Galilei, Galileo, Mechanics, 1665

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      <text>
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          <chap>
            <p type="main">
              <s>
                <pb xlink:href="070/01/019.jpg" pagenum="289"/>
              Weight G hanging at
                <emph type="italics"/>
              F,
                <emph.end type="italics"/>
              it hath been already demonſtrated, that
                <lb/>
              the ſaid
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orce D hath to the Weight ſo by it ſuſtained, that ſame
                <lb/>
              proportion which the Diſtance
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              C hath to the Diſtance C D:
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              Which is ſubduple proportion: Therefore the Moment D is ſub­
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              duple to the Moment of half of the Weight G ſuſtained by it:
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              Wherefore it followeth, that it is the fourth part of the Moment
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              of the whole Weight. </s>
              <s>And in the ſame manner the ſame thing is
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              demonſtrated, of the Moment
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              ; and it is but reaſonable, that the
                <lb/>
              Weight G being ſuſtained by the four points, A,
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              C, D, each of
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              them ſhould feel an equall part of the Labour.</s>
            </p>
            <p type="main">
              <s>Let us come now to apply this Conſideration to Pullies, and let
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              the Weight X be ſuppoſed to hang at the two Pullies A B and D E
                <lb/>
              entwining about them, and about the uppermoſt Pulley G H, the
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              Rope, as we ſee, I D E H G A B, ſuſtaining the whole Machine in
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              the point K. </s>
              <s>Now I ſay, that placing the Force in L, it ſhall be able
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              to ſuſtain the Weight X, if ſo be, it be equal to the fourth part of
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              it. </s>
              <s>For if we do imagine the two Diameters D E and A B, and the
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              Weights hanging at the middle points F and C, we ſhall have two
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              Leavers like to thoſe before deſcribed, the Fulciments of which an­
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              ſwer to the points D and A. </s>
              <s>Whereupon the Force placed in B,
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                <figure id="id.070.01.019.1.jpg" xlink:href="070/01/019/1.jpg" number="15"/>
                <lb/>
              or if you will, in L, ſhall be able to ſu­
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              ſtain the Weight X, being the fourth
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              part of it: And if we adde another Pul­
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              ley above the other two, making the
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              Rope or Cord to paſs along L M N, trans­
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              ferring the Force L into N, it ſhall be
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              able to bear the ſame Weight gravitating
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              downwards, the upper Pulley neither aug­
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              menting or diminiſhing the Force, as hath
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              been declared. </s>
              <s>And we will likewiſe
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              note, that to make the: Weight aſcend the
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                <arrow.to.target n="marg1112"/>
                <lb/>
              four Ropes B L, E H, D I, and A G
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              ought to paſs, whereupon the Mover will
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              be to begin, as much as thoſe Ropes are
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              long; and yet nevertheleſs the Weight
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              ſhall move but only as much as the length
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              of one of them: So that we may ſay by
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              way of advertiſement, and for confirma­
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              tion of what hatn been many times ſpo­
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              ken, namely, that look with what proportion the Labour of the
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                <arrow.to.target n="marg1113"/>
                <lb/>
              Mover is diminiſhed, the length of the Way, on the contrary, is
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              encreaſed with the ſame proportion</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1112"/>
              * Or four parts
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              of the ſame Rope</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1113"/>
              * The word
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              Gy­
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              rilla
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              ſignifieth a
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              Shiver, Rundle,
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              or ſmall Wheel
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              of a Pulley, tran­
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              ſlated by we
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              ſometimes Pul­
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              ley, ſometimes
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              Nut or Girill.</s>
            </p>
            <p type="main">
              <s>But if we would encreaſe the Force in ſexcuple proportion, it
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              will be requiſite that we adjoyn another ^{*} ſmall Pulley or Gyrill
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              to the inferiour Pulley which that you may the better underſtand </s>
            </p>
          </chap>
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    </archimedes>
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