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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        <div xml:id="echoid-div1494" type="section" level="1" n="359">
          <pb o="291" file="0393" n="429" rhead="MATHEMATICA. LIB. II. CAP. XII."/>
          <p>
            <s xml:id="echoid-s10562" xml:space="preserve">Ratio retardationis ex cohæſione, quæ æquabilis eſt , ad retardationem
              <note symbol="*" position="right" xlink:label="note-0393-01" xlink:href="note-0393-01a" xml:space="preserve">950.</note>
            inertia, in velocitate data, eſt compoſita ex ratione retardationis primæ ad
              <lb/>
            retardationem ex pondere reſpectivo, & </s>
            <s xml:id="echoid-s10563" xml:space="preserve">ratione retardationis hujus ad ſe-
              <lb/>
            cundam. </s>
            <s xml:id="echoid-s10564" xml:space="preserve">Vidimus rationes componentes dari, datur ergo & </s>
            <s xml:id="echoid-s10565" xml:space="preserve">compoſita, id
              <lb/>
              <note position="right" xlink:label="note-0393-02" xlink:href="note-0393-02a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig. 4.</note>
            eſt ſi hoc applicemus ad demonſtrata in ſcholio præcedenti , datur ratio AB ad BI; </s>
            <s xml:id="echoid-s10566" xml:space="preserve">unde deducitur ratio BI ad PR ; </s>
            <s xml:id="echoid-s10567" xml:space="preserve">qua data detegitur BP
              <note symbol="*" position="right" xlink:label="note-0393-03" xlink:href="note-0393-03a" xml:space="preserve"> 1013. 1014.</note>
            ſpatium quæſitum.</s>
            <s xml:id="echoid-s10568" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">1015. 1014.</note>
          <p>
            <s xml:id="echoid-s10569" xml:space="preserve">Corpus fluido ſpecifice levius, eodem modo in hoc ſurſum fertur, acgra-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0393-05" xlink:href="note-0393-05a" xml:space="preserve">1009.</note>
            vius fundum petit; </s>
            <s xml:id="echoid-s10570" xml:space="preserve">quare demonſtrata in hoc ſcholio, ad corpora fluidis ſpe-
              <lb/>
              <note position="right" xlink:label="note-0393-06" xlink:href="note-0393-06a" xml:space="preserve">1028.</note>
            cifice leviora, & </s>
            <s xml:id="echoid-s10571" xml:space="preserve">in his motu impreſſo deſcendentia referri debent.</s>
            <s xml:id="echoid-s10572" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1505" type="section" level="1" n="360">
          <head xml:id="echoid-head496" xml:space="preserve">SCHOLIUM. 7.</head>
          <head xml:id="echoid-head497" style="it" xml:space="preserve">De Corporibus in Fluidis cadentibus.</head>
          <p>
            <s xml:id="echoid-s10573" xml:space="preserve">COrpus quod in fluido ſponte cadit, continuo æquabiliter acceleratur , dum
              <note position="right" xlink:label="note-0393-07" xlink:href="note-0393-07a" xml:space="preserve">1029.</note>
            ſiſtentiam patitur, quæ eſt ut quadratum velocitatis .</s>
            <s xml:id="echoid-s10574" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">251. 950.</note>
          <p>
            <s xml:id="echoid-s10575" xml:space="preserve">Quæ motum hunc ſpectant etiam parabolâ, & </s>
            <s xml:id="echoid-s10576" xml:space="preserve">logarithmicâ exhiben-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0393-09" xlink:href="note-0393-09a" xml:space="preserve">954.</note>
            tur.</s>
            <s xml:id="echoid-s10577" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10578" xml:space="preserve">Sit QAR logarithmicæ BDH aſymtos; </s>
            <s xml:id="echoid-s10579" xml:space="preserve">ordinata hujus curvæ ad Aſymto-
              <lb/>
              <note position="right" xlink:label="note-0393-10" xlink:href="note-0393-10a" xml:space="preserve">1030.</note>
            ton perpendicularis AB; </s>
            <s xml:id="echoid-s10580" xml:space="preserve">quæ etiam eſt axis parabolæ BFQ, cujus para-
              <lb/>
              <note position="right" xlink:label="note-0393-11" xlink:href="note-0393-11a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig. 5.</note>
            metrum ponimus AB.</s>
            <s xml:id="echoid-s10581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10582" xml:space="preserve">Si AR repræſentat ſpatium cadendo percurſum, poſito in A puncto ex
              <lb/>
            quo corpus dimittitur, determinatur velocitas in puncto quocunque ut C,
              <lb/>
            ductâ CD ad AB parallelâ, &</s>
            <s xml:id="echoid-s10583" xml:space="preserve">per D ad RAQ parallelâ DEF, velocitatem
              <lb/>
            quæſitam deſignabit parabolæ ordinata EF, dum AQ velocitatem maxi-
              <lb/>
            mam exprimit, ad quam corpus non pertingit, niſi poſt percurſum ſpatium
              <lb/>
            AR in infinitum productum.</s>
            <s xml:id="echoid-s10584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10585" xml:space="preserve">Hæc patebunt ſi, ſumtis ad libitum ſpatiolis æqualibus infinite exiguis,
              <lb/>
            C c, G g demonſtremus augmenta velocitatum, quæ hìc f L & </s>
            <s xml:id="echoid-s10586" xml:space="preserve">k M expri-
              <lb/>
            munt, eſſe inter ſe inverſè ut lineæ FE & </s>
            <s xml:id="echoid-s10587" xml:space="preserve">KI, quas velocitates exprimere
              <lb/>
            dicimus, ſublatis partibus quæ ſunt ut ipſæ hæ lineæ FE & </s>
            <s xml:id="echoid-s10588" xml:space="preserve">KI .</s>
            <s xml:id="echoid-s10589" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">991. 993.
            <lb/>
          1029.</note>
        </div>
        <div xml:id="echoid-div1509" type="section" level="1" n="361">
          <head xml:id="echoid-head498" xml:space="preserve">f L, k M :: {E e/FE}, {Ii/KI} :: {CD/FE} = {BA/FE} -{BE/FE}, {GH/KI} = {BA/KI} - {BI/KI}</head>
          <note symbol="*" position="right" xml:space="preserve">995.</note>
          <note symbol="*" position="right" xml:space="preserve">983.</note>
          <p>
            <s xml:id="echoid-s10590" xml:space="preserve">Sed BE x BA = FE x FE; </s>
            <s xml:id="echoid-s10591" xml:space="preserve">ergo {BE/FE} = {FE/BA}. </s>
            <s xml:id="echoid-s10592" xml:space="preserve">Eodem modo
              <note symbol="*" position="right" xlink:label="note-0393-15" xlink:href="note-0393-15a" xml:space="preserve">la Hire
                <lb/>
              ſect. con.
                <lb/>
              lib. 3.
                <lb/>
              prop. 2.</note>
            = KI/BA}. </s>
            <s xml:id="echoid-s10593" xml:space="preserve">Idcirco</s>
          </p>
        </div>
        <div xml:id="echoid-div1511" type="section" level="1" n="362">
          <head xml:id="echoid-head499" xml:space="preserve">fL, kM :: {BA/FE}-{FE/BA}, {BA/KI} = {KI/BA}</head>
          <p>
            <s xml:id="echoid-s10594" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s10595" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10596" xml:space="preserve">Ut figurâ hac in computatione utamur, velocitas maxima ad quam corpus
              <lb/>
              <note position="right" xlink:label="note-0393-16" xlink:href="note-0393-16a" xml:space="preserve">1031.</note>
            pertingere poteſt, & </s>
            <s xml:id="echoid-s10597" xml:space="preserve">quæ QA repræſentatur, determinanda eſt:</s>
            <s xml:id="echoid-s10598" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10599" xml:space="preserve">Quærimus igitur velocitatem, qua conceſſa, retardatio ex ſecunda </s>
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