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="040/01/738.jpg" pagenum="46"/>
              ſuperficies A E, the Cylinder C F ſhall be leſſe than A E: For
                <lb/>
              if they were equal, its Superficies, by the laſt Propoſition would
                <lb/>
              be greater than the Superficies A E, and
                <lb/>
                <figure id="id.040.01.738.1.jpg" xlink:href="040/01/738/1.jpg" number="62"/>
                <lb/>
              much the more, if the ſaid Cylinder C F
                <lb/>
              were greater than A E. </s>
              <s>Let the Cylinder
                <lb/>
              I D be ſuppoſed equal to A E: There­
                <lb/>
              fore, by the precedent Propoſition, the
                <lb/>
              Superficies of the Cylinder I D ſhall be
                <lb/>
              to the Superficies A E, as the height I F
                <lb/>
              to the Mean-proportional betwixt I F &
                <lb/>
              A B. </s>
              <s>But the Superficies A E being by
                <lb/>
              Suppoſition equal to C F and I D, ha­
                <lb/>
              ving the ſame proportion to C F that the
                <lb/>
              height I F hath to C D: Therefore
                <lb/>
              C D is the Mean-Proportional between
                <lb/>
              I F and A B. Moreover, the Cylinder
                <lb/>
              I D being equal to the Cylinder A E,
                <lb/>
              they ſhall both have the ſame proporti­
                <lb/>
              on to the Cylinder C F: But I D is to
                <lb/>
              C F, as the height I F is to C D: Therefore the Cylinder A E
                <lb/>
              ſhall have the ſame proportion to the Cylinder C F, that the line
                <lb/>
              I F hath to C D; that is, that C D hath to A B: Which was to be
                <lb/>
              demonſtrated.
                <lb/>
                <arrow.to.target n="marg1042"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1042"/>
                <emph type="italics"/>
              Of Corn-ſacks
                <lb/>
              with a Board at
                <lb/>
              the Bottom, made
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              of the ſame Stuffe,
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              but different in
                <lb/>
              height, which are
                <lb/>
              the more capa­
                <lb/>
              cious.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>From hence is collected the Cauſe of an Accident, which the
                <lb/>
              Vulgar do not hearken to without admiration; and it is, how it
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              is poſſible that the ſame piece of ^{*}Cloth, being longer one way than
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              another, if a Sack be made thereof to hold Corn, as the uſual
                <lb/>
              manner is, with a Board at the bottom, will hold more, making
                <lb/>
              uſe of the leſſer breadth of the Cloth, for the height of the Sack, </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg1043"/>
                <lb/>
              and with the other encompaſſing the Board at the bottom, than if
                <lb/>
              it be made up the other way: As if for Example, the Cloth were
                <lb/>
              one way ſix foot, and the other way twelve, it will hold more,
                <lb/>
              when with the length of twelve one encompaſſeth the Board at the
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              bottom, the Sack being ſix foot high, than if it encompaſſed a
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              bottom of ſix foot, having twelve for its height. </s>
              <s>Now, by what
                <lb/>
              hath been demonſtrated, there is added to the Knowledge in ge­
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              neral that it holds more that way than this, the Specifick, and
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              particular Knowledge of how much it holdeth more: which is,
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              That it will hold more in proportion as it is lower, and leſſer, as
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              it is higher. </s>
              <s>And thus in the meaſures afore taken, the Cloth be­
                <lb/>
              ing twice as long as broad, when it is ſewed the length-ways it will
                <lb/>
              hold but half ſo much, as it will do the other way. </s>
              <s>And likewiſe
                <lb/>
                <arrow.to.target n="marg1044"/>
                <lb/>
              having a Mat to make a ^{*} Frale or Basket twenty five foot long,
                <lb/>
              and ſuppoſe ſeven broad; made up the long-way it will hold but
                <lb/>
              onely ſeven of thoſe meaſures, whereof the other way it will hold
                <lb/>
              five and twenty.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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