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

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          <pb o="92" file="0144" n="144" rhead="THEORIÆ"/>
          <p>
            <s xml:space="preserve">203. </s>
            <s xml:space="preserve">Interea hic illud poſtremo loco adnotabo, quod perti-
              <lb/>
              <note position="left" xlink:label="note-0144-01" xlink:href="note-0144-01a" xml:space="preserve">Acceſſum alte-
                <lb/>
              rius e binis ad
                <lb/>
              planum quod.
                <lb/>
              vis ulterius æ-
                <lb/>
              quari receſsui
                <lb/>
              ex vi mutua.</note>
            net ad duorum punctorum motum ibi uſui futurum: </s>
            <s xml:space="preserve">ſi duo
              <lb/>
            puncta moveantur viribus mutuis tantummodo, & </s>
            <s xml:space="preserve">ultra ipſa
              <lb/>
            aſſumatur planum quodcunque; </s>
            <s xml:space="preserve">acceſſus alterius ad illud pla-
              <lb/>
            num ſecundum directionem quamcunque, æquabitur receſſui al-
              <lb/>
            terius. </s>
            <s xml:space="preserve">Id ſponte conſequitur ex eo, quod eorum abſoluti mo-
              <lb/>
            tus ſint æquales, & </s>
            <s xml:space="preserve">contrarii; </s>
            <s xml:space="preserve">cum inde ſiat, ut ad directionem
              <lb/>
            aliam quamcunque redacti æquales itidem maneant, & </s>
            <s xml:space="preserve">contra-
              <lb/>
            rii, ut erant ante. </s>
            <s xml:space="preserve">Sed de æquilibrio, & </s>
            <s xml:space="preserve">motibus duorum
              <lb/>
            punctorum jam ſatis.</s>
            <s xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Tranſitus ad ſi-
            <lb/>
          ſtema puncto-
            <lb/>
          rum trium:
            <lb/>
          bina generalia
            <lb/>
          problemata.</note>
          <p>
            <s xml:space="preserve">204. </s>
            <s xml:space="preserve">Deveniendo ad ſyſtema trium punctorum, uti etiam pro
              <lb/>
            punctis quotcunque, res, ſi generaliter pertractari deberet, re-
              <lb/>
            duceretur ad hæc duo problemata, quorum alterum pertinet ad
              <lb/>
            vires, & </s>
            <s xml:space="preserve">alterum ad motus: </s>
            <s xml:space="preserve">1. </s>
            <s xml:space="preserve">Data poſitione, & </s>
            <s xml:space="preserve">diſtantia mu-
              <lb/>
            tua eorum punctorum, invenire magnitudinem, & </s>
            <s xml:space="preserve">directionem
              <lb/>
            vis, qua urgetur quodvis ex ipſis, compoſitæ a viribus, quibus
              <lb/>
            urgetur a reliquis, quarum ſingularum virium lex communis
              <lb/>
            datur per curvam ſiguræ primæ. </s>
            <s xml:space="preserve">2. </s>
            <s xml:space="preserve">Data illa lege virium ſi-
              <lb/>
            guræ primæ invenire motus eorum punctorum, quorum ſingula
              <lb/>
            cum datis velocitatibus projiciantur ex datis locis cum datis di-
              <lb/>
            rectionibus. </s>
            <s xml:space="preserve">Primum facile ſolvi poteſt, & </s>
            <s xml:space="preserve">poteſt etiam o-
              <lb/>
            pe curvæ ſiguræ 1 determinari lex virium generaliter pro o-
              <lb/>
            mnibus diſtantiis aſſumptis in quavis recta poſitionis datæ,
              <lb/>
            atque id tam geometrice determinando per puncta curvas,
              <lb/>
            quæ ejuſmodi legem exhibeant, ac determinent ſive magni-
              <lb/>
            tudinem vis abſolutæ, ſive magnitudines binarum virium, in
              <lb/>
            quas ea concipiatur reſoluta, & </s>
            <s xml:space="preserve">quarum altera ſit perpendi-
              <lb/>
            cularis datæ illi rectæ, altera ſecundum illam agat; </s>
            <s xml:space="preserve">quam
              <lb/>
            exhibendo tres formulas analyticas, quæ id præſtent. </s>
            <s xml:space="preserve">Secun-
              <lb/>
            dum omnino generaliter acceptum, & </s>
            <s xml:space="preserve">ita, ut ipſas curvas de-
              <lb/>
            ſcribendas liceat deſinire in quovis caſu vel conſtructione, vel
              <lb/>
            calculo, ſuperat (licet puncta ſint tantummodo tria) vires me-
              <lb/>
            thodorum adhuc cognitarum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi pro tribus punctis ſubſtituan-
              <lb/>
            tur tres maſſæ punctorum, eſt illud ipſum celeberrimum pro-
              <lb/>
            blema quod appellant trium corporum, uſque adeo quæſitum
              <lb/>
            per hæc noſtra tempora, & </s>
            <s xml:space="preserve">non niſi pro peculiaribus qui-
              <lb/>
            buſdam caſibus, & </s>
            <s xml:space="preserve">cum ingentibus limitationibus, nec ad
              <lb/>
            huc ſatis promoto ad accurationem calculo, ſolutum a pau-
              <lb/>
            ciſſimis noſtri ævi Geometris primi ordinis, uti diximus num.
              <lb/>
            </s>
            <s xml:space="preserve">122.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">205. </s>
            <s xml:space="preserve">Pro hoc ſecundo caſu illud eſt notiſſimum, ſi tria pun-
              <lb/>
              <note position="left" xlink:label="note-0144-03" xlink:href="note-0144-03a" xml:space="preserve">Theorema de
                <lb/>
              motu puncti ha-
                <lb/>
              bentis actionem
                <lb/>
              cum aliis binis.</note>
            cta ſint in ſig. </s>
            <s xml:space="preserve">21 A, C, B, & </s>
            <s xml:space="preserve">diſtantia A B duorum divi-
              <lb/>
            ſa ſemper bifariam in D, ac ducta C D, & </s>
            <s xml:space="preserve">aſſumpto ejus
              <lb/>
            triente D E, utcunque moveantur eadem puncta motibus com-
              <lb/>
              <note position="left" xlink:label="note-0144-04" xlink:href="note-0144-04a" xml:space="preserve">Fig. 21.</note>
            poſitis a projectionibus quibuſcunque, & </s>
            <s xml:space="preserve">mutuis viribus; </s>
            <s xml:space="preserve">pun-
              <lb/>
            ctum E debere vel quieſcere ſemper, vel progredi in directum
              <lb/>
            motu uniformi. </s>
            <s xml:space="preserve">Pendet id a generali theoremate de centro
              <lb/>
            gravitatis, cujus & </s>
            <s xml:space="preserve">ſuperius injecta eſt mentio, & </s>
            <s xml:space="preserve">de quo </s>
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