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

Table of contents

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[341.] Experimentum 3.
[342.] Experimentum 4.
[343.] SCHOLIUM, Demonſtrationes n. 914. & 915.
[344.] F f, F g :: FC aut IH, FH
[345.] CAPUT XII. De Retardatione Corporum in Fluidis motorum.
[346.] Machina, Qua Experimenta de Pendulorum Retardationibus inſtituuntur.
[347.] Experimentum.
[348.] SCHOLIUM 1. De Logarithmica.
[349.] Definitio 1.
[350.] Definitio 2.
[351.] AC, HI :: LM, RS ; & dividendo
[352.] TC, VM:: AC, LM.
[353.] C c, c E:: CA, AT, & M m, m O :: ML, LV.
[354.] SCHOLIUM 2. De Retardatione in genere.
[355.] SCHOLIUM 3. De Retardatione ex prima Cauſa.
[356.] SCHOLIUM 4. De Retardatione ex ſecunda Cauſâ.
[357.] SCHOLIUM 5. De ambabus Retardationibus conjunctim.
[358.] B Iq - PRq, PRq :: AI-AB = BI, AB.
[359.] SCHOLIUM. 6 De Corporibus in altum projectis.
[360.] SCHOLIUM. 7. De Corporibus in Fluidis cadentibus.
[361.] f L, k M :: {E e/FE}, {Ii/KI} :: {CD/FE} = {BA/FE} -{BE/FE}, {GH/KI} = {BA/KI} - {BI/KI}
[362.] fL, kM :: {BA/FE}-{FE/BA}, {BA/KI} = {KI/BA}
[363.] SCHOLIUM 8. Illuſtratio quorundam quæ ad retardationem ſpectant.
[364.] LIBRI II. Pars III. De Aëre, & aliis Fluidis Elaſticis. CAPUT XIII. Aërem Fluidorum proprietates habere.
[365.] Definitio 1.
[366.] Definitio 2.
[367.] Experimentum 1.
[368.] Experimentum 2.
[369.] Experimentum 3.
[370.] Experimentum 4.
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          <pb o="247" file="0343" n="376" rhead="MATHEMATICA. LIB. II. CAP. IX."/>
        </div>
        <div xml:id="echoid-div1300" type="section" level="1" n="331">
          <head xml:id="echoid-head460" xml:space="preserve">
            <emph style="sc">Definitio.</emph>
          2.</head>
          <p style="it">
            <s xml:id="echoid-s9194" xml:space="preserve">Flumen in eodem ſtatu manere, aut in ſtatu manente,
              <lb/>
              <note position="right" xlink:label="note-0343-01" xlink:href="note-0343-01a" xml:space="preserve">856.</note>
            dicitur, quando aqua uniformiter fluit, ita ut in eodem lo-
              <lb/>
            co ſemper ſit ad eandem altitudinem.</s>
            <s xml:id="echoid-s9195" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1302" type="section" level="1" n="332">
          <head xml:id="echoid-head461" xml:space="preserve">
            <emph style="sc">Definitio.</emph>
          3.</head>
          <p style="it">
            <s xml:id="echoid-s9196" xml:space="preserve">Sectio Fluminis vocatur planum Flumen ſecans perpen-
              <lb/>
              <note position="right" xlink:label="note-0343-02" xlink:href="note-0343-02a" xml:space="preserve">857.</note>
            diculariter ad fundum, & </s>
            <s xml:id="echoid-s9197" xml:space="preserve">ad quæ directionem in medio, ut
              <lb/>
            ponq.</s>
            <s xml:id="echoid-s9198" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9199" xml:space="preserve">Quando Flumen a lateribus terminatur, planis inter ſe pa-
              <lb/>
            rallelis, & </s>
            <s xml:id="echoid-s9200" xml:space="preserve">ad horizontem normalibus, & </s>
            <s xml:id="echoid-s9201" xml:space="preserve">fundus etiam eſt
              <lb/>
            planum, ſive horizontale, ſive inclinatum, ſectio Fluminis
              <lb/>
            cum tribus hiſce planis angulos rectos efficit, & </s>
            <s xml:id="echoid-s9202" xml:space="preserve">eſt paralle-
              <lb/>
            logrammum.</s>
            <s xml:id="echoid-s9203" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9204" xml:space="preserve">In omni Flumine in ſtatu manente, eadem aquæ quantitas
              <lb/>
              <note position="right" xlink:label="note-0343-03" xlink:href="note-0343-03a" xml:space="preserve">858.</note>
            per ſingulas ſectiones eodem tempore fluit. </s>
            <s xml:id="echoid-s9205" xml:space="preserve">Niſi enim in lo-
              <lb/>
            co quocunque eadem aquæ quantitas adfluat, quæ ex eo
              <lb/>
            defluit, in eodem ſtatu Flumen non manebit; </s>
            <s xml:id="echoid-s9206" xml:space="preserve">& </s>
            <s xml:id="echoid-s9207" xml:space="preserve">demon-
              <lb/>
            ſtratio hæc locum habet, quæcunque fuerit alvei irregula-
              <lb/>
            ritas, ex qua, alio reſpectu, multæ in Fluminis motu mu-
              <lb/>
            tationes oriuntur; </s>
            <s xml:id="echoid-s9208" xml:space="preserve">attritus ex. </s>
            <s xml:id="echoid-s9209" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s9210" xml:space="preserve">major eſt pro majore al-
              <lb/>
            vei inæqualitate.</s>
            <s xml:id="echoid-s9211" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9212" xml:space="preserve">Irregularitates in Fluminis motu in infinitum variari
              <lb/>
            poſſunt, & </s>
            <s xml:id="echoid-s9213" xml:space="preserve">regulæ circa illas tradi nequeunt; </s>
            <s xml:id="echoid-s9214" xml:space="preserve">ſepoſitis
              <lb/>
            ergo irregularitatibus omnibus Fluminum curſus exami-
              <lb/>
            nandus eſt; </s>
            <s xml:id="echoid-s9215" xml:space="preserve">niſi enim in hoc caſu motus leges notæ fue-
              <lb/>
            rint, de nullo judicium, vero fundamento nixum, ferri
              <lb/>
            poterit.</s>
            <s xml:id="echoid-s9216" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9217" xml:space="preserve">Ponimus ergo aquam fluere per canalem regularem, ſi-
              <lb/>
              <note position="right" xlink:label="note-0343-04" xlink:href="note-0343-04a" xml:space="preserve">859.</note>
            ne ſenſibili attritu; </s>
            <s xml:id="echoid-s9218" xml:space="preserve">canalem terminari ad latera planis pa-
              <lb/>
            rallelis inter ſe & </s>
            <s xml:id="echoid-s9219" xml:space="preserve">verticalibus; </s>
            <s xml:id="echoid-s9220" xml:space="preserve">fundumque etiam planum
              <lb/>
            eſſe & </s>
            <s xml:id="echoid-s9221" xml:space="preserve">ad horizontem inclinari.</s>
            <s xml:id="echoid-s9222" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9223" xml:space="preserve">Sit canalis A E; </s>
            <s xml:id="echoid-s9224" xml:space="preserve">ex receptaculo majori aqua in illum
              <lb/>
            fluat, maneatque in receptaculo ſemper ad eandem altitu-
              <lb/>
            dinem, ut Flumen ſit in ſtatu manenti. </s>
            <s xml:id="echoid-s9225" xml:space="preserve">Aqua juxta pla-
              <lb/>
            num inclinatum deſcendit & </s>
            <s xml:id="echoid-s9226" xml:space="preserve">acceleratur ; </s>
            <s xml:id="echoid-s9227" xml:space="preserve">quo,
              <note symbol="*" position="right" xlink:label="note-0343-05" xlink:href="note-0343-05a" xml:space="preserve">263.</note>
            æqualem aquæ quantitatem per ſingulas ſectiones </s>
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