Bošković, Ruđer Josip, Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium

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          <p>
            <s xml:space="preserve">
              <pb o="53" file="0105" n="105" rhead="PARS PRIMA"/>
            debeat. </s>
            <s xml:space="preserve"> Continetur autem id ipſum num. </s>
            <s xml:space="preserve">75, illius diſſertationis, ubi habetur hujuſmodi Problema: </s>
            <s xml:space="preserve">Invenire natu-
              <lb/>
            ram curvæ, cujus abſciſſis exprimentibus diſtantias, ordinatæ ex-
              <lb/>
            primant vires, mutatis diſtantiis utcunque mutatas, & </s>
            <s xml:space="preserve">in datis
              <lb/>
            quotcunque limitibus tranſeuntes e repulſrvis in attr
              <gap/>
            ctivas, ac
              <lb/>
            ex attractivis in repulſivas, in minimis autem diſtaǹtiis repulſi-
              <lb/>
            vas, & </s>
            <s xml:space="preserve">ita creſcentes, ut ſint pares extinguendæ cuicunque ve-
              <lb/>
            locitati utcunque magnœ. </s>
            <s xml:space="preserve">Propoſito problemate illud addo.
              <lb/>
            </s>
            <s xml:space="preserve">quoniam poſuimus mutatis diſtantiis utcunque mutatas, comple-
              <lb/>
            ctitur propoſitio etiam rationem, quæ ad rationem reciprocam du-
              <lb/>
            plicatam diſtantiarum accedat, quantum libuerit, in quibuſdam
              <lb/>
            ſatis magnis diſtantiis.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">118. </s>
            <s xml:space="preserve">His propoſitis numero illo 75, ſequenti numero pro-
              <lb/>
              <note position="right" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">Conditiones
                <lb/>
              ejus problema.
                <lb/>
              tis.</note>
            pono ſequentes ſex conditiones, quæ requirantur, & </s>
            <s xml:space="preserve">ſufficiant
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            ad habendam curvam, quæ quæritur. </s>
            <s xml:space="preserve">primo: </s>
            <s xml:space="preserve">ut ſit regularis, ac
              <lb/>
            ſimplex, & </s>
            <s xml:space="preserve">non compoſita ex aggregato arcuum diverſarum cur-
              <lb/>
            varum. </s>
            <s xml:space="preserve">Secundo: </s>
            <s xml:space="preserve">ut ſecet axem C` A C figuræ 1. </s>
            <s xml:space="preserve">tantum in pun-
              <lb/>
              <note position="right" xlink:label="note-0105-02" xlink:href="note-0105-02a" xml:space="preserve">Fig. 1</note>
            ctis quibuſdam datis ad binas diſtantias AE`, AE; </s>
            <s xml:space="preserve">AG`,
              <lb/>
            AG, & </s>
            <s xml:space="preserve">ita porro æquales binc, & </s>
            <s xml:space="preserve">inde. </s>
            <s xml:space="preserve">Tertio: </s>
            <s xml:space="preserve">ut ſin- gulis abſciſſis reſpondeant ſingulæ ordinatœ. </s>
            <s xml:space="preserve"> Quarto: </s>
            <s xml:space="preserve">ut ſumptis abſciſſis æqualibus binc, & </s>
            <s xml:space="preserve">inde ab A, reſpondeant or-
              <lb/>
            dinatæ æquales. </s>
            <s xml:space="preserve">Quinto: </s>
            <s xml:space="preserve">ut babeant rectam AB pro aſymptoto,
              <lb/>
            area aſymptotica BAED exiſtente infinita. </s>
            <s xml:space="preserve">Sexto: </s>
            <s xml:space="preserve">ut ar- cus binis quibuſcunque interſectionibus terminati poſſint variari,
              <lb/>
            ut libuerit, & </s>
            <s xml:space="preserve">ad quaſcunque diſtantias recedere ab axe C`AC,
              <lb/>
            ac accedere ad quoſcunque quarumcunque curvarum arcus, quan-
              <lb/>
            tum libuerit, eos ſecando, vel tangendo, vel oſculando ubicun-
              <lb/>
            que, & </s>
            <s xml:space="preserve">quomodocunque libuerit.</s>
            <s xml:space="preserve"/>
          </p>
          <note symbol="(c)" position="foot" xml:space="preserve">Qui velit ipſam rei determinationem videre, poterit bic in fine,
            <lb/>
          abi Supplemontorum §. 3. exbibebitur ſolutio problematis, quæ in memorata
            <lb/>
          diſſertatione continetar a num. 77. ad 110. Sed & numerorum orde, & fi-
            <lb/>
          gurarum mutabitur, at cam reliquis bujuſce operis cobæreat.</note>
          <note position="foot" xml:space="preserve">Addetur prœterea eidem §. poſtremum ſcbolium pertinens ad quæſtionem
            <lb/>
          agitatam ante bos aliquot annos Pariſiis; an vis matua inter materiæ par-
            <lb/>
          ticulas debeat omnino exprimi per ſolam aliquam diſtantiæ potentiam, an
            <lb/>
          poſſit per aliquam ejus ſunctionem; & conſtabit, poſſe utique per functio-
            <lb/>
          nem, ut bic ego præſto, quæ uti ſuperiore numero de curvis eſt dictum,
            <lb/>
          eſt in ſe æque ſimplex etiam, ubi nobis potentias ad ejus expreſſionem ad-
            <lb/>
          bibentibus videatur admodum compoſita.</note>
          <note symbol="(d)" position="foot" xml:space="preserve">Id, ut & quarta conditio, requiritur, ut curva utrinque ſit ſui
            <lb/>
          ſimilis, quod ipſam magis uniformem reddit; quanquam de illo crure,
            <lb/>
          quod eſt citra aſymptotum AB, nibil eſt, quod ſaliciti ſimus; cum ob vim
            <lb/>
          repulſivam imminutis diſtantiis ita in infinitum excreſcentem, non poſſ
            <gap/>
          ab-
            <lb/>
          ſciſſa diſtantiam exprimens unquam evadere zero, & abire in negativam.</note>
          <note symbol="(e)" position="foot" xml:space="preserve">Nam ſingulis diſtantiis ſingulæ vires reſpondent.</note>
          <note symbol="(f)" position="foot" xml:space="preserve">Id requiritur, quia in Mecbanica demonſtratur, aream curvœ, cujus
            <lb/>
          abſciſſæ exprimant diſtantias, & ordinatœ vires, exprimere incrementum,
            <lb/>
          vel decrementum quadrati velocitatis: quare ut illæ vires ſint pares extin-
            <lb/>
          guenàœ velocitati cuivis utcunque magnæ, debet illa area eſſe omni ſinit
            <gap/>
            <lb/>
            <gap/>
          ajor.</note>
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