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

Table of figures

< >
[Figure 201]
[Figure 202]
[Figure 203]
[Figure 204]
[Figure 205]
[Figure 206]
[Figure 207]
[Figure 208]
[Figure 209]
[Figure 210]
[Figure 211]
[Figure 212]
[Figure 213]
[Figure 214]
[Figure 215]
[Figure 216]
[Figure 217]
[Figure 218]
[Figure 219]
[Figure 220]
[Figure 221]
[Figure 222]
[Figure 223]
[Figure 224]
[Figure 225]
[Figure 226]
[Figure 227]
[Figure 228]
[Figure 229]
[Figure 230]
< >
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/1006.jpg" pagenum="312"/>
              ſeth to be raiſed by a leſſer, are the Pulley, the Inclined Plane, the
                <lb/>
              Wedg, the Capſten, or Wheel, the Screw, the Leaver, and ſome
                <lb/>
              others, for if we will not apply or compare them one to another,
                <lb/>
              we cannot well number more, and if we will apply them we need
                <lb/>
              not inſtance in ſo many.</s>
            </p>
            <p type="head">
              <s>The PVLLEY,
                <emph type="italics"/>
              Trochlea.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Let A B C be a Chord put about the Pulley D, to which let
                <lb/>
              the Weight E be faſtned; and firſt, ſuppoſing that two
                <lb/>
              men ſuſtain or pull up equally each of them one of the
                <lb/>
                <figure id="id.040.01.1006.1.jpg" xlink:href="040/01/1006/1.jpg" number="209"/>
                <lb/>
              ends of the ſaid Chord:
                <lb/>
              it is manifeſt, that if the
                <lb/>
              Weight weigheth 200
                <lb/>
              pounds, each of thoſe
                <lb/>
              men ſhal employ but the
                <lb/>
              half thereof, that is to ſay,
                <lb/>
              the Force that is requiſite
                <lb/>
              for ſuſtaining or raiſing
                <lb/>
              of 100 pounds, for each
                <lb/>
              of them ſhal bear but the
                <lb/>
              half of it.</s>
            </p>
            <p type="main">
              <s>Afterwards, let us ſup­
                <lb/>
              poſe that A, one of the
                <lb/>
              ends of this Chord, being
                <lb/>
              made faſt to ſome Nail,
                <lb/>
              the other C be again ſu­
                <lb/>
              ſtained by a Man; and it
                <lb/>
              is manifeſt, that this Man in C, needs not (no more than before)
                <lb/>
              for the ſuſtaining the Weight E, more Force than is requiſite for
                <lb/>
              the ſuſtaining of 100 pounds: becauſe the Nail at A doth the
                <lb/>
              ſame Office as the Man which we ſuppoſed there before. </s>
              <s>In fine,
                <lb/>
              let us ſuppoſe that this Man in C do pull the Chord to make the
                <lb/>
              Weight E to riſe, and it is manifeſt, that if he there employeth
                <lb/>
              the Force which is requiſite for the raiſing of 100 pounds to the
                <lb/>
              height of two feet, he ſhall raiſe this Weight E of 200 pounds to
                <lb/>
              the height of one foot: for the Chord A B C being doubled, as it
                <lb/>
              is, it muſt be pull'd two feet by the end C, to make the Weight E
                <lb/>
              riſe as much, as if two men did draw it, the one by the end A,
                <lb/>
              and the other by the end C, each of them the length of one foot
                <lb/>
              only.</s>
            </p>
            <p type="main">
              <s>There is alwaies one thing that hinders the exactneſs of the Cal­
                <lb/>
              culation, that is the ponderoſity of the Chord or Pulley, and the
                <lb/>
              difficulty that we meet with in making the Chord to ſlip, and in
                <lb/>
              bearing it: but this is very ſmall in compariſon of that which </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>