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

Table of Notes

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              <pb o="84" file="0136" n="136" rhead="THEORIÆ"/>
            alicubi intervallum inter duos proximos limites ſit etiam in
              <lb/>
              <note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">& reſpectu ori-
                <lb/>
              ginis abſciſſa-
                <lb/>
              rum, poſitos
                <lb/>
              o
                <unsure/>
              rdine quocun-
                <lb/>
              que.</note>
            quacunque ratione majus, quam ſit diſtantia præcedentis ab
              <lb/>
            origine abſciſſarum A, alibi in intervallo vel exiguo, vel in-
              <lb/>
            genti ſint quamplurimi inter ſe ita proximi, ut a ſe invicem
              <lb/>
            diſtent minus, quam pro quovis aſſumpto, aut dato interval-
              <lb/>
            lo. </s>
            <s xml:space="preserve">Id evidenter fluit ex eo ipſo, quod poſſint ſectiones cur-
              <lb/>
            væ cum axe haberi quotcunque, & </s>
            <s xml:space="preserve">ubicunque. </s>
            <s xml:space="preserve">Sed ex eo,
              <lb/>
            quod arcus curvæ ubicunque poſſint habere poſitiones quaſ-
              <lb/>
            cunque, cum ad datas curvas accedere poſſint, quantum li-
              <lb/>
            buerit, ſequitur, quod limites ipſi cohæſionis poſſint alii aliis
              <lb/>
            eſſe utcunque validiores, vel languidiores, atque id quocun-
              <lb/>
            que ordine, vel ſine ordine ullo; </s>
            <s xml:space="preserve">ut nimirum etiam ſint in mi-
              <lb/>
            noribus diſtantiis alicubi limites validiſſimi, tum in majori-
              <lb/>
            bus languidiores, deinde itidem in majoribus multo validio-
              <lb/>
            res, & </s>
            <s xml:space="preserve">ita porro; </s>
            <s xml:space="preserve">cum nimirum null’is ſit nexus neceſſarius
              <lb/>
            inter diſtantiam limitis ab origine abſciſſarum, & </s>
            <s xml:space="preserve">ejus vali-
              <lb/>
            ditatem pendentem ab inclinatione, & </s>
            <s xml:space="preserve">receſſu arcus ſecantis
              <lb/>
            reſpectu axis, quod probe notandum eſt, futurum nimirum uſui
              <lb/>
            ad oſtendendum, tenacitatem, ſive cohæſionem, a denſitate
              <lb/>
            non pendere.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">184. </s>
            <s xml:space="preserve">In utroque limitum genere ſieri poteſt, ut curva in
              <lb/>
              <note position="left" xlink:label="note-0136-02" xlink:href="note-0136-02a" xml:space="preserve">Quæ poſitio re-
                <lb/>
              ctæ tangentis
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              curvam in li-
                <lb/>
              mite rariſſima,
                <lb/>
              quæ frequentiſ-
                <lb/>
              f
                <unsure/>
              ima. Arcus
                <lb/>
              exigui hinc &
                <lb/>
              inde æquales,
                <lb/>
              & ſ
                <unsure/>
              imiles.</note>
            ipſo occurſu cum axe pro tangente habeat axem ipſum, ut ha-
              <lb/>
            beat ordinatam, ut aliam rectam aliquam inclinatam. </s>
            <s xml:space="preserve">In pri-
              <lb/>
            mo caſu maxime ad axem accedit, & </s>
            <s xml:space="preserve">initio ſaltem languidiſ-
              <lb/>
            ſimus eſt limes; </s>
            <s xml:space="preserve">in ſecundo maxime recedit, & </s>
            <s xml:space="preserve">initio ſaltem
              <lb/>
            eſt validifſimus; </s>
            <s xml:space="preserve">fed hi caſus debent eſſe rariſſimi, ſi uſpiam
              <lb/>
            funt: </s>
            <s xml:space="preserve">nam cum ibi debeat & </s>
            <s xml:space="preserve">axem ſecare curva, & </s>
            <s xml:space="preserve">progredi,
              <lb/>
            adeoque ſecari in puncto eodem ab ordinata producta, debe-
              <lb/>
            bit habere flexum contrarium, ſive mutare directionem flexus,
              <lb/>
            quod utique fit, ubi curva & </s>
            <s xml:space="preserve">rectam tangit ſimul, & </s>
            <s xml:space="preserve">ſecat.
              <lb/>
            </s>
            <s xml:space="preserve">Rariſſimos tamen debere eſſe ibi hos flexus, vel potius nul-
              <lb/>
            los, conſtat ex eo, quod flexus contrarii puncta in quovis
              <lb/>
            finito arcu datæ curvæ cujuſvis numero ſinito eſſe debent, ut
              <lb/>
            in Theoria curvarum demonſtrari poteſt, & </s>
            <s xml:space="preserve">alia puncta ſunt
              <lb/>
            infinita numero, adeoque illa cadere in interſectiones eſt infini-
              <lb/>
            ties improbabilius. </s>
            <s xml:space="preserve">Poſſunt tamen ſæpe cadere prope limi-
              <lb/>
            tes: </s>
            <s xml:space="preserve">nam in ſingulis contorſionibus curvæ ſaltem ſinguli fle-
              <lb/>
            xus contrarii eſſe debent. </s>
            <s xml:space="preserve">Porro quamcunque directionem ha-
              <lb/>
            buerit tangens, ſi accipiatur exiguus arcus hinc, & </s>
            <s xml:space="preserve">inde a
              <lb/>
            limite, vel maxime accedet ad rectam, vel habebit curva-
              <lb/>
            turam ad ſenſum æqualem, & </s>
            <s xml:space="preserve">ad ſenſum æquali lege progre-
              <lb/>
            dientem utrinque, adeoque vires in æquali diſtantia exigua
              <lb/>
            a limite erunt ad ſenſum hinc, & </s>
            <s xml:space="preserve">inde æquales; </s>
            <s xml:space="preserve">ſed diſtantiis
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            auctis poterunt & </s>
            <s xml:space="preserve">diu æqualitatem retinere, & </s>
            <s xml:space="preserve">cito etiam ab
              <lb/>
            ea recedere.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">185. </s>
            <s xml:space="preserve">Hi quidem ſunt limites per interſectionem curvæ
              <lb/>
              <note position="left" xlink:label="note-0136-03" xlink:href="note-0136-03a" xml:space="preserve">Tranſitus per
                <lb/>
              infinitum c
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              </note>
            cum axe, viribus evaneſcentibus in ipſo limite. </s>
            <s xml:space="preserve">At </s>
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