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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/866.jpg" pagenum="173"/>
            <p type="head">
              <s>PROBL. IV.
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              RO
                <emph type="italics"/>
              P.
                <emph.end type="italics"/>
              XVII.</s>
            </p>
            <p type="main">
              <s>A
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              erpendicular and
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              lane Inflected to it being
                <lb/>
              given, to aſſign a part in the given
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              lane, in
                <lb/>
              which after the Fall along the
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              erpendicular
                <lb/>
              the Motion may be made in a Time equal to
                <lb/>
              that in which the Moveable
                <emph type="italics"/>
              ex quiete
                <emph.end type="italics"/>
              paſſeth
                <lb/>
              the
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              erpendicular given.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Perpendicular be A B, and a Plane Inflected to it B E: It is
                <lb/>
              required in B E to aſſign a Space along which the Moveable af­
                <lb/>
              ter the Fall along A B may move in a Time equal to that in which
                <lb/>
              the ſaid Perpendicular A B is paſſed
                <emph.end type="italics"/>
              ex quiete.
                <emph type="italics"/>
              Let the Line A D be
                <lb/>
              parallel to the Horizon, with which let the Plane prolonged meet in D;
                <lb/>
              and ſuppoſe F B equal to B A; and as B D
                <lb/>
              is to D F, ſo let F D be to D E. </s>
              <s>I ſay, that
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.866.1.jpg" xlink:href="040/01/866/1.jpg" number="110"/>
                <lb/>
                <emph type="italics"/>
              the Time along B E after the Fall along A B
                <lb/>
              equalleth the Time along A B, out of Reſt
                <lb/>
              in A. </s>
              <s>For if we ſuppoſe A B to be the Time
                <lb/>
              along A B, D B ſhall be the Time along
                <lb/>
              D B. </s>
              <s>And becauſe, as B D is to D F, ſo is
                <lb/>
              F D to D E, D F ſhall be the Time along
                <lb/>
              the whole Plane D E, and B F along the
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              part B E out of D: But the Time along
                <lb/>
              B E after D B, is the ſame as after A B: Therefore the Time along B E
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              after A B ſhall be B F, that is, equal to the Time
                <emph.end type="italics"/>
              ex quiete
                <emph type="italics"/>
              in A:
                <lb/>
              Which was the Propoſition.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              ROBL. V. PROP. XVIII.</s>
            </p>
            <p type="main">
              <s>Any Space in the Perpendicular being given from
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              the aſſigned beginning of Motion that is
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              paſſed in a Time given, and any other leſſer
                <lb/>
              Time being alſo given, to find another Space in
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              the ſaid Perpendicular that may be paſſed in
                <lb/>
              the given leſſer Time.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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