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

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              <pb o="25" file="0077" n="77" rhead="PARS PRIMA."/>
            quod horas dirimit, binæ debebunt eſſe denſitates ſimul, nimi-
              <lb/>
            rum & </s>
            <s xml:space="preserve">ſimplex, & </s>
            <s xml:space="preserve">dupla, quæ ſunt reales binarum realium
              <lb/>
            ſerierum termini.</s>
            <s xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Unde huc
            <lb/>
          transferenda ſo-
            <lb/>
          lutio ipſa.</note>
          <p>
            <s xml:space="preserve">53. </s>
            <s xml:space="preserve">Id ipſum in diſſertatione De lege virium in Natura exi-
              <lb/>
            ſtentium ſatis, ni fallor, luculenter expoſui, ac geometricis fi-
              <lb/>
            guris illuſtravi, adjectis nonnullis, quæ eodem recidunt, & </s>
            <s xml:space="preserve">
              <lb/>
            quæ in applicatione ad rem, de qua agimus, & </s>
            <s xml:space="preserve">in cujus gra-
              <lb/>
            tiam hæc omnia ad legem continuitatis pertinentia allata ſunt,
              <lb/>
            proderunt infra; </s>
            <s xml:space="preserve">libet autem novem ejus diſſertationis nume-
              <lb/>
            ros huc transferre integros, incipiendo ab octavo, ſed numeros
              <lb/>
            ipſos, ut & </s>
            <s xml:space="preserve">ſchematum numeros mutabo hic, ut cum ſupe-
              <lb/>
            rioribus conſentiant.</s>
            <s xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Solutio peti
            <lb/>
          ta ex geometri-
            <lb/>
          co exemplo.</note>
          <p>
            <s xml:space="preserve">54. </s>
            <s xml:space="preserve">Sit in fig. </s>
            <s xml:space="preserve">8. </s>
            <s xml:space="preserve">circulus GMM'm, qui referatur ad
              <lb/>
            datam rectam A B per ordinatas H M ipſi rectæ perpendi-
              <lb/>
            culares; </s>
            <s xml:space="preserve">uti itidem perpendiculares ſint binæ tangentes
              <lb/>
              <note position="right" xlink:label="note-0077-03" xlink:href="note-0077-03a" xml:space="preserve">Fig. 8.</note>
            EGF, E'G'F'. </s>
            <s xml:space="preserve">Concipiantur igitur recta quædam indeſi-
              <lb/>
            nita ipſi rectæ A B perpendicularis, motu quodam continuo
              <lb/>
            delata ab A ad B. </s>
            <s xml:space="preserve">Ubi ea habuerit, poſitionem quamcum-
              <lb/>
            que CD, quæ præcedat tangentem EF, vel C'D', quæ con-
              <lb/>
            ſequatur tangentem E' F'; </s>
            <s xml:space="preserve">ordinata ad circulum nulla erit,
              <lb/>
            ſive erit impoſſibilis, & </s>
            <s xml:space="preserve">ut Geometræ loquuntur, imaginaria.
              <lb/>
            </s>
            <s xml:space="preserve">Ubic unque autem ea ſit inter binas tangentes EGF,
              <lb/>
            E'G'F', in HI, H'I', occurret circulo in binis punctis M,
              <lb/>
            m, vel M'm', & </s>
            <s xml:space="preserve">habebitur valor ordinatæ HM, Hm, vel
              <lb/>
            H'M', H'm'. </s>
            <s xml:space="preserve">Ordinata quidem ipſa reſpondet ſoli interval-
              <lb/>
            lo E E': </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi ipſa linea A B referat tempus; </s>
            <s xml:space="preserve">momentum E
              <lb/>
            eſt limes inter tempus præcedens continuum A E, quo or-
              <lb/>
            dinata non eſt, & </s>
            <s xml:space="preserve">tempus continuum E E' ſubſequens, quo
              <lb/>
            ordinata eſt; </s>
            <s xml:space="preserve">punctum E' eſt limes inter tempus præcedens
              <lb/>
            E E', quo ordinata eſt, & </s>
            <s xml:space="preserve">ſubſequens E'B, quo non eſt. </s>
            <s xml:space="preserve">
              <lb/>
            Vita igitur quædam ordinatæ eſt tempus E E': </s>
            <s xml:space="preserve">ortus habetur
              <lb/>
            in E, interitus in E'. </s>
            <s xml:space="preserve">Quid autem in ipſo ortu, & </s>
            <s xml:space="preserve">interitu? </s>
            <s xml:space="preserve">
              <lb/>
            Habetur-ne quoddam eſſe ordinatæ, an non eſſe? </s>
            <s xml:space="preserve">Habetur uti-
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            que eſſe, nimirum E G, vel E'G', non autem non eſſe. </s>
            <s xml:space="preserve">O-
              <lb/>
            ritur tota finitæ magnitudinis ordinata E G, interit tota fi-
              <lb/>
            nitæ magnitudinis E'G', nec tamen ibi conjungit eſſe, & </s>
            <s xml:space="preserve">non
              <lb/>
            eſſe, nec ullum abſurdum ſecum trahit. </s>
            <s xml:space="preserve">Habetur momento E
              <lb/>
            primus terminus ſeriei ſequentis ſine ultimo ſeriei præceden-
              <lb/>
            tis, & </s>
            <s xml:space="preserve">habetur momento E' ultimus terminus ſeriei præceden-
              <lb/>
            tis ſine primo termino ſeriei ſequentis.</s>
            <s xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Solutio ex me-
            <lb/>
          taphyſica con-
            <lb/>
          ſideratione.</note>
          <p>
            <s xml:space="preserve">55. </s>
            <s xml:space="preserve">Quare autem id ipſum accidat, ſi metaphyſica conſi-
              <lb/>
            deratione rem perpendimus, ſtatim patebit. </s>
            <s xml:space="preserve">Nimirum veri
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            nihili nullæ ſunt veræ proprietates: </s>
            <s xml:space="preserve">entis realis veræ, & </s>
            <s xml:space="preserve">
              <lb/>
            reales proprietates ſunt. </s>
            <s xml:space="preserve">Quævis realis ſeries initium rea-
              <lb/>
            le habere debet, & </s>
            <s xml:space="preserve">finem, ſive primum, & </s>
            <s xml:space="preserve">ultimum termi-
              <lb/>
            num. </s>
            <s xml:space="preserve">Id, quod non eſt, nullam habet veram proprietatem,
              <lb/>
            nec proinde ſui generis ultimum terminum, aut primum exi-
              <lb/>
            git. </s>
            <s xml:space="preserve">Series præcedens ordinatæ nullius, ultimum terminum </s>
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