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

Table of figures

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/887.jpg" pagenum="194"/>
                <emph type="italics"/>
              ſhall be the Time of the whole A F, and E C the Time of A I: And be­
                <lb/>
              cauſe in the Equicrural Triangle A E D the Side A E is equal to the
                <lb/>
              Side E D, E D ſhall be the Time along A F, and E C is the Time along
                <lb/>
              A I: Therefore C D, that is A B ſhall be the Time along A F
                <emph.end type="italics"/>
              ex qui­
                <lb/>
              ete
                <emph type="italics"/>
              in A; which is the ſame as if we ſaid, that A B is the Time along
                <lb/>
              A G out of G, or out of H: Which was to be done.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>PROBL.
                <emph type="italics"/>
              XIII. P
                <emph.end type="italics"/>
              RO
                <emph type="italics"/>
              P. XXXIV.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>An inclined
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              lane and Perpendicular whoſe ſub­
                <lb/>
              lime term is the ſame being given, to find a
                <lb/>
              more ſublime point in the Perpendicular pro­
                <lb/>
              longed out of which a Moveable falling, and
                <lb/>
              being turned along the inclined
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              lane, may
                <lb/>
              paſſe them both in the ſame Time, as it doth
                <lb/>
              the ſole inclined
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              lane
                <emph type="italics"/>
              ex quiete
                <emph.end type="italics"/>
              in its ſuperi­
                <lb/>
              our Term.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the inclined Plane and Perpendicular be A B and A C, whoſe
                <lb/>
              Term A is the ſame. </s>
              <s>It is required in the Perpendicular prolonged
                <lb/>
              from A to find a ſublime point, out of which the Moveable deſcen­
                <lb/>
              ding, and being turned along the Plane A B, may paſſe the aſſigned part
                <lb/>
              of the Perpendicular and the Plane A B in the ſame Time, as it would the
                <lb/>
              ſole Plane A B out of Reſt in A.
                <emph.end type="italics"/>
              </s>
            </p>
            <figure id="id.040.01.887.1.jpg" xlink:href="040/01/887/1.jpg" number="133"/>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Ho­
                <lb/>
              rizontal Line
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              be B C, and
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              let A N be
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              cut equal to
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              A C; and as
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              A B is to B N,
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              ſo let A L be
                <lb/>
              to L C: and
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              unto A L let
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              A I be equal,
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              and unto A C
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              and B I let C
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              E be a third
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              proportional,
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              marked in the
                <lb/>
              Perpendicular A C produced. </s>
              <s>I ſay, that C E is the Space acquired;
                <lb/>
              ſo that the Perpendicular being extended above A, and the part A X
                <lb/>
              equal to C E being taken, a Moveable out of X will paſſe both the
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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