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

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              neſe
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              territories, and many other places, where very great ſuits
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              and differences ariſe, which not being to be determined with in­
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              telligible reaſons, come oftentimes to be decided, by force of
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              armes; and inſtead of flowing their Grounds with Waters, they
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              cruelly flow them with the ſhedding of humane blood, impiouſly
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              inverting the courſe of Peace and Juſtice, ſowing ſuch diſorders
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              and feuds, as that they are ſometimes accompanied with the ru­
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              ine of whole Cities, or elſe unprofitably charge them with vain,
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              and ſometimes prejudicial expences.</s>
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              <s>PROPOS. IV. THEOR. II.</s>
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              If a River increaſe in quick height, the quantitie of
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              Water which the River diſchargeth after the in­
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              creaſe, hath the Proportion compounded of the
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              Proportions of the Quick height to the Quick
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              height, and of the velocity to the velocity.
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              <s>Let there be a River, which whilſt it is low, runneth thorow
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              the Regulator D F, with the Quick height A B, and after­
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              wards let a Flood come; and then let it run with the height
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              D B, I ſay, that the quantity of the Water that is diſcharged
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              through D F, to that which diſchargeth through A F, hath the
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              proportion compounded of the proportions of the velocity
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              through D F to the velocity through A F, and of the height
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              D B to the height A B. </s>
              <s>As the velocity through D F is to the
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              velocity through A F, ſo let the line R be to the line S; and as
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              the height D B is to the height A B; ſo let the line S be to the
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              line T. </s>
              <s>And let a Section be ſuppoſed L M N equal to the
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              Section D F in height and length, but let it be in velocity equal
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              to the Section AF. </s>
              <s>Therefore the quantity of the Water that run­
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              neth through D F to that which runneth through L N, ſhall be </s>
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