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

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              <pb o="127" file="0179" n="179" rhead="PARS SECUNDA."/>
            bi, una cum æqualitate actionis, & </s>
            <s xml:space="preserve">reactionis æqualium, rem
              <lb/>
            totam perficient. </s>
            <s xml:space="preserve">Sit enim maſſa, ſive quantitas materiæ,
              <lb/>
            globi præcurrentis = q, inſequentis = Q; </s>
            <s xml:space="preserve">celeritas illius = c,
              <lb/>
            hujus = C: </s>
            <s xml:space="preserve">quantitas motus illius ante colliſionem erit cq,
              <lb/>
            hujus CQ; </s>
            <s xml:space="preserve">nam celeritas ducta per numerum punctorum ex-
              <lb/>
            hibet ſummam motuum punctorum omnium, ſive quantitatem
              <lb/>
            motus; </s>
            <s xml:space="preserve">unde etiam fit, ut quantitas motus per maſſam divi-
              <lb/>
            ſa exhibeat celeritatem. </s>
            <s xml:space="preserve">Ob actionem, & </s>
            <s xml:space="preserve">reactionem æquales,
              <lb/>
            hæc quantitas erit eadem etiam poſt colliſionem, poſt quam
              <lb/>
            motus totus utriuſque maſſæ, erit CQ + cq. </s>
            <s xml:space="preserve">Quoniam autem
              <lb/>
            progrediuntur cum æquali celeritate; </s>
            <s xml:space="preserve">celeritas illa habebitur; </s>
            <s xml:space="preserve">ſi
              <lb/>
            quantitas motus dividatur per totam quantitatem materiæ; </s>
            <s xml:space="preserve">quæ
              <lb/>
            idcirco erit {CQ + cq/Q + q}. </s>
            <s xml:space="preserve">Nimirum ad habendam velocitatem
              <lb/>
            communem poſt colliſionem, oportebit ducere ſingulas maſſas in
              <lb/>
            ſuas celeritates, & </s>
            <s xml:space="preserve">productorum ſummam dividere per ſummam
              <lb/>
            maſſarum.</s>
            <s xml:space="preserve"/>
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          <p>
            <s xml:space="preserve">269. </s>
            <s xml:space="preserve">Si alter globus q quieſcat; </s>
            <s xml:space="preserve">ſatis erit illius celeritatem
              <lb/>
              <note position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">Ejus extenſio
                <lb/>
              ad omnes ca-
                <lb/>
              ſus: ce eritas
                <lb/>
              amiſſa, vel ac-
                <lb/>
              quiſlta.</note>
            c conſiderare = o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi moveatur motu contrario motui prio-
              <lb/>
            ris globi; </s>
            <s xml:space="preserve">ſatis erit illi valorem negativum tribuere; </s>
            <s xml:space="preserve">ut adeo
              <lb/>
            & </s>
            <s xml:space="preserve">hic, & </s>
            <s xml:space="preserve">in ſequentibus formula inventa pro illo primo ca-
              <lb/>
            ſu globorum in eandem progredientium plagam, omnes caſus
              <lb/>
            contineat. </s>
            <s xml:space="preserve">In eo autem ſi libeat invenire celeritatem amiſſam a
              <lb/>
            globo Q, & </s>
            <s xml:space="preserve">celeritatem acquiſitam a globo q, ſatis erit redu-
              <lb/>
            cere ſingulas formulas C - {CQ + cq/Q + q}, &</s>
            <s xml:space="preserve">{CQ + cq/Q + q} - c
              <lb/>
            ad eundem denominatorem, ac habebitur {Cq - cq/Q + q}, & </s>
            <s xml:space="preserve">
              <lb/>
            {CQ - cQ/Q + q}, ex quibus deducitur hujuſmodi theorema: </s>
            <s xml:space="preserve">ut ſum-
              <lb/>
            ma maſſarum ad maſſam alteram, ita differentia celeritatum ad
              <lb/>
            celeritatem ab altera acquiſitam, quæ in eo caſu accelerabit mo-
              <lb/>
            tum præcurrentis, & </s>
            <s xml:space="preserve">retardabit motum conſequentis.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">270. </s>
            <s xml:space="preserve">Ex hiſce, quæ pertinent ad corpora mollia, facile eſt
              <lb/>
              <note position="right" xlink:label="note-0179-02" xlink:href="note-0179-02a" xml:space="preserve">Tranſitus ad
                <gap/>
              -
                <lb/>
              laſticorum col-
                <lb/>
              liſiones.</note>
            progredi ad perfecte elaſtica. </s>
            <s xml:space="preserve">In iis poſt compreſſionem maxi-
              <lb/>
            mam, & </s>
            <s xml:space="preserve">mutationem figuræ inductam ab ipſa, quæ habetur,
              <lb/>
            ubi ad æquales velocitates eſt ventum, agent adhuc in ſe invi-
              <lb/>
            cem bini globi, donec deveniant ad ſiguram priorem, & </s>
            <s xml:space="preserve">hæc
              <lb/>
            actio duplicabit effectum priorem. </s>
            <s xml:space="preserve">Ubi ad ſphæricam figuram
              <lb/>
            deventum fuerit, quod fit receſſu mutuo oppoſitarum ſuperficie-
              <lb/>
            rum, quæ in compreſſione ad ſe invicem acceſſerant, pergent
              <lb/>
            utique a ſe invicem recedere aliquanto magis eædem ſuperficies,
              <lb/>
            & </s>
            <s xml:space="preserve">figura producetur, ſed oppoſita jam vi mutua inter partes
              <lb/>
            ejuſdem globi incipient retrahi, & </s>
            <s xml:space="preserve">productio perget fieri, ſed
              <lb/>
            uſque lentius, donec ad maximam quandam productionem </s>
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