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-s2699" xml:space="preserve">
              <pb o="49" file="0067" n="67" rhead=""/>
            metam infra quam nullus reflexus axem ſecat (vel perpendicularis
              <lb/>
            iqſius reflexum BZ ad Z terminari). </s>
            <s xml:id="echoid-s2700" xml:space="preserve">quia ſemper Cv &</s>
            <s xml:id="echoid-s2701" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2702" xml:space="preserve">CZ;
              <lb/>
            </s>
            <s xml:id="echoid-s2703" xml:space="preserve">adeóque CK &</s>
            <s xml:id="echoid-s2704" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2705" xml:space="preserve">CZ.</s>
            <s xml:id="echoid-s2706" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2707" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s2708" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2709" xml:space="preserve">Patet eſſe KN = KC.
              <lb/>
            </s>
            <s xml:id="echoid-s2710" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2711" xml:space="preserve">Patet fore PN (2 CQ), CN, CK {.</s>
            <s xml:id="echoid-s2712" xml:space="preserve">./.</s>
            <s xml:id="echoid-s2713" xml:space="preserve">.}</s>
          </p>
          <p>
            <s xml:id="echoid-s2714" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s2715" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2716" xml:space="preserve">Ductâ tangente BT, productâque CNE, patet ſecan-
              <lb/>
            tem CE diftantiæ CK duplam eſſe; </s>
            <s xml:id="echoid-s2717" xml:space="preserve">& </s>
            <s xml:id="echoid-s2718" xml:space="preserve">EN = 2 KZ.</s>
            <s xml:id="echoid-s2719" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2720" xml:space="preserve">X. </s>
            <s xml:id="echoid-s2721" xml:space="preserve">5. </s>
            <s xml:id="echoid-s2722" xml:space="preserve">Manifeſtum eſt incidentis ad F (hoc eſt ad diſtantiam 60
              <lb/>
              <note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">Fig. 64.</note>
            graduum à vertice) reflexum per verticem B tranſire; </s>
            <s xml:id="echoid-s2723" xml:space="preserve">proindéque
              <lb/>
            reflexos omnium intra BF incidentium axem intra ſpacium BZ decuſſa-
              <lb/>
            re; </s>
            <s xml:id="echoid-s2724" xml:space="preserve">ſed omnes _extra_ BF reflexos ultra B cum eo convenire.</s>
            <s xml:id="echoid-s2725" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2726" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s2727" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2728" xml:space="preserve">Perſpicuum eſt duorum hujuſmodi quorumvis ad eaſdem
              <lb/>
              <note position="right" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">Fig. 65.</note>
            axis partes incidentium (ut ipſorum MNP, QRS) reflexos (ut
              <lb/>
            GNK, HRL,) productos ſe prius decuſſare, quàm axem. </s>
            <s xml:id="echoid-s2729" xml:space="preserve">Nam,
              <lb/>
            ductis CR, CN, eſt C ρ &</s>
            <s xml:id="echoid-s2730" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2731" xml:space="preserve">Cv, adeóque CL &</s>
            <s xml:id="echoid-s2732" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2733" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s2734" xml:space="preserve">unde ne-
              <lb/>
            ceſſariò rectæ NK, RL, ſe decuſſabunt, puta ad X.</s>
            <s xml:id="echoid-s2735" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2736" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s2737" xml:space="preserve">Hinc ipſi convexis partibus incidentium reflexi, NG, RH,
              <lb/>
            antrorſum procurrentes divergunt; </s>
            <s xml:id="echoid-s2738" xml:space="preserve">adeóque nunquam uno plures
              <lb/>
            idem oculi centrum permeant. </s>
            <s xml:id="echoid-s2739" xml:space="preserve">unde ſpeculum convexum unicam lon-
              <lb/>
            ginqui radiantis imaginem reddit.</s>
            <s xml:id="echoid-s2740" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2741" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s2742" xml:space="preserve">7. </s>
            <s xml:id="echoid-s2743" xml:space="preserve">Notetur autem angulum GXR (vel KXL ) à duobus
              <lb/>
            reflexis comprehenſum æquare duplum angulum NCR (hoc eſt
              <lb/>
            duplum exceſſum angulorum incidentiæ) . </s>
            <s xml:id="echoid-s2744" xml:space="preserve">Nam ang. </s>
            <s xml:id="echoid-s2745" xml:space="preserve">KXL = ang.
              <lb/>
            </s>
            <s xml:id="echoid-s2746" xml:space="preserve">ALR - ang. </s>
            <s xml:id="echoid-s2747" xml:space="preserve">AKN = 2 ang. </s>
            <s xml:id="echoid-s2748" xml:space="preserve">ACR - 2 ang. </s>
            <s xml:id="echoid-s2749" xml:space="preserve">ACN = 2 ang. </s>
            <s xml:id="echoid-s2750" xml:space="preserve">
              <lb/>
            NCR.</s>
            <s xml:id="echoid-s2751" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2752" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s2753" xml:space="preserve">Pro Sequentibus hujuſmodi _Lemma_ proponemus: </s>
            <s xml:id="echoid-s2754" xml:space="preserve">In trian-
              <lb/>
            gulo quopiam ABC recta AD biſecet angulum BAC; </s>
            <s xml:id="echoid-s2755" xml:space="preserve">dico fore
              <lb/>
              <note position="right" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve">Fig. 66.</note>
            AB + AC &</s>
            <s xml:id="echoid-s2756" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2757" xml:space="preserve">2 A D.</s>
            <s xml:id="echoid-s2758" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2759" xml:space="preserve">In _Iſoſcele_ res clara eſt; </s>
            <s xml:id="echoid-s2760" xml:space="preserve">in alio proinde ſit AC &</s>
            <s xml:id="echoid-s2761" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2762" xml:space="preserve">AB; </s>
            <s xml:id="echoid-s2763" xml:space="preserve">centró-
              <lb/>
            que A per B ducatur circulus BXY ſecans ipſam. </s>
            <s xml:id="echoid-s2764" xml:space="preserve">AD in X, & </s>
            <s xml:id="echoid-s2765" xml:space="preserve">AC
              <lb/>
            in Y. </s>
            <s xml:id="echoid-s2766" xml:space="preserve">Subtenſa BX ducatur, ipſamque AC ſecet in V; </s>
            <s xml:id="echoid-s2767" xml:space="preserve">fiátque
              <lb/>
            VT ad AD parallela. </s>
            <s xml:id="echoid-s2768" xml:space="preserve">denuo ſubtenſa XY connectatur. </s>
            <s xml:id="echoid-s2769" xml:space="preserve">Et quoni-
              <lb/>
            am ang. </s>
            <s xml:id="echoid-s2770" xml:space="preserve">XVC major eſt angulo XYV, vel angulo BXD, vel </s>
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