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

Table of Notes

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              <pb o="176" file="0228" n="228" rhead="THEORIÆ"/>
            evinco, caſum, quo punctum aliquod materiæ occupet quovis
              <lb/>
            momento temporis punctum ſpatii, quod alio quopiam quo-
              <lb/>
            cunque occuparit vel ipſum, vel aliud punctum quodcunque,
              <lb/>
            eſſe infinities improbabilem, conſiderato nimirum numero pun-
              <lb/>
            ctorum materiæ finito, numero momentorum poſſibilium in-
              <lb/>
            finito èjus generis, cujus ſunt infinita puncta in una recta,
              <lb/>
            qui numerus momentorum bis ſumitur, ſemel cum conſidera-
              <lb/>
            tur puncti dati materiæ cujuſcunque momentum quodvis, & </s>
            <s xml:space="preserve">
              <lb/>
            iterum cum conſideratur momentum quodvis, quo aliud quod-
              <lb/>
            piam materiæ punctum alicubi fuerit, ac iis collatis cum nu-
              <lb/>
            mero punctorum ſpatii habentis extenſionem in longum, la-
              <lb/>
            tum, & </s>
            <s xml:space="preserve">profundum, qui idcirco debet eſſe infinitus ordinis
              <lb/>
            tertii reſpectu ſuperiorum. </s>
            <s xml:space="preserve">Deinde ab omnium corporum mo-
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            tu circa centrum commune gravitatis, vel quieſcens, vel uni-
              <lb/>
            formiter progrediens in recta linea, quies actualis itidem a Na-
              <lb/>
            tura excluditur.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">384. </s>
            <s xml:space="preserve">Verum ipſam quietem excludit alia mihi proprietas,
              <lb/>
              <note position="left" xlink:label="note-0228-01" xlink:href="note-0228-01a" xml:space="preserve">Q
                <unsure/>
              uies exclufa
                <lb/>
              etiam a conti-
                <lb/>
              nuitate omnium
                <lb/>
              motuum: pro-
                <lb/>
              blema generale
                <lb/>
              eo pertinens.</note>
            quam omnibus itidem materiæ punctis, & </s>
            <s xml:space="preserve">omnium corporum
              <lb/>
            centris gravitatis communem cenſeo, nimirum continuitas
              <lb/>
            motuum, de qua egi num. </s>
            <s xml:space="preserve">883, & </s>
            <s xml:space="preserve">alibi. </s>
            <s xml:space="preserve">Quodvis materiæ
              <lb/>
            punctum ſecluſis motibus liberis, qui oriuntur ab imperio
              <lb/>
            liberorum ſpirituum, debet deſcribere curvam quandam li-
              <lb/>
            neam continuam, cujus determinatio reducitur ad hujuſmodi
              <lb/>
            problema generale: </s>
            <s xml:space="preserve">Dato numero punctorum materiæ, ac pro
              <lb/>
            ſingulis dato puncto loci, quod occupent dato quopiam mo-
              <lb/>
            mento temporis, ac data directione, & </s>
            <s xml:space="preserve">velocitate motus ini-
              <lb/>
            tialis, ſi tum primo projiciuntur, vel tangentialis, ſi jam an-
              <lb/>
            te fuerunt in motu, ac data lege virium expreſſa per curvam
              <lb/>
            aliquam continuam, cujuſmodi eſt curva figuræ 1, quæ me-
              <lb/>
            am hanc Theoriam continet, invenire ſingulorum punctorum
              <lb/>
            trajectorias, lineas nimirum, per quas ea moventur ſingula. </s>
            <s xml:space="preserve">Id
              <lb/>
            problema mechanicum quam ſublime ſit, quam omnem huma-
              <lb/>
            næ mentis excedat vim, ille ſatis intelliget, qui in Mechanica
              <lb/>
            verſatus non nihil noverit, trium etiam corporum motus, ad-
              <lb/>
            modum ſimplici etiam vi præditorum, nondum eſſe generali-
              <lb/>
            ter definitos, uti monui num. </s>
            <s xml:space="preserve">204, & </s>
            <s xml:space="preserve">conſideret immenſum
              <lb/>
            punctorum numerum, ac altiſſimam curvæ virium tantis flexi-
              <lb/>
            bus circa axem circumvolutæ elevationem.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">385. </s>
            <s xml:space="preserve">Sed licet ejuſmodi problema vires omnes humanæ
              <lb/>
              <note position="left" xlink:label="note-0228-02" xlink:href="note-0228-02a" xml:space="preserve">Quid curvæ de-
                <lb/>
              ſcriptæ a pun-
                <lb/>
              ctis non ha-
                <lb/>
              beant. Proble-
                <lb/>
              m
                <unsure/>
              a inverſum
                <lb/>
              datis particulis
                <lb/>
              deſcriptis tem-
                <lb/>
              puſculo utcun-
                <lb/>
              que parvo.</note>
            mentis excedat; </s>
            <s xml:space="preserve">adhuc tamen unuſquiſque Geometra videbit
              <lb/>
            facile, problema eſſe prorſus determinatum, & </s>
            <s xml:space="preserve">curvas ejuſ-
              <lb/>
            modi fore omnes continuas ſine ullo ſaltu, ſi in lege virium
              <lb/>
            nullus ſit ſaltus. </s>
            <s xml:space="preserve">Quin immo & </s>
            <s xml:space="preserve">illud arbitror, in ejuſmodi
              <lb/>
            curvis nec ullas uſquam cuſpides occurrere; </s>
            <s xml:space="preserve">nam nodos nul-
              <lb/>
            los eſſe conſequitur ex eo, quod nullum materiæ punctum re-
              <lb/>
            deat ad idem punctum ſpatii, in quo ipſum aliquando fuerit,
              <lb/>
            adeoque nullus habeatur regreſſus, qui tamen ad nodum eſt ne-
              <lb/>
            ceſſarius. </s>
            <s xml:space="preserve">Hujuſmodi curvæ neceſſariæ eſſent omnes, & </s>
            <s xml:space="preserve"/>
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