Galilei, Galileo, Mechanics, 1665

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              <s>
                <pb xlink:href="070/01/018.jpg" pagenum="288"/>
              Force in
                <emph type="italics"/>
              F,
                <emph.end type="italics"/>
              that it may raiſe the Weight, muſt move upwards, which
                <lb/>
              to exanimate Movers, as being for the moſt part Grave Bodies, is al­
                <lb/>
                <figure id="id.070.01.018.1.jpg" xlink:href="070/01/018/1.jpg" number="13"/>
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              together impoſſible, or at leaſt more laborious,
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              than the making of the ſame
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orce down­
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              wards: Therefore to help this inconvenience,
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              a Remedy hath been found by adjoyning an­
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              other Nut or Pulley above, as in the adjacent
                <lb/>
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              igure is ſeen, where the Rope C E
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              hath
                <lb/>
              been made to paſs about the upper Pulley
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              G
                <lb/>
              upheld by the Hook L, ſo that the Rope paſſing
                <lb/>
              to H, and thither transferring the
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orce E, it
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              ſhall be able to move the Weight X by pulling
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              downwards, but not that it may be leſſer than
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              it was in E:
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              or the Motions of the
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orce
                <lb/>
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              H, hanging at the equal Diſtances
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              D and
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              D G of the upper Pulley, do alwaies continue
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              equal; nor doth that upper Pulley (as hath
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              been ſhewn above) come to produce any di­
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              minution in the Labour. </s>
              <s>Moreover it having been neceſſary by
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              the addition of the upper Pulley to introduce the Appendix B, by
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              which it is ſuſtained, it will prove of ſome benefit to us to raiſe
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              the other A, to which one end of the Rope was faſtned, transferring
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              it to a Ring annexed to the lower part of the
                <emph type="italics"/>
              F
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              rame of the upper
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              Pulley, as we ſee it done in M. </s>
              <s>Now finally, this Machine com­
                <lb/>
              pounded of upper and lower Pullies, is that which the Greeks call
                <lb/>
                <arrow.to.target n="marg1111"/>
                <lb/>
                <foreign lang="grc">Τποχίλιον.</foreign>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1109"/>
              *Called by ſome
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              a Nut.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1110"/>
              * Or two ends of
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              the ſame Rope.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1111"/>
              In Latine
                <emph type="italics"/>
              Tro­
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              chlea.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>We have hitherto explained, how by help of Pullies one may
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              double the
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orce, it remaineth that with the greateſt brevity poſ­
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              ſible, we ſhew the way how to encreaſe it according to any Multi­
                <lb/>
              plicity. </s>
              <s>And firſt we will ſpeak of the Multiplicity according to
                <lb/>
              the even numbers, and then the odde: To ſhew how we may mul­
                <lb/>
              tiply the
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orce in a quadruple Proportion, we will propound the
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              following Speculation as the Soul of all that followeth.</s>
            </p>
            <p type="main">
              <s>Take two Leavers, A B, C D, with the
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              ulciments in the ex­
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                <figure id="id.070.01.018.2.jpg" xlink:href="070/01/018/2.jpg" number="14"/>
                <lb/>
              treams A and C; and at the middles
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              of each of them let the Grave G hang,
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              ſuſtained by two
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orces of equal Mo­
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              ment placed in B and D. </s>
              <s>I ſay, that
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              the Moment of each of them will
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              equal the Moment of the fourth part
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              of the Weight G.
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              or the two
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              or­
                <lb/>
              ces B and D bearing equally, it is
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              manifeſt, that the
                <emph type="italics"/>
              F
                <emph.end type="italics"/>
              orce D hath not
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              contraſted with more then one half of the Weight G: But if the
                <lb/>
                <emph type="italics"/>
              F
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              orce D do by benefit of the Leaver D C ſuſtain the half of the </s>
            </p>
          </chap>
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