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

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          <pb o="293" file="0345" n="345" rhead="SUPPLEMENTA. §. V."/>
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          <head style="it" xml:space="preserve">§ V. De Æquilibrio binarum maſſarum connexarum
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          invicem per bina alia puncta </head>
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            <s xml:space="preserve">86. </s>
            <s xml:space="preserve">COntinetur autem, quod pertinet ad momentum in
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              <note position="right" xlink:label="note-0345-01" xlink:href="note-0345-01a" xml:space="preserve">Propoſitio pro-
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              blematis de æ-
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              quilibrio pun-
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              ctorum qua-
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              tuor, quorum
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              bina extrema
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              habeant quaſ
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              -
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              cunque maſſas
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              cum viribus ex-
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              ternis ſibi pro-
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              portionalibus,
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              & altera e me-
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              diis vim a ful.
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              cro.</note>
            vecte, & </s>
            <s xml:space="preserve">ad æquilibrium, ſequentis problematis
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            ſolutione. </s>
            <s xml:space="preserve">Sit in fig. </s>
            <s xml:space="preserve">75 quivis numerus punctorum materiæ
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            in A, qui dicatur A, in D quivis alius, qui dicatur D, & </s>
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            puncta ea omnia ſecundum directiones AZ, DX parallelas
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            rectæ datæ CF ſollicitentur ſimul viribus, quæ ſint æquales
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            inter omnia puncta ſita in A, itidem inter omnia ſita in D,
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            licet vires in A ſint utcunque diverſæ a viribus in D. </s>
            <s xml:space="preserve">Sint
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            autem in C, & </s>
            <s xml:space="preserve">B bina puncta, quæ in ſe invicem, & </s>
            <s xml:space="preserve">in
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            illa puncta ſita in A, & </s>
            <s xml:space="preserve">D mutuo agant, ac ejuſmodi mutuis
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            actionibus impediri debeat omnis actio virium illarum in A,
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            & </s>
            <s xml:space="preserve">D, & </s>
            <s xml:space="preserve">omnis motus puncti B: </s>
            <s xml:space="preserve">motus autem puncti C im-
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              <note position="right" xlink:label="note-0345-02" xlink:href="note-0345-02a" xml:space="preserve">Fig. 75.</note>
            pediri debeat actione contraria ſulcri cujuſdam, in quod ipſum
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            agat ſecundum directionem compoſitam ex actionibus omnium
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            virium, quas habet: </s>
            <s xml:space="preserve">quæritur ratio, quam habere debent ſum-
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            mæ virium A, & </s>
            <s xml:space="preserve">D ad hoc, ut habeatur id æquilibrium, & </s>
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            quantitas, ac quæritur directio vis, qua fulcrum urgeri debet a
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            puncto C.</s>
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            <s xml:space="preserve">87. </s>
            <s xml:space="preserve">Exprimant AZ, & </s>
            <s xml:space="preserve">DX vires illas parallelas ſingulo-
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              <note position="right" xlink:label="note-0345-03" xlink:href="note-0345-03a" xml:space="preserve">Vis ex binis
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              extremis in al-
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              terum e me-
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              diis.</note>
            rum punctorum poſitorum in A, & </s>
            <s xml:space="preserve">D. </s>
            <s xml:space="preserve">Ut ipſæ elidantur,
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            debebunt in iis haberi vires AG, DK contrariæ, & </s>
            <s xml:space="preserve">æquales
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            ipſis AZ, DX. </s>
            <s xml:space="preserve">Quoniam eæ debent oriri a ſolis actionibus
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            punctorum C, & </s>
            <s xml:space="preserve">B agentium in A ſecundum rectas AC,
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            AB, & </s>
            <s xml:space="preserve">in D ſecundum rectas DC, DB, ductis ex G rectis
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            GI, GH parallelis BA, AC uſque ad rectas AC, BA, & </s>
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            ex K rectis KM, KL parallelis BD, DC, uſque ad re-
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            ctas DC, BD; </s>
            <s xml:space="preserve">patet, in A vim AG debere componi ex
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            viribus AI, AH, quarum prima quodvis punctum in A
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            repellat a C, ſecunda attrahat ad B, & </s>
            <s xml:space="preserve">in D vim DK com-
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            poni itidem ex viribus DM, DL, quarum prima quodvis
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            punctum ſitum in D repellat a C, ſecunda attrahat ad B.
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            </s>
            <s xml:space="preserve">Hinc ob actionem reactioni æqualem debebit punctum C re-
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            pelli a quovis puncto ſito in A ſecundum directionem AC
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            vi æquali IA, & </s>
            <s xml:space="preserve">a quovis puncto ſito in D ſecundum directio-
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              <note symbol="(f)" position="foot" xlink:label="note-0345-04" xlink:href="note-0345-04a" xml:space="preserve">Excerpta bæc ſunt ex Synopſi Phyſicæ Generalis P. Caroli Benve-
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              nuti Soc. Jeſu num. 146, cui banc ſolutionem ibi imprineendam tradide-
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              sam.</note>
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