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

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          <chap>
            <p type="main">
              <s>
                <pb xlink:href="068/01/054.jpg" pagenum="40"/>
              ſuppoſed equal to the Section A, in magnitude; but of velocity
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              equal to the Section B, and let it be G, and as the Section A is
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                <figure id="id.068.01.054.1.jpg" xlink:href="068/01/054/1.jpg" number="7"/>
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              to the Section B, ſo let the line F be to the line D; and as the
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              velocity A, is to the velocity by B, ſo let the line D be to the
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              line R: Therefore the Water which paſſeth thorow A, ſhall be
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              to that which paſſeth through G (in regard the Sections A and
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              G are of equal bigneſs, but of unequal velocity) as the velocity
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              through A, to the velocity through G; But as the velocity
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              through A, is to the velocity through G, ſo is the velocity through
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              A, to the velocity through B; namely, as the line D, to the
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              line R: therefore the quantity of the Water which paſſe the
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              through A, ſhall be to the quantity which paſſeth through G, as
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              the line D is to the line R; but the quantity which paſſeth
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              through G, is to that which paſſeth through B, (in regard the
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              Sections G, and B, are equally ſwift) as the Section G to the Se­
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              ction B; that is, as the Section A, to the Section B; that is, as
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              the line F, to the line D: Therefore by the equal and perturbed
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              proportionality, the quantity of the Water which paſſeth through
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              A, hath the ſame proportion to that which paſſeth through B,
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              that the line F hath to the line R; but F to R, hath a proportion
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              compounded of the proportions of F to D, and of D to R; that
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              is, of the Section A to the Section B; and of the velocity through
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              A, to the velocity through B. </s>
              <s>Therefore alſo the quantity of
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              Water which paſſeth through the Section A, ſhall have a propor­
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              tion to that which paſſeth through the Section B, compounded of
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              the proportions of the Section A, to the Section B; and of
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              the velocity through A, to the velocity through B: And
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              therefore in two Sections of Rivers, the quantity of Water which
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              paſſeth by the firſt,
                <emph type="italics"/>
              &c.
                <emph.end type="italics"/>
              which was to be demonſtrated.</s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              COROLLARIE.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>The ſame followeth, though the quantity of the Water which
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              paſſeth through the Section A, be equal to the quantity of
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              Water which paſſeth through the Section B, as is manifeſt by the
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              ſame demonſtration.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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