Galilei, Galileo, Mechanics, 1665

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="070/01/014.jpg" pagenum="284"/>
              with a Machine to overcome a Reſiſtance, though great, with a
                <lb/>
              ſmall Force, in regard, that we ſhall manifeſtly prove that the ſame
                <lb/>
              Force placed in F, might in the ſame Time conveigh the ſame
                <lb/>
              Weight, with the ſame Motion, unto the ſame Diſtance, without
                <lb/>
              any Machine at all: For ſuppoſing, for example, that the Reſiſtance
                <lb/>
              of the Grave H be ten times greater than the Force placed in F, it
                <lb/>
                <figure id="id.070.01.014.1.jpg" xlink:href="070/01/014/1.jpg" number="9"/>
                <lb/>
              will be requiſite for the mo­
                <lb/>
              ving of the ſaid Reſiſtance,
                <lb/>
              that the Line F B be decuple
                <lb/>
              to B D; and conſequently,
                <lb/>
              that the Circumference of the
                <lb/>
              Circle F G C be alſo decuple
                <lb/>
              to the Circumference E A D:
                <lb/>
              and becauſe when the Force
                <lb/>
              ſhall be moved once along the
                <lb/>
              whole Circumference of the
                <lb/>
              Circle F G C, the Barrel EAD,
                <lb/>
              about which the Rope is be-laid which draweth the Weight, ſhall
                <lb/>
              likewiſe have given one onely turn; it is manifeſt, that the Weight
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              H ſhall not have been moved more than the tenth part of that way
                <lb/>
              which the Mover ſhall have gone. </s>
              <s>If therefore the Force that is to
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              move a Reſiſtance that is greater than it ſelf, for ſuch an aſſigned
                <lb/>
              Space by help of this Machine, muſt of neceſſity move ten times as
                <lb/>
              far, there is no doubt, but that dividing that Weight into ten parts,
                <lb/>
              each of them ſhall be equall to the Force, and conſequently, might
                <lb/>
              have been tranſported one at a Time, as great a Space as that
                <lb/>
              which it ſelf did move, ſo that making ten journeys, each equal to
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              the Circumference E A D, it ſhall not have gone any farther than
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              if it did move but once alone about the Circumference F G C;
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              and ſhall have conveighed the ſame Weight H to the ſame Di­
                <lb/>
              ſtance. </s>
              <s>The benefit therefore that is to be derived from theſe
                <lb/>
              Machines is, that they carry all the Weight together, but not with
                <lb/>
              leſſe Labour, or with greater Expedition, or a greater Way than
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              the ſame Force might have done conveying it by parcels.</s>
            </p>
            <p type="head">
              <s>Of PULLIES.</s>
            </p>
            <p type="main">
              <s>The Inſtruments, whoſe Natures are reducible unto the Bal­
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              lance, as to their Principle and Foundation, and others little
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              differing from them, have been already deſcribed; now for
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              the underſtanding of that which we have to ſay touching Pullies,
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              it is requiſite, that we conſider in the firſt place another way to uſe
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              the Leaver, which will conduce much towards the inveſtigation of
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              the Force of Pullies, and towards the underſtanding of other Me­
                <lb/>
              chanical Effects. </s>
              <s>The uſe of the Leaver above declared ſuppoſed </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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