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

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          <pb o="280" file="0332" n="332" rhead="SUPPLEMENTA §. III."/>
          <p>
            <s xml:space="preserve">in æquatione P - Ry - Ty= o, ſive P - Qy= o, patet po-
              <lb/>
              <note position="left" xlink:label="note-0332-01" xlink:href="note-0332-01a" xml:space="preserve">& cohærentia
                <lb/>
              cum omnibus
                <lb/>
              præcedentibus
                <lb/>
              conditionibus.</note>
            ſitis ſucceſſive pro x valoribus M1, M2, M3 &</s>
            <s xml:space="preserve">c, debere va-
              <lb/>
            lores ordinatæ y eſſe ſucceſſive N1, N2, N3 &</s>
            <s xml:space="preserve">c; </s>
            <s xml:space="preserve">ac proin-
              <lb/>
            de debere curvam tranſire per data illa puncta in datis il-
              <lb/>
            lis curvis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">tamen valor Q adhuc habebit omnes conditio-
              <lb/>
            nes præcedentes. </s>
            <s xml:space="preserve">Nam imminuta z ultra quoſcunque limites,
              <lb/>
            minuentur ſinguli ejus termini ultra quoſcunque limites, cum
              <lb/>
            minuantur termini ſinguli valoris T, qui ita aſſumpti ſunt, & </s>
            <s xml:space="preserve">
              <lb/>
            minuantur pariter termini valoris R, qui omnes ſunt ducti in
              <lb/>
            z, & </s>
            <s xml:space="preserve">præterea nullus erit communis diviſor quantitatum P, & </s>
            <s xml:space="preserve">
              <lb/>
            Q, cum nullus ſit quantitatum P, & </s>
            <s xml:space="preserve">R + T.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">38. </s>
            <s xml:space="preserve">Porro ſi bina proxima ex punctis aſſumptis in arcubus
              <lb/>
              <note position="left" xlink:label="note-0332-02" xlink:href="note-0332-02a" xml:space="preserve">Inde conta-
                <lb/>
              ctus, oſcula,
                <lb/>
              acceſſus quivis.</note>
            curvarum ad eandem axis partem concipiantur accedere ad ſe
              <lb/>
            invicem ultra quoſcumque limites, & </s>
            <s xml:space="preserve">tandem congruere, ſa-
              <lb/>
            ctis nimirum binis M æqualibus, & </s>
            <s xml:space="preserve">pariter æqualibus binis
              <lb/>
            N; </s>
            <s xml:space="preserve">jam curva quæſita ibidem tanget arcum curvæ datæ : </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            ſi tria ejuſmodi puncta congruant, eam oſculabitur: </s>
            <s xml:space="preserve">quin im-
              <lb/>
            mo illud præſtari poterit, ut coeant quot libuerit puncta, ubi
              <lb/>
            libuerit, & </s>
            <s xml:space="preserve">habeantur oſcula ordinis cujus libuerit, & </s>
            <s xml:space="preserve">ut libue.
              <lb/>
            </s>
            <s xml:space="preserve">rit ſibi invicem proxima, arcu curvæ datæ accedente, ut li-
              <lb/>
            buerit, & </s>
            <s xml:space="preserve">in quibus libuerit diſtantiis ad arcus, quos libuerit
              <lb/>
            curvarum, quarum libuerit, & </s>
            <s xml:space="preserve">tamen ipſa curva ſervante omnes
              <lb/>
            illas ſex conditiones requiſitas ad exponendam legem illam vi-
              <lb/>
            rium repulſivarum, ac attractivarum, & </s>
            <s xml:space="preserve">datos limites.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">39. </s>
            <s xml:space="preserve">Cum vero adhuc infinitis modis variari poſſit valor T;
              <lb/>
            </s>
            <s xml:space="preserve">
              <note position="left" xlink:label="note-0332-03" xlink:href="note-0332-03a" xml:space="preserve">Adhuc indeter-
                <lb/>
              minatio relicta
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              pro infinitis
                <lb/>
              modis.</note>
            infinitis modis idem præſtari poterit: </s>
            <s xml:space="preserve">ac proinde infinitis mo-
              <lb/>
            dis inveniri poterit curva ſimplex datis conditionibus ſatisfa-
              <lb/>
            ciens. </s>
            <s xml:space="preserve">Q. </s>
            <s xml:space="preserve">E. </s>
            <s xml:space="preserve">F.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">40. </s>
            <s xml:space="preserve">Coroll. </s>
            <s xml:space="preserve">1. </s>
            <s xml:space="preserve">Curva poterit contingere axem C'AC in
              <lb/>
              <note position="left" xlink:label="note-0332-04" xlink:href="note-0332-04a" xml:space="preserve">Poſſe & axem
                <lb/>
              contingere, oſ-
                <lb/>
              culari &c.</note>
            quot libuerit punctis, & </s>
            <s xml:space="preserve">contingere ſimul, ac ſecare in iiſdem,
              <lb/>
            ac proinde eum oſculari quocunque oſculi genere. </s>
            <s xml:space="preserve">Nam ſi bi-
              <lb/>
            næ quævis e diſtantiis limitum fiant æquales; </s>
            <s xml:space="preserve">curva continget
              <lb/>
            rectam C'A, evaneſcente arcu inter binos limites; </s>
            <s xml:space="preserve">ut ſi pun-
              <lb/>
            ctum I abiret in L, evaneſcente arcu IKL; </s>
            <s xml:space="preserve">haberetur con-
              <lb/>
            tactus in L, repulſio per arcum H I perpetuo decreſceret, & </s>
            <s xml:space="preserve">
              <lb/>
            in ipſo contactu I L evaneſceret, tum non tranſiret in attra-
              <lb/>
            ctionem, ſed iterum creſceret repulſio ipſa per arcum LM.
              <lb/>
            </s>
            <s xml:space="preserve">Idem autem accideret attractioni, ſi coeuntibus punctis LN,
              <lb/>
            evaneſceret arcus repulſivus LMN.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">41. </s>
            <s xml:space="preserve">Si autem tria puncta coirent, ut LNP; </s>
            <s xml:space="preserve">curva contin-
              <lb/>
              <note position="left" xlink:label="note-0332-05" xlink:href="note-0332-05a" xml:space="preserve">Poſſe contin-
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              gere ſimul, &
                <lb/>
              ſecare.</note>
            geret ſimul axem C'AC, & </s>
            <s xml:space="preserve">ab eodem ſimul ſecaretur, ac
              <lb/>
            proinde haberet in eodem puncto contactus ſlexum contrarium.
              <lb/>
            </s>
            <s xml:space="preserve">Haberetur autem ibidem tranſitus ab attractione ad repulſio-
              <lb/>
            nem, vel vice verſa, adeoque verus limes.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">42. </s>
            <s xml:space="preserve">Eodem pacto poſſunt congruere puncta quatuor, quin-
              <lb/>
              <note position="left" xlink:label="note-0332-06" xlink:href="note-0332-06a" xml:space="preserve">Quid congru-
                <lb/>
              entia interſe-
                <lb/>
              ctionum pluri-
                <lb/>
              um.</note>
            que, quotcunque : </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi congruat numerus punctorum par;
              <lb/>
            </s>
            <s xml:space="preserve">habebitur contactus: </s>
            <s xml:space="preserve">ſi impar; </s>
            <s xml:space="preserve">contactus ſimul, & </s>
            <s xml:space="preserve">ſectio. </s>
            <s xml:space="preserve">
              <lb/>
            Sed quo plura puncta coibunt ; </s>
            <s xml:space="preserve">eo magis curva accedet </s>
          </p>
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