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

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              <pb o="188" file="0240" n="240" rhead="THEORIÆ"/>
            ſionis, juxta num. </s>
            <s xml:space="preserve">179; </s>
            <s xml:space="preserve">unde fit, ut ſi interſectionum ſe con-
              <lb/>
            ſequentium aſſumatur numerus par; </s>
            <s xml:space="preserve">dimidium ſit limitum co-
              <lb/>
            hæſionis. </s>
            <s xml:space="preserve">Hinc quoniam in ſolutione problematis expoſiti num.
              <lb/>
            </s>
            <s xml:space="preserve">117 oſtenſum eſt, curvam ſimplicem illam meam habere poſ-
              <lb/>
            ſe quencunque demum interſectionum numerum; </s>
            <s xml:space="preserve">poterit uti-
              <lb/>
            que etiam pro duobus tantummodo punctis haberi quicunque
              <lb/>
            numerus diſtantiarum differentium a ſe invicem cum cohæſio-
              <lb/>
            ne. </s>
            <s xml:space="preserve">Poterunt autem ejuſmodi cohæſiones ipſæ eſſe diverſiſſi-
              <lb/>
            mæ a ſe invicem ſoliditatis, ac nexus, limitibus vel validiſſi-
              <lb/>
            mis, vel languidiſſimis utcunque, prout nimirum ibi curva ſe-
              <lb/>
            cuerit axem fere ad perpendiculum, & </s>
            <s xml:space="preserve">longiſſime abierit, vel
              <lb/>
            potius ad illum inclinetur plurimum, & </s>
            <s xml:space="preserve">parum admodum diſ-
              <lb/>
            cedat; </s>
            <s xml:space="preserve">nam in priore eorum caſuum vires repulſivæ imminu-
              <lb/>
            tis, & </s>
            <s xml:space="preserve">attractivæ auctis utcunque parum diſtantiis, ingentes
              <lb/>
            erunt; </s>
            <s xml:space="preserve">in poſteriore plurimum immutatis, perquam exiguæ. </s>
            <s xml:space="preserve">
              <lb/>
            Poterunt autem etiam e remotioribus limitibus aliqui eſſe mul-
              <lb/>
            to languidiores, & </s>
            <s xml:space="preserve">alii multo validiores aliquibus e propiori-
              <lb/>
            bus; </s>
            <s xml:space="preserve">ut idcirco cohæſionis vis nihil omnino pendeat a denſi-
              <lb/>
            tate, ſed cohæſio poſſit in denſioribus corporibus eſſe vel mul-
              <lb/>
            to magis, vel multo minus valida, quam in rarioribus, & </s>
            <s xml:space="preserve">id
              <lb/>
            in ratione quacunque.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">412. </s>
            <s xml:space="preserve">Quæ de binis punctis ſunt dicta, multo magis de maſ-
              <lb/>
              <note position="left" xlink:label="note-0240-01" xlink:href="note-0240-01a" xml:space="preserve">In maſſis nu-
                <lb/>
              merus limitum
                <lb/>
              multo major:
                <lb/>
              problema pro
                <lb/>
              iis inveniendis
                <lb/>
              quomodo ſol-
                <lb/>
              vendum.</note>
            ſis continentibus plurima puncta, dicenda ſunt. </s>
            <s xml:space="preserve">In iis numerus
              <lb/>
            limitum eſt adhuc major in immenſum, & </s>
            <s xml:space="preserve">diſcrimen utique
              <lb/>
            majus. </s>
            <s xml:space="preserve">Inventio omnium poſitionum pro dato punctorum nu-
              <lb/>
            mero, in quibus tota maſſa haberet limitem quendam virium,
              <lb/>
            eſſet problema moleſtum, & </s>
            <s xml:space="preserve">calculus ad id ſolvendum neceſſa-
              <lb/>
            rius in immenſum excreſceret, exiſtente aliquo majore puncto-
              <lb/>
            rum numero. </s>
            <s xml:space="preserve">Sed tamen data virium lege ſolvi utique poſſet.
              <lb/>
            </s>
            <s xml:space="preserve">Satis eſſet aſſumere poſitiones omnium punctorum reſpectu cu-
              <lb/>
            juſdam puncti in quadam arbitraria recta ad arbitrium collo-
              <lb/>
            cati, & </s>
            <s xml:space="preserve">ſubſtitutis ſingulorum binariorum diſtantiis a ſe invi-
              <lb/>
            cem in æquatione curvæ primæ pro abſciſſa, ac valoribus iti-
              <lb/>
            dem aſſumptis pro viribus ſingulorum punctorum pro ordina-
              <lb/>
            tis, eruere totidem æquationes, tum reducere vires ſingulas
              <lb/>
            fingulorum punctorum ad tres datas directiones, & </s>
            <s xml:space="preserve">ſummam
              <lb/>
            omnium eandem directionem habentium in quovis puncto po-
              <lb/>
            nere = o: </s>
            <s xml:space="preserve">orirentur æquationes, quæ paullatim eliminatis va-
              <lb/>
            loribus incognitis aſſumptis, demum ad æquationes perducerent
              <lb/>
            definientes punctorum diſtantias neceſſarias ad æquilibrium, & </s>
            <s xml:space="preserve">
              <lb/>
            reſpectivam quietem, quæ altiſſimæ eſſent, & </s>
            <s xml:space="preserve">plurimas habe-
              <lb/>
            rent radices; </s>
            <s xml:space="preserve">nam æquationes, quo altiores ſunt, eo plures ra-
              <lb/>
            dices habere poſſunt, ac ſingulis radicibus ſinguli limites exhi-
              <lb/>
            berentur, vel ſingulæ poſitiones exhibentes vim nullam. </s>
            <s xml:space="preserve">In-
              <lb/>
            ter ejuſmodi poſitiones illæ, in quibus repulſioni in minoribus
              <lb/>
            diſtantiis habitæ, ſuccederent attractiones in majoribus, exhi-
              <lb/>
            berent limites cohæſionis, qui adhuc eſſent quam plurimi, & </s>
            <s xml:space="preserve">
              <lb/>
            inter ſe magis diverſi, quam limites ad duo tantummodo </s>
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