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-div113" type="section" level="1" n="19">
          <p>
            <s xml:id="echoid-s5964" xml:space="preserve">
              <pb o="91" file="0109" n="109" rhead=""/>
            &</s>
            <s xml:id="echoid-s5965" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5966" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s5967" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s5968" xml:space="preserve">dividendóque CB. </s>
            <s xml:id="echoid-s5969" xml:space="preserve">BK&</s>
            <s xml:id="echoid-s5970" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5971" xml:space="preserve">CB. </s>
            <s xml:id="echoid-s5972" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s5973" xml:space="preserve">adeóque BK
              <lb/>
            &</s>
            <s xml:id="echoid-s5974" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5975" xml:space="preserve">BZ; </s>
            <s xml:id="echoid-s5976" xml:space="preserve">hoc eſt punctum K magìs quàm Z à centro elongatur.</s>
            <s xml:id="echoid-s5977" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5978" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5979" xml:space="preserve">Haud diſſimilis in aliis caſibus erìt _Demonſtratio_; </s>
            <s xml:id="echoid-s5980" xml:space="preserve">ut in hoc, ubi
              <lb/>
              <note position="right" xlink:label="note-0109-01" xlink:href="note-0109-01a" xml:space="preserve">Fig. 140.</note>
            I &</s>
            <s xml:id="echoid-s5981" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5982" xml:space="preserve">R, ad convexas; </s>
            <s xml:id="echoid-s5983" xml:space="preserve">eſt enim hîc (ut in præcedente) KB. </s>
            <s xml:id="echoid-s5984" xml:space="preserve">AB&</s>
            <s xml:id="echoid-s5985" xml:space="preserve">lt;
              <lb/>
            </s>
            <s xml:id="echoid-s5986" xml:space="preserve">KN. </s>
            <s xml:id="echoid-s5987" xml:space="preserve">AN. </s>
            <s xml:id="echoid-s5988" xml:space="preserve">adeóque (ſupra monſtratis inſiſtendo) CK.</s>
            <s xml:id="echoid-s5989" xml:space="preserve">CZ&</s>
            <s xml:id="echoid-s5990" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5991" xml:space="preserve">
              <lb/>
            KB. </s>
            <s xml:id="echoid-s5992" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s5993" xml:space="preserve">vel permutando CK. </s>
            <s xml:id="echoid-s5994" xml:space="preserve">KB&</s>
            <s xml:id="echoid-s5995" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5996" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s5997" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s5998" xml:space="preserve">dividendóque
              <lb/>
            CB. </s>
            <s xml:id="echoid-s5999" xml:space="preserve">KB&</s>
            <s xml:id="echoid-s6000" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6001" xml:space="preserve">CB. </s>
            <s xml:id="echoid-s6002" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s6003" xml:space="preserve">unde KB&</s>
            <s xml:id="echoid-s6004" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6005" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s6006" xml:space="preserve">adeóque punctum K
              <lb/>
            centro ſemper vicinius eſt quàm Z.</s>
            <s xml:id="echoid-s6007" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6008" xml:space="preserve">XVI. </s>
            <s xml:id="echoid-s6009" xml:space="preserve">Hæc autem cùm, modo ſuo mutatis mutandis, ad omnes
              <lb/>
            caſus transferri poſſint, habentur indè determinati refractorum limites,
              <lb/>
            hoc eſt apparentia radiantium punctorum A loca, reſpectu oculi cen-
              <lb/>
            trum habentis in axe AC ſitum; </s>
            <s xml:id="echoid-s6010" xml:space="preserve">juxta doctrinam à nobis toties in-
              <lb/>
            culcatam.</s>
            <s xml:id="echoid-s6011" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6012" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s6013" xml:space="preserve">Id autem hîc in duobus caſibus (utroque nimirum ad circuli
              <lb/>
            cavas) peculiare venit obſervandum cùm ſit CB = CR, omnes
              <lb/>
            refractos in ipſo puncto Z (ut ſuprà definito) retrò protractos con-
              <lb/>
            gregari. </s>
            <s xml:id="echoid-s6014" xml:space="preserve">Nam ob AB. </s>
            <s xml:id="echoid-s6015" xml:space="preserve">BC :</s>
            <s xml:id="echoid-s6016" xml:space="preserve">: AB. </s>
            <s xml:id="echoid-s6017" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s6018" xml:space="preserve">: BZ. </s>
            <s xml:id="echoid-s6019" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s6020" xml:space="preserve">erit divi-
              <lb/>
            dendo AC. </s>
            <s xml:id="echoid-s6021" xml:space="preserve">BC :</s>
            <s xml:id="echoid-s6022" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s6023" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s6024" xml:space="preserve">quapropter ad punctum quodvis N
              <lb/>
            adſumptum connexis AN, ZN, erit ZN. </s>
            <s xml:id="echoid-s6025" xml:space="preserve">AN :</s>
            <s xml:id="echoid-s6026" xml:space="preserve">: (CZ. </s>
            <s xml:id="echoid-s6027" xml:space="preserve">CN :</s>
            <s xml:id="echoid-s6028" xml:space="preserve">: )
              <lb/>
            CZ. </s>
            <s xml:id="echoid-s6029" xml:space="preserve">CR. </s>
            <s xml:id="echoid-s6030" xml:space="preserve">unde ZN refractus erit incidentis AN.</s>
            <s xml:id="echoid-s6031" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6032" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s6033" xml:space="preserve">Hinc etiam ſi fuerit AB = CR, conſequetur punctum Z
              <lb/>
              <note position="right" xlink:label="note-0109-02" xlink:href="note-0109-02a" xml:space="preserve">Fig. 141.</note>
            à centro infinitè diſtare; </s>
            <s xml:id="echoid-s6034" xml:space="preserve">quia nempe tum ob AB. </s>
            <s xml:id="echoid-s6035" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s6036" xml:space="preserve">: BZ. </s>
            <s xml:id="echoid-s6037" xml:space="preserve">CZ,
              <lb/>
            erit BZ = CZ; </s>
            <s xml:id="echoid-s6038" xml:space="preserve">id quod fieri nequit, niſi punctum Z ità elongetur
              <lb/>
            infinitè.</s>
            <s xml:id="echoid-s6039" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6040" xml:space="preserve">XIX. </s>
            <s xml:id="echoid-s6041" xml:space="preserve">_Conſectantur_ & </s>
            <s xml:id="echoid-s6042" xml:space="preserve">hæc: </s>
            <s xml:id="echoid-s6043" xml:space="preserve">Si punctorum radiantium A, _a_ limites
              <lb/>
              <note position="right" xlink:label="note-0109-03" xlink:href="note-0109-03a" xml:space="preserve">Fig. 142,
                <lb/>
              143.</note>
            ſint puncta Z, ζ, erit AC. </s>
            <s xml:id="echoid-s6044" xml:space="preserve">AB + BZ. </s>
            <s xml:id="echoid-s6045" xml:space="preserve">CZ = _a_ C. </s>
            <s xml:id="echoid-s6046" xml:space="preserve">_a_B + Bζ.
              <lb/>
            </s>
            <s xml:id="echoid-s6047" xml:space="preserve">C ζ.</s>
            <s xml:id="echoid-s6048" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6049" xml:space="preserve">Nam è præmiſſis facilè conſtat eſſe
              <lb/>
            tam AC. </s>
            <s xml:id="echoid-s6050" xml:space="preserve">AB + BZ. </s>
            <s xml:id="echoid-s6051" xml:space="preserve">CZ = \q̇uam _a_ C. </s>
            <s xml:id="echoid-s6052" xml:space="preserve">_a_ B + B ζ. </s>
            <s xml:id="echoid-s6053" xml:space="preserve">C ζ = }I. </s>
            <s xml:id="echoid-s6054" xml:space="preserve">R.</s>
            <s xml:id="echoid-s6055" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6056" xml:space="preserve">XX. </s>
            <s xml:id="echoid-s6057" xml:space="preserve">Unde Cζ &</s>
            <s xml:id="echoid-s6058" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6059" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s6060" xml:space="preserve">Nam ob BC. </s>
            <s xml:id="echoid-s6061" xml:space="preserve">AB &</s>
            <s xml:id="echoid-s6062" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6063" xml:space="preserve">BC. </s>
            <s xml:id="echoid-s6064" xml:space="preserve">_a_B.
              <lb/>
            </s>
            <s xml:id="echoid-s6065" xml:space="preserve">componendóque AC. </s>
            <s xml:id="echoid-s6066" xml:space="preserve">AB &</s>
            <s xml:id="echoid-s6067" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6068" xml:space="preserve">_a_ C. </s>
            <s xml:id="echoid-s6069" xml:space="preserve">_a_ B. </s>
            <s xml:id="echoid-s6070" xml:space="preserve">erit BZ. </s>
            <s xml:id="echoid-s6071" xml:space="preserve">CZ &</s>
            <s xml:id="echoid-s6072" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6073" xml:space="preserve">BC α B. </s>
            <s xml:id="echoid-s6074" xml:space="preserve">
              <lb/>
            Cζ. </s>
            <s xml:id="echoid-s6075" xml:space="preserve">dividendóque BC. </s>
            <s xml:id="echoid-s6076" xml:space="preserve">CZ &</s>
            <s xml:id="echoid-s6077" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6078" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s6079" xml:space="preserve">Cζ. </s>
            <s xml:id="echoid-s6080" xml:space="preserve">adeóque Cζ &</s>
            <s xml:id="echoid-s6081" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6082" xml:space="preserve">
              <lb/>
            C Z.</s>
            <s xml:id="echoid-s6083" xml:space="preserve"/>
          </p>
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