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

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            <pb xlink:href="040/01/609.jpg" pagenum="42"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              COROLLARIE.
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              </s>
            </p>
            <p type="main">
              <s>Hence it is manifeſt, that Sections of the ſame River (which
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              are no other than the vulgar meaſures of the River) have
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              betwixt themſelves reciprocal proportions to their veloci­
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              ties; for in the firſt Propoſition we have demonſtrated that the
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              Sections of the ſame River, diſcharge equal quantities of Water
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              in equal times; therefore, by what hath now been demonſtrated
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              the Sections of the ſame River ſhall have reciprocal proportion
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              to their velocities; And therefore the ſame running water chan­
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              geth meaſure, when it changeth velocity; namely, increaſeth the
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              meaſure, when it decreaſeth the velocity, and decreaſeth the
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              meaſure, when it increaſeth the velocity.</s>
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            <p type="main">
              <s>On which principally depends all that which hath been ſaid
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              above in the
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              Diſcourſe,
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              and obſerved in the
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              Corollaries
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              and
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              Ap­
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              pendixes
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              ; and therefore is worthy to be well underſtood and
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              heeded.</s>
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            <p type="head">
              <s>PROPOSITION IV.</s>
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            <p type="main">
              <s>
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              If a River fall into another River, the height of the
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              firſt in its own Chanel ſhall be to the height that it
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              ſhall make in the ſecond Chanel, in a proportion
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              compounded of the proportions of the breadth of
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              the Chanel of the ſecond, to the breadth of the
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              Chanel of the firſt, and of the velocitie acquired in
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              the Chanel of the ſecond, to that which it had in
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              its proper and first Chanel.
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              </s>
            </p>
            <p type="main">
              <s>Let the River A B, whoſe height is A C, and breadth C B,
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              that is, whoſe Section is A C B; let it enter, I ſay, into a­
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              nother River as broad as the line E F, and let it therein make
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              the riſe or height D E, that is to ſay, let it have its Section in
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              the River whereinto it falls D E F; I ſay, that the height A C
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              hath to the height D E the proportion compounded of the pro­
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              portions of the breadth E F, to the breadth C B, and of the ve­
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              locity through D F, to the velocity through A B. </s>
              <s>Let us ſup­
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              poſe the Section G, equal in velocity to the Section A B, and in
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              breadth equal to E F, which carrieth a quantity of Water e­
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              qual to that which the Section A B carrieth, in equal times,
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              and conſequently, equal to that which D F carrieth. </s>
              <s>Moreover,
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              as the breadth E F is to the breadth C B, ſo let the line H be to </s>
            </p>
          </chap>
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