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

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              <pb o="129" file="0181" n="181" rhead="PARS SECUNDA"/>
            prioribus. </s>
            <s xml:space="preserve">Erit nimirum illa quæ pertinet ad globum Q =
              <lb/>
            {rCq - rcq/Q + q} , & </s>
            <s xml:space="preserve">quæ pertinet ad globum q, erit = {rCQ - rcQ/Q + q},
              <lb/>
            adeoque velocitas illius poſt congreſſum erit C - {rCq - rcq/Q + q},
              <lb/>
            & </s>
            <s xml:space="preserve">hujus c + {rCQ - rcQ/Q + q}; </s>
            <s xml:space="preserve">quæ formulæ i
              <unsure/>
            tidem reducuntur
              <lb/>
            ad eoſdem denominatores; </s>
            <s xml:space="preserve">ac tum ex hiſce formulis, tum e
              <lb/>
            ſuperioribus quam plurima elegantiſſima theoremata deducun-
              <lb/>
            tur, quæ quidem pa ſſim inveniuntur in elementaribus libris,
              <lb/>
            & </s>
            <s xml:space="preserve">ego ipſe aliquanto uberius perſecutus ſum in Supplementis
              <lb/>
            Stayanis ad lib. </s>
            <s xml:space="preserve">2, §. </s>
            <s xml:space="preserve">2; </s>
            <s xml:space="preserve">ſed hic ſatis eſt, fundamenta ipſa,
              <lb/>
            & </s>
            <s xml:space="preserve">primarias formulas derivaſſe ex eadem Theoria, & </s>
            <s xml:space="preserve">ex pro-
              <lb/>
            prietatibus centri gravitatis, ac motuum oppoſitorum æqua-
              <lb/>
            ſium, deductis ex Theoria eadem; </s>
            <s xml:space="preserve">nec niſi binos, vel ternos
              <lb/>
            evolvam caſus uſui futuros infra, antequam ad obliquam col-
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            liſionem, ac reflexionem motuum gradum faciam.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">273. </s>
            <s xml:space="preserve">Si globus perfecte elaſticus incurrat in globum itidem
              <lb/>
              <note position="right" xlink:label="note-0181-01" xlink:href="note-0181-01a" xml:space="preserve">Caſus, in quo
                <lb/>
              globus perfecte
                <lb/>
              elaſticus incur-
                <lb/>
              rit in alium.</note>
            quieſcentem, erit c = o, adeoque velocitas contraria priori per-
              <lb/>
            tinens ad incurrentem, quæ erat {2Cq - 2cq/Q + q}, erit {2Cq/Q+q}; </s>
            <s xml:space="preserve">ve-
              <lb/>
            locitas acquiſita a quieſcente, quæ erat {2CQ - 2cQ/Q + q}, erit
              <lb/>
            {2CQ/Q+q}; </s>
            <s xml:space="preserve">unde habebitur hoc theorema: </s>
            <s xml:space="preserve">ut ſumma maſf
              <unsure/>
            arum ad
              <lb/>
            duplam maſſam quieſcentis, vel incurrentis, ita celeritas incurrentis
              <lb/>
            ad celeritatem amiſſam a ſecundo, vel acquiſitam a primo; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi
              <lb/>
            maſſæ æquales fuerint, fit ea ratio æqualitatis; </s>
            <s xml:space="preserve">ac proinde glo-
              <lb/>
            bus incurrens totam ſuam velocitatem amittit, acquirendo ni-
              <lb/>
            mirum æqualem contrariam, a qua ea elidatur, & </s>
            <s xml:space="preserve">globus quie-
              <lb/>
            ſcens acquirit velocitatem, quam ante habuerat globus incurrens.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">274. </s>
            <s xml:space="preserve">Si globus imperfecte elaſticus incurrat in globum quie-
              <lb/>
              <note position="right" xlink:label="note-0181-02" xlink:href="note-0181-02a" xml:space="preserve">Caſus triplex
                <unsure/>
                <lb/>
              globi incurren-
                <lb/>
              tis in planum
                <lb/>
              immobile.</note>
            ſcentem immenſum, & </s>
            <s xml:space="preserve">qui habeatur pro abſolute infinito, cu-
              <lb/>
            jus idcirco ſuperficies habetur pro plana, in formula velocita-
              <lb/>
            tis acquiſitæ a globo quieſcente {rCQ - rcQ/Q + q}, cum evaneſcat Q
              <lb/>
            reſpectu q abſolute infiniti, & </s>
            <s xml:space="preserve">proinde {Q/Q + q} evadat = o, tota
              <lb/>
            formula evaneſcit, adeoque ipſe haberi poteſt pro plano im-
              <lb/>
            mobili. </s>
            <s xml:space="preserve">In formula vero velocitatis, quam in partem oppoſi-
              <lb/>
            tam acquiret globus incurrens, {rCq -rcq/Q + q}, evadit c = </s>
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