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

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            <p type="main">
              <s>
                <pb xlink:href="068/01/085.jpg" pagenum="71"/>
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                <lb/>
              Book^{*} of the meaſure of Running Watets;) but yet doth not
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              run thorowout with the ſame velocity: Hence it is, that the vul­
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              gar meaſures of the ſaid River, in divers parts of its Chanel, are
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              alwaies divers; inſomuch, that if a River paſſing through its cha­
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              nel had ſuch velocity, that it ran 100 Braces in the 1/60 of an hour­
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              and afterwards the ſaid River ſhould be reduced to ſo much tardi,
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              ty of motion, as that in the ſame time it ſhould not run more than
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              one Brace, it would be neceſſary that that ſame River ſhould be­
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              come 100. times bigger in that place where it was retarded; I
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              mean, 100. times bigger than it was in the place where it was
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              ſwifter. </s>
              <s>And let it be kept well in mind, that this point rightly
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              underſtood, will clear the underſtanding to diſcover very many
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              accidents worthy to be known. </s>
              <s>But for this time let it ſuffice,
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              that we have onely declared that which makes for our purpoſe,
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              referring apprehenſive and ſtudious Wits to the peruſal of my
                <lb/>
              aforenamed Treatiſe; for therein he ſhall finde profit and delight
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              both together.</s>
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            <p type="margin">
              <s>
                <margin.target id="marg973"/>
              * He here intends
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              the Demonſtrati­
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              ons following, at
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              the end of the firſt
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              Book</s>
            </p>
            <p type="main">
              <s>Now applying all to our principal intent, I ſay, That by what
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              hath been declared it is manifeſt, that if the
                <emph type="italics"/>
              Brent
                <emph.end type="italics"/>
              were 40. Bra­
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              ces broad, and 2 1/2 high, in ſome one part of its Chanel, that after­
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              wards the ſame Water of the
                <emph type="italics"/>
              Brent
                <emph.end type="italics"/>
              falling into the Lake, andpaſ­
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              ſing thorow the ſame to the Sea, it ſhould loſe ſo much of its ve­
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              locity, that it ſhould run but one Brace, in the time wherein
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              whilſt it was in its Chanel at the place aforeſaid, it ran 100. Bra­
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              ces. </s>
              <s>It would be abſolutely neceſſary, that increaſing in mea­
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              ſure, it ſhould become an hundred times ^{*} thicker; and therefore
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                <arrow.to.target n="marg974"/>
                <lb/>
              if we ſhould ſuppoſe that the Lake were 20000. Braces, the
                <lb/>
                <emph type="italics"/>
              Brent
                <emph.end type="italics"/>
              that already hath been ſuppoſed in its Chanel 100. Braces,
                <lb/>
              being brought into the Lake, ſhould be 100. times 100. Brates;
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              that is, ſhall be 10000. Braces in thickneſs, and conſequently ſhall
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              be in height half a Brace; that is, 100/200 of a Brace, and not 1/2. of a
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              Brace, as was concluded in the Argument.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg974"/>
              * Deeper.</s>
            </p>
            <p type="main">
              <s>Now one may ſee into what a groſs errour of 99. in 100. one
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              may fall through the not well underſtanding the true quantity
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              of Running Water, which being well underſtood, doth open a
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              direct way to our judging aright in this moſt conſiderable affair.</s>
            </p>
            <p type="main">
              <s>And therefore admitting that wich hath been demonſtrated,
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              I fay, that I would (if it did concern me) greatly encline to con­
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              ſult upon the returning of the
                <emph type="italics"/>
              Brent
                <emph.end type="italics"/>
              again into the Lake: For it
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              being moſt evident, that the
                <emph type="italics"/>
              Brent
                <emph.end type="italics"/>
              in the Chanel of its mouth, is
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              much ſwifter than the
                <emph type="italics"/>
              Brent
                <emph.end type="italics"/>
              being brought into the Lake, it will
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              certainly follow thereupon, that the thickneſs of the Water of
                <lb/>
                <emph type="italics"/>
              Brent
                <emph.end type="italics"/>
              in the Lake, ſhall be ſo much greater than that of
                <emph type="italics"/>
              Brent
                <emph.end type="italics"/>
              in
                <lb/>
                <emph type="italics"/>
              Brent,
                <emph.end type="italics"/>
              by how much the
                <emph type="italics"/>
              Bront
                <emph.end type="italics"/>
              in
                <emph type="italics"/>
              Brent
                <emph.end type="italics"/>
              is ſwifter than thh
                <emph type="italics"/>
              Brent
                <emph.end type="italics"/>
                <lb/>
              in the Lake.</s>
            </p>
          </chap>
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