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

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              <pb o="51" file="0103" n="103" rhead="PARS PRIMA."/>
            natura abſtiacte conſiderata, multo magis rationi conſenta-
              <lb/>
            neum eſt, cenſere lineam illam, quæ vires exprimat, eſſe
              <lb/>
            unam ex iis, quæ axem ſecant, quam ex iis, quæ non ſecant,
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            adeoque & </s>
            <s xml:space="preserve">ejuſmodi eſſe virium legem, ut attractiones, & </s>
            <s xml:space="preserve">re-
              <lb/>
            pulſiones exhibeat ſimul pro diverſis diſtantiis, quam ut alte-
              <lb/>
            ras tantummodo referat; </s>
            <s xml:space="preserve">uſque adeo rei natura conſiderata non
              <lb/>
            ſolam attractionem, vel ſolam repulſionem, ſed utramque no-
              <lb/>
            bis objicit ſimul.</s>
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          </p>
          <p>
            <s xml:space="preserve">113. </s>
            <s xml:space="preserve">Sed eodem argumento licet ulterius qucque progredi,
              <lb/>
              <note position="right" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">Ulterior per-
                <lb/>
              quiſitio: curva-
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              rum genera:
                <lb/>
              quo altiores,
                <lb/>
              eo in pluribus
                <lb/>
              punctis ſecabi-
                <lb/>
              les a recta-</note>
            & </s>
            <s xml:space="preserve">primum etiam difficultatis caput amovere, quod a ſectio-
              <lb/>
            num, & </s>
            <s xml:space="preserve">idcirco etiam arcuum jam attractivorum, jam repul-
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            ſivoruin multiplicitate deſumitur. </s>
            <s xml:space="preserve">Curvas lineas Geometræ
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            in quaſdam claſſes dividunt ope analyſeos, quæ earum natu-
              <lb/>
            ram exprimit per illas, quas Analyſtæ appellant, æquationes,
              <lb/>
            & </s>
            <s xml:space="preserve">quæ ad varios gradus aſcendunt. </s>
            <s xml:space="preserve">Æquationes primi gra-
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            dus exprimunt rectas; </s>
            <s xml:space="preserve">æquationes ſecundi gradus curvas pri-
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            mi generis; </s>
            <s xml:space="preserve">æquationes tertii gradus curvas ſecundi generis,
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            atque ita porro; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſunt curvæ, quæ omnes gradus tranſcen-
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            dunt finitæ Algebræ, & </s>
            <s xml:space="preserve">quæ idcirco dicuntur tranſcendentes.
              <lb/>
            </s>
            <s xml:space="preserve">Porro illud demonſtrant Geometræ in Analyſi ad Geometriam
              <lb/>
            applicata, lineas, quæ exprimuntur per æquationen
              <gap/>
            primi gra-
              <lb/>
            dus, poſſe ſecari a recta in unico puncto; </s>
            <s xml:space="preserve">quæ æquationem
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            habent gradus ſecundi, tertii, & </s>
            <s xml:space="preserve">ita porro, ſecari poſſe a re-
              <lb/>
            cta in punctis duobus, tribus, & </s>
            <s xml:space="preserve">ita porro: </s>
            <s xml:space="preserve">unde fit, ut cur-
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            va noni, vel nonageſimi noni generis ſecari poſſit a recta in
              <lb/>
            punctis decem, vel centum.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">114. </s>
            <s xml:space="preserve">Jam vero curvæ primi generis ſunt tantummodo tres
              <lb/>
              <note position="right" xlink:label="note-0103-02" xlink:href="note-0103-02a" xml:space="preserve">Quo altiores, eo
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              itidem in im-
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              menſum plu
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              es
                <lb/>
              in eodem ge-
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              nere.</note>
            conicæ ſectiones, ellipſis, parabola, hyperbola, adnumerato
              <lb/>
            ellipſibus etiam circulo, quæ quidem veteribus quoque Geo-
              <lb/>
            metris innotuerunt. </s>
            <s xml:space="preserve">Curvas ſecundi generis enumeravit New-
              <lb/>
            tonus omnium primus, & </s>
            <s xml:space="preserve">ſunt circiter octoginta; </s>
            <s xml:space="preserve">curvarum
              <lb/>
            generis tertii nemo adhuc numerum exhibuit accuratum, & </s>
            <s xml:space="preserve">
              <lb/>
            mirum ſane, quantus ſit is ipſe illarum numerus. </s>
            <s xml:space="preserve">Sed quo
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            altius aſſurgit curvæ genus, eo plures in eo genere ſunt cur-
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            væ, progreſſione ita in immenſum creſcente, ut ubi aliquan-
              <lb/>
            to altius aſcenderit genus ipſum, numerus curvarum omnem
              <lb/>
            ſuperet humanæ imaginationis vim. </s>
            <s xml:space="preserve">Idem nimirum ibi ac-
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            cidit, quod in combinationibus terminorum, de quibus ſupra
              <lb/>
            mentionem fecimus, ubi diximus a 24 litterulis omnes exhi-
              <lb/>
            beri voces linguarum omnium, & </s>
            <s xml:space="preserve">quæ fuerunt, aut ſunt, & </s>
            <s xml:space="preserve">
              <lb/>
            quæ eſſe poſſunt.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">115. </s>
            <s xml:space="preserve">Inde jam pronum eſt argumentationem hujuſmodi in-
              <lb/>
              <note position="right" xlink:label="note-0103-03" xlink:href="note-0103-03a" xml:space="preserve">Deductio inde
                <lb/>
              plurimarum in-
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              terſectionum,
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              axis, & curvæ,
                <lb/>
              exprimentis vi-
                <lb/>
              res.</note>
            ſtituere. </s>
            <s xml:space="preserve">Numerus linearum, quæ axem ſecare poſſint in pun-
              <lb/>
            ctis quamplurimis, eſt in immenſum major earum numero,
              <lb/>
            quæ non poſſint, niſi in paucis, vel unico: </s>
            <s xml:space="preserve">igitur ubi agitur
              <lb/>
            de linea exprimente legem virium, ei, qui nihil aliunde ſciat,
              <lb/>
            in immenſum probabilius erit, ejuſmodi lineam eſſe ex </s>
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