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

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            <s xml:space="preserve">169. </s>
            <s xml:space="preserve">Arcus intermedii, qui ſe contorquent circa axem,
              <lb/>
              <note position="left" xlink:label="note-0130-01" xlink:href="note-0130-01a" xml:space="preserve">Arcus inter-
                <lb/>
              medii.</note>
            poffunt etiam alicubi, ubi ad ipſum devenerint, retro redire,
              <lb/>
            tangendo ipſum, atque id ex utralibet parte, & </s>
            <s xml:space="preserve">poffent itidem
              <lb/>
            ante ipſum contactum inflecti, & </s>
            <s xml:space="preserve">redire retro, mutando acceſ-
              <lb/>
            ſum in receffum, ut in fig. </s>
            <s xml:space="preserve">I. </s>
            <s xml:space="preserve">videre eſt in arcu P efq R.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">170. </s>
            <s xml:space="preserve">Si gravitas generalis legem vis proportionalis inverſe
              <lb/>
              <note position="left" xlink:label="note-0130-02" xlink:href="note-0130-02a" xml:space="preserve">Arcus poſtre-
                <lb/>
              mus gravitatis
                <lb/>
              fortaffe non a-
                <lb/>
              ſymptoticus.</note>
            quadrato diſtantiæ, quam non accurate fervat, ſed quampro-
              <lb/>
            xime, uti diximus in pri
              <gap/>
            re parte, retinet ad ſenſum non mu-
              <lb/>
            tatam ſolum per totum planetarium, & </s>
            <s xml:space="preserve">cometarium ſyſtema,
              <lb/>
            fieri utique poterit, ut curva virium non habeat illud poſtre-
              <lb/>
            mum crus aſymptoticum TV, habens pro aſymptoto ipſam
              <lb/>
            rectam AC, ſed iterum ſecet axem, & </s>
            <s xml:space="preserve">ſe contorqueat circa
              <lb/>
            ipſum. </s>
            <s xml:space="preserve">Tum vero inter alios caſus innumeros, qui haberi poſ-
              <lb/>
            fent, unum cenſeo ſpeciminis gratia hic non omittendum; </s>
            <s xml:space="preserve">in-
              <lb/>
            credibile enim eſt, quam ferax caſuum, quorum ſinguli ſunt
              <lb/>
            notatu digniffimi, unica etiam hujuſmodi curva eſſe poffit.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">171. </s>
            <s xml:space="preserve">Si in fig. </s>
            <s xml:space="preserve">14. </s>
            <s xml:space="preserve">in axe C`C ſint ſegmenta AA`, A`A`` nu-
              <lb/>
              <note position="left" xlink:label="note-0130-03" xlink:href="note-0130-03a" xml:space="preserve">Series curva-
                <lb/>
              rum ſimilium,
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              cum ſerie Mun-
                <lb/>
              dorum magni.</note>
            mero quocunque, quorum poſteriora ſint in immenſum majo-
              <lb/>
            ra reſpectu præcedentium, & </s>
            <s xml:space="preserve">per ſingula tranſeant aſympto-
              <lb/>
              <note position="foot" xlink:label="note-0130-04" xlink:href="note-0130-04a" xml:space="preserve">quarumlibet ſinguli occurſus cum axe in curvis per eas hac eadem lege geni-
                <lb/>
              tis bina crura aſymptotica generant, cruribus ipſis jacentibus, vel, ut hic,
                <lb/>
              ad eandem axis partem, ubi curva genitrix ab eo regreditur retro poſt ap-
                <lb/>
              pulſum, vel etiam ad partes oppoſitas, ubi curva genitrix ipſum ſecet, ac
                <lb/>
              tranſiliat: cumque poſſit eadem curva altiorum generun
                <gap/>
              ſecari in punctis
                <lb/>
              plurimis a recta, vel contingi; poterunt utique haberi & rami aſymptotici
                <lb/>
              in curva eadem continua, quo libuerit dato numero.</note>
              <note position="foot" xlink:label="note-0130-05" xlink:href="note-0130-05a" xml:space="preserve">Nam ex
                <gap/>
              pſa Geometrica continuitate, quam perſecutus ſum in diſſerta-
                <lb/>
              tione De Lege Continuitatis, & in diſſertatione De Transformatione Locorum
                <lb/>
              Geometricorum adjecta Sectionibus Conicis, exhibui neceſſitatem generalem
                <lb/>
              ſecundi illius cruris aſymptotici redeuntis ex inſinito. Quotieſcunque enim
                <lb/>
              curva aliqua ſaltem algebraica habet aſymptoticum crus aliquod, debet ne-
                <lb/>
              ceſſario habere & alterum ipſi reſpondens, & habens pro aſymptoto eandem
                <lb/>
              rectam: ſed id habere poteſt vel ex eadem parte, vel ex oppoſita; & crus
                <lb/>
              ipſum jacere poteſt vel ad eaſdem plagas partis utriuſlibet cum priore cru-
                <lb/>
              re, vel ad oppoſitas, adeoque cruris redeuntis ex infinito poſitiones qua-
                <lb/>
              tuor eſſe poſſunt. Si in fig. 13 crus ED abeat in infinitum, exiftente aſym-
                <lb/>
              ptoto ACA`, poteſt regredi ex parte A vel ut HI, quod crus jacet ad
                <lb/>
              eandem plagam, vel ut KL, quod jacet ad oppoſitam: & ex parte A`,
                <lb/>
              vel ut MN, ex eadem plaga, vel ut OP, ex oppoſita. In poſteriore ex
                <lb/>
              iis duabus diſſertationibus profero exempla omnium ejuſmodi regreſſuum;
                <lb/>
              ac ſecundi, & quarti caſus exempla exhibet etiam ſuperior geneſis, ſi cur-
                <lb/>
              va generans contingat axem, vel ſecet, ulterius progreſsa reſp
                <gap/>
              ctu ipſius.
                <lb/>
              Inde autem ſit, ut crura aſymptotica rectilineam habentia aſymptotum eſſe
                <lb/>
              non poſſint, niſi numero pari, ut & radices imaginariæ in æquationibus
                <lb/>
              algebraicis.</note>
              <note position="foot" xlink:label="note-0130-06" xlink:href="note-0130-06a" xml:space="preserve">Verum hic in curva virium, in qua arcus ſemper debet progredi, ut
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              ſingulis diſtantiis, ſive abſciſſis, ſingulæ vires, ſive ordinatæ reſpondeant,
                <lb/>
              caſus primus, & tertius haberi non poſſunt. Nam ordinata RQ cruris DE
                <lb/>
              occurreret alicubi in S, S` cruribus etiam HI, MN; adeoque relinquentur
                <lb/>
              ſoli quartus, & ſecundus, quorum uſus erit infra.</note>
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