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="158" file="0210" n="210" rhead="THEORIÆ"/>
            {AxAPxPQ-AxAP
              <emph style="super">2</emph>
            /PQ}. </s>
            <s xml:space="preserve">Eodem pacto actio in P ex ne-
              <lb/>
            xu cum B erit {BxBPxPQ = BxPB
              <emph style="super">2</emph>
            /PQ}, & </s>
            <s xml:space="preserve">ita porro. </s>
            <s xml:space="preserve">Iis o-
              <lb/>
            mnibus poſitis = o, diviſor communis PQ abit, & </s>
            <s xml:space="preserve">omnia po-
              <lb/>
            ſitiva æquantur ne gativis. </s>
            <s xml:space="preserve">Erit igitur AxAPxPQ +
              <lb/>
            BxBPxPQ &</s>
            <s xml:space="preserve">c = AxAP
              <emph style="super">2</emph>
            + BxBP
              <emph style="super">2</emph>
            &</s>
            <s xml:space="preserve">c; </s>
            <s xml:space="preserve">quare PQ =
              <lb/>
            {AxAP
              <emph style="super">2</emph>
            + BxBP
              <emph style="super">2</emph>
            &</s>
            <s xml:space="preserve">c/AxAP + BxBP &</s>
            <s xml:space="preserve">c}, quæ formula eſt eadem, ac formula
              <lb/>
            centri oſcillationis, ac habetur hujuſmodi theorema: </s>
            <s xml:space="preserve">Diſtantia
              <lb/>
            centri percuſſionis a puncto converſionis æquatur diſtantiæ centri
              <lb/>
            oſcillationis a puncto ſuſpenſionis; </s>
            <s xml:space="preserve">adeoque hic locum habent in
              <lb/>
            hoc caſu, quæcunque de centro oſcillationis ſuperius dicta
              <lb/>
            ſunt.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">346. </s>
            <s xml:space="preserve">Quod ſi quis quærat vim percuſſionis in Q, hic habe-
              <lb/>
              <note position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">Determinatio
                <lb/>
              vi
                <gap/>
              percuſſionis
                <lb/>
              in ipſo centro.</note>
            bit QP. </s>
            <s xml:space="preserve">AP:</s>
            <s xml:space="preserve">:AxAP. </s>
            <s xml:space="preserve">{AxAP
              <emph style="super">2</emph>
            /PQ}, quæ erit vis in Q ex
              <lb/>
            nexu cum A. </s>
            <s xml:space="preserve">Eodem pacto invenientur vires ex reliquis: </s>
            <s xml:space="preserve">ade-
              <lb/>
            oque ſumma virium erit {AxAP
              <emph style="super">2</emph>
            + BxBP
              <emph style="super">2</emph>
            /PQ} &</s>
            <s xml:space="preserve">c, ſive ob PQ
              <lb/>
            = {AxAP
              <emph style="super">2</emph>
            + BxBP
              <emph style="super">2</emph>
            /AxAP + BxBP &</s>
            <s xml:space="preserve">c}, ſumma illa erit AxAP + BxRP
              <lb/>
            &</s>
            <s xml:space="preserve">c; </s>
            <s xml:space="preserve">nimirum ejuſmodi vis erit æqualis ſummæ virium, quæ
              <lb/>
            requiruntur ad ſiſtendos omnes motus maſſarum A, B &</s>
            <s xml:space="preserve">c cum
              <lb/>
            illis di verſis velocitatibus progredientium, videlicet ejuſmodi,
              <lb/>
            quæ in maſſa percuſſionem excipiente poſſit producere quanti-
              <lb/>
            tatem motus æqualem toti motui, qui ſiſtitur in maſſis omni-
              <lb/>
            bus, quod congruit cum lege actionis, & </s>
            <s xml:space="preserve">reactionis æqualium,
              <lb/>
            & </s>
            <s xml:space="preserve">cum conſervatione ejuſdem quantitatis motus in eandem
              <lb/>
            plagam, de quibus egimus num. </s>
            <s xml:space="preserve">265, & </s>
            <s xml:space="preserve">264.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">347. </s>
            <s xml:space="preserve">Haberent hic locum alia ſane multa, quæ pertinent ad
              <lb/>
              <note position="left" xlink:label="note-0210-02" xlink:href="note-0210-02a" xml:space="preserve">Omitti hic
                <lb/>
              multa, quæ ad
                <lb/>
              hanc Theoriam
                <lb/>
              pertinerent, ad
                <lb/>
              quam pertinet
                <lb/>
              univerſa Me-
                <lb/>
              chanica.</note>
            ſummas virium, quibus agunt maſſæ, compoſitarum e viri-
              <lb/>
            bus, quibus agunt puncta, vel a Newtono, vel ab aliis de-
              <lb/>
            monſtrata, & </s>
            <s xml:space="preserve">magni uſus in Mechanica, & </s>
            <s xml:space="preserve">Phyſica: </s>
            <s xml:space="preserve">hujuſ-
              <lb/>
            modi ſunt ea omnia, quæ Newtonus habet ſectione 12, & </s>
            <s xml:space="preserve">13
              <lb/>
            libri 1 Princip. </s>
            <s xml:space="preserve">de attractionibus corporum ſphæricorum, & </s>
            <s xml:space="preserve">
              <lb/>
            non ſphæricorum, quæ componantur ex attractionibus particu-
              <lb/>
            larum; </s>
            <s xml:space="preserve">ubi habentur præclariſſima theoremata tam pro viribus
              <lb/>
            quibuſcunque generaliter, quam pro certis virium legibus, ut
              <lb/>
            illud, quod pertinet ad rationem reciprocam duplicatam diſtan-
              <lb/>
            tiarum, in qua globus globum trahit, tanquam ſi omnis ma-
              <lb/>
            teria eſſet compenetrata in centris eorundem; </s>
            <s xml:space="preserve">punctum </s>
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