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-s4440" xml:space="preserve">
              <pb o="71" file="0089" n="89" rhead=""/>
            & </s>
            <s xml:id="echoid-s4441" xml:space="preserve">demittatur NQ ad AC perpendicularis, erit CQ = F - E. </s>
            <s xml:id="echoid-s4442" xml:space="preserve">‖
              <lb/>
            Nam (ut ſuprà) eft CA. </s>
            <s xml:id="echoid-s4443" xml:space="preserve">CK:</s>
            <s xml:id="echoid-s4444" xml:space="preserve">: F. </s>
            <s xml:id="echoid-s4445" xml:space="preserve">E. </s>
            <s xml:id="echoid-s4446" xml:space="preserve">quare dividendo erit CA
              <lb/>
            - CK. </s>
            <s xml:id="echoid-s4447" xml:space="preserve">CK:</s>
            <s xml:id="echoid-s4448" xml:space="preserve">: F - E. </s>
            <s xml:id="echoid-s4449" xml:space="preserve">E. </s>
            <s xml:id="echoid-s4450" xml:space="preserve">Item hîc erit ANq - ACq =
              <lb/>
            2 AC x CQ + CNq. </s>
            <s xml:id="echoid-s4451" xml:space="preserve">adeóque 2 AC x CQ + CNq. </s>
            <s xml:id="echoid-s4452" xml:space="preserve">CNq
              <lb/>
            :</s>
            <s xml:id="echoid-s4453" xml:space="preserve">: AC. </s>
            <s xml:id="echoid-s4454" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s4455" xml:space="preserve">hoc eſt, (ob CNq = 2 AC x E.) </s>
            <s xml:id="echoid-s4456" xml:space="preserve">2 AC x CQ
              <lb/>
            + 2 AC x E. </s>
            <s xml:id="echoid-s4457" xml:space="preserve">2 AC x E:</s>
            <s xml:id="echoid-s4458" xml:space="preserve">: AC. </s>
            <s xml:id="echoid-s4459" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s4460" xml:space="preserve">hoc eſt CQ + E. </s>
            <s xml:id="echoid-s4461" xml:space="preserve">E:</s>
            <s xml:id="echoid-s4462" xml:space="preserve">:
              <lb/>
            AC. </s>
            <s xml:id="echoid-s4463" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s4464" xml:space="preserve">quare dividendo CQ. </s>
            <s xml:id="echoid-s4465" xml:space="preserve">E:</s>
            <s xml:id="echoid-s4466" xml:space="preserve">: AC - CK. </s>
            <s xml:id="echoid-s4467" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s4468" xml:space="preserve">ergo
              <lb/>
            F - E = CQ: </s>
            <s xml:id="echoid-s4469" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s4470" xml:space="preserve">E. </s>
            <s xml:id="echoid-s4471" xml:space="preserve">D.</s>
            <s xml:id="echoid-s4472" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4473" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s4474" xml:space="preserve">porrò, ſi duorum quorumvis radiorum AN, AR reflexi
              <lb/>
            NK, RL axem ſecent punctis K, L; </s>
            <s xml:id="echoid-s4475" xml:space="preserve">erit CK. </s>
            <s xml:id="echoid-s4476" xml:space="preserve">CL:</s>
            <s xml:id="echoid-s4477" xml:space="preserve">: ARq -
              <lb/>
            ACq. </s>
            <s xml:id="echoid-s4478" xml:space="preserve">ANq - ACq. </s>
            <s xml:id="echoid-s4479" xml:space="preserve">Nam ob CK. </s>
            <s xml:id="echoid-s4480" xml:space="preserve">AC:</s>
            <s xml:id="echoid-s4481" xml:space="preserve">: CNq. </s>
            <s xml:id="echoid-s4482" xml:space="preserve">ANq
              <lb/>
            - ACq. </s>
            <s xml:id="echoid-s4483" xml:space="preserve">& </s>
            <s xml:id="echoid-s4484" xml:space="preserve">AC. </s>
            <s xml:id="echoid-s4485" xml:space="preserve">CL:</s>
            <s xml:id="echoid-s4486" xml:space="preserve">: ARq - ACq. </s>
            <s xml:id="echoid-s4487" xml:space="preserve">CNq. </s>
            <s xml:id="echoid-s4488" xml:space="preserve">erit ex æquo
              <lb/>
            perturbatè CK. </s>
            <s xml:id="echoid-s4489" xml:space="preserve">CL:</s>
            <s xml:id="echoid-s4490" xml:space="preserve">: ARq - ACq. </s>
            <s xml:id="echoid-s4491" xml:space="preserve">ANq - ACq.</s>
            <s xml:id="echoid-s4492" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4493" xml:space="preserve">X. </s>
            <s xml:id="echoid-s4494" xml:space="preserve">Hinc ſi radius AR ſit ipſo AN obliquior; </s>
            <s xml:id="echoid-s4495" xml:space="preserve">erit CK &</s>
            <s xml:id="echoid-s4496" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4497" xml:space="preserve">CL.
              <lb/>
            </s>
            <s xml:id="echoid-s4498" xml:space="preserve">Nam ARq - ACq &</s>
            <s xml:id="echoid-s4499" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4500" xml:space="preserve">ANq - ACq.</s>
            <s xml:id="echoid-s4501" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4502" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s4503" xml:space="preserve">Hinc palàm eſt reflexos NK, RL ſeſe priùs quàm axem
              <lb/>
            decuſſare.</s>
            <s xml:id="echoid-s4504" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4505" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s4506" xml:space="preserve">Accipiantur porrò bini pares arcus NR, RX; </s>
            <s xml:id="echoid-s4507" xml:space="preserve">& </s>
            <s xml:id="echoid-s4508" xml:space="preserve">inciden-
              <lb/>
            tium AN, AR, AX reflexi cum axe conveniant punctis K, L, M;
              <lb/>
            </s>
            <s xml:id="echoid-s4509" xml:space="preserve">dico ſpatium LM, obliquiorum occurſibus interjectum, majus eſſe
              <lb/>
            ſpatio LK, quod rectiorum continetur occurſibus. </s>
            <s xml:id="echoid-s4510" xml:space="preserve">Nam è ſuprà
              <lb/>
            monſtratis conſtat eſſe ANq + AXq &</s>
            <s xml:id="echoid-s4511" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4512" xml:space="preserve">2 ARq. </s>
            <s xml:id="echoid-s4513" xml:space="preserve">proindeque fo-
              <lb/>
              <note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">Fig. 102;</note>
            re ANq + AXq - 2 ACq &</s>
            <s xml:id="echoid-s4514" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4515" xml:space="preserve">2 ARq - 2 ACq. </s>
            <s xml:id="echoid-s4516" xml:space="preserve">ac indè
              <lb/>
            ANq. </s>
            <s xml:id="echoid-s4517" xml:space="preserve">- ACq. </s>
            <s xml:id="echoid-s4518" xml:space="preserve">ARq - ACq &</s>
            <s xml:id="echoid-s4519" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4520" xml:space="preserve">ARq - ACq. </s>
            <s xml:id="echoid-s4521" xml:space="preserve">AXq -
              <lb/>
            ACq. </s>
            <s xml:id="echoid-s4522" xml:space="preserve">hoc eſt CL. </s>
            <s xml:id="echoid-s4523" xml:space="preserve">CK &</s>
            <s xml:id="echoid-s4524" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4525" xml:space="preserve">CM. </s>
            <s xml:id="echoid-s4526" xml:space="preserve">CL. </s>
            <s xml:id="echoid-s4527" xml:space="preserve">vel CM. </s>
            <s xml:id="echoid-s4528" xml:space="preserve">CL &</s>
            <s xml:id="echoid-s4529" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4530" xml:space="preserve">CL.
              <lb/>
            </s>
            <s xml:id="echoid-s4531" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s4532" xml:space="preserve">quare CM + CK &</s>
            <s xml:id="echoid-s4533" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4534" xml:space="preserve">2 CL. </s>
            <s xml:id="echoid-s4535" xml:space="preserve">& </s>
            <s xml:id="echoid-s4536" xml:space="preserve">ideò LM &</s>
            <s xml:id="echoid-s4537" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4538" xml:space="preserve">KL.</s>
            <s xml:id="echoid-s4539" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4540" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s4541" xml:space="preserve">Hinc rectiùs ingruens lux à reflectione verſus axem conden-
              <lb/>
            fatior evadit.</s>
            <s xml:id="echoid-s4542" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4543" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s4544" xml:space="preserve">Quidnì demùm rurſus ex his inferatur, viſibilis A imaginem
              <lb/>
            @irca reflexorum metam Z, oculo uſpiam in AZ conſtituto, appa-
              <lb/>
            rere?</s>
            <s xml:id="echoid-s4545" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4546" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">Adverſatur ſaltem (id quod experiendo deprehendetur) ocu-
              <lb/>
            lo uſpiam in ZB collocato confuſiorem apparentiam objici; </s>
            <s xml:id="echoid-s4548" xml:space="preserve"/>
          </p>
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