh to be perpetuated. </s>
              <s>And
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              here (as hath been done in the other Inſtruments, and ſhall be in
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              thoſe that follow) we will not paſſe without conſidering how that
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              the journey that the Force maketh, is double to the Moment of the
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              Weight. </s>
              <s>For in caſe the Weight ſhall be moved ſo far, till that
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              the Line B C come to arrive with it's points B and C, at the points
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              A and F, it is neceſſary that the two equal Ropes be diſtended in
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              one ſole Line F H, and conſequently, when the Weight ſhall have
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              aſcended along the Intervall B A, the Force ſhall have been moved
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              twice as far, that is, from
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              unto H. </s>
              <s>Then conſidering that the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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