Galilei, Galileo, Mechanics, 1665

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="070/01/015.jpg" pagenum="285"/>
              the Weight to be at one extream, and the Force at the other, and
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              the Fulciment placed in ſome point between the extreams: but we
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              may make uſe of the Leaver another way, yet, placing, as we ſee,
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              the Fulciment in the extream A, the Force in the other extream C,
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              and ſuppoſing the Weight D to hang by ſome point in the midſt,
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                <figure id="id.070.01.015.1.jpg" xlink:href="070/01/015/1.jpg" number="10"/>
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              as here we ſee by the point B, in
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              this example it's manifeſt, that if
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              the Weight did hang at a point
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              Equi-diſtant from the two ex­
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              treams A and C, as at the point F,
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              the labour of ſuſtaining it would
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              be equally divided betwixt the
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              two points A and C, ſo that half
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              the Weight would be felt by the
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              Force C, the other half being ſu­
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              ſtained by the Fulciment A: but if the Grave Body ſhall be hanged
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              at another place, as at B, we ſhall ſhew that the Force in C is ſuffi­
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              cient to ſuſtain the Weight in B, as it hath the ſame proportion
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              to it, that the Diſtance, A B hath to the Diſtance A C. </s>
              <s>For De­
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              monſtration of which, let us imagine the Line B A to be continued
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              right out unto G, and let the Diſtance B A be equall to A G, and
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              let the Weight hanging at G, be ſuppoſed equall to D: It is ma­
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              nifeſt, that by reaſon of the equality of the Weights D and E, and
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              of the Diſtances G A and A B, the Moment of the Weight E
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              ſhall equalize the Moment of the Weight D, and is ſufficient to
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              ſuſtain it: Therefore whatever Force ſhall have Moment equall to
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              that of the Weight E, and that ſhall be able to ſuſtain it, ſhall be
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              ſufficient likewiſe to ſuſtain the Weight D: But for ſuſtaining the
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              Weight E, let there be placed in the point C ſuch a Force, whoſe
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              Moment hath that proportion to the Weight E, that the Diſtance
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              G A hath to the Diſtance A C, it ſhall be ſufficient to ſuſtain it:
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              Therefore the ſame Force ſhall likewiſe be able to ſuſtain the
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              Weight D, whoſe Moment is equall to the of E: But look what
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              Proportion the Line G A hath to the Line A C; and A B alſo hath
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              the ſame to the ſaid A C, G A having been ſuppoſed equall to A B:
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              And becauſe the Weights E and D are equall, each of them ſhall
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              have the ſame proportion to the Force placed in C: Therefore the
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              Force in C is concluded to equall the Moment of the Weight D,
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              as often as it hath unto it the ſame proportion that the Diſtance B A
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              hath to the Diſtance C A. </s>
              <s>And by moving the Weight, with the
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              Leaver uſed in this manner, it is gathered in this alſo, as well as in
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              the other Inſtruments, that what is gained in Force is loſt in Velo­
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              city: for the Force C raiſing the Leaver, and transferring it to A I,
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              the Weight is moved the Space B H, which is as much leſſer than
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              the Space C I paſſed by the Force, as the Diſtance A B is leſſer </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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