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

Table of figures

< >
< >
page |< < (49) of 389 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="0" n="0">
          <p>
            <s xml:space="preserve">
              <pb o="49" file="0101" n="101" rhead="PARS PRIMA."/>
            hil ſane obeſſet, cum poſitivo argumento evincatur & </s>
            <s xml:space="preserve">repul-
              <lb/>
              <note position="right" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve">verſi ſint ge,
                <lb/>
              neris: ſed eſſe
                <lb/>
              ejuſdem, uti
                <lb/>
              ſunt poſitiva,
                <lb/>
              & negativa.</note>
            ſio, & </s>
            <s xml:space="preserve">attractio, uti vidimus; </s>
            <s xml:space="preserve">at id ipſum eft omnino falſum.
              <lb/>
            </s>
            <s xml:space="preserve">Utraque vis ad eandem pertinet ſpeciem, cum altera reſpectu
              <lb/>
            alterius negativa ſit, & </s>
            <s xml:space="preserve">negativa a poſitivis ſpecie non diffe-
              <lb/>
            rant. </s>
            <s xml:space="preserve">Alteram negativam eſſe reſpectu alterius, patet inde,
              <lb/>
            quod tantummodo differant in directione, quæ in altera eſt
              <lb/>
            prorſus oppoſita directioni alterius; </s>
            <s xml:space="preserve">in altera enim habetur de-
              <lb/>
            terminatio ad acceſſum, in altera ad receſſum, & </s>
            <s xml:space="preserve">uti receſſus,
              <lb/>
            & </s>
            <s xml:space="preserve">acceſſus ſunt poſitivum, ac negativum; </s>
            <s xml:space="preserve">ita ſunt pariter & </s>
            <s xml:space="preserve">
              <lb/>
            determinationes ad ipſos. </s>
            <s xml:space="preserve">Quod autem negativum, & </s>
            <s xml:space="preserve">poſiti-
              <lb/>
            vum ad eandem pertineant ſpeciem, id ſane patet vel ex eo
              <lb/>
            principio: </s>
            <s xml:space="preserve">magis, & </s>
            <s xml:space="preserve">minus non differunt ſpecie. </s>
            <s xml:space="preserve">Nam a po-
              <lb/>
            ſitivo per continuam ſubtractionem, nimirum diminutionem,
              <lb/>
            habentur prius minora poſitiva, tum zero, ac demum negati-
              <lb/>
            va, continuando ſubtractionem eandem.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">109. </s>
            <s xml:space="preserve">Id facile patet exemplis ſolitis. </s>
            <s xml:space="preserve">Eat aliquis contra flu-
              <lb/>
              <note position="right" xlink:label="note-0101-02" xlink:href="note-0101-02a" xml:space="preserve">Probatio h
                <gap/>
                <lb/>
              jus a progreſ.
                <lb/>
              ſu, & regreſſu.
                <lb/>
              in fluvio.</note>
            vii directionem verſus locum aliquem ſuperiori alveo proxi-
              <lb/>
            mum, & </s>
            <s xml:space="preserve">ſingulis minutis perficiat remis, vel vento 100 hexa-
              <lb/>
            pedas, dum a curſu fluvii retroagitur per hexapedas 40; </s>
            <s xml:space="preserve">is
              <lb/>
            habet progreſſum hexapedarum 60 ſingulis minutis. </s>
            <s xml:space="preserve">Creſcat au-
              <lb/>
            tem continuo impetus fluvii ita, ut retroagatur per 50, tum
              <lb/>
            per 60, 70, 80, 90, 100, 110, 120 &</s>
            <s xml:space="preserve">c. </s>
            <s xml:space="preserve">Is progredietur per 50,
              <lb/>
            40, 30, 20, 10, nihil; </s>
            <s xml:space="preserve">tum regredietur per 10, 20, quæ erunt
              <lb/>
            negativa priorum; </s>
            <s xml:space="preserve">nam erat prius 100 - 50, 100 - 60, 100
              <lb/>
            - 70, 100 - 80, 100 - 90, tum 100 - 100=0, 100-
              <lb/>
            110= - 10, 100 - 120= - 20, & </s>
            <s xml:space="preserve">ita porro. </s>
            <s xml:space="preserve">Continua
              <lb/>
            imminutione, ſive ſubtractione itum eſt a poſitivis in negati-
              <lb/>
            va, a progreſſu ad regreſſum, in quibus idcirco eadem ſpe-
              <lb/>
            cies manſit, non duæ diverſæ.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">110. </s>
            <s xml:space="preserve">Idem autem & </s>
            <s xml:space="preserve">algebraicis formulis, & </s>
            <s xml:space="preserve">geometricis li-
              <lb/>
              <note position="right" xlink:label="note-0101-03" xlink:href="note-0101-03a" xml:space="preserve">Probatio ex
                <lb/>
              Algebra, &
                <lb/>
              Geometria:
                <lb/>
              applicatio ad
                <lb/>
              omnes quanti-
                <lb/>
              tates variabi-
                <lb/>
              les.</note>
            neis ſatis manifeſte oſtenditur. </s>
            <s xml:space="preserve">Sit formula 10 - x, & </s>
            <s xml:space="preserve">pro
              <lb/>
            x ponantur valores 6, 7, 8, 9, 10, 11, 12 &</s>
            <s xml:space="preserve">c.</s>
            <s xml:space="preserve">; valor for-
              <lb/>
            mulæ exhibebit 4, 3, 2, 1, 0, - 1, -2 &</s>
            <s xml:space="preserve">c.</s>
            <s xml:space="preserve">, quod eodem
              <lb/>
            redit, ubi erat ſuperius in progreſſu, & </s>
            <s xml:space="preserve">regreſſu, qui exprime-
              <lb/>
            rentur ſimul per formulam 10 - x. </s>
            <s xml:space="preserve">Eadem illa formula per
              <lb/>
            continuam mutationem valoris x migrat e valore poſitivo in
              <lb/>
            negativum, qui æque ad eandem formulam pertinent. </s>
            <s xml:space="preserve">Eodem
              <lb/>
            pacto in Geometria in fig. </s>
            <s xml:space="preserve">11, ſi duæ lineæ MN, OP refe-
              <lb/>
              <note position="right" xlink:label="note-0101-04" xlink:href="note-0101-04a" xml:space="preserve">Fig. 11.</note>
            rantur invicem per ordinatas AB, CD &</s>
            <s xml:space="preserve">c parallelas inter
              <lb/>
            ſe, ſecent autem ſe in E; </s>
            <s xml:space="preserve">continuo motu ipſius ordinatæ a
              <lb/>
            poſitivo abitur in negativum, mutata directione AB, CD,
              <lb/>
            quæ hic habentur pro poſitivis, in FG, HI, poſt evaneſcen-
              <lb/>
            tiam in E. </s>
            <s xml:space="preserve">Ad eandem lineam continuam OEP æque per-
              <lb/>
            tinet omnis ea ordinatarum ſeries, nec eſt altera linea, alter
              <lb/>
            locus geometricus O E, ubi ordinatæ ſunt poſitivæ, ac EP,
              <lb/>
            ubi ſunt negativæ. </s>
            <s xml:space="preserve">Jam vero variabilis quantitatis cujuſvis
              <lb/>
            natura, & </s>
            <s xml:space="preserve">lex plerumque per formulam aliquam analyticam,
              <lb/>
            ſemper per ordinatas ad lineam aliquam exprimi poteſt; </s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum