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

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            ventum ſuerit, quæ deinde incipiet minui, & </s>
            <s xml:space="preserve">globus ad ſphæ-
              <lb/>
            ricam figuram accedet iterum, ac iterum comprimetur motu
              <lb/>
            quodam oſcillatorio, ac partium trepidatione hinc, & </s>
            <s xml:space="preserve">in-
              <lb/>
            de a figura ſphærica, uti ſupra vidimus etiam duo puncta cir-
              <lb/>
            ca diſtantiam limitis cohæſionis oſcillare hinc, & </s>
            <s xml:space="preserve">inde; </s>
            <s xml:space="preserve">ſed id
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            ad colliſionem, & </s>
            <s xml:space="preserve">motus centrorum gravitatis nihil pertinebit,
              <lb/>
            quorum ſtatus a viribus mutuis nihil turbatur; </s>
            <s xml:space="preserve">actio autem
              <lb/>
            unius globi in alterum ſtatim ceſſabit poſt regreſſum ad figu-
              <lb/>
            ram ſphærcam, poſt quem ſuperficies alterius poſtica, & </s>
            <s xml:space="preserve">alte-
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            rius antica in centra jam retractæ, ulteriore centrorum diſceſ-
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            ſu a ſe invicem incipient ita diſtare, ut vires in ſe invicem
              <lb/>
            non exerant, quarum effectus ſentiri poſſit; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">hypotheſis per-
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            fecte elaſticorum eſt, ut tantus ſit mutuæ actionis effectus in
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            recuperanda, quantus fuit in amittenda figura.</s>
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          <p>
            <s xml:space="preserve">271 Duplicato igitur effectu, globus Q amittet celeritatem
              <lb/>
              <note position="left" xlink:label="note-0180-01" xlink:href="note-0180-01a" xml:space="preserve">Formulæ pro
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              perfecte elaſti-
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                <gap/>
              is.</note>
            {2Cq - 2 cq,/Q + q}, & </s>
            <s xml:space="preserve">globus q acquiret celeritatem {2CQ - 2 cQ.</s>
            <s xml:space="preserve">/Q + q}
              <lb/>
            Quare illius celeritas poſt colliſionem erit C - {2 CQ - 2 cQ/Q + q}
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            ſive {Cq - Cq + 2 cq/Q + q}; </s>
            <s xml:space="preserve">hujus vero erit c + {2CQ - 2 cQ/Q + q} =
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            {cQ - cQ + 2 Cq/Q + q}, & </s>
            <s xml:space="preserve">motus fient in eandem plagam, vel glo-
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            bus alter quieſcet, vel fient in plagas oppoſitas; </s>
            <s xml:space="preserve">prout deter-
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            minatis valoribus Q, q, C, c, formulæ valor evaſerit poſiti-
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            vus, nullus, vel negativus.</s>
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          </p>
          <p>
            <s xml:space="preserve">272. </s>
            <s xml:space="preserve">Quod ſi elaſticitas fuerit imperſecta, & </s>
            <s xml:space="preserve">vis in amitten-
              <lb/>
              <note position="left" xlink:label="note-0180-02" xlink:href="note-0180-02a" xml:space="preserve">Formulæ pro
                <lb/>
              imperfecte ela-
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                <gap/>
                <gap/>
              cis-</note>
            da ad vim in recuperanda figura fuerit in aliqua ratione data,
              <lb/>
            erit & </s>
            <s xml:space="preserve">effectus prioris ad effectum poſterioris itidem in ra-
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            tione data, nimirum in ratione ſubduplicata prioris. </s>
            <s xml:space="preserve">Nam
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            ubi per idem ſpatium agunt vires, & </s>
            <s xml:space="preserve">velocitas oritur, vel
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            extinguitur tota, ut hic reſpectiva velocitas extinguitur in
              <lb/>
            compreſſione, oritur in reſtitutione figuræ, quadrata veloci-
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            tatum ſunt ut areæ, quas deſcribunt ordinatæ viribus pro-
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            portionales juxta num. </s>
            <s xml:space="preserve">176, & </s>
            <s xml:space="preserve">hinc areæ erunt in ratione vi-
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            rium, ſi, viribus conſtantibus, ſint conſtantes & </s>
            <s xml:space="preserve">ordinatæ, cum
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            inde fiat, ut ſcalæ celeritatum ab iis deſcriptæ ſint rectangu-
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            la. </s>
            <s xml:space="preserve">Sit igitur rationis conſtantis illarum virium ratio ſubdu-
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            plicata m ad n, & </s>
            <s xml:space="preserve">erit effectus in amittenda figura ad ſum-
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            mam effectuum in tota colliſione, ut m ad m + n, quæ ratio
              <lb/>
            ſi ponatur eſſe I
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            ad r, ut ſit r = {m +n,/m} ſatis erit, effectus il-
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            los inventos pro globis mollibus, ſive celeritatem ab altero a-
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            miſſam, ab altero acquiſitam, non duplicare, ut in perfecte e-
              <lb/>
            laſticis, ſed multiplicare per r, ut habeantur velocitates acqui-
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            ſitæ in partes contrarias, & </s>
            <s xml:space="preserve">componendæ cum </s>
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