Castelli, Benedetto, Of the mensuration of running waters, 1661
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              being equally ſwift) ſhall be in proportion as the Section
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              L
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              N, to
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              the Section A F; that is, as D B, to A B; that is as the line S, to
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              the line T: Therefore by equal proportion, the quantity of the
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              water which runneth through D F, ſhall be in proportion to that
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              which runneth through A F, as R is to T; that is, compounded of
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              the proportions of the height D B, to the height A B, and of the
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              velocity through
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              D F,
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              to the velocity through
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              A F
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              ; and therefore
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              if a River diſcharge a certain quantity,
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              &c.
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              which was to be de­
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              monſtrated.</s>
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              <s>ANNOTATION.</s>
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              <s>The ſame might have been demonſtrated by the ſecond
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              Propoſition above demonſtrated, as is manifeſt.</s>
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              <s>PROPOSITION VI.</s>
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              If two equal ſtreams of the ſame Torrent, fall into a
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              River at divers times, the heights made in the Ri­
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              ver by the Torrent, ſhall have between them­
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              ſelves the reciprocal proportion of the velocities
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              acquired in the River.
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              <s>Let A and B, be two equal ſtreams of the ſame Torrent,
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              which falling into a River at divers times, make the heights
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              C D, and F G; that is the ſtream A, maketh the height
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              C D, and the ſtream B, maketh the height F G; that is, Let
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              their Sections in the River, into which they are fallen, be C E,
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              and FH; I ſay, that the height C D, ſhall be to the height F G,
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              in reciprocal proportion, as the velocity through F H, to the ve­
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              locity through C E; for the quantity of water which paſſeth
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              through A, being equal to the quantity which paſſeth through B,
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              in equal times; alſo the quantity which paſſeth through C E, ſhall
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              be equal to that which paſſeth through F H: And therefore the
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              proportion that the Section C E, hath to the Section F H; ſhall
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              be the ſame that the velocity through F H, hath to the velocity
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              through C E; But the Section C E, is to the Section F H, as
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              C D, to F G, by reaſon they are of the ſame breadth: Therefore
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              C D, ſhall be to F G, in reciprocal proportion, as the velocity
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              through F H, is to the velocity through C E, and therefore if two
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              equal ſtreams of the ſame Torrent,
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              &c.
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              which was to be de­
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              monſtrated.</s>
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