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

Page concordance

< >
Scan Original
131 79
132 80
133 81
134 82
135 83
136 84
137 85
138 86
139 87
140 88
141 89
142 90
143 91
144 92
145 93
146 94
147 95
148 96
149 97
150 98
151 99
152 100
153 101
154 102
155 103
156 104
157 105
158 106
159 107
160 108
< >
page |< < (101) 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="101" file="0153" n="153" rhead="PARS SECUNDA."/>
            ſummæ, vel differentiæ binarum ordinatarum pertinentium ad
              <lb/>
            eas abſciſſas, prout fuerint ejuſdem directionis, vel contrariæ, & </s>
            <s xml:space="preserve">
              <lb/>
            eam ducere ex parte attractiva, vel repulſiva, prout ambæ or-
              <lb/>
            dinatæ figuræ 1, vel earum major, attractiva fuerit, vel repul-
              <lb/>
            ſiva. </s>
            <s xml:space="preserve">Habebitur autem aſymptotus b Y c, & </s>
            <s xml:space="preserve">ultra ipſam crus
              <lb/>
            aſymptoticum D E, citra ipſam autem crus itidem aſymptoti-
              <lb/>
            cum d g attractivum reſpectu A, cui attractivum, ſed directio-
              <lb/>
            nis mutatæ reſpectu CC', ut in fig. </s>
            <s xml:space="preserve">ſuperiore diximus, ad par-
              <lb/>
            tes oppoſitas A debet eſſe aliud g' d', habens aſymptotum c' b'
              <lb/>
            tranſeuntem per X; </s>
            <s xml:space="preserve">ac utrumque crus debet continuari uſque ad
              <lb/>
            A, ubi curva ſecabit axem. </s>
            <s xml:space="preserve">Hoc poſtremum patet ex eo, quod
              <lb/>
            vires oppoſitæ in A debeant elidi; </s>
            <s xml:space="preserve">illud autem prius ex eo, quod
              <lb/>
            ſi a ſit prope Y, & </s>
            <s xml:space="preserve">ad ipſum in infinitum accedat, repulſio ab
              <lb/>
            Y creſcat in infinitum, vi, quæ provenit ab X, manente fi-
              <lb/>
            nita; </s>
            <s xml:space="preserve">adeoque tam ſumma, quam differentia debet eſſe vis re-
              <lb/>
            pulſiva reſpectu Y, & </s>
            <s xml:space="preserve">proinde attractiva reſpectu A, quæ immi-
              <lb/>
            nutis in infinitum diſtantiis ab Y augebitur in infinitum. </s>
            <s xml:space="preserve">Qua-
              <lb/>
            re ordinata a g in acceſſu ad b Y c creſcet in infinitum; </s>
            <s xml:space="preserve">unde
              <lb/>
            conſequitur, arcum g d fore aſymptoticum reſpectu Y c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ea-
              <lb/>
            dem erit ratio pro a' g', & </s>
            <s xml:space="preserve">arcu g' d' reſpectu b' X c'.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">219. </s>
            <s xml:space="preserve">Poterit autem etiam arcus curvæ interceptus aſymptotis
              <lb/>
              <note position="right" xlink:label="note-0153-01" xlink:href="note-0153-01a" xml:space="preserve">Ejus curvæ pro-
                <lb/>
              prietates: diſcri-
                <lb/>
              mina pro muta-
                <lb/>
              ta diſtantia pu
                <gap/>
              -
                <lb/>
              ctorum: collatio
                <lb/>
              cum curva ca-
                <lb/>
              ſus alterius.</note>
            b Y c, b' X c', ſive cruribus d g, d' g' ſecare alicubi axem, ut exhibet
              <lb/>
            figura 26; </s>
            <s xml:space="preserve">quin immo & </s>
            <s xml:space="preserve">in locis pluribus, ſi nimirum AY ſit
              <lb/>
            ſatis major, quam AE figuræ 1, ut ab Y habeatur alicubi citra
              <lb/>
            A attractio, & </s>
            <s xml:space="preserve">ab X repulſio, vel ab X repulſio major, quam
              <lb/>
            repulſio ab Y. </s>
            <s xml:space="preserve">Ceterum ſola inſpectione poſtremarum duarum
              <lb/>
              <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,
              <lb/>
            vel curvam, ſola diſtantia punctorum X, Y. </s>
            <s xml:space="preserve">Utraque enim fi-
              <lb/>
            gura derivata eſt a figura 1, & </s>
            <s xml:space="preserve">in fig. </s>
            <s xml:space="preserve">25 aſſumpta eſt XY æ-
              <lb/>
            qualis AE figuræ 1, in fig. </s>
            <s xml:space="preserve">26 æqualis AI, ejuſdem quæ varia-
              <lb/>
            tio uſque adeo mutavit figuræ genitæ ductum ; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">aſſumptis ali-
              <lb/>
            is, atque aliis diſtantiis punctorum X, Y, aliæ, atque aliæ cur-
              <lb/>
            v æ novæ provenirent, quæ inter ſe collatæ, & </s>
            <s xml:space="preserve">cum illis, quæ
              <lb/>
            habentur in recta CAC' perpendiculari ad XAY, uti eſt in
              <lb/>
            fig. </s>
            <s xml:space="preserve">24; </s>
            <s xml:space="preserve">ac multo magis cum iis, quæ pertinentes ad alias re-
              <lb/>
            ctas mente concipi poſſunt, ſatis confirmant id, quod ſupra in-
              <lb/>
            nui de tanta multitudine, & </s>
            <s xml:space="preserve">varietate legum provenientium a
              <lb/>
            ſola etiam duorum punctorum agentium in tertium diſpoſitio-
              <lb/>
            ne diverſa; </s>
            <s xml:space="preserve">ut & </s>
            <s xml:space="preserve">illud itidem patet ex ſola etiam harum trium
              <lb/>
            curvarum delineatione, quanta ſit ubique conformitas in arcu
              <lb/>
            illo attractivo T p V, ubique conjuncta cum tanto diſcrimine in
              <lb/>
            arcu ſe circa axem contorquente.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">220. </s>
            <s xml:space="preserve">Verum ex tanto diſcriminum numero unum ſeligam
              <lb/>
              <note position="right" xlink:label="note-0153-03" xlink:href="note-0153-03a" xml:space="preserve">Tria genera
                <lb/>
              hujus caſus no-
                <lb/>
              tatu digniſſima.</note>
            maxime notatu dignum, & </s>
            <s xml:space="preserve">maximo nobis uſui futurum infe-
              <lb/>
            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-
              <lb/>
            que arcus conſequenter accepti alicubi GHI, IKL, LMN,
              <lb/>
              <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-
              <lb/>
              <note position="right" xlink:label="note-0153-05" xlink:href="note-0153-05a" xml:space="preserve">Fig. 28.
                <lb/>
              29. 30.</note>
            nantur autem bina puncta B', B hinc, & </s>
            <s xml:space="preserve">inde ab A in fig. </s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum