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

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page |< < (295) of 389 > >|
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              <pb o="295" file="0347" n="347" rhead="SUPPLEMENTA. §. V."/>
            earum directiones, adeoque RC, NC ipſis æquales, & </s>
            <s xml:space="preserve">paral-
              <lb/>
            lelæ expriment vires illas tertiam, & </s>
            <s xml:space="preserve">quartam puncti C. </s>
            <s xml:space="preserve">Pro-
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            ducantur autem DC, AC, donec occurrant in O, & </s>
            <s xml:space="preserve">T re-
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            ctis ex N, & </s>
            <s xml:space="preserve">R parallelis ipſi CF, ſive ipſis GAZ, KDX,
              <lb/>
            & </s>
            <s xml:space="preserve">demittantur AF, DE, NQ, RS perpendicula in ipſam
              <lb/>
            FC productam, qua opus eſt, quæ occurrat rectis AB, DB
              <lb/>
            in V, P.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">90. </s>
            <s xml:space="preserve">Inprimis ob ſingula latera ſingulis lateribus parallela erunt
              <lb/>
              <note position="right" xlink:label="note-0347-01" xlink:href="note-0347-01a" xml:space="preserve">Vires ſub nova
                <lb/>
              expreſſione in-
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              de reſultante.</note>
            ſimilia triangula IAG, CTR, & </s>
            <s xml:space="preserve">triangula MDK, CON.
              <lb/>
            </s>
            <s xml:space="preserve">Quare erit ut IG, ſive AH, ad CR, ſive NB, vel AXAH,
              <lb/>
            nimirum ut 1 ad A, ita AG ad TR, & </s>
            <s xml:space="preserve">ita AI ad TC. </s>
            <s xml:space="preserve">
              <lb/>
            Erit igitur TR æqualis GA, ſive AZ ductæ in A, & </s>
            <s xml:space="preserve">CT
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            æqualis IA ductæ in A: </s>
            <s xml:space="preserve">adeoque illa exprimet ſummam om-
              <lb/>
            nium virium AZ omnium punctorum in A, hæc vim illam
              <lb/>
            primam puncti C, nimirum AXIA. </s>
            <s xml:space="preserve">Eodem prorſus argu-
              <lb/>
            mento, cum ſit MK, ſive DL ad CN, ſive RB, vel
              <lb/>
            DXDL, nimirum 1 ad D, ita DK ad ON, & </s>
            <s xml:space="preserve">ita DM
              <lb/>
            ad OC; </s>
            <s xml:space="preserve">erit NO æqualis KD, ſive DX ductæ in D, & </s>
            <s xml:space="preserve">
              <lb/>
            OC æqualis MD ductæ in D, adeoque illa exprimet ſummam
              <lb/>
            omnium virium DX omnium punctorum in D, hæc vim il-
              <lb/>
            lam ſccundam puncti C, nimirum DXDM. </s>
            <s xml:space="preserve">Quare jam erunt
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            Summa virium parallelarum in A - - - - - - - TR
              <lb/>
            Summa virium parallelarum in D - - - - - - - NO
              <lb/>
            Binæ vires in B - - - - - - - - - - - BN, BR
              <lb/>
            Quatuor vires in C - - - - - - CT, OC, RC, NC</s>
          </p>
          <p>
            <s xml:space="preserve">91. </s>
            <s xml:space="preserve">Jam vero patet, ex tertia R C, & </s>
            <s xml:space="preserve">prima CT com-
              <lb/>
              <note position="right" xlink:label="note-0347-02" xlink:href="note-0347-02a" xml:space="preserve">Vis in ſulcrum
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              cui æqualis.</note>
            poni vim RT æqualem ſummæ virium parallelarum A; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex
              <lb/>
            quarta NC, ac ſecunda OC componi vim NO æqualem
              <lb/>
            ſummæ virium parallelarum in D. </s>
            <s xml:space="preserve">Quare patet, ab unico
              <lb/>
            puncto C fulcrum urgeri vi, quæ eandem directionem habeat,
              <lb/>
            quam habent vires parallelæ in A, & </s>
            <s xml:space="preserve">D, & </s>
            <s xml:space="preserve">æquetur earum
              <lb/>
            ſummæ, nimirum urgeri eodem modo, quo urgeretur, ſi om-
              <lb/>
            nia illa puncta, quæ ſunt in D, & </s>
            <s xml:space="preserve">A, cum his viribus eſſent
              <lb/>
            in C, & </s>
            <s xml:space="preserve">ſulcrum per ſe ipſa immediate urgerent.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">92. </s>
            <s xml:space="preserve">Præterea ob paralleliſmum itidem omnium laterum ſi-
              <lb/>
              <note position="right" xlink:label="note-0347-03" xlink:href="note-0347-03a" xml:space="preserve">Proportio, quæ
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              vectem exhibet.</note>
            milia erunt triangula 1.</s>
            <s xml:space="preserve">° CNO, DPC: </s>
            <s xml:space="preserve">2.</s>
            <s xml:space="preserve">° CNQ, PDE:
              <lb/>
            </s>
            <s xml:space="preserve">3.</s>
            <s xml:space="preserve">° CPR, VCN: </s>
            <s xml:space="preserve">4.</s>
            <s xml:space="preserve">° CRS, VNQ: </s>
            <s xml:space="preserve">5.</s>
            <s xml:space="preserve">° CVA, TCR: </s>
            <s xml:space="preserve">
              <lb/>
            6.</s>
            <s xml:space="preserve">° VAF, CRS. </s>
            <s xml:space="preserve">Ea exhibent ſequentes ſex proportiones,
              <lb/>
            quarum binæ ſingulis verſibus continentur.</s>
            <s xml:space="preserve"/>
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          <p>
            <s xml:space="preserve">ON. </s>
            <s xml:space="preserve">CP:</s>
            <s xml:space="preserve">:NC. </s>
            <s xml:space="preserve">PD:</s>
            <s xml:space="preserve">:NQ. </s>
            <s xml:space="preserve">DE</s>
          </p>
          <p>
            <s xml:space="preserve">CP. </s>
            <s xml:space="preserve">CV:</s>
            <s xml:space="preserve">:CR. </s>
            <s xml:space="preserve">NV:</s>
            <s xml:space="preserve">:RS. </s>
            <s xml:space="preserve">NQ</s>
          </p>
          <p>
            <s xml:space="preserve">CV. </s>
            <s xml:space="preserve">RT:</s>
            <s xml:space="preserve">:VA. </s>
            <s xml:space="preserve">RC:</s>
            <s xml:space="preserve">:AF. </s>
            <s xml:space="preserve">RS</s>
          </p>
          <p>
            <s xml:space="preserve">Porro ex iis componendo primas, & </s>
            <s xml:space="preserve">poſtremas, ac demendo
              <lb/>
            in illis CP, CV; </s>
            <s xml:space="preserve">in his QN, RS communes tam antece-
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            dentibus, quam conſequentibus, ſit ex æqualitate nimirum per-
              <lb/>
            turbata ON. </s>
            <s xml:space="preserve">RT:</s>
            <s xml:space="preserve">:AF . </s>
            <s xml:space="preserve">DE. </s>
            <s xml:space="preserve">Nempe ſumma omnium
              <lb/>
            virium parallelarum in D, cui æquatur ON, ad ſummam </s>
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