Bošković, Ruđer Josip, Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium
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              <pb o="130" file="0182" n="182" rhead="THEORIÆ"/>
            & </s>
            <s xml:space="preserve">Q evaneſcit itidem reſpectu q. </s>
            <s xml:space="preserve">Hinc habetur {rCq/q}, ſive rC,
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            nimirum ob r = {m + n/m} fit ({m + n/m}) x C, cujus prima pars
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            {m/m} x C, ſive C, eſt illa, quæ amittitur, ſive acquiritur in
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            partem oppoſitam in comprimenda figura, & </s>
            <s xml:space="preserve">{n/m} x C eſt illa,
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            quæ acquiritur in recuperanda, ubi ſi ſit n = o, quod accidit
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            nimirum in perfecte mollibus; </s>
            <s xml:space="preserve">habetur ſola pars prima; </s>
            <s xml:space="preserve">ſi
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            m = n, quod accidit in perſecte elaſticis, eſt {n/m} x C = C, ſe-
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            cunda pars æqualis primæ; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in reliquis caſibus eſt, ut m ad
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            n, ita illa pars prima C, ſive præcedens velocitas, quæ per
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            primam partem acquiſitam eliditur, ad partem ſecundam, quæ
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            remanet in plagam oppoſitam. </s>
            <s xml:space="preserve">Quamobrem habetur ejuſmodi
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            theorema. </s>
            <s xml:space="preserve">Si incurrat ad perpendiculum in planum immobile
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            globus perfecte mollis, acquirit velocitatem contrariam æqualem ſuæ
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            priori, & </s>
            <s xml:space="preserve">quieſcit; </s>
            <s xml:space="preserve">ſi perfecte elaſticus, acquirit duplam ſuæ,
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            nimirum æqualem in compreſſione, qua motus omnis ſiſtitur, & </s>
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            æqualem in recuperanda figura, cum qua reſilit; </s>
            <s xml:space="preserve">ſi fuerit im-
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            perfecte elaſticus in ratione m ad n, in illa eadem ratione erit
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            velocitas priori ſuæ contraria acquiſita, dum figura mutatur, quæ
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            priorem ipſam velocitatem extinguit, ad velocitatem, quam ac-
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            quirit, dum figura reſtituitur, & </s>
            <s xml:space="preserve">cum qua reſilit.</s>
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            <s xml:space="preserve">275. </s>
            <s xml:space="preserve">Eſt & </s>
            <s xml:space="preserve">aliud theorema aliquanto operoſius, ſed genera-
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              <note position="left" xlink:label="note-0182-01" xlink:href="note-0182-01a" xml:space="preserve">Summa qua-
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              dratorum velo-
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              citatis ducto-
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              rum in maſſas
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              manens in per-
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              fecte elaſticis.</note>
            le, & </s>
            <s xml:space="preserve">elegans, ab Hugenio inventum pro perfectæ elaſticis,
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            quod nimirum ſumma quadratorum velocitatis ductorum in
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            maſſas poſt congreſſum remaneat eadem, quæ fuerat ante i-
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            pſum. </s>
            <s xml:space="preserve">Nam Velocitates poſt congreſſum ſunt C - {2q/Q + q} x
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            (C - c), & </s>
            <s xml:space="preserve">c+{2Q/Q + q} x (C - c); </s>
            <s xml:space="preserve">quadrata ducta in
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            maſſas continent ſingula ternos terminos: </s>
            <s xml:space="preserve">primi erunt QCC
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            + qcc; </s>
            <s xml:space="preserve">ſecundi erunt (-CC+C c) x {4Qq/Q + q} + (cC - cc)
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            x {4Qq/Q + q}, quorum ſumma evadit (- CC + 2Cc - cc)
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            x {4Qq/Q + q}; </s>
            <s xml:space="preserve">poſtremi erunt {4Qqq/(Q + q)
              <emph style="super">2</emph>
            } x (CC-2Cc + cc), & </s>
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              <lb/>
            {4 qQQ/(Q+q)
              <emph style="super">2</emph>
            } x CC - 2Cc + cc), ſive ſimul {4(Q + q) x Qq/(Q+q)
              <emph style="super">2</emph>
            </s>
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