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-s5750" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5751" xml:space="preserve">Si fuerit AN &</s>
            <s xml:id="echoid-s5752" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5753" xml:space="preserve">CR, refractus N _a_ cum AC retrò tractus
              <lb/>
              <note position="right" xlink:label="note-0107-01" xlink:href="note-0107-01a" xml:space="preserve">Fig. 132.</note>
            conveniet.</s>
            <s xml:id="echoid-s5754" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5755" xml:space="preserve">Nam CK&</s>
            <s xml:id="echoid-s5756" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5757" xml:space="preserve">NK. </s>
            <s xml:id="echoid-s5758" xml:space="preserve">(utin priore caſu).</s>
            <s xml:id="echoid-s5759" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5760" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5761" xml:space="preserve">Etiam hîc ſi AN = CR, refractus N _a_ fit ipſi AC paralle-
              <lb/>
            lus.</s>
            <s xml:id="echoid-s5762" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5763" xml:space="preserve">Nam erit CK = NK. </s>
            <s xml:id="echoid-s5764" xml:space="preserve">quod in hoc caſu niſi K infinitè diſtet con-
              <lb/>
            tingere nequit.</s>
            <s xml:id="echoid-s5765" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5766" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5767" xml:space="preserve">Si AN&</s>
            <s xml:id="echoid-s5768" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5769" xml:space="preserve">CR; </s>
            <s xml:id="echoid-s5770" xml:space="preserve">refractus N _a_ prorsùm excurrens axi oc-
              <lb/>
            currit.</s>
            <s xml:id="echoid-s5771" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5772" xml:space="preserve">Nam hîc CK&</s>
            <s xml:id="echoid-s5773" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5774" xml:space="preserve">NK.</s>
            <s xml:id="echoid-s5775" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5776" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5777" xml:space="preserve">Si AB&</s>
            <s xml:id="echoid-s5778" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5779" xml:space="preserve">CR; </s>
            <s xml:id="echoid-s5780" xml:space="preserve">omnes refracti directè progredientes ad AC
              <lb/>
              <note position="right" xlink:label="note-0107-02" xlink:href="note-0107-02a" xml:space="preserve">Fig. 133.</note>
            convergunt. </s>
            <s xml:id="echoid-s5781" xml:space="preserve">Erit enim quivis incidens AN&</s>
            <s xml:id="echoid-s5782" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5783" xml:space="preserve">CR.</s>
            <s xml:id="echoid-s5784" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5785" xml:space="preserve">5. </s>
            <s xml:id="echoid-s5786" xml:space="preserve">Quum AN = CR, evidens eſt omnes arcui BN incidentes
              <lb/>
            retrorſum verſus CA refractos convergere; </s>
            <s xml:id="echoid-s5787" xml:space="preserve">omnes autem ad partes
              <lb/>
            NT cadentes antrorſum verſus CB refringi.</s>
            <s xml:id="echoid-s5788" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5789" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s5790" xml:space="preserve">Hinc apparet ſub iſtis duobus generalibus caſibus tres à diverſo
              <lb/>
              <note position="right" xlink:label="note-0107-03" xlink:href="note-0107-03a" xml:space="preserve">Fig. 134,
                <lb/>
              135, 136.</note>
            puncti radiantis intervallo ſubnaſcentes ſpeciales caſus comprehendi;
              <lb/>
            </s>
            <s xml:id="echoid-s5791" xml:space="preserve">nempe vel omnes ab axe poſt refractionem progredientes divergunt,
              <lb/>
            vel omnes ad ipſum convergunt, vel aliqui divergunt, alii convergunt,
              <lb/>
            his intercedente medio quodam ad illum parallelo. </s>
            <s xml:id="echoid-s5792" xml:space="preserve">quæ ſubnotâſſe
              <lb/>
            diſcrimina videbatur operæ pretium ac determinâſſe. </s>
            <s xml:id="echoid-s5793" xml:space="preserve">Subdimus
              <lb/>
            etiam quoad reliquos generales caſus ſimpliciùs ſeſe rem habere; </s>
            <s xml:id="echoid-s5794" xml:space="preserve">
              <lb/>
            ſcilicet eodem ſemper modo: </s>
            <s xml:id="echoid-s5795" xml:space="preserve">Omnes enim ad cavum denſius inci-
              <lb/>
            dentium refracti directè procedentes ab axe divergunt; </s>
            <s xml:id="echoid-s5796" xml:space="preserve">Ut & </s>
            <s xml:id="echoid-s5797" xml:space="preserve">omnes
              <lb/>
            eorum, qui convexo ratiori impungunt; </s>
            <s xml:id="echoid-s5798" xml:space="preserve">id quod è generaliſſimis re-
              <lb/>
            fractionum legibus immediatè ſequitur, & </s>
            <s xml:id="echoid-s5799" xml:space="preserve">è ſimplice ſecundum illas
              <lb/>
            linearum ductu diluceſcit. </s>
            <s xml:id="echoid-s5800" xml:space="preserve">His admonitis in orbitam regreſſi pergi-
              <lb/>
            mus.</s>
            <s xml:id="echoid-s5801" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5802" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s5803" xml:space="preserve">E præmiſſo Theoremate non dificilè conficitur hoc _Problema:_
              <lb/>
            </s>
            <s xml:id="echoid-s5804" xml:space="preserve">Dato in axe puncto K, refractum deſignare, qui per hoc ipſum tran-
              <lb/>
            ſeat.</s>
            <s xml:id="echoid-s5805" xml:space="preserve">‖</s>
          </p>
          <p>
            <s xml:id="echoid-s5806" xml:space="preserve">Hoc nempe pacto. </s>
            <s xml:id="echoid-s5807" xml:space="preserve">Reperiatur punctum G, ut ſit KG. </s>
            <s xml:id="echoid-s5808" xml:space="preserve">AG :</s>
            <s xml:id="echoid-s5809" xml:space="preserve">:
              <lb/>
              <note position="right" xlink:label="note-0107-04" xlink:href="note-0107-04a" xml:space="preserve">Lect. 10.
                <lb/>
              Num. 25.
                <lb/>
              Fig. 137.</note>
            CK. </s>
            <s xml:id="echoid-s5810" xml:space="preserve">CR. </s>
            <s xml:id="echoid-s5811" xml:space="preserve">item fiat GF. </s>
            <s xml:id="echoid-s5812" xml:space="preserve">FA :</s>
            <s xml:id="echoid-s5813" xml:space="preserve">: CK. </s>
            <s xml:id="echoid-s5814" xml:space="preserve">CR (:</s>
            <s xml:id="echoid-s5815" xml:space="preserve">: KG. </s>
            <s xml:id="echoid-s5816" xml:space="preserve">AG). </s>
            <s xml:id="echoid-s5817" xml:space="preserve">tum
              <lb/>
            centro F, intervallo FG deſcribatur circulus refringentem interſecans
              <lb/>
            ad N; </s>
            <s xml:id="echoid-s5818" xml:space="preserve">erit connexa NK incidentis AN refractus.</s>
            <s xml:id="echoid-s5819" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5820" xml:space="preserve">Nam ducatur FN; </s>
            <s xml:id="echoid-s5821" xml:space="preserve">& </s>
            <s xml:id="echoid-s5822" xml:space="preserve">ob KG. </s>
            <s xml:id="echoid-s5823" xml:space="preserve">AG :</s>
            <s xml:id="echoid-s5824" xml:space="preserve">: GF. </s>
            <s xml:id="echoid-s5825" xml:space="preserve">FA. </s>
            <s xml:id="echoid-s5826" xml:space="preserve">erit permu-
              <lb/>
            tatim KG. </s>
            <s xml:id="echoid-s5827" xml:space="preserve">GF :</s>
            <s xml:id="echoid-s5828" xml:space="preserve">: AG. </s>
            <s xml:id="echoid-s5829" xml:space="preserve">FA. </s>
            <s xml:id="echoid-s5830" xml:space="preserve">dividendóque KF. </s>
            <s xml:id="echoid-s5831" xml:space="preserve">GF :</s>
            <s xml:id="echoid-s5832" xml:space="preserve">: GF. </s>
            <s xml:id="echoid-s5833" xml:space="preserve">FA.
              <lb/>
            </s>
            <s xml:id="echoid-s5834" xml:space="preserve">hoc eſt KF. </s>
            <s xml:id="echoid-s5835" xml:space="preserve">FN :</s>
            <s xml:id="echoid-s5836" xml:space="preserve">: FN. </s>
            <s xml:id="echoid-s5837" xml:space="preserve">FA. </s>
            <s xml:id="echoid-s5838" xml:space="preserve">quare triangula KFN, </s>
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