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

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                <pb xlink:href="068/01/057.jpg" pagenum="43"/>
              the line I; and as the velocity of D F is to the velocity of A B,
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              ſo let the line I be to the line L; becauſe therefore the two
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              Sections A B and G are equally ſwift, and diſcharge equal quan­
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              tity of Water in equal times, they ſhall be equal Sections; and
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                <figure id="id.068.01.057.1.jpg" xlink:href="068/01/057/1.jpg" number="9"/>
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              therefore the height of A
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              B
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              to the height of G, ſhall be as the
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              breadth of G, to the breadth of A
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              B,
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              that is, as E F to C
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              B,
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              that is, as the line H to the line I: but becauſe the Water which
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              paſſeth through G, is equal to that which paſſeth through D E F,
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              therefore the Section G, to the Section D E F, ſhall have the re­
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              ciprocal proportion of the velocity through D E F, to the velo­
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              city through G; but alſo the height of G, is to the height D E,
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              as the Section G, to the Section D E F: Therefore the height of
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              G, is to the height D E, as the velocity through D E F, is to the
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              velocity through G; that is, as the velocity through D E F, is to
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              the velocity through A
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              B
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              ; That is, finally, as the line I, to the
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              line L; Therefore, by equal proportion, the height of
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              A B,
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              that
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              is, A C, ſhall be to the height D E; as H to L, that is, com­
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              pounded of the proportions of the breadth E F, to the breadth
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              C
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              B,
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              and of the velocity through D F, to the velocity through
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              A
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              B
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              : So that if a River fall into another River, &c. </s>
              <s>which was
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              to be demonſtrated.</s>
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