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

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/896.jpg" pagenum="203"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              ROBL. XVI.
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              RO
                <emph type="italics"/>
              P.
                <emph.end type="italics"/>
              XXXVIII.</s>
            </p>
            <p type="main">
              <s>Two Horizontal Planes cut by the Perpendicular
                <lb/>
              being given, to find a ſublime point in the
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              er­
                <lb/>
              pendicular, out of which Moveables falling
                <lb/>
              and being reflected along the Horizontal
                <lb/>
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              lanes may in Times equal to the Times of
                <lb/>
              the Deſcents along the ſaid Horizontal
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              lanes,
                <lb/>
              namely, along the upper and along the lower,
                <lb/>
              paſſe Spaces that have to each other any given
                <lb/>
              proportion of the leſſer to the greater.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              LET the Planes C D and B E be interſected by the Perpendicular
                <lb/>
              A C B, and let the given proportion of the leſſe to the greater be
                <lb/>
              N to F G. </s>
              <s>It is required in the Perpendicular A B to find a point
                <lb/>
              on high, out of which a Moveable falling, and reflected along C D may
                <lb/>
              in a Time equal to the Time of its Fall, paſſe a Space, that ſhall have
                <lb/>
              unto the Space paſſed by the other Moveable coming out of the ſame ſub­
                <lb/>
              lime point in a Time equal to the Time of its Fall with a Reflex Motion
                <lb/>
              along the Plane B E the ſame proportion as the given Line N batb to
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.896.1.jpg" xlink:href="040/01/896/1.jpg" number="143"/>
                <lb/>
                <emph type="italics"/>
              F G. </s>
              <s>Let G H be
                <lb/>
              made equal to the
                <lb/>
              ſaid N; and as F H
                <lb/>
              is to H G, ſo let
                <lb/>
              B C be to C L. </s>
              <s>I ſay,
                <lb/>
              L is the ſublime
                <lb/>
              point required. </s>
              <s>For
                <lb/>
              taking C M double
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              to C L, draw L M
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              meeting the Plane
                <lb/>
              B E in O; B O
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              ſhall be double to
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              B L: And becauſe,
                <lb/>
              as F H is to H G, ſo is B C to C L; therefore, by Compoſition and In­
                <lb/>
              verſion, as H G, that is, N is to G F, ſo is C L to L B, that is, C M to
                <lb/>
              B O: But becauſe C M is double to L C; let the Space C M be that
                <lb/>
              which by the Moveable coming from L after the Fall L C is paſſed along
                <lb/>
              the Plane C D; and by the ſame reaſon B O is that which is paſſed after
                <lb/>
              the Fall L B in a Time equal to the Time of the Fall along L B; foraſ­
                <lb/>
              much as B O is double to B L: Therefore the Propoſition is manifeſt.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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