Galilei, Galileo, Mechanics, 1665

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      <text>
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            <p type="main">
              <s>
                <pb xlink:href="070/01/020.jpg" pagenum="290"/>
              we will ſet before you the preſent Contemplation. </s>
              <s>Suppoſe, there­
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              fore, that A B, C D, and E F are three Leavers; and that on the
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              middle points of them G, H, and I the Weight K doth hang in
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              common, ſo that every one of them ſhall ſuſtain the third part of
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                <figure id="id.070.01.020.1.jpg" xlink:href="070/01/020/1.jpg" number="16"/>
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              it: And becauſe the Power in
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              B, ſuſtaining with the Leaver
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              B A thependent Weight in G,
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              hapneth to be the half of the
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              ſaid Weight, and it hath been
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              already ſaid, that it ſuſtaineth
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              the third part of the Weight
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              K: Therefore the Moment of
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              the Force B is equal to half of
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              the third part of the Weight K; that is, to the ſixth part of it:
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              And the ſame ſhall be demonſtrated of the other Forces D and F:
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              From whence we may eaſily gather, that putting three Gyrils or
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              Rundles into the inferiour Pulley, and two or three into the upper­
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                <figure id="id.070.01.020.2.jpg" xlink:href="070/01/020/2.jpg" number="17"/>
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              moſt, we may multiply the Force accor­
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                <arrow.to.target n="marg1114"/>
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              ding to our ^{*}
                <emph type="italics"/>
              Senarius.
                <emph.end type="italics"/>
              And if we would
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              encreaſe it according to any other even
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              Number, the Gyrils of the Pulley below
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              muſt be multiplyed according to the half
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              of that Number, according to which the
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              Force is to be multiplyed, circumpoſing
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              the Rope about the Pulleys, ſo as that one
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              of the ends be faſtned to the upper Pul­
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              ley, and let the Force be in the other; as
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              in this Figure adjoyning may manifeſtly
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              be gathered.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1114"/>
              * Or in Sexcuple
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              proportion.</s>
            </p>
            <p type="main">
              <s>Now paſſing to the Declaration of the
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              manner how to multiply the Force ac­
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              cording to the odd Numbers, and begin­
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                <figure id="id.070.01.020.3.jpg" xlink:href="070/01/020/3.jpg" number="18"/>
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              ning at the triple proportion: firſt, let us
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              propoſe the preſent Contemplation, as
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              that, on the underſtanding of which the
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              knowledge of all the Work in hand
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              doth depend. </s>
              <s>Let therefore the Leaver
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              be A B, its Fulciment A, and from the
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              middle of it, that is, at the point C let
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              the Grave D be hanged; and let it be ſu­
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              ſtained by two equal Forces; and let one of them be applied to the
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              point C, and the other to the term B. </s>
              <s>I ſay, that each of thoſe Powers
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              have Moment equal to the third part of the Weight D. </s>
              <s>For the
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              Force in C ſuſtaineth a Weight equal to it ſelf, being placed in the
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              ſame Line in which the Weight D doth hang & Gravitate: But the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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