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

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              <pb o="101" file="0153" n="153" rhead="PARS SECUNDA."/>
            ſummæ, vel differentiæ binarum ordinatarum pertinentium ad
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            eas abſciſſas, prout fuerint ejuſdem directionis, vel contrariæ, & </s>
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            eam ducere ex parte attractiva, vel repulſiva, prout ambæ or-
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            dinatæ figuræ 1, vel earum major, attractiva fuerit, vel repul-
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            ſiva. </s>
            <s xml:space="preserve">Habebitur autem aſymptotus b Y c, & </s>
            <s xml:space="preserve">ultra ipſam crus
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            aſymptoticum D E, citra ipſam autem crus itidem aſymptoti-
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            cum d g attractivum reſpectu A, cui attractivum, ſed directio-
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            nis mutatæ reſpectu CC', ut in fig. </s>
            <s xml:space="preserve">ſuperiore diximus, ad par-
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            tes oppoſitas A debet eſſe aliud g' d', habens aſymptotum c' b'
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            tranſeuntem per X; </s>
            <s xml:space="preserve">ac utrumque crus debet continuari uſque ad
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            A, ubi curva ſecabit axem. </s>
            <s xml:space="preserve">Hoc poſtremum patet ex eo, quod
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            vires oppoſitæ in A debeant elidi; </s>
            <s xml:space="preserve">illud autem prius ex eo, quod
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            ſi a ſit prope Y, & </s>
            <s xml:space="preserve">ad ipſum in infinitum accedat, repulſio ab
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            Y creſcat in infinitum, vi, quæ provenit ab X, manente fi-
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            nita; </s>
            <s xml:space="preserve">adeoque tam ſumma, quam differentia debet eſſe vis re-
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            pulſiva reſpectu Y, & </s>
            <s xml:space="preserve">proinde attractiva reſpectu A, quæ immi-
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            nutis in infinitum diſtantiis ab Y augebitur in infinitum. </s>
            <s xml:space="preserve">Qua-
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            re ordinata a g in acceſſu ad b Y c creſcet in infinitum; </s>
            <s xml:space="preserve">unde
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            conſequitur, arcum g d fore aſymptoticum reſpectu Y c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ea-
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            dem erit ratio pro a' g', & </s>
            <s xml:space="preserve">arcu g' d' reſpectu b' X c'.</s>
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          <p>
            <s xml:space="preserve">219. </s>
            <s xml:space="preserve">Poterit autem etiam arcus curvæ interceptus aſymptotis
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              <note position="right" xlink:label="note-0153-01" xlink:href="note-0153-01a" xml:space="preserve">Ejus curvæ pro-
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              prietates: diſcri-
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              mina pro muta-
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              ta diſtantia pu
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              -
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              ctorum: collatio
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              cum curva ca-
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              ſus alterius.</note>
            b Y c, b' X c', ſive cruribus d g, d' g' ſecare alicubi axem, ut exhibet
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            figura 26; </s>
            <s xml:space="preserve">quin immo & </s>
            <s xml:space="preserve">in locis pluribus, ſi nimirum AY ſit
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            ſatis major, quam AE figuræ 1, ut ab Y habeatur alicubi citra
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            A attractio, & </s>
            <s xml:space="preserve">ab X repulſio, vel ab X repulſio major, quam
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            repulſio ab Y. </s>
            <s xml:space="preserve">Ceterum ſola inſpectione poſtremarum duarum
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              <note position="right" xlink:label="note-0153-02" xlink:href="note-0153-02a" xml:space="preserve">Fig. 26.</note>
            figurarum patebit, quantum diſcrimen inducat in legem virium,
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            vel curvam, ſola diſtantia punctorum X, Y. </s>
            <s xml:space="preserve">Utraque enim fi-
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            gura derivata eſt a figura 1, & </s>
            <s xml:space="preserve">in fig. </s>
            <s xml:space="preserve">25 aſſumpta eſt XY æ-
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            qualis AE figuræ 1, in fig. </s>
            <s xml:space="preserve">26 æqualis AI, ejuſdem quæ varia-
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            tio uſque adeo mutavit figuræ genitæ ductum ; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">aſſumptis ali-
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            is, atque aliis diſtantiis punctorum X, Y, aliæ, atque aliæ cur-
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            v æ novæ provenirent, quæ inter ſe collatæ, & </s>
            <s xml:space="preserve">cum illis, quæ
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            habentur in recta CAC' perpendiculari ad XAY, uti eſt in
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            fig. </s>
            <s xml:space="preserve">24; </s>
            <s xml:space="preserve">ac multo magis cum iis, quæ pertinentes ad alias re-
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            ctas mente concipi poſſunt, ſatis confirmant id, quod ſupra in-
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            nui de tanta multitudine, & </s>
            <s xml:space="preserve">varietate legum provenientium a
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            ſola etiam duorum punctorum agentium in tertium diſpoſitio-
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            ne diverſa; </s>
            <s xml:space="preserve">ut & </s>
            <s xml:space="preserve">illud itidem patet ex ſola etiam harum trium
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            curvarum delineatione, quanta ſit ubique conformitas in arcu
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            illo attractivo T p V, ubique conjuncta cum tanto diſcrimine in
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            arcu ſe circa axem contorquente.</s>
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          </p>
          <p>
            <s xml:space="preserve">220. </s>
            <s xml:space="preserve">Verum ex tanto diſcriminum numero unum ſeligam
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              <note position="right" xlink:label="note-0153-03" xlink:href="note-0153-03a" xml:space="preserve">Tria genera
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              hujus caſus no-
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              tatu digniſſima.</note>
            maxime notatu dignum, & </s>
            <s xml:space="preserve">maximo nobis uſui futurum infe-
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            rius. </s>
            <s xml:space="preserve">Sit in fig. </s>
            <s xml:space="preserve">27 C'AC axis idem, ac in fig. </s>
            <s xml:space="preserve">1, & </s>
            <s xml:space="preserve">quin-
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            que arcus conſequenter accepti alicubi GHI, IKL, LMN,
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              <note position="right" xlink:label="note-0153-04" xlink:href="note-0153-04a" xml:space="preserve">Fig. 27.</note>
            NO P, PQR ſint æquales prorſus inter ſe, ac ſimiles. </s>
            <s xml:space="preserve">Po-
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              <note position="right" xlink:label="note-0153-05" xlink:href="note-0153-05a" xml:space="preserve">Fig. 28.
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              29. 30.</note>
            nantur autem bina puncta B', B hinc, & </s>
            <s xml:space="preserve">inde ab A in fig. </s>
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