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

Table of Notes

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            longior AC habebit repulſionem, & </s>
            <s xml:space="preserve">BC brevior attractionem,
              <lb/>
            ac rhombus erit KGNC, & </s>
            <s xml:space="preserve">vis dirigetur verſus O. </s>
            <s xml:space="preserve">Quod
              <lb/>
            ſi alicubi ante in loco adhuc propiore O diſtantiæ A C, BC
              <lb/>
            æquarentur abſciſſis A R, AI figuræ 1; </s>
            <s xml:space="preserve">ibi iterum eſſet limes;
              <lb/>
            </s>
            <s xml:space="preserve">ſed ante eum locum rediret iterum repulſio pro minore di-
              <lb/>
            ſtantia, attractio pro majore, & </s>
            <s xml:space="preserve">iterum rhombi diameter ja-
              <lb/>
            ceret verſus verticem axis conjugati E. </s>
            <s xml:space="preserve">Generaliter autem
              <lb/>
            ubi ſemiaxis transverſus æquatur diſtantiæ cujuſpiam limitis
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            cohæſionis, & </s>
            <s xml:space="preserve">diſtantia punctorum a centro ellipſeos, ſive ejus
              <lb/>
            eccentricitas eſt major, quam intervallum dicti limitis a plu-
              <lb/>
            ribus ſibi proximis hinc, & </s>
            <s xml:space="preserve">inde, ac maneat æqualitas ar-
              <lb/>
            cuum, habebuntur in ſingulis quadrantibus perimetri ellipſeos
              <lb/>
            tot limites, quot limites tranſibit eccentricitas hinc translata
              <lb/>
            in axem figuræ 1, a limite illo nominato, qui terminet in
              <lb/>
            fig. </s>
            <s xml:space="preserve">1 ſemiaxem tranſverſum hujus ellipſeos; </s>
            <s xml:space="preserve">ac præterea ha-
              <lb/>
            bebuntur limites in verticibus amborum ellipſeos axium; </s>
            <s xml:space="preserve">erit-
              <lb/>
            que incipiendo ab utrovis vertice axis conjugati in gyrum per
              <lb/>
            ipſam perimetrum is limes primus cohæſionis, tum illi proximus
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            eſſet non cohæſionis, deinde alter cohæſionis, & </s>
            <s xml:space="preserve">ita porro,
              <lb/>
            donec redeatur ad primum, ex quo incœptus fuerit gyrus, vi
              <lb/>
            in tranſitu per quemvis ex ejuſmodi limitibus mutante dire-
              <lb/>
            ctionem in oppoſitam. </s>
            <s xml:space="preserve">Quod ſi ſemiaxis hujus ellipſeos æque-
              <lb/>
            tur diſtantiæ limitis non cohæſionis ſiguræ 1; </s>
            <s xml:space="preserve">res eodem or-
              <lb/>
            dine pergit cum hoc ſolo diſcrimine, quod primus limes, qui
              <lb/>
            habetur in vertice ſemiaxis conjugati ſit limes non cohæſionis,
              <lb/>
            tum eundo in gyrum ipſi proximus ſit cohæſionis limes, de-
              <lb/>
            inde iterum non cohæſionis, & </s>
            <s xml:space="preserve">ita porro.</s>
            <s xml:space="preserve"/>
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          <p>
            <s xml:space="preserve">234. </s>
            <s xml:space="preserve">Verum eſt adhuc alia quædam analogia cum iis limiti-
              <lb/>
              <note position="left" xlink:label="note-0160-01" xlink:href="note-0160-01a" xml:space="preserve">Perimetri plu-
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              rium ellipſi
                <gap/>
                <gap/>
                <lb/>
              æquivalentes li.
                <lb/>
              mitibus.</note>
            bus; </s>
            <s xml:space="preserve">ſi conſiderentur plures ellipſes iiſdem illis focis, quarum
              <lb/>
            ſemiaxes ordine ſuo æquentur diſtantiis, in altera cujuſpiam e
              <lb/>
            limitibus cohæſionis ſiguræ 1, in altera limitis non cohæſio-
              <lb/>
            nis ipſi proximi, & </s>
            <s xml:space="preserve">ita porro alternatim, communis autem
              <lb/>
            illa eccentricitas ſit adhuc etiam minor quavis amplitudine ar-
              <lb/>
            cuum interceptorum limitibus illis figuræ 1, ut nimirum ſin-
              <lb/>
            gulæ ellipſium perimetri habeant quaternos tantummodo limi-
              <lb/>
            tes in quatuor verticibus axium. </s>
            <s xml:space="preserve">Ipſæ ejuſmodi perimetri to-
              <lb/>
            tæ erunt quidam veluti limites relate ad acceſſum, & </s>
            <s xml:space="preserve">receſſum
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            a centro. </s>
            <s xml:space="preserve">Punctum collocatum in quavis perimetro habebit
              <lb/>
            determinationem ad motum ſecundum directionem perimetri
              <lb/>
            ejuſdem; </s>
            <s xml:space="preserve">at collocatum inter binas perimetros diriget ſemper
              <lb/>
            vim ſuam ita, ut tendat verſus perimetrum definitam per li-
              <lb/>
            mitem cohæſionis figuræ 1, & </s>
            <s xml:space="preserve">recedat a perimetro definita per
              <lb/>
            limitem non cohæſionis; </s>
            <s xml:space="preserve">ac proinde punctum a perimetro pri-
              <lb/>
            mi generis dimotum conabitur ad illam redire; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">dimotum
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            a perimetro ſecundi generis, ſponte illam adhuc magis fugiet,
              <lb/>
            ac recedet.</s>
            <s xml:space="preserve"/>
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          <p>
            <s xml:space="preserve">236. </s>
            <s xml:space="preserve">Sint enim in fig. </s>
            <s xml:space="preserve">33. </s>
            <s xml:space="preserve">ellipſium FEOH, F'E'O'H',
              <lb/>
              <note position="left" xlink:label="note-0160-02" xlink:href="note-0160-02a" xml:space="preserve">Demonſtratio.</note>
            F''E''O''H'' ſemiaxes DO, DO', DO'' æquales primus </s>
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