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

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          <pb o="155" file="0207" n="207" rhead="PARS, SECUNDA."/>
          <p>
            <s xml:space="preserve">336. </s>
            <s xml:space="preserve">Deinde debet centrum gravitatis jacere inter punctum ſuſ-
              <lb/>
              <note position="right" xlink:label="note-0207-01" xlink:href="note-0207-01a" xml:space="preserve">Centrum gr
                <gap/>
              -
                <lb/>
              vitatis debere
                <lb/>
              eſſe inter bina
                <lb/>
              reliqua ex iis
                <lb/>
              punctis.</note>
            penſionis, & </s>
            <s xml:space="preserve">centrum oſcillationis. </s>
            <s xml:space="preserve">Sint enim in fig. </s>
            <s xml:space="preserve">64 pun-
              <lb/>
            cta A, P, G, Q eadem, ac in fig. </s>
            <s xml:space="preserve">63, ducanturque AG,
              <lb/>
            AQ, & </s>
            <s xml:space="preserve">A a perpendicularis ad PQ; </s>
            <s xml:space="preserve">ſumma autem omnium
              <lb/>
            maſſarum ductarum in ſuas diſtanti
              <lb/>
            as a recta quapiam, vel
              <lb/>
              <note position="right" xlink:label="note-0207-02" xlink:href="note-0207-02a" xml:space="preserve">Fig. 64.</note>
            plano, vel in earum quadrata, deſignetur præfixa litera ſ ſoli
              <lb/>
            termino pertinente ad maſſam A, ut contractiores evadant de-
              <lb/>
            monſtrationes. </s>
            <s xml:space="preserve">Erit ex formula inventa PQ = {ſ.</s>
            <s xml:space="preserve">AxAP
              <emph style="super">2</emph>
            /MxGP} Por-
              <lb/>
            ro eſt AG
              <emph style="super">2</emph>
            = AP
              <emph style="super">2</emph>
            + GP
              <emph style="super">2</emph>
            -2GPx P a, adeoque AP
              <emph style="super">2</emph>
            =
              <lb/>
            AG
              <emph style="super">2</emph>
            -GP
              <emph style="super">2</emph>
            + 2GPxPa, & </s>
            <s xml:space="preserve">ſ. </s>
            <s xml:space="preserve">AxGP
              <emph style="super">2</emph>
            eſt MxGP
              <emph style="super">2</emph>
            ,
              <lb/>
            ob GP conſtantem; </s>
            <s xml:space="preserve">ac ſ. </s>
            <s xml:space="preserve">AxPa eſt = MxGP, cum P a
              <lb/>
            ſit æqualis diſtantiæ maſſæ a plano perpendiculari rectæ QP
              <lb/>
            tranſeunte per P, & </s>
            <s xml:space="preserve">eorum productorum ſumma æquetur
              <lb/>
            diſtantiæ centri gravitatis ductæ in ſummam maſſarum; </s>
            <s xml:space="preserve">adeo-
              <lb/>
            que ſ. </s>
            <s xml:space="preserve">Ax2GPxPa erit =2MxGP
              <emph style="super">2</emph>
            . </s>
            <s xml:space="preserve">Quare {ſ. </s>
            <s xml:space="preserve">AxAP
              <emph style="super">2</emph>
            /MxGP}
              <lb/>
            erit = {ſ. </s>
            <s xml:space="preserve">AxAG
              <emph style="super">2</emph>
            -MxGP
              <emph style="super">2</emph>
            + 2MxGP
              <emph style="super">2</emph>
            /MxGP} = {ſ. </s>
            <s xml:space="preserve">AxAG
              <emph style="super">2</emph>
            /MxGP}
              <lb/>
            + GP. </s>
            <s xml:space="preserve">Erit igitur PQ major, quam PG, exceſſu GQ =
              <lb/>
            {ſ. </s>
            <s xml:space="preserve">AxAG
              <emph style="super">2</emph>
            /MxGP}.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">337. </s>
            <s xml:space="preserve">Ex illo exceſſu facile conſtat, mutato utcunque puncto
              <lb/>
              <note position="right" xlink:label="note-0207-03" xlink:href="note-0207-03a" xml:space="preserve">Valor conſtans
                <lb/>
              producti ex bi-
                <lb/>
              nis diſtantiis
                <lb/>
              centri gravita-
                <lb/>
              tis ab iiſdem.</note>
            ſuſpenſionis, rectangulum ſub binis diſtantiis centri gravitatis
              <lb/>
            ab ipſo, & </s>
            <s xml:space="preserve">a centro oſcillationis fore conſtans. </s>
            <s xml:space="preserve">Cum enim ſit
              <lb/>
            QG = {ſ.</s>
            <s xml:space="preserve">AxAG
              <emph style="super">2</emph>
            /MxGP}, erit GQxGP = {ſ.</s>
            <s xml:space="preserve">AxAG
              <emph style="super">2</emph>
            /M}, quod pro-
              <lb/>
            ductum eſt conſtans, & </s>
            <s xml:space="preserve">habetur hujuſmodi elegans theorema:
              <lb/>
            </s>
            <s xml:space="preserve">ſingulæ maſſæ ducantur in quadrata ſuarum diſtantiarum a cen-
              <lb/>
            tro gravitatis communi, & </s>
            <s xml:space="preserve">dividatur omnium ejuſmodi produ-
              <lb/>
            ctorum ſumma per ſummam maſſarum, ac habebitur productum
              <lb/>
            ſub binis diſtantiis centri gravitatis a centro ſuſpenſionis, & </s>
            <s xml:space="preserve">a
              <lb/>
            centro oſcillationis.</s>
            <s xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Manente pun-
            <lb/>
          cto ſuſpenſionis
            <lb/>
          & centro gra-
            <lb/>
          vitatis, manere
            <lb/>
          centrum oſcil-
            <lb/>
          lationis.</note>
          <p>
            <s xml:space="preserve">338. </s>
            <s xml:space="preserve">Inde autem primo eruitur illud: </s>
            <s xml:space="preserve">manente puncto ſuſpen-
              <lb/>
            ſionis, & </s>
            <s xml:space="preserve">centro gravitatis, debere etiam centrum oſcillationis
              <lb/>
            manere nibil mutatum; </s>
            <s xml:space="preserve">utcunque totum ſyſtema, ſervata reſpe-
              <lb/>
            ctiva omnium maſſarum; </s>
            <s xml:space="preserve">diſtantia, & </s>
            <s xml:space="preserve">poſitione ad ſe invicem con-
              <lb/>
            vertatur intra idem planum circa ipſum gravitatis centrum; </s>
            <s xml:space="preserve">nam
              <lb/>
            illa GP inventa eo pacto pendet tantummodo a diſtantiis,
              <lb/>
            quas ſingulæ maſſæ habent a centro gravitatis.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">339. </s>
            <s xml:space="preserve">Sed & </s>
            <s xml:space="preserve">illud ſponte conſequitur: </s>
            <s xml:space="preserve">centrum oſcillationis, & </s>
            <s xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0207-05" xlink:href="note-0207-05a" xml:space="preserve">Centrum oſcil-
                <lb/>
              lationis, & pun-
                <lb/>
              ctum ſuſpenſio-
                <lb/>
              nis reciprocari.</note>
            centrum ſuſpenſionis reciprocari ita, ut, ſi fiat ſuſpenſio per id
              <lb/>
            punctum, quod fuerat centrum oſcillationis; </s>
            <s xml:space="preserve">evadat </s>
          </p>
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