Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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              <pb o="249" file="0345" n="378" rhead="MATHEMATICA. LIB. II. CAP. IX."/>
            pendiculares ducantur, eo hæ breviores erunt, quo magis
              <lb/>
            ab r diſtabunt, omniumque breviſſima erit sv; </s>
            <s xml:id="echoid-s9255" xml:space="preserve">ideoque
              <lb/>
            particularum, in linea rs, celeritates eo minores ſunt, quo
              <lb/>
            magis hæ ad ſuperficiem Fluminis accedunt, & </s>
            <s xml:id="echoid-s9256" xml:space="preserve">aqua infe-
              <lb/>
              <note position="right" xlink:label="note-0345-01" xlink:href="note-0345-01a" xml:space="preserve">864.</note>
            rior celerius ſuperiori movetur.</s>
            <s xml:id="echoid-s9257" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9258" xml:space="preserve">Harum tamen aquarum in progreſſu fluminis ad æqualita-
              <lb/>
              <note position="right" xlink:label="note-0345-02" xlink:href="note-0345-02a" xml:space="preserve">865.</note>
            tem continuo magis accedunt celeritates. </s>
            <s xml:id="echoid-s9259" xml:space="preserve">Nam celeritatum
              <lb/>
            harum quadrata ſunt ut rt ad sv, quarum linearum dif-
              <lb/>
            ferentia, recedendo a fluminis origine, continuo minuitur,
              <lb/>
            propter imminutam altitudinem rs, dum lineæ ipſæ
              <note symbol="*" position="right" xlink:label="note-0345-03" xlink:href="note-0345-03a" xml:space="preserve">860.</note>
            gentur. </s>
            <s xml:id="echoid-s9260" xml:space="preserve">Quod cum in quadratis obtineat, multo magis in
              <lb/>
            ipſis celeritatibus locum habet, quarum differentia ergo et-
              <lb/>
            iam minuitur, dum ipſæ creſcunt.</s>
            <s xml:id="echoid-s9261" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9262" xml:space="preserve">Si fundi inclinatio in principio fluminis mutetur ut ſit
              <lb/>
              <note position="right" xlink:label="note-0345-04" xlink:href="note-0345-04a" xml:space="preserve">866.</note>
            yZ, & </s>
            <s xml:id="echoid-s9263" xml:space="preserve">major aquæ quantitas in canalem fluat, altior erit
              <lb/>
            ubique in flumine, ſed non mutatur celeritas aquæ in loco quo-
              <lb/>
            cunque. </s>
            <s xml:id="echoid-s9264" xml:space="preserve">Hæc enim celeritas non ab altitudine aquæ in flu-
              <lb/>
            mine pendet, ſed, ut demonſtratum, a diſtantia inter par-
              <lb/>
            riculam motam & </s>
            <s xml:id="echoid-s9265" xml:space="preserve">planum horizontale per aquæ ſu-
              <lb/>
            perficiem in origine fluminis tranſiens; </s>
            <s xml:id="echoid-s9266" xml:space="preserve">quæ diſtantia per-
              <lb/>
            pendiculari ut rt aut sv menſuratur; </s>
            <s xml:id="echoid-s9267" xml:space="preserve">hæ autem adfluxu a-
              <lb/>
            quæ non variantur, ſi modo maneat aquæ ſuperficies in re-
              <lb/>
            ceptaculo.</s>
            <s xml:id="echoid-s9268" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9269" xml:space="preserve">Claudatur canalis pars ſuperior obſtaculo ut X, quod quan-
              <lb/>
              <note position="right" xlink:label="note-0345-05" xlink:href="note-0345-05a" xml:space="preserve">867.</note>
            tumvis parum infra aquæ ſuperficiem deſcendat; </s>
            <s xml:id="echoid-s9270" xml:space="preserve">aqua o-
              <lb/>
            mnis quæ adfluit perfluere non poterit, adſcendet idcirco;
              <lb/>
            </s>
            <s xml:id="echoid-s9271" xml:space="preserve">ſed eo celeritas aquæ infra cataractam non augetur ,
              <note symbol="*" position="right" xlink:label="note-0345-06" xlink:href="note-0345-06a" xml:space="preserve">866.</note>
            tinuoque accumulatur aqua adfluens; </s>
            <s xml:id="echoid-s9272" xml:space="preserve">quæ ergo ita
              <lb/>
            adſcendit ut ſupra impedimentum aut ripas fluminis de-
              <lb/>
            fluat. </s>
            <s xml:id="echoid-s9273" xml:space="preserve">Si vero ripæ eleventur & </s>
            <s xml:id="echoid-s9274" xml:space="preserve">impedimentum continue-
              <lb/>
            tur, ſupra lineam it aquæ altitudo excreſcet, antea enim
              <lb/>
            hujus celeritas augeri nequit: </s>
            <s xml:id="echoid-s9275" xml:space="preserve">in quo caſu totius aquæ in
              <lb/>
            receptaculo altitudo augebitur; </s>
            <s xml:id="echoid-s9276" xml:space="preserve">cum enim ponamus
              <lb/>
            flumen in ſtatu manenti neceſſe eſt ut aliunde continuo in
              <lb/>
            receptaculum tantum aquæ adfluat, quantum ex illo in flu-
              <lb/>
            men defluit; </s>
            <s xml:id="echoid-s9277" xml:space="preserve">imminuta verò aquæ defluentis </s>
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