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

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            patet, ad idem loci punctum N per hæc parallelogramma de-
              <lb/>
            ſinitum debere devenire punctum mobile, quod prius percurrat
              <lb/>
            PA, tum AM parallelam, & </s>
            <s xml:space="preserve">æqualem PB; </s>
            <s xml:space="preserve">tum MN paral-
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            lelam, & </s>
            <s xml:space="preserve">æqualem PC, atque ita porro additis quotcunque
              <lb/>
            aliis motibus, vel viribus, quæ per nova parallela, & </s>
            <s xml:space="preserve">æqualia
              <lb/>
            parallelogrammorum latera debeant componi.</s>
            <s xml:space="preserve"/>
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          <p>
            <s xml:space="preserve">259. </s>
            <s xml:space="preserve">Deveniretur quidem ad idem punctum N, ſi alio etiam
              <lb/>
              <note position="right" xlink:label="note-0173-01" xlink:href="note-0173-01a" xml:space="preserve">Demonſtratio
                <lb/>
              generalis m
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              -
                <lb/>
              thodi-</note>
            ordine componerentur ii motus, vel vires, ut compoſitis viri-
              <lb/>
            bus PA, PC per parallelogrammum PAOC, tum vi PO
              <lb/>
            cu m vi PB per novum parallelogrammum, quod itidem ha-
              <lb/>
            beret cuſpidem in N; </s>
            <s xml:space="preserve">ſed eo deveniretur alia via PAON.
              <lb/>
            </s>
            <s xml:space="preserve">Hoc autem ipſum, quod tam multis viis, quam multas diver-
              <lb/>
            ſæ plurium compoſitiones motuum, ac virium exhibere poſ-
              <lb/>
            ſunt, eodem ſemper deveniri debeat, ſic generaliter demonſtro. </s>
            <s xml:space="preserve">
              <lb/>
            Si aſſumatur ultra omnia puncta, ad quæ per ejuſmodi com-
              <lb/>
            poſitiones deveniri poteſt, planum quodcunque; </s>
            <s xml:space="preserve">ubi punctum
              <lb/>
            mobile percurrit lineolam pertinentem ad quencunque determi-
              <lb/>
            natum motum, habet eundem perpendicularem acceſſum ad id
              <lb/>
            planum, vel receſſum ab eo, quocunque tempuſculo id fiat,
              <lb/>
            ſive aliquo e prioribus, ſive aliquo e poſtremis, vel mediis. </s>
            <s xml:space="preserve">
              <lb/>
            Nam ea lineola ex quocunque puncto diſcedat, ad quod deven-
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            tum jam ſit, habet ſemper eandem & </s>
            <s xml:space="preserve">longitudinem, & </s>
            <s xml:space="preserve">di-
              <lb/>
            rectionem, cum eidem e componentibus parallela eſſe debeat,
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            & </s>
            <s xml:space="preserve">æqualis. </s>
            <s xml:space="preserve">Quare ſumma ejuſmodi acceſſuum, ac ſumma
              <lb/>
            receſſuum erit eadem in fine omnium tempuſculorum, quo-
              <lb/>
            cunque ordine diſponantur lineolæ hæ parallelæ, & </s>
            <s xml:space="preserve">æquales
              <lb/>
            lineolis componentibus, adeoque etiam id, quod prodit demen-
              <lb/>
            do receſſuum ſummam a ſumma acceſſuum, vel vice verſa, erit
              <lb/>
            idem, & </s>
            <s xml:space="preserve">diſtantia puncti poſtremi, ad quod deventum eſt ab
              <lb/>
            illo eodem plano, erit eadem. </s>
            <s xml:space="preserve">Inde autem ſponte jam fluit
              <lb/>
            id, quod demonſtrandum erat, nimirum punctum illud eſſe
              <lb/>
            idem ſemper. </s>
            <s xml:space="preserve">Si enim ad duo puncta duabus diverſis viis de-
              <lb/>
            veniretur, aſſumpto plano perpendiculari ad rectam, quæ illa
              <lb/>
            duo puncta jungeret, diſtantia perpendicularis ab ipſo non eſſet
              <lb/>
            utique eadem pro utroque, cum altera diſtantia deberet alterius
              <lb/>
            eſſe pars.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">260. </s>
            <s xml:space="preserve">Porro ſimilis admodum eſt etiam methodus, qua utor
              <lb/>
              <note position="right" xlink:label="note-0173-02" xlink:href="note-0173-02a" xml:space="preserve">Theorema de
                <lb/>
              ſtatu centri gra-
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              vitatis manen-
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              te etiam ubi
                <lb/>
              agant utcunque
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              vires mutuæ,
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              ac ejus demon-
                <lb/>
              ſtrationis ini-
                <lb/>
              tium.</note>
            ad demonſtrandum præclariſſimum Newtoni theorema, in quod
              <lb/>
            coaleſcunt ſimul duo, quæ ſuperius innui, & </s>
            <s xml:space="preserve">huc reducun-
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            tur. </s>
            <s xml:space="preserve">Si quotcunque materiæ puncta utcunque diſpoſita, & </s>
            <s xml:space="preserve">in
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              <gap/>
            uotcunque utcunque disjunctas maſſas coaleſcentia babeant ve-
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            locitates quaſcunque cum directionibus quibuſcunque, & </s>
            <s xml:space="preserve">præte-
              <lb/>
            rea urgeantur viribus mutuis quibuſcunque, quæ in binis qui-
              <lb/>
            buſque punctis æqualiter agant in plagas oppoſitas; </s>
            <s xml:space="preserve">centrum com-
              <lb/>
            mune gravitatis omnium vel quieſcet, vel movebitur uniformiter
              <lb/>
            in directum eodem motu, quem baberet, ſi nulla adeſſet mu-
              <lb/>
            tua punctorum actio in ſe invicem. </s>
            <s xml:space="preserve">Hoc autem theorema ſic
              <lb/>
            generaliter, & </s>
            <s xml:space="preserve">admodum facile, ac luculenter demonſtratur.</s>
            <s xml:space="preserve"/>
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