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

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          <pb o="279" file="0331" n="331" rhead="SUPPLEMENTA. §. III."/>
          <p>
            <s xml:space="preserve">33. </s>
            <s xml:space="preserve">Patet igitur, utcunque affumpto Q cum datis conditio-
              <lb/>
              <note position="right" xlink:label="note-0331-01" xlink:href="note-0331-01a" xml:space="preserve">Poſt eas con-
                <lb/>
              ditiones rema-
                <lb/>
              nere inde
                <gap/>
                <gap/>
              r-
                <lb/>
              minationem
                <lb/>
              parem cuicun-
                <lb/>
              que acceſſui ad
                <lb/>
              quaſvis cur-
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              vas in punctis
                <lb/>
              datis quibuſ-
                <lb/>
              vis.</note>
            nibus, ſatisfieri primis quinque conditionibus curvæ . </s>
            <s xml:space="preserve">Jam ve-
              <lb/>
            ro poteſt valor Q variari inſinitis modis ita, ut adhuc im-
              <lb/>
            pleat ſemper conditiones, cum quibus aſſumptus eſt. </s>
            <s xml:space="preserve">Ac pro-
              <lb/>
            inde arcus curvæ intercepti interſectionibus poterunt inſinitis
              <lb/>
            modis variari ita, ut primæ quinque ipſius curvæ conditiones
              <lb/>
            impleantur; </s>
            <s xml:space="preserve">unde fit, ut poſſint etiam variari ita, ut ſextam
              <lb/>
            conditionem impleant.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">34. </s>
            <s xml:space="preserve">Si enim dentur quotcunque, & </s>
            <s xml:space="preserve">quicunque arcus, qua-
              <lb/>
              <note position="right" xlink:label="note-0331-02" xlink:href="note-0331-02a" xml:space="preserve">Quid requira-
                <lb/>
              tur, ut trans-
                <lb/>
              eat per quævis
                <lb/>
              earum puncta.</note>
            rumcunque curvarum, modo ſint ejuſmodi, ut ab aſymptoto
              <lb/>
            A B perpetuo recedant, adeoque nulla recta ipſi aſymptoto pa-
              <lb/>
            rallela eos arcus ſecet in pluribus, quam in unico puncto, & </s>
            <s xml:space="preserve">
              <lb/>
            in iis aſſumantur puncta quotcunque, utcunque inter ſe proxi-
              <lb/>
            ma; </s>
            <s xml:space="preserve">poterit admodum facile aſſumi valor P ita, ut curva per
              <lb/>
            omnia ejuſmodi puncta tranſeat, & </s>
            <s xml:space="preserve">idem poterit infinitis mo-
              <lb/>
            dis variari ita, ut adhuc ſemper curva tranſeat per eadem illa
              <lb/>
            puncta.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">35. </s>
            <s xml:space="preserve">Sit enim numerus punctorum aſſumptorum quicunque
              <lb/>
              <note position="right" xlink:label="note-0331-03" xlink:href="note-0331-03a" xml:space="preserve">Quomodo id
                <lb/>
              præſtandum.</note>
            =r, & </s>
            <s xml:space="preserve">a ſingulis ejuſmodi punctis demittantur rectæ pa-
              <lb/>
            rallelæ A B uſque ad axem C' A C, quæ debent eſſe ordina-
              <lb/>
            tæ curvæ quæ ſitæ, & </s>
            <s xml:space="preserve">ſingulæ abſciffæ ab A uſque ad ejuſmo-
              <lb/>
            di ordinatas dicantur M1, M2, M3 &</s>
            <s xml:space="preserve">c, ſingulæ autem
              <lb/>
            ordinatæ N'1, N'2, N'3 &</s>
            <s xml:space="preserve">c. </s>
            <s xml:space="preserve">Aſſumatur autem quædam
              <lb/>
            quantitas Az
              <emph style="super">v</emph>
            + Bz
              <emph style="super">r-1</emph>
            + Cz
              <emph style="super">r-2</emph>
            .</s>
            <s xml:space="preserve">..</s>
            <s xml:space="preserve">. + Gz, quæ ponatur = R.
              <lb/>
            </s>
            <s xml:space="preserve">Tum alia aſſumatur quantitas T ejuſmodi , ut evaneſcente
              <lb/>
            z evaneſcat quivis ejus terminus, & </s>
            <s xml:space="preserve">ut nullus ſit diviſor com-
              <lb/>
            munis valoris P, & </s>
            <s xml:space="preserve">valoris R + T, quod facile fiet, cum in-
              <lb/>
            noteſcant omnes diviſores quantitatis P . </s>
            <s xml:space="preserve">Ponatur autem Q
              <lb/>
            = R + T, & </s>
            <s xml:space="preserve">jam æquatio ad curvam erit P - Ry - Ty
              <lb/>
            = o. </s>
            <s xml:space="preserve">Ponantur in hac æquatione ſucceſſive M1, M2, M3 &</s>
            <s xml:space="preserve">c
              <lb/>
            pro x, & </s>
            <s xml:space="preserve">N 1, N 2, N 3 &</s>
            <s xml:space="preserve">c. </s>
            <s xml:space="preserve">pro y. </s>
            <s xml:space="preserve">Habebuntur æqua-
              <lb/>
            tiones numero r, quæ ſingulæ continebunt valores A , B,
              <lb/>
            C, . </s>
            <s xml:space="preserve">. </s>
            <s xml:space="preserve">. </s>
            <s xml:space="preserve">. </s>
            <s xml:space="preserve">G, unius tantum dimenſionis ſingulos, numero pa-
              <lb/>
            riter r, & </s>
            <s xml:space="preserve">præterea datos valores M1, M2, M3 &</s>
            <s xml:space="preserve">c, N1,
              <lb/>
            N2, N3 &</s>
            <s xml:space="preserve">c, ac valores arbitrarios, qui in T ſunt coeffi-
              <lb/>
            cientes ipſius z.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">36. </s>
            <s xml:space="preserve">Per illas æquationes numero r admodum facile deter-
              <lb/>
              <note position="right" xlink:label="note-0331-04" xlink:href="note-0331-04a" xml:space="preserve">Progreſſus ul-
                <lb/>
              terior.</note>
            minabuntur illi valores A, B, C . </s>
            <s xml:space="preserve">. </s>
            <s xml:space="preserve">. </s>
            <s xml:space="preserve">. </s>
            <s xml:space="preserve">G, qui ſunt pari-
              <lb/>
            ter numero r, aſſumendo in prima æquatione, juxta metho-
              <lb/>
            dos notiſſimas, & </s>
            <s xml:space="preserve">elementares valorem A, & </s>
            <s xml:space="preserve">eum fubſtituen-
              <lb/>
            do in æquationibus omnibus ſequentibus, quo pacto habebun-
              <lb/>
            tur æquationes r - 1. </s>
            <s xml:space="preserve">Hæ autem ejecto valore B reducentur
              <lb/>
            ad r - 2, & </s>
            <s xml:space="preserve">ita porro, donec ad unicam ventum fuerit, in
              <lb/>
            qua determinato valore Q, per ipſum ordine retrogrado de-
              <lb/>
            terminabuntur valores omnes præcedentes, ſinguli in ſingulis
              <lb/>
            æquationibus.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">37. </s>
            <s xml:space="preserve">Determinatis hoc pacto valoribus A, B, C . </s>
            <s xml:space="preserve">. </s>
            <s xml:space="preserve">. </s>
            <s xml:space="preserve">. </s>
            <s xml:space="preserve">G</s>
          </p>
          <note position="right" xml:space="preserve">Conclufio,</note>
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