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

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/922.jpg" pagenum="229"/>
            <p type="head">
              <s>PROBL. II. PROP. V.</s>
            </p>
            <p type="main">
              <s>In the Axis of a given Parabola prolonged to find
                <lb/>
              a ſublime point out of which the Moveable
                <lb/>
              falling ſhall deſcribe the ſaid Parabola.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Parabola be A B, its Amplitude H B, and its prolonged
                <lb/>
              Axis H E; in which a Sublimity is to be found, out of which the
                <lb/>
              Moveable falling, and converting the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              conceived in A
                <lb/>
              along the Horizontal Line, deſcribeth the Parabola A B. </s>
              <s>Draw the
                <lb/>
              Horizontal Line A G, which ſhall be Parallel to B H, and ſuppoſing A F
                <lb/>
              equal to A H draw the Right Line F B, which toucheth the Parabola in
                <lb/>
              B, and cutteth the Horizontal Line A G in G; and unto F A and A G
                <lb/>
              let A E be a third Proportional. </s>
              <s>I ſay, that E is the ſublime Point re­
                <lb/>
              quired, out of which the Moveable falling
                <emph.end type="italics"/>
              ex quiete
                <emph type="italics"/>
              in E, and the
                <emph.end type="italics"/>
              Im­
                <lb/>
              petus
                <emph type="italics"/>
              conceived in A being converted along the Horizontal Line over­
                <lb/>
              taking the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              of the Deſcent
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.922.1.jpg" xlink:href="040/01/922/1.jpg" number="154"/>
                <lb/>
                <emph type="italics"/>
              in H
                <emph.end type="italics"/>
              ex quiete
                <emph type="italics"/>
              in A, deſcribeth the
                <lb/>
              Parabola A B. </s>
              <s>For if we ſuppoſe
                <lb/>
              E A to be the Meaſure of the Time
                <lb/>
              of the Fall from E to A, and of
                <lb/>
              the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              acquired in A, A G
                <lb/>
              (that is a Mean-proportional be­
                <lb/>
              tween E A and A F) ſhall be the
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              Time and the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              coming
                <lb/>
              from F to A, or from A to H. </s>
              <s>And
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              becauſe the Moveable coming out of
                <lb/>
              E in the Time E A with the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              acquired in A paſſeth in the Ho­
                <lb/>
              rizontal Lation with an Equable Motion the double of E A; There­
                <lb/>
              fore likewiſe moving with the ſame
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              it ſhall in the Time A G
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              paſs the double of G A, to wit, the Mean-proportional B H (for the
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              Spaces paſſed with the ſame Equable Motion are to one another as the
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              Times of the ſaid Motions:) And along the Perpendicular A H ſhall
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              be paſſed with a Motion
                <emph.end type="italics"/>
              ex quiete
                <emph type="italics"/>
              in the ſame Time G A: Therefore
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              the Amplitude H B, and Altitude A H are paſſed by the Moveable in the
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              ſame Time: Therefore the Parabola A B ſhall be deſcribed by the
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              Deſcent of the Project coming from the Sublimity E: Which was re­
                <lb/>
              quired.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>COROLLARY.</s>
            </p>
            <p type="main">
              <s>Hence it appeareth that the half of the
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              aſe or Amplitude of the
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              Semiparabola (which is the fourth part of the Amplitude of
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              the whole Parabola) is a Mean-proportional betwixt its Al­
                <lb/>
              titude and the Sublimity out of which the Moveable falling
                <lb/>
              deſcribeth it.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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