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

Table of handwritten notes

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            perimetri ejus ellipſeos, tum ob AC, CB ſimul æquales in
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              <note position="right" xlink:label="note-0159-01" xlink:href="note-0159-01a" xml:space="preserve">trum verſus
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              vertices axis
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              conjugati.</note>
            ellipſi axi tranſverſo, ſive duplo ſemiaxi DO; </s>
            <s xml:space="preserve">erit AC tan-
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            to longior, quam ipſa DO, quanto BC brevior; </s>
            <s xml:space="preserve">adeoque ſi
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            jam in fig. </s>
            <s xml:space="preserve">1 ſint Au, A z æquales hiſce AC, BC; </s>
            <s xml:space="preserve">habebun-
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            tur ibi utique u y, z t itidem æquales inter ſe. </s>
            <s xml:space="preserve">Quare hic at-
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            tractio CL æquabitur repulſioni CM, & </s>
            <s xml:space="preserve">LI MC eritrhom-
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            bus, in quo inclinatio IC ſecabit bifariam angulum LCM;
              <lb/>
            </s>
            <s xml:space="preserve">ac proinde ſi ea utrinque producatur in P, & </s>
            <s xml:space="preserve">Q; </s>
            <s xml:space="preserve">angulus
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            AC P, qui eſt idem, ac LC I, erit æqualis angulo BC Q,
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            qui eſt ad verticem oppoſitus angulo IC M. </s>
            <s xml:space="preserve">Quæ cum in el-
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            lipſi ſit notiſſima proprietas tangentis relatæ ad focos; </s>
            <s xml:space="preserve">erit i-
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            pſa PQ tangens. </s>
            <s xml:space="preserve">Quamobrem dirigetur vis puncti C in latus
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            ſecundum tangentem, ſive ſecundum directionem arcus ellipti-
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            ci, atque id, ubicunque fuerit punctum in perimetro ipſa,
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            verſus verticem propiorem axis conjugati, & </s>
            <s xml:space="preserve">ſibi relictum ibit
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            per ipſam perimetrum verſus eum verticem, niſi quatenus
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            ob vim centrifugam motum non nihil adhuc magis incurva-
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            bit.</s>
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          <note position="right" xml:space="preserve">Ana
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          ogía ver-
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          ticum binorum
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          axium cum li-
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          mitibus curvæ
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          virium.</note>
          <p>
            <s xml:space="preserve">232. </s>
            <s xml:space="preserve">Quamobrem hic jam licebit contemplari in hac curva
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            perimetro viciſſitudinem limitum prorſus analogorum limiti-
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            bus cohæſionis, & </s>
            <s xml:space="preserve">non co
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            æſionis, qui habentur in axe recti-
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            lineo curvæ primigeniæ figuræ 1. </s>
            <s xml:space="preserve">Erunt limites quidam in E,
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            in F, in H, in O, in quibus nimirum vis erit nulla, cum in
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            omnibus punctis C intermediis ſit aliqua. </s>
            <s xml:space="preserve">Sed in E, & </s>
            <s xml:space="preserve">H
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            erunt ejuſmodi, ut ſi utravis ex parte punctum dimoveatur,
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            per ipſam perimetrum, debeat redire verſus ipſos ejuſmodi li-
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            mites, ſicut ibi accidit in limitibus cohæſionis; </s>
            <s xml:space="preserve">at in F, & </s>
            <s xml:space="preserve">O
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            erit ejuſmodi, ut in utramvis partem, quantum libuerit, pa-
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            rum inde punctum dimotum fuerit, ſponte debeat inde magis uſ-
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            que recedere, prorſus ut ibi accidit in limitibus non cohæſionis.</s>
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          </p>
          <note position="right" xml:space="preserve">Quando limi-
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          tes contrario
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          modo poſiti:
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          caſus elegantiſ-
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          ſimi alternatio-
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          nis plurium li-
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          mitum in peri-
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          metro ellipſe-
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          os.</note>
          <p>
            <s xml:space="preserve">233. </s>
            <s xml:space="preserve">Contrarium accideret, ſi DO æquaretur diſtantiæ li-
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            mitis non cohæſionis: </s>
            <s xml:space="preserve">tum enim diſtantia BC minor haberet
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            attractionem C K, diſtantia major AC repulſionem CN, & </s>
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              <lb/>
            vis compoſita per diagonalem CG rhombi CN GK haberet
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            itidem directionem tangentis ellipſeos; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in verticibus qui-
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            dem axis utriuſque haberetur limes quidam, ſed punctum in
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            perimetro collocatum tenderet verſus vertices axis transverſi,
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            non verſus vertices axis conjugati, & </s>
            <s xml:space="preserve">hi referrent limites co-
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            hæſionis, illi e contrario limites non cohæſionis. </s>
            <s xml:space="preserve">Sed adhuc
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            major analogia in perimetro harum ellipſium habebitur cum
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            axe curvæ primigeniæ figuræ 1; </s>
            <s xml:space="preserve">ſi fuerit DO æqualis diſtan-
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            tiæ limitis cohæſionis AN illius, & </s>
            <s xml:space="preserve">DB in hac major, quam
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            in fig. </s>
            <s xml:space="preserve">1 amplitudo N L, N P; </s>
            <s xml:space="preserve">multo vero magis, ſi ipſa hu-
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            jus DB ſuperet plures ejuſmodi amplitudines, ac arcuum æquali-
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            tas maneat hinc, & </s>
            <s xml:space="preserve">inde. </s>
            <s xml:space="preserve">per totum ejuſmodi ſpatium. </s>
            <s xml:space="preserve">Ubi e
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            nim AC hujus figuræ fiet æqualis abſciſſæ AP illius, etiam
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            BC hujus fiet pariter æqualis AL illius. </s>
            <s xml:space="preserve">Quare in ejuſmodi
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            loco habebitur limes, & </s>
            <s xml:space="preserve">ante ejuſmodi locum verſus A </s>
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