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

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            <s xml:space="preserve">333. </s>
            <s xml:space="preserve">Is valor erit variabilis pro varia inclinatione ob valores
              <lb/>
              <note position="left" xlink:label="note-0206-01" xlink:href="note-0206-01a" xml:space="preserve">Initium appli-
                <lb/>
              cationis ad o-
                <lb/>
              ſcillationes in
                <lb/>
              latus ponderum
                <lb/>
              jacentium in
                <lb/>
              eodem plano.</note>
            ſinuum q, & </s>
            <s xml:space="preserve">g variatos, niſi QP tranſeat per G, quo caſu
              <lb/>
            ſit q = g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quidem ubi G accedit in infinitum ad P R, de-
              <lb/>
            creſcente g in infinitum, ſi PQ non tranſeat per G, manen-
              <lb/>
            te finito q, valor {q/g} excreſcit in infinitum; </s>
            <s xml:space="preserve">contra vero appel-
              <lb/>
            lente QP ad P R, evadit q = o, & </s>
            <s xml:space="preserve">g remanet aliquid, adeo-
              <lb/>
            que {q/g} evaneſcit. </s>
            <s xml:space="preserve">Id vero accidit, quia in appulſu G ad verti-
              <lb/>
            calem totum ſyſtema vim acceleratricem in infinitum immi-
              <lb/>
            nuit, & </s>
            <s xml:space="preserve">lentiſſime acceleratur; </s>
            <s xml:space="preserve">adeoque ut radius PQ adhuc
              <lb/>
            obliquus ſit ipſi in ea particula oſcillationis infiniteſima iſo-
              <lb/>
            chronus, nimirum æque parum acceleratus, debet in infini-
              <lb/>
            tum produci. </s>
            <s xml:space="preserve">Contra vero appellente PQ ad PR ipſius ac-
              <lb/>
            celeratio minima eſſe debet, dum adhuc acceleratio radii P G
              <lb/>
            obliqui eſt in immenſum major, quam ipſa; </s>
            <s xml:space="preserve">adeoque brevita-
              <lb/>
            te ſua ipſe radius compenſare debet accelerationis imminutio-
              <lb/>
            nem.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">334. </s>
            <s xml:space="preserve">Quare ut habeatur pendulum ſimplex conſtantis longi-
              <lb/>
              <note position="left" xlink:label="note-0206-02" xlink:href="note-0206-02a" xml:space="preserve">Finis ejuſdem
                <lb/>
              cum formula
                <lb/>
              generali.</note>
            tudinis, & </s>
            <s xml:space="preserve">in quacunque inclinatione iſochronum compoſito,
              <lb/>
            debet radius PQ ita aſſumi, ut tranſeat per centrum gravita-
              <lb/>
            tis G, quo unico caſu fit conſtanter q = g, & </s>
            <s xml:space="preserve">formula evadit
              <lb/>
            conſtans QP = {AxAP
              <emph style="super">2</emph>
            + BxBP
              <emph style="super">2</emph>
            /MxGP} &</s>
            <s xml:space="preserve">c, quæ eſt formula ge-
              <lb/>
            neralis pro oſcillationibus in latus maſſarum quotcumque, & </s>
            <s xml:space="preserve">
              <lb/>
            quomodocunque collocatarum in eodem plano perpendiculari
              <lb/>
            ad axem rotationis, qui caſus generaliter continet caſum maſ-
              <lb/>
            ſarum jacentium in eadem recta tranſeunte per punctum ſuſ-
              <lb/>
            penſionis, quem prius eruimus.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">335. </s>
            <s xml:space="preserve">Inde autem pro hujuſmodi caſibus plura corollaria de-
              <lb/>
              <note position="left" xlink:label="note-0206-03" xlink:href="note-0206-03a" xml:space="preserve">Corollarium
                <lb/>
              pro poſitione
                <lb/>
              centri oſcilla-
                <lb/>
              tionis, & gra-
                <lb/>
              vitatis ex ea-
                <lb/>
              dem parte a
                <lb/>
              puncto ſuſpen.
                <lb/>
              ſionis.</note>
            ducuntur. </s>
            <s xml:space="preserve">Inprimis patet: </s>
            <s xml:space="preserve">gravitatis centrum debere jacere in
              <lb/>
            recta, quæ a centro ſuſpenſionis ducitur per centrum oſcillationis,
              <lb/>
            uti demonſtratum eſt num. </s>
            <s xml:space="preserve">334. </s>
            <s xml:space="preserve">Sed & </s>
            <s xml:space="preserve">debet jacere ad eandem
              <lb/>
            partem cum ipſo centro oſcillationis. </s>
            <s xml:space="preserve">Nam utcumque mutetur ſi-
              <lb/>
            tus maſſarum per illud planum, manentibus puncto ſuſpenſio-
              <lb/>
            nis P, & </s>
            <s xml:space="preserve">centro gravitatis G, ſignum valoris quadrati cujuſ-
              <lb/>
            vis A P, BP manebit ſemper idem. </s>
            <s xml:space="preserve">Quare formula valoris
              <lb/>
            ſui ſignum mutare non poterit; </s>
            <s xml:space="preserve">adeoque ſi in uno aliquo ca-
              <lb/>
            ſu jaceat Q reſpectu P ad eandem plagam, ad quam jacet G;
              <lb/>
            </s>
            <s xml:space="preserve">debebit jacere ſemper. </s>
            <s xml:space="preserve">Jacet autem ad eandem plagam in ca-
              <lb/>
            ſu, in quo concipiatur, omnes maſſas abire in ipſum centrum
              <lb/>
            gravitatis, quo caſu pendulum evadit ſimplex, & </s>
            <s xml:space="preserve">centrum o-
              <lb/>
            ſcillationis cadit in ipſum centrum gravitatis, in quo ſunt
              <lb/>
            maſſæ. </s>
            <s xml:space="preserve">Jacebit igitur ſemper ad eandem partem cum G.</s>
            <s xml:space="preserve"/>
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