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

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          <p>
            <s xml:id="echoid-s10116" xml:space="preserve">
              <pb o="51" file="0229" n="244" rhead=""/>
            CN + DB. </s>
            <s xml:id="echoid-s10117" xml:space="preserve">P. </s>
            <s xml:id="echoid-s10118" xml:space="preserve">hoc eſt DB. </s>
            <s xml:id="echoid-s10119" xml:space="preserve">DC:</s>
            <s xml:id="echoid-s10120" xml:space="preserve">: DC x DB. </s>
            <s xml:id="echoid-s10121" xml:space="preserve">CN x P. </s>
            <s xml:id="echoid-s10122" xml:space="preserve">hoc
              <lb/>
            eſt DB x DC. </s>
            <s xml:id="echoid-s10123" xml:space="preserve">DC q:</s>
            <s xml:id="echoid-s10124" xml:space="preserve">: DC x DB. </s>
            <s xml:id="echoid-s10125" xml:space="preserve">CN x P. </s>
            <s xml:id="echoid-s10126" xml:space="preserve">Quaproptcr eſt
              <lb/>
            DC q = CN x P; </s>
            <s xml:id="echoid-s10127" xml:space="preserve">ergò patet _curvam_ DNN _eſſe parabolam_, cu-
              <lb/>
            jus _parameter_ P, _vertex_ D; </s>
            <s xml:id="echoid-s10128" xml:space="preserve">_diameter_ ipſi BA parallela.</s>
            <s xml:id="echoid-s10129" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10130" xml:space="preserve">Dedit hoc _Gregorius
              <unsure/>
            _ à S. </s>
            <s xml:id="echoid-s10131" xml:space="preserve">_Vincentio_, ſed operosâ (ſi probè
              <note symbol="* it" position="right" xlink:label="note-0229-01" xlink:href="note-0229-01a" xml:space="preserve">In Lib. de
                <lb/>
              Spirali.</note>
            prolixitate, demonſtratum.</s>
            <s xml:id="echoid-s10132" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10133" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s10134" xml:space="preserve">Adjicimus; </s>
            <s xml:id="echoid-s10135" xml:space="preserve">Si reliquis iiſdem poſitis, ità ferantur CX, & </s>
            <s xml:id="echoid-s10136" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0229-02" xlink:href="note-0229-02a" xml:space="preserve">Fig. 48.</note>
            DY, ut jam ſemper habeant BE, BC rationem eandem (puta quam
              <lb/>
            BD ad R) erunt etiam interſectiones ad _par abolam_.</s>
            <s xml:id="echoid-s10137" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10138" xml:space="preserve">Nam biſecetur DB in G, ducatúrque GV ad BE parallela, ſe-
              <lb/>
            cans curvam DNN in V; </s>
            <s xml:id="echoid-s10139" xml:space="preserve">& </s>
            <s xml:id="echoid-s10140" xml:space="preserve">quoniam eſt BC. </s>
            <s xml:id="echoid-s10141" xml:space="preserve">R:</s>
            <s xml:id="echoid-s10142" xml:space="preserve">: BE. </s>
            <s xml:id="echoid-s10143" xml:space="preserve">BD:</s>
            <s xml:id="echoid-s10144" xml:space="preserve">:
              <lb/>
            CN. </s>
            <s xml:id="echoid-s10145" xml:space="preserve">CD. </s>
            <s xml:id="echoid-s10146" xml:space="preserve">erit BC x CD = R x CN. </s>
            <s xml:id="echoid-s10147" xml:space="preserve">ergò (ſecundum benè
              <lb/>
            notam _parabolæ proprietatem_) eſt curva DNN _parabola_, cujus _para-_
              <lb/>
            _meter_ R, _diameter_ GV.</s>
            <s xml:id="echoid-s10148" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10149" xml:space="preserve">Proletaria ſunt forſan iſta; </s>
            <s xml:id="echoid-s10150" xml:space="preserve">ſed non perinde notata occurunt hæc:</s>
            <s xml:id="echoid-s10151" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10152" xml:space="preserve">XVI. </s>
            <s xml:id="echoid-s10153" xml:space="preserve">Si reliquis ſimiliter poſitis, recta CX non jam ad ipſam BA,
              <lb/>
              <note position="right" xlink:label="note-0229-03" xlink:href="note-0229-03a" xml:space="preserve">Fig. 49.</note>
            ſed ad aliam poſitione datam (DH) feratur parallela; </s>
            <s xml:id="echoid-s10154" xml:space="preserve">sitque per-
              <lb/>
            petuò BE. </s>
            <s xml:id="echoid-s10155" xml:space="preserve">DC:</s>
            <s xml:id="echoid-s10156" xml:space="preserve">: DB. </s>
            <s xml:id="echoid-s10157" xml:space="preserve">R; </s>
            <s xml:id="echoid-s10158" xml:space="preserve">erunt _interſectiones_ N ad _hyperbolam_.</s>
            <s xml:id="echoid-s10159" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10160" xml:space="preserve">Nam ductâ NG ad BA parallelâ, nuncupentur DB = _b_. </s>
            <s xml:id="echoid-s10161" xml:space="preserve">BH =
              <lb/>
            _h_; </s>
            <s xml:id="echoid-s10162" xml:space="preserve">DG = _x_. </s>
            <s xml:id="echoid-s10163" xml:space="preserve">GN = _y_. </s>
            <s xml:id="echoid-s10164" xml:space="preserve">Eſtque _x.</s>
            <s xml:id="echoid-s10165" xml:space="preserve">y:</s>
            <s xml:id="echoid-s10166" xml:space="preserve">: b_. </s>
            <s xml:id="echoid-s10167" xml:space="preserve">{_by_/_x_} = BE. </s>
            <s xml:id="echoid-s10168" xml:space="preserve">item _h._
              <lb/>
            </s>
            <s xml:id="echoid-s10169" xml:space="preserve">_b:</s>
            <s xml:id="echoid-s10170" xml:space="preserve">: y._ </s>
            <s xml:id="echoid-s10171" xml:space="preserve">{_by_/_h_} = GC. </s>
            <s xml:id="echoid-s10172" xml:space="preserve">quare CD = _x_ - {_by_/_h_}. </s>
            <s xml:id="echoid-s10173" xml:space="preserve">Eſt igitur (ex hypotheſi)
              <lb/>
            {_by_/_x_}._</s>
            <s xml:id="echoid-s10174" xml:space="preserve">x_ - {_by_/_h_}:</s>
            <s xml:id="echoid-s10175" xml:space="preserve">: _b. </s>
            <s xml:id="echoid-s10176" xml:space="preserve">r_; </s>
            <s xml:id="echoid-s10177" xml:space="preserve">unde talis ordinabitur æquatio; </s>
            <s xml:id="echoid-s10178" xml:space="preserve">_y x_ + {_bry_/_b_} =
              <lb/>
            {_h_/_b_}_x x_. </s>
            <s xml:id="echoid-s10179" xml:space="preserve">ponendóq; </s>
            <s xml:id="echoid-s10180" xml:space="preserve">{_hr_/_b_} = _m_; </s>
            <s xml:id="echoid-s10181" xml:space="preserve">erit _yx_ + _my_ = {_m_/_r_}_x x_; </s>
            <s xml:id="echoid-s10182" xml:space="preserve">eſt ergò
              <lb/>
            curva DNN _hyperbola_, quæ ſuprà habetur determinata.</s>
            <s xml:id="echoid-s10183" xml:space="preserve"/>
          </p>
          <note symbol="* it" position="right" xml:space="preserve">In 10 hujus.</note>
          <p>
            <s xml:id="echoid-s10184" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s10185" xml:space="preserve">Quinetiam ſi (reliquis, ut in præcedente, ſuppoſitis) ità
              <lb/>
            jam feratur CX, ut ſemper habeat BE ad BC rationem eandem, quam
              <lb/>
            BD ad R; </s>
            <s xml:id="echoid-s10186" xml:space="preserve">erunt itidem interſectiones N ad _hyperbolam_.</s>
            <s xml:id="echoid-s10187" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10188" xml:space="preserve">Nam ductâ NG ad AB parallelâ, nominentur rectæ, ut in præ-
              <lb/>
            eunte; </s>
            <s xml:id="echoid-s10189" xml:space="preserve">èſtque jam BC = _b_ - _x_ + {_by_/_b_}; </s>
            <s xml:id="echoid-s10190" xml:space="preserve">atque {_by_/_x_}._</s>
            <s xml:id="echoid-s10191" xml:space="preserve">b_ - _x_ </s>
          </p>
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    </echo>
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