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-
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              <note position="right" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">omnes maſſæ
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              ſint in eodem
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              plano perpen-
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              diculari ad a-
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              xem rotationis
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              tranſitus ad cen-
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              trum percuſſio-
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              nis.</note>
            nis, & </s>
            <s xml:space="preserve">centro oſcillationis. </s>
            <s xml:space="preserve">At ubi in diverſis ſunt planis,
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            vel in plano non perpendiculari ad axem rotationis, oportet
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            ſingulas maſſas connectere cum binis punctis axis, & </s>
            <s xml:space="preserve">cum cen-
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            tro oſcillationis, ubi jam occurrit ſyſtema quatuor maſſarum
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            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-
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            quiſitio eſt operoſior, ſed multo ſœcundior, & </s>
            <s xml:space="preserve">ad problema-
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            ta plurima rite ſolvenda magni uſus; </s>
            <s xml:space="preserve">ſed quæ hucuſque protu-
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            li, ſpeciminis loco abunde ſunt; </s>
            <s xml:space="preserve">mirum enim, quo in hujuſ-
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            modi
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            Theoria promovenda, & </s>
            <s xml:space="preserve">ad Mechanicam applicanda
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            progredi liceat. </s>
            <s xml:space="preserve">Sic etiam in determinando centro percuſſio-
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            nis, virgam tantummodo rectilineam conſiderabo, ſpeciminis
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            loco futuram, ſive maſſas in eadem recta linea ſitas, & </s>
            <s xml:space="preserve">mu-
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            tuis actionibus inter ſe connexas.</s>
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            <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
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              <note position="right" xlink:label="note-0209-02" xlink:href="note-0209-02a" xml:space="preserve">Præparatio ad
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              inveniendum
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              centrum percuſ-
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              ſionis maſſarum
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              jacentium in e-
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              adem recta.</note>
            in recta quadam, quæ concipiatur revoluta circa punctum P
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            in ea ſitum, & </s>
            <s xml:space="preserve">quæratur in eadem recta punctum quoddam
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            Q, cujus motu impedito debeat impediri omnis motus ea-
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            rumdem maſſarum per mutuas actiones; </s>
            <s xml:space="preserve">quod punctum appel-
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            latur centrum percuſſionis. </s>
            <s xml:space="preserve">Quoniam ſyſtema totum gyrat ci
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            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-
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            tionales diſtantiis a puncto P, adeoque ſingularum motus, qui
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            per mutuas vires motrices extingui debent, poterunt exprimi
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            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
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            connexæ cum punctis P, & </s>
            <s xml:space="preserve">Q, & </s>
            <s xml:space="preserve">quoniam velocitas puncti
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            P erat nulla; </s>
            <s xml:space="preserve">ibi omnium actionum ſumma debebit eſſe = o:
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            </s>
            <s xml:space="preserve">ſumma autem earum, quæ habentur in Q, elidetur a vi ex-
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            terna percuſſionem ſuſtinente.</s>
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          <p>
            <s xml:space="preserve">345. </s>
            <s xml:space="preserve">Quoniam actiones debent eſſe perpendiculares eidem
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              <note position="right" xlink:label="note-0209-04" xlink:href="note-0209-04a" xml:space="preserve">Calculus cum
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              ejus determina-
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              tione.</note>
            rectæ jungenti maſſas, erit per theorema numeri 314, ut PQ
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            ad AQ, ita actio in A = AxAP, ad actionem in P =
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            {AxAPxAQ/PQ}, ſive ob AQ = PQ-AP, erit ea actio
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              <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
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              ſe, ſed adhuc in eodem plano jacentium, perſecutus fueram ante aliquot
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              annos; quod ſibi a me communicatum exhibuit in ſua Synopſi Phyſicæ
                <lb/>
              Generali
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              s P. Benvenutus, ut ibidem ipſe innuit. Id inde excerptum ha
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              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
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              ante tres menſes jam ibidem imprimeretur, quæ quidem adjecta eſt in ip-
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              ſa prima editione in fine operis. Ibi & theoriam trium maſſarum extendi
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              ad caſum maſſarum quatuor ita; ut inde generaliter deduci poſſit & æqui-
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              librium, & centrum oſcillationis, & centrum percuſſionis, pro maſſis quot-
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              cunque, & utcunque diſpoſitis.</note>
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