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

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            <s xml:space="preserve">
              <pb o="156" file="0208" n="208" rhead="THEORIÆ"/>
            centrum illud, quod fuerat punctuna ſuſpenſionis; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alterius di-
              <lb/>
            ſtantia a centro gravitatis mutata, mutetur & </s>
            <s xml:space="preserve">alterius diſtantia
              <lb/>
            in eadem ratione reciproca. </s>
            <s xml:space="preserve">Cum enim earum diſtantiarum re-
              <lb/>
            ctangulum debeat eſſe conſtans; </s>
            <s xml:space="preserve">ſi pro ſecunda ponatur valor,
              <lb/>
            quem habuerat prima; </s>
            <s xml:space="preserve">debet pro prima obvenire valor, quem
              <lb/>
            habuerat ſecunda, & </s>
            <s xml:space="preserve">altera debet æquari quantitati conſtanti
              <lb/>
            diviſæ per alteram.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">340. </s>
            <s xml:space="preserve">Conſequitur etiam illud: </s>
            <s xml:space="preserve">Altera ex iis binis diſtantiis
              <lb/>
              <note position="left" xlink:label="note-0208-01" xlink:href="note-0208-01a" xml:space="preserve">Altera ex iis
                <lb/>
              diſtantiis eva-
                <lb/>
              neſcente, abire
                <lb/>
              alteram in in-
                <lb/>
              ſ
                <gap/>
              nitum.</note>
            evaneſcente, abibit altera in infinitum, niſi omnes maſſæ in uni-
              <lb/>
            co puncto ſint ſimul compenetratæ. </s>
            <s xml:space="preserve">Nam ſine ejuſmodi compe-
              <lb/>
            netratione ſumma omnium productorum ex maſſis, & </s>
            <s xml:space="preserve">quadra-
              <lb/>
            tis diſtantiarum a centro gravitatis, remanet ſemper finita
              <lb/>
            quantitas: </s>
            <s xml:space="preserve">adeoque remanet finita etiam, ſi dividatur per ſum-
              <lb/>
            mam maſſarum, & </s>
            <s xml:space="preserve">quotus, manente diviſo finito, creſcit in
              <lb/>
            infinitum; </s>
            <s xml:space="preserve">ſi diviſor in infinitum decreſcat.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">341. </s>
            <s xml:space="preserve">Hinc vero iterum deducitur: </s>
            <s xml:space="preserve">Suſpenſione ſacta per i-
              <lb/>
              <note position="left" xlink:label="note-0208-02" xlink:href="note-0208-02a" xml:space="preserve">Suſpenſione fa-
                <lb/>
              cta per centrum
                <lb/>
              gravitatis, nul-
                <lb/>
              lum haberi mo-
                <lb/>
              tum.</note>
            pſum centrum gravitatis nullum motum conſequi. </s>
            <s xml:space="preserve">Evaneſcit enim
              <lb/>
            in eo caſu diſtantia centri gravitatis a puncto ſuſpenſionis, a-
              <lb/>
            deoque diſtantia centri oſcillationis creſcit in infinitum, & </s>
            <s xml:space="preserve">
              <lb/>
            celeritas oſcillationis evadit nulla.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">342. </s>
            <s xml:space="preserve">Quoniam utraque diſtantia ſimul evaneſcere non poteſt,
              <lb/>
              <note position="left" xlink:label="note-0208-03" xlink:href="note-0208-03a" xml:space="preserve">Quæ diſtantia
                <lb/>
              centri oſcilla-
                <lb/>
              tionis omnium
                <lb/>
              minima pro da-
                <lb/>
              ta poſitione mu-
                <lb/>
              tua maſſarum
                <lb/>
              datarum; ma-
                <lb/>
                <gap/>
                <gap/>
              imam haberi
                <lb/>
              nullam.</note>
            poteſt autem centrum oſcillationis abire in infinitum; </s>
            <s xml:space="preserve">nulla
              <lb/>
            erit maxima e longitudinibus penduli ſimplicis iſochroni pen-
              <lb/>
            dulo facto per ſuſpenſionem dati ſyſtematis; </s>
            <s xml:space="preserve">ſed aliqua debet
              <lb/>
            eſſe minima, ſuſpenſrone quadam inducente omnium celerri-
              <lb/>
            mam dati ſyſtematis oſcillationem. </s>
            <s xml:space="preserve">Ea vero minima debet eſ-
              <lb/>
            ſe, ubi illæ binæ diſtantiæ æquantur inter ſe: </s>
            <s xml:space="preserve">ibi enim evadit
              <lb/>
            minima earum ſumma, ubi altera creſcente, & </s>
            <s xml:space="preserve">altera decre-
              <lb/>
            ſcente, incrementa prius minora decrementis, incipiunt eſſe
              <lb/>
            majora, adeoque ubi ea æquantur inter ſe. </s>
            <s xml:space="preserve">Quoniam autem il-
              <lb/>
            læ binæ diſtantiæ mutantur in eadem ratione, utut reciproca;
              <lb/>
            </s>
            <s xml:space="preserve">incrementum alterius infiniteſimum erit ad alterius decremen-
              <lb/>
            tum in ratione ipſarum, nec ea æquari poterunt inter ſe, niſi
              <lb/>
            ubi ipſæ diſtantiæ inter ſe æquales fiant. </s>
            <s xml:space="preserve">Tum vero illarum
              <lb/>
            productum evadit utriusl ibet quadratum, & </s>
            <s xml:space="preserve">longitudo penduli
              <lb/>
            ſimplicis iſochroni æquat ur eorum ſummæ; </s>
            <s xml:space="preserve">ac proinde habe-
              <lb/>
            tur hujuſmodi theorema: </s>
            <s xml:space="preserve">Singulæ maſſæ ducantur in quadrata
              <lb/>
            ſuarum diſtantiarum a centro gravitatis, ac productorum ſumma
              <lb/>
            dividatur per ſummam maſſarum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">dupla radix quadrata quo-
              <lb/>
            ti exhibebit minimam penduli ſimplicis iſocbroni longitudinem. </s>
            <s xml:space="preserve">
              <lb/>
            Vel Geometrice ſic: </s>
            <s xml:space="preserve">Pro quavis maſſa capiatur recta, quæ ad
              <lb/>
            diſtantiam cujuſvis maſſæ a centro gravitatis ſit in ratione ſub-
              <lb/>
            duplicata ejuſdem maſſæ ad maſſarum ſummam: </s>
            <s xml:space="preserve">inveniatur re-
              <lb/>
            cta, cujus quadratum æquetur quadratis omnium ejuſmodi recta-
              <lb/>
            rum ſimul: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ipſius duplum dabit quæſitam longitudinem me-
              <lb/>
            diam, quæ breviſſimam præſtet oſcillationem.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">343. </s>
            <s xml:space="preserve">Hæc quidem omnia locum habent, ubi omnes maſſæ
              <lb/>
              <note position="left" xlink:label="note-0208-04" xlink:href="note-0208-04a" xml:space="preserve">Superiora ha-
                <lb/>
              bere locum tan-
                <lb/>
              tummodo, ubi</note>
            ſint in unico plano perpendiculari ad axem rotationis, ut </s>
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