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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="068/01/052.jpg" pagenum="38"/>
            <p type="head">
              <s>AXIOME I.</s>
            </p>
            <p type="main">
              <s>Sections equal, and equally ſwift, diſcharge equal quantities
                <lb/>
              of Water in equal times.</s>
            </p>
            <p type="head">
              <s>AXIOME II.</s>
            </p>
            <p type="main">
              <s>Sections equally ſwift, and that diſcharge equal quantity of
                <lb/>
              Water, in equal time, ſhall be equal.</s>
            </p>
            <p type="head">
              <s>AXIOME III.</s>
            </p>
            <p type="main">
              <s>Sections equal, and that diſcharge equal quantities of Water
                <lb/>
              in equal times, ſhall be equally ſwift.</s>
            </p>
            <p type="head">
              <s>AXIOME IV.</s>
            </p>
            <p type="main">
              <s>When Sections are unequal, but equally ſwift, the quanti­
                <lb/>
              ty of the Water that paſſeth through the firſt Section,
                <lb/>
              ſhall have the ſame proportion to the quantity that paſ­
                <lb/>
              ſeth through the Second, that the firſt Section hath to the ſecond
                <lb/>
              Section. </s>
              <s>Which is manifeſt, becauſe the velocity being the
                <lb/>
              ſame, the difference of the Water that paſſeth ſhall be according
                <lb/>
              to the difference of the Sections.</s>
            </p>
            <p type="head">
              <s>AXIOME V.</s>
            </p>
            <p type="main">
              <s>If the Sections ſhall be equal, and of unequal velocity, the
                <lb/>
              quantity of the Water that paſſeth through the firſt, ſhall
                <lb/>
              have the ſame proportion to that which paſſeth through the
                <lb/>
              ſecond, that the velocity of the firſt Section, ſhall have to the
                <lb/>
              velocity of the ſecond Section. </s>
              <s>Which alſo is manifeſt, becauſe
                <lb/>
              the Sections being equal, the difference of the Water which
                <lb/>
              paſſeth, dependeth on the velocity.</s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PETITION.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>A Section of a River being given, we may ſuppoſe another
                <lb/>
              equal to the given, of different breadth, heigth, and ve­
                <lb/>
              locity.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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