Castelli, Benedetto, Of the mensuration of running waters, 1661

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="068/01/058.jpg" pagenum="44"/>
            <p type="head">
              <s>PROPOSITION V.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              If a River diſcharge a certain quantitie of Water
                <lb/>
              in a certain time; and after that there come into it
                <lb/>
              a Flood, the quantity of Water which is diſchar­
                <lb/>
              ged in as much time at the Flood, is to that which
                <lb/>
              was diſcharged before, whilſt the River was low,
                <lb/>
              in a proportion compounded of the proportions of
                <lb/>
              the velocity of the Flood, to the velocity of the first
                <lb/>
              Water, and of the height of the Flood, to the
                <lb/>
              height of the first Water.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Suppoſe a River, which whilſt it is low, runs by the Section
                <lb/>
              AF; and after a Flood cometh into the ſame, and runneth
                <lb/>
              through the Section D F, I ſay, that the quantity of the Wa­
                <lb/>
              ter which is diſcharged through D F, is to that which is diſcharged
                <lb/>
                <figure id="id.068.01.058.1.jpg" xlink:href="068/01/058/1.jpg" number="10"/>
                <lb/>
              through A F, in a proportion compounded of the proportions of
                <lb/>
              the velocity through D F, to the velocity through A F, and of
                <lb/>
              the height D
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              to the height A
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              ; As the velocity through DF
                <lb/>
              is to the velocity through A F, ſo let the line R, to the line S;
                <lb/>
              and as the height D
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              is to the height A
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              ſo let the line S, to
                <lb/>
              the line T; and let us ſuppoſe a Section L M N, equal to D F
                <lb/>
              in height and breadth; that is L M equal to D
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              and M N equal
                <lb/>
              to
                <emph type="italics"/>
              B F
                <emph.end type="italics"/>
              ; but let it be in velocity equal to the Section A F, there­
                <lb/>
              fore the quantity of Water which runneth through D F, ſhall be
                <lb/>
              to that which runneth through LN, as the velocity through DF,
                <lb/>
              is to the velocity through L N, that is, to the velocity through
                <lb/>
                <emph type="italics"/>
              A F
                <emph.end type="italics"/>
              ; and the line R being to the line S, as the velocity through
                <lb/>
              D
                <emph type="italics"/>
              F,
                <emph.end type="italics"/>
              to the velocity through
                <emph type="italics"/>
              A F
                <emph.end type="italics"/>
              ; therefore the quantity which
                <lb/>
              runneth through D
                <emph type="italics"/>
              F,
                <emph.end type="italics"/>
              to that which runneth through L N, ſhall
                <lb/>
              have the proportion of R to S; but the quantity which runneth
                <lb/>
              through L N, to that which runneth through
                <emph type="italics"/>
              A F,
                <emph.end type="italics"/>
              (the Sections </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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