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

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              <pb o="157" file="0209" n="209" rhead="PARS SECUNDA."/>
            mirum ſingulæ maſſæ poſſint connecti cum puncto ſuſpenſio-
              <lb/>
              <note position="right" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">omnes maſſæ
                <lb/>
              ſint in eodem
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              plano perpen-
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              diculari ad a-
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              xem rotationis
                <gap/>
                <lb/>
              tranſitus ad cen-
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              trum percuſſio-
                <lb/>
              nis.</note>
            nis, & </s>
            <s xml:space="preserve">centro oſcillationis. </s>
            <s xml:space="preserve">At ubi in diverſis ſunt planis,
              <lb/>
            vel in plano non perpendiculari ad axem rotationis, oportet
              <lb/>
            ſingulas maſſas connectere cum binis punctis axis, & </s>
            <s xml:space="preserve">cum cen-
              <lb/>
            tro oſcillationis, ubi jam occurrit ſyſtema quatuor maſſarum
              <lb/>
            in ſe mutuo agentium; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">relatio virium, quæ in latus agant extra planum, in quo tres e maſſis jaceant, quæ per-
              <lb/>
            quiſitio eſt operoſior, ſed multo ſœcundior, & </s>
            <s xml:space="preserve">ad problema-
              <lb/>
            ta plurima rite ſolvenda magni uſus; </s>
            <s xml:space="preserve">ſed quæ hucuſque protu-
              <lb/>
            li, ſpeciminis loco abunde ſunt; </s>
            <s xml:space="preserve">mirum enim, quo in hujuſ-
              <lb/>
            modi
              <lb/>
            Theoria promovenda, & </s>
            <s xml:space="preserve">ad Mechanicam applicanda
              <lb/>
            progredi liceat. </s>
            <s xml:space="preserve">Sic etiam in determinando centro percuſſio-
              <lb/>
            nis, virgam tantummodo rectilineam conſiderabo, ſpeciminis
              <lb/>
            loco futuram, ſive maſſas in eadem recta linea ſitas, & </s>
            <s xml:space="preserve">mu-
              <lb/>
            tuis actionibus inter ſe connexas.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">344. </s>
            <s xml:space="preserve">Sint in fig. </s>
            <s xml:space="preserve">65 maſſæ A, B, C, D connexæ inter ſe
              <lb/>
              <note position="right" xlink:label="note-0209-02" xlink:href="note-0209-02a" xml:space="preserve">Præparatio ad
                <lb/>
              inveniendum
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              centrum percuſ-
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              ſionis maſſarum
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              jacentium in e-
                <lb/>
              adem recta.</note>
            in recta quadam, quæ concipiatur revoluta circa punctum P
              <lb/>
            in ea ſitum, & </s>
            <s xml:space="preserve">quæratur in eadem recta punctum quoddam
              <lb/>
            Q, cujus motu impedito debeat impediri omnis motus ea-
              <lb/>
            rumdem maſſarum per mutuas actiones; </s>
            <s xml:space="preserve">quod punctum appel-
              <lb/>
            latur centrum percuſſionis. </s>
            <s xml:space="preserve">Quoniam ſyſtema totum gyrat ci
              <lb/>
            rca
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              <note position="right" xlink:label="note-0209-03" xlink:href="note-0209-03a" xml:space="preserve">Fig. 65.</note>
            P, ſingulæ maſſæ habebunt velocitates A a, B b &</s>
            <s xml:space="preserve">c propor-
              <lb/>
            tionales diſtantiis a puncto P, adeoque ſingularum motus, qui
              <lb/>
            per mutuas vires motrices extingui debent, poterunt exprimi
              <lb/>
            per AxAP, BxBP &</s>
            <s xml:space="preserve">c. </s>
            <s xml:space="preserve">Quare vires motrices in iis de-
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            bebunt eſſe proportionales iis motibus. </s>
            <s xml:space="preserve">Concipiantur ſingulæ
              <lb/>
            connexæ cum punctis P, & </s>
            <s xml:space="preserve">Q, & </s>
            <s xml:space="preserve">quoniam velocitas puncti
              <lb/>
            P erat nulla; </s>
            <s xml:space="preserve">ibi omnium actionum ſumma debebit eſſe = o:
              <lb/>
            </s>
            <s xml:space="preserve">ſumma autem earum, quæ habentur in Q, elidetur a vi ex-
              <lb/>
            terna percuſſionem ſuſtinente.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">345. </s>
            <s xml:space="preserve">Quoniam actiones debent eſſe perpendiculares eidem
              <lb/>
              <note position="right" xlink:label="note-0209-04" xlink:href="note-0209-04a" xml:space="preserve">Calculus cum
                <lb/>
              ejus determina-
                <lb/>
              tione.</note>
            rectæ jungenti maſſas, erit per theorema numeri 314, ut PQ
              <lb/>
            ad AQ, ita actio in A = AxAP, ad actionem in P =
              <lb/>
            {AxAPxAQ/PQ}, ſive ob AQ = PQ-AP, erit ea actio
              <lb/>
              <note symbol="(q)" position="foot" xlink:label="note-0209-05" xlink:href="note-0209-05a" xml:space="preserve">Syſtema binarum maſſarum cum binis punctis connexarum, & inter
                <lb/>
              ſe, ſed adhuc in eodem plano jacentium, perſecutus fueram ante aliquot
                <lb/>
              annos; quod ſibi a me communicatum exhibuit in ſua Synopſi Phyſicæ
                <lb/>
              Generali
                <lb/>
              s P. Benvenutus, ut ibidem ipſe innuit. Id inde excerptum ha
                <lb/>
              betur hic in Supplementis §. 5.</note>
              <note position="foot" xlink:label="note-0209-06" xlink:href="note-0209-06a" xml:space="preserve">Habetur autem poſt idem ſupplementum & Epiſtola, quam delatus Flo-
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              rentiam ſcripſi ad P. Scherfferum, dum hoc ipſum opus relictum Viennæ
                <lb/>
              ante tres menſes jam ibidem imprimeretur, quæ quidem adjecta eſt in ip-
                <lb/>
              ſa prima editione in fine operis. Ibi & theoriam trium maſſarum extendi
                <lb/>
              ad caſum maſſarum quatuor ita; ut inde generaliter deduci poſſit & æqui-
                <lb/>
              librium, & centrum oſcillationis, & centrum percuſſionis, pro maſſis quot-
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              cunque, & utcunque diſpoſitis.</note>
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