Galilei, Galileo, Mechanics, 1665

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    <archimedes>
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          <chap>
            <p type="main">
              <s>
                <pb xlink:href="070/01/021.jpg" pagenum="291"/>
              Force in B ſuſtaineth a part of the Weight D double to it ſelf, its
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              Diſtance from the Fulciment A, that is, the Line B A being dou­
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              ble to the Diſtance A C at which the Grave hangeth: But becauſe
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              the two Forces in B and C are ſuppoſed to be equal to each other:
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              Therefore the part of the Weight D, which is ſuſtained by the
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              Force in B, is double to the part ſuſtained by the Force in C. </s>
              <s>If
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              therefore, of the Grave D two parts be made, the one double to
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              the remainder, the greater is ſuſtained by the Force in B, and the
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              leſſer by the Force in C: But this leſſer is the third part of the
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              Weight D: Therefore the Moment of the Force in C is equal to
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              the Moment of the third part of the Weight D; to which, of
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              conſequence, the Force B ſhall be equal, we having ſuppoſed it
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              equal to the other Force C: Wherefore our intention is manifell,
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              which we were to demonſtrate, how that each of the two Powers
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              C and B is equal to the third part of the Weight D. </s>
              <s>Which be­
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              ing demonſtrated, we will paſs forwards to the Pulleys, and will
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              deſcribe the inferiour Gyrils of A C B, voluble about the Center
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              G, and the Weight H hanging thereat, we will draw the other up­
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              per one E F, winding about them both the Rope D F E A C B I,
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              of which let the end D be faſtned to the inferiour Pulley, and to
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                <figure id="id.070.01.021.1.jpg" xlink:href="070/01/021/1.jpg" number="19"/>
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              the other I let the Force be applyed:
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              Which, I ſay, ſuſtaining or moving the
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              Weight H, ſhall feele no more than the
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              third part of the Gravity of the ſame. </s>
              <s>For
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              conſidering the contrivance of this Ma­
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              chine, we ſhall find that the Diameter A B
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              ſupplieth the place of a Leaver, in whoſe
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              term B the Force I is applied, and in the
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              other A the
                <emph type="italics"/>
              F
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              uiciment is placed, at the mid­
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              dle G the Grave H is hanged, and another
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                <emph type="italics"/>
              F
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              orce D applied at the ſame place: ſo that
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                <arrow.to.target n="marg1115"/>
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              the Weight is faſtned to the ^{*} three Ropes
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              I B,
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              F
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              D, and E A, which with equal Labour
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              ſuſtain the Weight. </s>
              <s>Now, by what hath
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              already been contemplated, the two
                <emph type="italics"/>
              F
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              orces
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              D and B being applied, one, to the midſt of the Leaver A B, and
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              the other to the extream term B, it is manifeſt, that each of them
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              holdeth no more but the third part of the Weight H: Therefore
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              the Power I, having a Moment equal to the third part of the
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              Weight H, ſhall be able to ſuſtain and move it: but yet the Way
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              of the
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              F
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              orce in I ſhall be triple to the Way that the Weight ſhall
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              paſs; the ſaid Force being to diſtend it ſelf according to the
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              Length of the three Ropes I B,
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              F
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              D, and E A, of which one alone
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              meaſureth the Way of the Weight H.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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