Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/1010.jpg" pagenum="316"/>
              ſtrument: which difficulty is more ſenſible in it than in thoſe afore­
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              going, foraſmuch as it hath greater Force.</s>
            </p>
            <p type="head">
              <s>The LEAVER,
                <emph type="italics"/>
              Vectis.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>I Have deferred to ſpeak of the Leaver until the laſt, in regard
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              that it is of all Engines for raiſing of Weights, the moſt diffi­
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              cult to be explained.</s>
            </p>
            <p type="main">
              <s>Let us ſuppoſe that C H is a Leaver, in ſuch manner ſupported
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              at the point O, (by means of an Iron Pin that paſſeth thorow it
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              acroſs, or otherwiſe) that it may turn about on this point O, its
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              part C deſcribing the Semicircle A B C D E, and its part H the
                <lb/>
                <figure id="id.040.01.1010.1.jpg" xlink:href="040/01/1010/1.jpg" number="214"/>
                <lb/>
              Semicircle F G H I K; and that
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              the Weight which we would
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              raiſe by help of it were in H,
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              and the Force in C, the Line
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              C O being ſuppoſed triple of
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              O H. </s>
              <s>Then let us conſider that
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              in the Time whilſt the Force
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              that moveth this Leaver deſcri­
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              beth the whole Semicircle
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              A B C D E, and acteth accord­
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              ing to the Line A B C D E, al­
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              though that the Weight deſcri­
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              beth likewiſe the Semicircle
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              F G H I K, yet it is not raiſed to
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              the length of this curved Line
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              F G H I K, but only to that of the Line F O K; inſomuch that the
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              Proportion that the Force which moveth this Weight ought to
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              have to its Ponderoſity ought not to be meaſured by that which is
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              between the two Diameters of theſe Circles, or between their two
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              Circumferences, as it hath been ſaid above of the Wheel, but ra­
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              ther by that which is betwixt the Circumference of the greater,
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              and the Diameter of the leſſer. </s>
              <s>Furthermore let us conſider, that
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              there is a neceſſity that this Force needeth not to be ſo great, at
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              ſuch time as it is near to A, or near to E, for the turning of the
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              Leaver, as then when it is near to B, or to D; nor ſo great when
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              it is near to B or D, as then when it is near to C: of which the rea­
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              ſon is, that the Weights do there mount leſs: as it is eaſie to un­
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              derſtand, if having ſuppoſed that the Line C O H is parallel to the
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              Horizon, and that A O F cutteth it at Right Angles, we take the
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              point G equidiſtant from the points F and H, and the point B equi­
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              diſtant from A and C; and that having drawn G S perpendicular
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              to F O, we obſerve that the Line F S (which ſheweth how much
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              the Weight mounteth in the Time that the Force operates along </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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