Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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        <div xml:id="echoid-div399" type="section" level="1" n="42">
          <head xml:id="echoid-head45" xml:space="preserve">APPENDICUL A.</head>
          <p>
            <s xml:id="echoid-s13071" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13072" xml:space="preserve">Cum pridem ante plures annos illuſtris Viri, _Chriſtiani Hugenii,_
              <lb/>
            _Cyclometrica_ luſtrarem, ac in eo verſatus adverterem ad id
              <lb/>
            negotii duas præſertim ab ipſo methodos adhiberi; </s>
            <s xml:id="echoid-s13073" xml:space="preserve">quarum una _Cir-_
              <lb/>
            _culi ſegmentum_ duobus parabolicis (uni inſcripto, alteri adſcripto)
              <lb/>
            medium eſſe monſtrans, illius inde magnitudini limites præſcribit;
              <lb/>
            </s>
            <s xml:id="echoid-s13074" xml:space="preserve">altera _Parabolici ſegmenti, & </s>
            <s xml:id="echoid-s13075" xml:space="preserve">Parallelogrammi_ æquè altorum cen-
              <lb/>
            tris gravitatum medium interjacere centrum gravitatis circularis ſeg-
              <lb/>
            menti oſtendens, alteros exindè limites, adſignat; </s>
            <s xml:id="echoid-s13076" xml:space="preserve">incidit mihi cogi-
              <lb/>
            tatio poſſe loco parabolæ in prima methodo, nec non vice Parallelo-
              <lb/>
            grammi in ſecunda, paraboliformium aliquam circulari ſegmento cir-
              <lb/>
            cumſcriptibilem uſurpari, ſic ut res aliquanto propiùs attingatur; </s>
            <s xml:id="echoid-s13077" xml:space="preserve">id
              <lb/>
            mox verum eſſe re perpensâ comperi; </s>
            <s xml:id="echoid-s13078" xml:space="preserve">quin&</s>
            <s xml:id="echoid-s13079" xml:space="preserve">prætereà notavi facilèſup-
              <lb/>
            pares methodos _Hyperbolici ſegmenti dimenſioni_ accommodari. </s>
            <s xml:id="echoid-s13080" xml:space="preserve">Quo-
              <lb/>
            rum demonſtratio (præ aliis fortaſſe, quæ excogitari poſſent) brevis
              <lb/>
            & </s>
            <s xml:id="echoid-s13081" xml:space="preserve">clara cùm è ſuprà poſitis conſequatur aut pendeat, eam (alioquin
              <lb/>
            opinor haud injucundam) hîc viſum eſt apponere.</s>
            <s xml:id="echoid-s13082" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s13083" xml:space="preserve">II. </s>
            <s xml:id="echoid-s13084" xml:space="preserve">Adſumimus autem hæc pervulgata; </s>
            <s xml:id="echoid-s13085" xml:space="preserve">quorúmque demonſtratio-
              <lb/>
            nes è præmonſtratis haud difficilè variis modis colligantur; </s>
            <s xml:id="echoid-s13086" xml:space="preserve">ſi _parabo-_
              <lb/>
              <note position="left" xlink:label="note-0272-01" xlink:href="note-0272-01a" xml:space="preserve">Fig. 133.</note>
            _liformis_ BAE (cujus _Axis_ AD, _Baſis_ vel ordinata BDE, _Tan-_
              <lb/>
            _gens_ BT; </s>
            <s xml:id="echoid-s13087" xml:space="preserve">_Gravitatis centrum_ K) exponens ſit {_n_/_m_}; </s>
            <s xml:id="echoid-s13088" xml:space="preserve">erit _Area_ BAE
              <lb/>
            = {_m_/_n_ + _m_} AD x BE; </s>
            <s xml:id="echoid-s13089" xml:space="preserve">& </s>
            <s xml:id="echoid-s13090" xml:space="preserve">TD = {_m_/_n_} AD, & </s>
            <s xml:id="echoid-s13091" xml:space="preserve">KD = {_m_/_n_ + 2 _m_} AD.</s>
            <s xml:id="echoid-s13092" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13093" xml:space="preserve">III. </s>
            <s xml:id="echoid-s13094" xml:space="preserve">Sint duæ quævis curvæ AEB, AFB (quarum communis
              <lb/>
              <note position="left" xlink:label="note-0272-02" xlink:href="note-0272-02a" xml:space="preserve">Fig. 134.</note>
            axis AD, ordinata DB) ità ſe habentes, ut ductâ quâcunque rectâ
              <lb/>
            EFG ad BD parallelâ, quæ lineas expoſitas punctis E, F, G ſecet, po-
              <lb/>
            ſitóque quòd rectæ ES, FT tangant curvas, (illa curvam AEB, </s>
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