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

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            <s xml:space="preserve">257. </s>
            <s xml:space="preserve">Atque hic illud quidem accidit, quod in numerorum
              <lb/>
              <note position="left" xlink:label="note-0172-01" xlink:href="note-0172-01a" xml:space="preserve">Similis diffi-
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              cultas in ſum-
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              ma, & multi-
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              plicatione plu-
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              rium numero-
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              rum, & in vi
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              compoſita ex
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              pluribus: me-
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              thodus compo-
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              nendi ſimul o-
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              mnes.</note>
            ſumma, & </s>
            <s xml:space="preserve">multiplicatione experimur, ut nimirum quocunque
              <lb/>
            ordine accipiantur numeri, vel ſinguli, ut addantur numero
              <lb/>
            jam invento, vel ipſum multiplicent, vel plurium aggregata
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            ſeorſum addita, vel multiplicata; </s>
            <s xml:space="preserve">ſemper ad eundem demum
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            deveniatur numerum poſt omnes, qui dati fuerant, adhibitos
              <lb/>
            ſemel ſingulos; </s>
            <s xml:space="preserve">ac in ſumma patet facile deveniri eodem, & </s>
            <s xml:space="preserve">in
              <lb/>
            multiplicatione poteſt res itidem demonſtrari etiam generali-
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            ter, ſed ea huc non pertinent. </s>
            <s xml:space="preserve">Pertinet autem huc magis aliud
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            ejuſmodi exemplum petitum a compoſitione virium, in qua
              <lb/>
            itidem ſi multæ vires componantur communi methodo compo-
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            nendo inter ſe duas per diagonalem parallelogrammi, cujus la-
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            tera eas exprimant, tum hanc diagonalem cum tertia, & </s>
            <s xml:space="preserve">ita
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            porro; </s>
            <s xml:space="preserve">quocunque ordine res procedat, ſemper ad eandem de-
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            mum poſt omnes adhibitas devenitur. </s>
            <s xml:space="preserve">Hujuſmodi compoſitio-
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            ne plurimarum virium generali jam indigebimus, & </s>
            <s xml:space="preserve">ad abſo-
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            lutam demonſtrationem requiritur generalis expreſſio compoſi-
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            tionis virium quotcunque, qua uti ſoleo. </s>
            <s xml:space="preserve">Compono nimirum
              <lb/>
            generaliter motus, qui ſunt virium effectus, & </s>
            <s xml:space="preserve">ex effectu com-
              <lb/>
            poſito metior vim, ut e ſpatiolo, quod dato tempuſculo vi ali-
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            qua percurreretur, ſolet ipſa vis ſimplex quælibet æſtimari. </s>
            <s xml:space="preserve">Aſ-
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            ſumo illud, quod & </s>
            <s xml:space="preserve">rationi eſt conſentaneum, & </s>
            <s xml:space="preserve">experimentis
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            conſtat, & </s>
            <s xml:space="preserve">facile etiam demonſtratur conſentire cum communi
              <lb/>
            methodo componendi vires, ac motus per parallelogramma, ni-
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            mirum punctum ſolicitatum ſimul initio cujuſvis tempuſculi
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            actione conjuncta virium quarumcunque, quarum directio, & </s>
            <s xml:space="preserve">
              <lb/>
            magnitudo toto tempuſculo perſeveret eadem, fore in fine ejus
              <lb/>
            tempuſculi in eo loci puncto, in quo eſſet, ſi ſingulæ eadem
              <lb/>
            intenſitate, & </s>
            <s xml:space="preserve">directione egiſſent aliæ poſt alias totidem tempu-
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            ſculis, quot ſunt ipſæ vires, ceſſante omni nova ſolicitatione,
              <lb/>
            & </s>
            <s xml:space="preserve">omni velocitate jam producta a vi qualibet poſt ſuum tem-
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            puſculum: </s>
            <s xml:space="preserve">tum rectam, quæ conjungit primum illud punctum
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            cum hoc poſtremo, aſſumo pro menſura vis ex omnibus com-
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            poſitæ, quæ cum eadem perſeveret per totum tempuſculum;
              <lb/>
            </s>
            <s xml:space="preserve">punctum mobile utique per unicam illam eandem rectam ab-
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            iret. </s>
            <s xml:space="preserve">Quod ſi & </s>
            <s xml:space="preserve">velocitatem aliquam habuerit initio illius
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            tempuſculi jam acquiſitam ante; </s>
            <s xml:space="preserve">aſſumo itidem, fore in eo
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            puncto loci, in quo eſſet, ſi altero tempuſculo percurreret ſpa-
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            tiolum, ad quod determinatur ab illa velocitate, altero ſpa-
              <lb/>
            tiolum, ad quod determinatur a vi, ſive aliis totidem tempuſ-
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            culis percurreret ſpatiola, ad quorum ſingula determinatur a vi-
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            ribus ſingulis.</s>
            <s xml:space="preserve"/>
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          <p>
            <s xml:space="preserve">258. </s>
            <s xml:space="preserve">Huc recidere methodum componendi per parallelogram-
              <lb/>
              <note position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">Conſenſus ejus
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              methodi cum
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              communi per
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              parallelogram-
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              ma.</note>
            ma facile conſtat; </s>
            <s xml:space="preserve">ſi enim in fig. </s>
            <s xml:space="preserve">41 componendi ſint plures
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            motus, vel vires expreſſæ a rectis PA, PB, PC &</s>
            <s xml:space="preserve">c, & </s>
            <s xml:space="preserve">in-
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            cipiendo a binis quibuſque PA, PB, eæ componantur per
              <lb/>
            parallelogrammum PAMB, tum vis compoſita PM cum
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              <note position="left" xlink:label="note-0172-03" xlink:href="note-0172-03a" xml:space="preserve">Fig. 41.</note>
            tertia PC per parallelogrammum PMNC, & </s>
            <s xml:space="preserve">ita porro;</s>
            <s xml:space="preserve"/>
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