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-s5838" xml:space="preserve">
              <pb o="90" file="0108" n="108" rhead=""/>
            aſſimilantur. </s>
            <s xml:id="echoid-s5839" xml:space="preserve">unde NK. </s>
            <s xml:id="echoid-s5840" xml:space="preserve">KF :</s>
            <s xml:id="echoid-s5841" xml:space="preserve">: AN. </s>
            <s xml:id="echoid-s5842" xml:space="preserve">NF. </s>
            <s xml:id="echoid-s5843" xml:space="preserve">ſeu permutando NK.
              <lb/>
            </s>
            <s xml:id="echoid-s5844" xml:space="preserve">AN :</s>
            <s xml:id="echoid-s5845" xml:space="preserve">: KF. </s>
            <s xml:id="echoid-s5846" xml:space="preserve">NF. </s>
            <s xml:id="echoid-s5847" xml:space="preserve">erat autem priùs KF. </s>
            <s xml:id="echoid-s5848" xml:space="preserve">NF :</s>
            <s xml:id="echoid-s5849" xml:space="preserve">: GF. </s>
            <s xml:id="echoid-s5850" xml:space="preserve">FA :</s>
            <s xml:id="echoid-s5851" xml:space="preserve">: CK. </s>
            <s xml:id="echoid-s5852" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0108-01" xlink:href="note-0108-01a" xml:space="preserve">Fig. 137.</note>
            CR. </s>
            <s xml:id="echoid-s5853" xml:space="preserve">eſt igitur NK. </s>
            <s xml:id="echoid-s5854" xml:space="preserve">AN :</s>
            <s xml:id="echoid-s5855" xml:space="preserve">: CK. </s>
            <s xml:id="echoid-s5856" xml:space="preserve">CR. </s>
            <s xml:id="echoid-s5857" xml:space="preserve">unde (juxta dictum Theo-
              <lb/>
            rema) conſtat factum.</s>
            <s xml:id="echoid-s5858" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5859" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s5860" xml:space="preserve">Ad conſtructionem iſtam advertentes animum, hujuſmodi
              <lb/>
            facilè _Conſectaria_ deducetis:</s>
            <s xml:id="echoid-s5861" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5862" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5863" xml:space="preserve">Si circulus GNH_refringentem_ contingat ad H; </s>
            <s xml:id="echoid-s5864" xml:space="preserve">ipſius AH
              <lb/>
            (perpendicularis utique) refractus in K terminabitur; </s>
            <s xml:id="echoid-s5865" xml:space="preserve">& </s>
            <s xml:id="echoid-s5866" xml:space="preserve">aliorum
              <lb/>
            incidentium refracti ad unas ipſius K partes (ultra nempe vel citra
              <lb/>
            K reſpectu centri, pro diverſitate caſuum ab ipſius A poſitione reſul-
              <lb/>
            tantium) cadent.</s>
            <s xml:id="echoid-s5867" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5868" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5869" xml:space="preserve">Si dictus ille circulus _refringenti_ non occurrat omninò, _Problema_
              <lb/>
            conſtructionem reſpuet; </s>
            <s xml:id="echoid-s5870" xml:space="preserve">nec ullus refractus punctum K permeabit.</s>
            <s xml:id="echoid-s5871" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5872" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5873" xml:space="preserve">Si circulus GNH_refringenti_ coincidat (id quod facilè concipi
              <lb/>
            poteſt, & </s>
            <s xml:id="echoid-s5874" xml:space="preserve">in aliquo reverà caſu contingit) omnes refracti in punctum
              <lb/>
            K confluent.</s>
            <s xml:id="echoid-s5875" xml:space="preserve">‖ Hæc & </s>
            <s xml:id="echoid-s5876" xml:space="preserve">alia conſtructionem iſtam conſectantur ſoler-
              <lb/>
            ter expanſem; </s>
            <s xml:id="echoid-s5877" xml:space="preserve">quorum ſaltem nonnulla haud abs re fuerit exertiùs
              <lb/>
            oſtendi; </s>
            <s xml:id="echoid-s5878" xml:space="preserve">velut hoc imprimìs palmarium.</s>
            <s xml:id="echoid-s5879" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5880" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s5881" xml:space="preserve">Si fuerit AB. </s>
            <s xml:id="echoid-s5882" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s5883" xml:space="preserve">: BZ. </s>
            <s xml:id="echoid-s5884" xml:space="preserve">CZ; </s>
            <s xml:id="echoid-s5885" xml:space="preserve">dico punctum Z eſſe limi-
              <lb/>
            tem, ultra vel citra quem nullus refractus axim interſecat; </s>
            <s xml:id="echoid-s5886" xml:space="preserve">ſeu per-
              <lb/>
            pendicularis ipſius AB refractum in Z terminari.</s>
            <s xml:id="echoid-s5887" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5888" xml:space="preserve">Nam cujuſvis incidentis AN refractus axi occurrat in K, erit ideò
              <lb/>
            CK. </s>
            <s xml:id="echoid-s5889" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s5890" xml:space="preserve">: NK. </s>
            <s xml:id="echoid-s5891" xml:space="preserve">NA. </s>
            <s xml:id="echoid-s5892" xml:space="preserve">ergò quum ſit CR. </s>
            <s xml:id="echoid-s5893" xml:space="preserve">CZ :</s>
            <s xml:id="echoid-s5894" xml:space="preserve">: AB. </s>
            <s xml:id="echoid-s5895" xml:space="preserve">BZ;
              <lb/>
            </s>
            <s xml:id="echoid-s5896" xml:space="preserve">erit CK. </s>
            <s xml:id="echoid-s5897" xml:space="preserve">CR + CR. </s>
            <s xml:id="echoid-s5898" xml:space="preserve">CZ = NK. </s>
            <s xml:id="echoid-s5899" xml:space="preserve">NA + AB. </s>
            <s xml:id="echoid-s5900" xml:space="preserve">BZ.</s>
            <s xml:id="echoid-s5901" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5902" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5903" xml:space="preserve">Eſt autem (in prima figura, ubi puncta Z, & </s>
            <s xml:id="echoid-s5904" xml:space="preserve">K ſunt ad partes
              <lb/>
              <note position="left" xlink:label="note-0108-02" xlink:href="note-0108-02a" xml:space="preserve">Fig. 138.</note>
            centri, vel ubi refracti ad axem directè procurrentes convergunt)
              <lb/>
            BK&</s>
            <s xml:id="echoid-s5905" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5906" xml:space="preserve">NK, & </s>
            <s xml:id="echoid-s5907" xml:space="preserve">AB&</s>
            <s xml:id="echoid-s5908" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5909" xml:space="preserve">AN; </s>
            <s xml:id="echoid-s5910" xml:space="preserve">adeóque BK. </s>
            <s xml:id="echoid-s5911" xml:space="preserve">AB &</s>
            <s xml:id="echoid-s5912" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5913" xml:space="preserve">NK. </s>
            <s xml:id="echoid-s5914" xml:space="preserve">NA.
              <lb/>
            </s>
            <s xml:id="echoid-s5915" xml:space="preserve">ergò CK. </s>
            <s xml:id="echoid-s5916" xml:space="preserve">CR + CR. </s>
            <s xml:id="echoid-s5917" xml:space="preserve">CZ&</s>
            <s xml:id="echoid-s5918" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5919" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s5920" xml:space="preserve">AB + AB. </s>
            <s xml:id="echoid-s5921" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s5922" xml:space="preserve">hoc eſt
              <lb/>
            C K. </s>
            <s xml:id="echoid-s5923" xml:space="preserve">CZ&</s>
            <s xml:id="echoid-s5924" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5925" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s5926" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s5927" xml:space="preserve">vel inversè permutando BK. </s>
            <s xml:id="echoid-s5928" xml:space="preserve">CK&</s>
            <s xml:id="echoid-s5929" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5930" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s5931" xml:space="preserve">
              <lb/>
            C Z. </s>
            <s xml:id="echoid-s5932" xml:space="preserve">dividendóque BC. </s>
            <s xml:id="echoid-s5933" xml:space="preserve">CK&</s>
            <s xml:id="echoid-s5934" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5935" xml:space="preserve">BC. </s>
            <s xml:id="echoid-s5936" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s5937" xml:space="preserve">ergò CK &</s>
            <s xml:id="echoid-s5938" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5939" xml:space="preserve">CZ; </s>
            <s xml:id="echoid-s5940" xml:space="preserve">
              <lb/>
            adeóque punctum K ſupra Z exiſtit, verſus centrum; </s>
            <s xml:id="echoid-s5941" xml:space="preserve">quod erat pro-
              <lb/>
            poſitum oſtendere.</s>
            <s xml:id="echoid-s5942" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5943" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5944" xml:space="preserve">In ſecundâ verò figurá ubi puncta Z, K ad alteras ſupra punctum
              <lb/>
              <note position="left" xlink:label="note-0108-03" xlink:href="note-0108-03a" xml:space="preserve">Fig. 139.</note>
            A partes à centro averſas cadunt) connectatur ſubtenſa BN, & </s>
            <s xml:id="echoid-s5945" xml:space="preserve">du-
              <lb/>
            catur AS ad KN parallela; </s>
            <s xml:id="echoid-s5946" xml:space="preserve">hæc ſecabit angulum BA N, majorem
              <lb/>
            ipſo BK N, vel BA S; </s>
            <s xml:id="echoid-s5947" xml:space="preserve">& </s>
            <s xml:id="echoid-s5948" xml:space="preserve">cùm angulus ABNfit obtuſus, èrit AN
              <lb/>
            &</s>
            <s xml:id="echoid-s5949" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5950" xml:space="preserve">AS. </s>
            <s xml:id="echoid-s5951" xml:space="preserve">adeóque KN. </s>
            <s xml:id="echoid-s5952" xml:space="preserve">AN&</s>
            <s xml:id="echoid-s5953" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5954" xml:space="preserve">KN. </s>
            <s xml:id="echoid-s5955" xml:space="preserve">AS :</s>
            <s xml:id="echoid-s5956" xml:space="preserve">: KB. </s>
            <s xml:id="echoid-s5957" xml:space="preserve">AB. </s>
            <s xml:id="echoid-s5958" xml:space="preserve">erit etiam hîc
              <lb/>
            igitur (ut ſupra)C K. </s>
            <s xml:id="echoid-s5959" xml:space="preserve">CZ&</s>
            <s xml:id="echoid-s5960" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5961" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s5962" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s5963" xml:space="preserve">vel permutatim CK. </s>
            <s xml:id="echoid-s5964" xml:space="preserve"/>
          </p>
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