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

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            <s xml:space="preserve">
              <pb o="300" file="0352" n="352" rhead="EPISTOLA"/>
            itidem, ac e ſuperioribus etiam Theorematis facile deduci-
              <lb/>
              <note position="left" xlink:label="note-0352-01" xlink:href="note-0352-01a" xml:space="preserve">ciltus invenien-
                <lb/>
              da.</note>
            tur, centrum oſcillationis jacere infra centrum globi, per {2/5}
              <lb/>
            tertiæ proportionalis poſt diſtantiam puncti ſuſpenſionis a cen-
              <lb/>
            tro globi, & </s>
            <s xml:space="preserve">radium; </s>
            <s xml:space="preserve">pro filo autem conſiderato ut recta qua-
              <lb/>
            dam habetur centrum gravitatis in medio ipſo filo, & </s>
            <s xml:space="preserve">cen-
              <lb/>
            trum oſcillationis, ſuſpenſione facta per fili extremum eſt in
              <lb/>
            fine ſecundi trientis longitudinis ejuſdem fili, quod itidem ex
              <lb/>
            formula generali facillime deducitur. </s>
            <s xml:space="preserve">Inde centrum oſcillationis
              <lb/>
            commune globi, & </s>
            <s xml:space="preserve">fili nullo negotio definietur per corolla-
              <lb/>
            rium ſuperius.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">101. </s>
            <s xml:space="preserve">Sit Longitudo fili a, maſſa ſeu pondus b, radius globi r,
              <lb/>
              <note position="left" xlink:label="note-0352-02" xlink:href="note-0352-02a" xml:space="preserve">Calculus &
                <lb/>
              formula pro
                <lb/>
              pendulo globi
                <lb/>
              pendentis e fi-
                <lb/>
              lo.</note>
            maſſa ſeupondus p: </s>
            <s xml:space="preserve">erit diſtantia centri gravitatis fili ab axe con-
              <lb/>
            verſionis erit {1/2} a, diſtantia centri oſcillationis ejuſdem {2/3} a.
              <lb/>
            </s>
            <s xml:space="preserve">Quare productum illud pertinens ad filum erit {1/3} a
              <emph style="super">2</emph>
            b. </s>
            <s xml:space="preserve">Pro
              <lb/>
            globo erit diſtantia centri gravitatis a + r, quæ ponatur =m; </s>
            <s xml:space="preserve">
              <lb/>
            Diſtantia centri oſcillationis erit m + {2/5} x {r r/m}. </s>
            <s xml:space="preserve">Quare produ-
              <lb/>
            ctum pertinens ad globum erit m
              <emph style="super">2</emph>
            p + {2/5} r r p. </s>
            <s xml:space="preserve">Horum ſum-
              <lb/>
            ma eſt m
              <emph style="super">2</emph>
            p + {2/5} r r p + {1/3} a
              <emph style="super">2</emph>
            b. </s>
            <s xml:space="preserve">Porro cum centra gravitatis
              <lb/>
            fili, & </s>
            <s xml:space="preserve">globi jaceant in directum cum puncto ſuſpenſionis, ad
              <lb/>
            habendam diſtantiam centri gravitatis communis ductam in
              <lb/>
            ſummam maſſarum ſatis erit ducere ſingularum partium maſ-
              <lb/>
            ſas in ſuorum centrorum diſtantias, ac habebitur m p + {1/2} a b. </s>
            <s xml:space="preserve">
              <lb/>
            Quare formula pro centro oſcillationis utriuſque ſimul, erit
              <lb/>
            {m
              <emph style="super">2</emph>
            p + {2/5} r r p + {1/3} a
              <emph style="super">2</emph>
            b/m p + {1/2} a b.</s>
            <s xml:space="preserve">}</s>
          </p>
          <p>
            <s xml:space="preserve">102. </s>
            <s xml:space="preserve">Hic autem notandum illud, ad centrum oſcillationis
              <lb/>
              <note position="left" xlink:label="note-0352-03" xlink:href="note-0352-03a" xml:space="preserve">Non licere hic
                <lb/>
              concipere maſ-
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              ſas ſingulas ut
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              collectas in ſuis
                <lb/>
              centris oſcilla-
                <lb/>
              tionis, aut gra-
                <lb/>
              vitatis, aut aliis
                <lb/>
              intermediis do-
                <lb/>
              cumentum uti-
                <lb/>
              le.</note>
            commune habendum non licere ſingularum partium maſſas con-
              <lb/>
            cipere, ut collectas in ſuis ſingulas aut centris oſcillationis, aut
              <lb/>
            centris gravitatis. </s>
            <s xml:space="preserve">In primo caſu numerator colligeretur ex ſum-
              <lb/>
            ma omnium productorum, quæ fierent ducendo ſingulas maſſas
              <lb/>
            in quadrata diſtantiarum centri oſcillationis ſui; </s>
            <s xml:space="preserve">in ſecundo in
              <lb/>
            quadrata diſtantiarum ſui centri gravitatis. </s>
            <s xml:space="preserve">In illo nimirum ha-
              <lb/>
            beretur plus juſto, in hoc minus. </s>
            <s xml:space="preserve">Sed nec poſſunt concipi ut
              <lb/>
            collectæ in aliquo puncto intermedio, cujus diſtantia ſit media
              <lb/>
            continue proportionalis inter illas diſtantias; </s>
            <s xml:space="preserve">nam in eo caſu nu-
              <lb/>
            merator maneret idem, at denominator non eſſet idem, qui ut
              <lb/>
            idem perſeveraret, oporteret concipere maſſas ſingulas collectas
              <lb/>
            in ſuis centris gravitatis, non ultra ipſa. </s>
            <s xml:space="preserve">Inde autem patet, non
              <lb/>
            ſemper licere concipere maſſas ingentes in ſuo gravitatis centro,
              <lb/>
            & </s>
            <s xml:space="preserve">idcirco, ubi in Theoria centri oſcillationis, vel percuſſionis
              <lb/>
            dico maſſam exiſtentem in quodam puncto, intelligi debet, ut
              <lb/>
            monui in ipſo opere, tota maſſa ibi compenetrata vel concipi
              <lb/>
            maſſula extenſionis infiniteſimæ, ut maſſæ compenetratæ in uni-
              <lb/>
            co ſuo puncto æquivaleat.</s>
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