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

Table of figures

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/1007.jpg" pagenum="313"/>
              raiſeth it, and cannot be eſtimated ſave wthin a ſmall matter.</s>
            </p>
            <p type="main">
              <s>Moreover, it is neceſſary to obſerve, that it is nothing but the
                <lb/>
              redoubling of the Chord, and not the Pulley, that cauſeth this
                <lb/>
              Force: for if we faſten yet another Pulley towards A, about
                <lb/>
              which we paſs the Chord A B C H, there will be required no leſs
                <lb/>
              Force to draw H towards K, and ſo to lift up the Weight E, than
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              there was before to draw C towards G. </s>
              <s>But if to theſe two Pul­
                <lb/>
              leys we add yet another towards D, to which we faſten the Weight,
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              and in which we make the Chord to run or ſlip, juſt as we did in
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              the firſt, then we ſhall need no more Force to lift up this Weight
                <lb/>
              of 200 pounds than to lift up 50 pounds without the Pulley: be­
                <lb/>
              cauſe that in drawing four feet of Chord we lift it up but one
                <lb/>
              foot. </s>
              <s>And ſo in multiplying of the Pulleys one may raiſe the great­
                <lb/>
              eſt Weights with the leaſt Forces. </s>
              <s>It is requiſite alſo to obſerve,
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              that a little more Force is alwaies neceſſary for the raiſing of a
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              Weight than for the ſuſtaining of it: which is the reaſon why I
                <lb/>
              have ſpoken here diſtinctly of the one and of the other.</s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              The Inclined
                <emph.end type="italics"/>
              PLANE.</s>
            </p>
            <p type="main">
              <s>If not having more Force than ſufficeth to raiſe 100 pounds, one
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              would nevertheleſs raiſe this Body F, that weigheth 200 pounds,
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              to the height of the Line B A, there needs no more but to draw
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              or rowl it along the Inclined Plane C A, which I ſuppoſe to be
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              twice as long as the Line
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                <figure id="id.040.01.1007.1.jpg" xlink:href="040/01/1007/1.jpg" number="210"/>
                <lb/>
              A B, for by this means,
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              for to make it arrive at
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              the point A, we muſt
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              there employ the Force
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              that is neceſſary for the
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              raiſing 100 pounds twice
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              as high, and the more inclined this Plane ſhall be made, ſo much
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              the leſs Force ſhall there need to raiſe the Weight F. </s>
              <s>But yet there
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              is to be rebated from this Calculation the difficulty that there is
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              in moving the Body F, along the Plane A C, if that Plane were
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              laid down upon the Line B C, all the parts of which I ſuppoſe to
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              be equidiſtant from the Center of the Earth.</s>
            </p>
            <p type="main">
              <s>It is true, that this impediment being ſo much leſs as the Plane is
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              more united, more hard, more even, and more polite; it cannot
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              likewiſe be eſtimated but by gueſs, and it is not very conſide­
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              rable.</s>
            </p>
            <p type="main">
              <s>We need not neither much to regard that the Line B C being a
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              part of a Circle that hath the ſame Center with the Earth, the
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              Plane A C ought to be (though but very little) curved, and to
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              have the Figure of part of a Spiral, deſcribed between two Circles, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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