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

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              to adjuſt the Ciſtern ſo, that the exceſs above the ordinary wa­
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              ter, diſcharge into the publick Fountains, that ſo the particular
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              participants may have alwayes the ſame abundance of
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              water.</s>
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              <s>APPENDIX XI.</s>
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              <s>Much more difficult is the diviſion of the waters which
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              ſerve to water the fields, it not being poſſible to obſerve
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              ſo commodiouſly, what quantity of water the whole
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              Ditch ſends forth in one determinate time, as may be done in
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              Fountains: Yet nevertheleſs, if the ſecond propoſition by us a
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              little below demonſtrated, be well underſtood, there may be
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              thence taken a very ſafe and juſt way to diſtribute ſuch waters.
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              <s>The Propoſition therefore by us demonſtrated is this: If there
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              be two Sections, (namely two mouths of Rivers) the quantity of
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              the water which paſſeth by the firſt, hath a proportion to that
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              which paſſeth by the ſecond, compounded of the proportions of
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              the firſt Section to the ſecond, and of the velocity through
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              the firſt, to the velocity through the ſecond: As I will declare
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              for example by help of practice, that I may be underſtood by
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              all, in a matter ſo important. </s>
              <s>Let the two mouths of the
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              Rivers be A, and B, and let
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              the mouth A be in meaſure
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              and content thirty two feet,
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              and the mouth B, eight feet.
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              <s>Here you muſt take notice,
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              that it is not alwayes true, that
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              the Water which paſſeth by A,
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              hath the ſame proportion to that which paſſeth by B, that the
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              mouth A hath to the mouth B; but onely when the velocityes
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              by each of thoſe paſſages are equal: But if the velocityes ſhall
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              be unequal, it may be that the ſaid mouths may emit equal
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              quantity of Water in equal times, though their meaſure be un­
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              equal; and it may be alſo, that the bigger doth diſcharge a great­
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              er quantity of Water: And laſtly, it may be, that the leſs mouth
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              diſchargeth more Water than the greater; and all this is mani­
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              feſt by the things noted in the beginning of this diſcourſe, and
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              by the ſaid ſecond Propoſition. </s>
              <s>Now to examine the propor­
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              tion of the Water that paſſeth by one Ditch, to that which paſ­
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              ſeth by another, that this being known, the ſame Waters and
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              mouths of Ditches may be then adjuſted; we are to keep ac­
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              count not onely of the greatneſs of the mouths or paſſages of the
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              Water, but of the velocity alſo; which we will do, by firſt find­
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              ing two numbers that have the ſame proportion between them­</s>
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