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