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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/732.jpg" pagenum="40"/>
            <p type="margin">
              <s>
                <margin.target id="marg1034"/>
                <emph type="italics"/>
              How infinite points
                <lb/>
              are aſſigned in a
                <lb/>
              finite Line.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1035"/>
              Continuum
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              com­
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              pounded of Indivi­
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              ſibles.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I know not what the Peripateticks would ſay, in regard
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              that the Conſiderations you have propoſed would be, for the moſt
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              part, new unto them, and as ſuch, it is requiſite that they be exa­
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              mined: and it may be, that they would find you anſwers, and
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              powerful Solutions, to unty theſe knots, which I, by reaſon of the
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              want of time and ingenuity proportionate, cannot for the preſent
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              reſolve. </s>
              <s>Therefore, ſuſpending this particular for this time, I
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              would gladly underſtand how the introduction of theſe Indiviſi­
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              bles facilitateth the knowledge of Condenſation, and Rarefa­
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              ction, avoiding at the ſame time a
                <emph type="italics"/>
              Vacuum,
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              and the Penetration of
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              Bodies.</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>I alſo much long to underſtand the ſame, it being to
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              my Capacity ſo obſcure: with this
                <emph type="italics"/>
              proviſo,
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              that I be not couzen­
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              ed of hearing (as
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              Simplicius
                <emph.end type="italics"/>
              ſaid but even now) the Reaſons of
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                <emph type="italics"/>
              Ariſtotle
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              in confutation of a
                <emph type="italics"/>
              Vacuum,
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              and conſequently the Solu­
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              tions which you bring, as ought to be done, whilſt that you ad­
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              mit what he denieth.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>I will do both the one and the other. </s>
              <s>And as to the firſt
                <lb/>
              it's neceſſary, that like as in favour of Rarefaction, we make uſe of
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              the Line deſcribed by the leſſer Circle bigger than its own Cir­
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              cumference, whilſt it was moved at the Revolution of the greater;
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              ſo, for the underſtanding of Condenſation, we ſhall ſhew, how that,
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              at the converſion made by the leſſer Circle, the greater deſcribeth
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              a Right-line leſs than its Circumference; for the clearer explicati­
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              on of which, let us ſet before us the conſideration of that which
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              befalls in the Poligons. </s>
              <s>In a deſcription like to that other; ſup­
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              poſe two Hexagons about the common Center L, which let be
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              A B C, and H I K, with the Parallel-lines H O M, and A B C, up­
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              on which they are to make their Revolutions; and the Angle I, of
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              the leſſer Poligon, reſting at a ſtay, turn the ſaid Poligon till ſuch
                <lb/>
              time as I K fall upon the Parallel, in which motion the point K
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              ſhall deſcribe the Arch K M, and the Side K I, ſhall unite with the
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              part I M; while this is in doing, you muſt obſerve what the Side
                <lb/>
              C B of the greater Poligon will do. </s>
              <s>And becauſe the Revolution
                <lb/>
              is made upon the Point I, the Line I B with its term B ſhall de­
                <lb/>
              ſcribe, turning backward the Arch B b, below the Parallel c A, ſo
                <lb/>
              that when the Side K I ſhall fall upon the Line M I, the Line B C
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              ſhall fall upon the Line b c, advancing forwards only ſo much as
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              is the Line B c, and retiring back the part ſubtended by the Arch
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              B b, which falls upon the Line B A, and intending to continue af­
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              ter the ſame manner the Revolution of the leſſer Poligon, this will
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              deſcribe, and paſs upon its Parallel, a Line equal to its Perimeter;
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              but the greater ſhall paſs a Line leſs than its Perimeter, the quan­
                <lb/>
              tity of ſo many of the lines
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              b as it hath Sides, wanting one;
                <lb/>
              and that ſame line ſhall be very near equal to that deſcribed by </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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