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

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              <s>
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              I ſay that the proportion of the ſuperficies of the Veſſel A D is
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              in proportion to the meaſure of the ſection of the Emiſſary
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              H L, as the velocity of the Emiſſary or Cock to the line A F;
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              which is manifeſt, for that the Water in the Veſsel moving by
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              the line A F; as far as F, and the whole maſs of Water A G
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              diſcharging it ſelf, and in the ſame time the ſame quantity of
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              Water being diſcharged by the ſection of the Emiſſary H L; it
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              is neceſſary by what I have demonſtrated in the third Propoſition,
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              and alſo explained in the beginning of this Treatiſe, that the ve­
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              locity by the Emiſſary or Cock be in proportion to the velocity
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              of the abatement, as the ſuperficies of the Veſſel to the mea­
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              ſure of the ſection of the Emiſſary, which was to be demon­
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              ſtrated.</s>
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              <s>That which hath been demonſtrated in the Veſſel, falls out ex­
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              actly alſo in our Lake of
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              Perugia,
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              and its Emiſsary; and becauſe
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              the immenſity of the ſuperficies of the Lake is in proportion to
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              the ſuperficies of the Emiſsary or Sluice, as many millions to
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              one, as may be eaſily calculated; it is manifeſt, that ſuch abate­
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              ment ſhall be imperceptible, and almoſt nothing, in two dayes
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              ſpace, nay in four or ſix: and all this will be true, when we
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              ſuppoſe that for that time there entreth no other Water into the
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              Lake from Ditches or Rivolets, which falling into the Lake would
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              render ſuch abatement yet leſs.</s>
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              <s>Now we ſee, that it's neceſsary to examine ſuch abatements
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              and riſings, with excellent reaſons, or at leaſt, with accurate ex­
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              periments, before we reſolve and conclude any thing; and how
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              farre the vulgar are diſtant from a right judgment in ſuch
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              matters.</s>
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              <s>APPENDIX XIII.</s>
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              <s>For greater confirmation of all this which I have ſaid, I
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              will inſtance in another like caſe, which alſo I met with here­
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              tofore, wherein, for that the buſineſs was not rightly un­
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              derſtood, many diſorders, vaſt expences, and conſiderable miſ­
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              chiefs have followed. </s>
              <s>There was heretofore an Emiſsary or
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              Sluice made to drain the Waters, which from Rains, Springs, and
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              Rivolets fall into a Lake; to the end, the ſhores adjoyning on
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              the Lake, ſhould be free from the overflowing of the Waters;
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              but becauſe perhaps the enterprize was not well managed and
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              carried on, it fell out, that the Fields adjacent to the ſaid Chanel
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              could not drain, but continued under water; to which diſorders
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              a preſent remedy hath been uſed, namely, in a time convenient
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              to ſtop up the Sluice, by meanes of certain Floodgates kept on
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              purpoſe for that end; and thus abating the Level of the Water </s>
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          </chap>
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