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

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/923.jpg" pagenum="230"/>
            <p type="head">
              <s>PROBL. III.
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              RO
                <emph type="italics"/>
              P.
                <emph.end type="italics"/>
              VI.</s>
            </p>
            <p type="main">
              <s>The Sublimity and Altitude of a Semiparabola
                <lb/>
              being given to find its Amplitude.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let A C be perpendicular to the
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.923.1.jpg" xlink:href="040/01/923/1.jpg" number="155"/>
                <lb/>
                <emph type="italics"/>
              Horizontal Line D C, in
                <lb/>
              which let the Altitude C B and
                <lb/>
              the Sublimity B A be given: It is
                <lb/>
              required in the Horizontal Line
                <lb/>
              D C to find the Amplitude of the
                <lb/>
              Semiparabola that is deſcribed out of
                <lb/>
              the Sublimity B A with the Alti­
                <lb/>
              tude B C. </s>
              <s>Take a Mean proportional
                <lb/>
              between C B and B A, to which let
                <lb/>
              C D be double, I ſay, that C D is
                <lb/>
              the Amplitude required. </s>
              <s>The which
                <lb/>
              is manifeſt by the precedent Propoſition.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>THEOR. IV. PROP. VII.</s>
            </p>
            <p type="main">
              <s>In Projects which deſcribe Semiparabola's of the
                <lb/>
              ſame Amplitude, there is leſs
                <emph type="italics"/>
              Impetus
                <emph.end type="italics"/>
              required
                <lb/>
              in that which deſcribeth that whoſe Ampli­
                <lb/>
              tude is double to its Altitude, than in any
                <lb/>
              other.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              For let the Semiparabola be B D, whoſe Amplitude C D is dou­
                <lb/>
              ble to its Altitude C B; and in its Axis extended on high let B A
                <lb/>
              be ſuppoſed equal to the Altitude B C; and draw a Line from
                <lb/>
              A to D which toucheth the Semiparabola in D, and ſhall cut the Hori­
                <lb/>
              zontal Line B E in E; and B E ſhall be equal to B C or to B A: It is
                <lb/>
              manifeſt that it is deſcribed by the Project whoſe Equable Horizontal
                <emph.end type="italics"/>
                <lb/>
              Impetus
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              is ſuch as is that gained in B of a thing falling from Reſt in A,
                <lb/>
              and the
                <emph.end type="italics"/>
              Impetus
                <emph type="italics"/>
              of the Natural Motion downwards, ſuch as is that of
                <lb/>
              a thing coming to C
                <emph.end type="italics"/>
              ex quiete
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              in B. </s>
              <s>Whence it is manifeſt, that the
                <emph.end type="italics"/>
                <lb/>
              Impetus
                <emph type="italics"/>
              compounded of them, and that ſtriketh in the Term D is as the
                <lb/>
              Diagonal A E, that is
                <emph.end type="italics"/>
              potentia
                <emph type="italics"/>
              equal to them both. </s>
              <s>Now let there be
                <lb/>
              another Semiparabola G D, whoſe Amplitude is the ſame C D, and the
                <lb/>
              Altitude C G leſs, or greater than the Altitude B C, and let H D touch
                <lb/>
              the ſame, cutting the Horizontal Line drawn by G in the point K; and
                <lb/>
              as H G is to G K, ſo let K G be to G L: by what hath been demonſtrated
                <lb/>
              G L ſhall be the Altitude from which the Project falling deſcribeth the
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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