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-s3054" xml:space="preserve">
              <pb o="55" file="0073" n="73" rhead=""/>
            ductæ XN reflexus (puta NP) ipſi BC parallelus erit. </s>
            <s xml:id="echoid-s3055" xml:space="preserve">Nam con-
              <lb/>
            nexis XC, XL; </s>
            <s xml:id="echoid-s3056" xml:space="preserve">quoniam CN = HL, & </s>
            <s xml:id="echoid-s3057" xml:space="preserve">CX = LX; </s>
            <s xml:id="echoid-s3058" xml:space="preserve">& </s>
            <s xml:id="echoid-s3059" xml:space="preserve">anguli
              <lb/>
            XCL, XLC pares ſunt; </s>
            <s xml:id="echoid-s3060" xml:space="preserve">erit XH = XN. </s>
            <s xml:id="echoid-s3061" xml:space="preserve">quapropter erit NP
              <lb/>
            ad XH, vel BC parallelus: </s>
            <s xml:id="echoid-s3062" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s3063" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3064" xml:space="preserve">F.</s>
            <s xml:id="echoid-s3065" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3066" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s3067" xml:space="preserve">Ex hac conſtructione, cum præmiſſi lemmatis ſolutione colla-
              <lb/>
            tâ diluceſcet hujuſmodi non ultra quatuor reflexos per idem quodcun-
              <lb/>
            que punctum, ceu X, tranſire; </s>
            <s xml:id="echoid-s3068" xml:space="preserve">quorum duo ad unas axis partes inci-
              <lb/>
            dentibus, reliqui ad alteras conveniunt. </s>
            <s xml:id="echoid-s3069" xml:space="preserve">adparebit ctiam ſi CN
              <lb/>
            major ſit, quam ut ci par HL rectâ GF, Semicirculóque GEF
              <lb/>
            intercipi poſſit; </s>
            <s xml:id="echoid-s3070" xml:space="preserve">quòd ad axis partes, ad quas ipſum X ponitur, om-
              <lb/>
              <note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">Fig. 75.</note>
            nino nullus per hoc punctum reflexus meabit; </s>
            <s xml:id="echoid-s3071" xml:space="preserve">quinetiam ſi CN
              <lb/>
            tanta ſit, ut ci par una tantùm ejuſmodi recta poſſit intercipi, quòd
              <lb/>
            unicus per ipſum X reflexus iter ſuſcipiet. </s>
            <s xml:id="echoid-s3072" xml:space="preserve">tales, inquam, expoſiti
              <lb/>
            problematis determinationes hanc conſtructionem haud obſcurè ſe-
              <lb/>
            quuntur; </s>
            <s xml:id="echoid-s3073" xml:space="preserve">quas certè tu meliùs uno mentis (haud dormitantis) ictu
              <lb/>
            perſpexeris, quàm ego pluribus verbis explicâro.</s>
            <s xml:id="echoid-s3074" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3075" xml:space="preserve">X. </s>
            <s xml:id="echoid-s3076" xml:space="preserve">Exhinc itaque denuò rectam (ſeurectas) ſatìs definivimus, in
              <lb/>
            qua (vel ìn quibus) puncti radiantis lmago, reſpectu visûs utcunque
              <lb/>
            poſitione datum centrum habentis, conſiſtit. </s>
            <s xml:id="echoid-s3077" xml:space="preserve">ad ejus jam præciſiorem
              <lb/>
            locum inveſtigandum accingemur; </s>
            <s xml:id="echoid-s3078" xml:space="preserve">in iſtarum rectâ quâpiam exiſten-
              <lb/>
            tem.</s>
            <s xml:id="echoid-s3079" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3080" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s3081" xml:space="preserve">Huc adnotetur imprimìs, quòd ſi duorum ad eaſdem axis par-
              <lb/>
            tes incidentium parallelorum (NP, RS) reflexi ſint N Π, R σ;
              <lb/>
            </s>
            <s xml:id="echoid-s3082" xml:space="preserve">erit arcus NR, vel PS arcûs Π σ ſubtriplus. </s>
            <s xml:id="echoid-s3083" xml:space="preserve">Concurrant enim dicti
              <lb/>
            reflexi in X; </s>
            <s xml:id="echoid-s3084" xml:space="preserve">& </s>
            <s xml:id="echoid-s3085" xml:space="preserve">Connectatur recta R Π. </s>
            <s xml:id="echoid-s3086" xml:space="preserve">& </s>
            <s xml:id="echoid-s3087" xml:space="preserve">quoniam, è præmonitis,
              <lb/>
              <note position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve">Fig. 76.</note>
            angulus NX R duplus eſt anguli arcui NR ad centrum inſiſtentis;
              <lb/>
            </s>
            <s xml:id="echoid-s3088" xml:space="preserve">crit idem angulus NXR anguli N Π R quadruplus. </s>
            <s xml:id="echoid-s3089" xml:space="preserve">quapropter erit
              <lb/>
            ang. </s>
            <s xml:id="echoid-s3090" xml:space="preserve">NXR - ang. </s>
            <s xml:id="echoid-s3091" xml:space="preserve">N Π R triplus anguli N Π R, hoc eſt angulus
              <lb/>
            XR Π anguli N Π R triplus. </s>
            <s xml:id="echoid-s3092" xml:space="preserve">unde quoque triplus erit arcus Π σ ipſius
              <lb/>
            NR : </s>
            <s xml:id="echoid-s3093" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s3094" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3095" xml:space="preserve">D.</s>
            <s xml:id="echoid-s3096" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3097" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s3098" xml:space="preserve">Iiſdem ſtantibus dico fore RX (obliquioris reflexi partem
              <lb/>
            incidentiæ concursûſque punctis interceptam) majorem quadrante to-
              <lb/>
            tius reflexi R σ. </s>
            <s xml:id="echoid-s3099" xml:space="preserve">Nam, ductis ſubtenſis NR, Π σ; </s>
            <s xml:id="echoid-s3100" xml:space="preserve">erit I. </s>
            <s xml:id="echoid-s3101" xml:space="preserve">3 :</s>
            <s xml:id="echoid-s3102" xml:space="preserve">:
              <lb/>
            arc. </s>
            <s xml:id="echoid-s3103" xml:space="preserve">NR. </s>
            <s xml:id="echoid-s3104" xml:space="preserve">Π σ. </s>
            <s xml:id="echoid-s3105" xml:space="preserve">&</s>
            <s xml:id="echoid-s3106" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3107" xml:space="preserve">recta NR. </s>
            <s xml:id="echoid-s3108" xml:space="preserve">Π σ :</s>
            <s xml:id="echoid-s3109" xml:space="preserve">: RX. </s>
            <s xml:id="echoid-s3110" xml:space="preserve">X Π &</s>
            <s xml:id="echoid-s3111" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3112" xml:space="preserve">RX. </s>
            <s xml:id="echoid-s3113" xml:space="preserve">X σ (quia
              <lb/>
            ſcilicet eſt X Π &</s>
            <s xml:id="echoid-s3114" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3115" xml:space="preserve">X σ). </s>
            <s xml:id="echoid-s3116" xml:space="preserve">igitur eſt X σ minor triplâ RX; </s>
            <s xml:id="echoid-s3117" xml:space="preserve">compo-
              <lb/>
            nendóque minor erit R σ quadruplâ RX: </s>
            <s xml:id="echoid-s3118" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s3119" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3120" xml:space="preserve">D.</s>
            <s xml:id="echoid-s3121" xml:space="preserve"/>
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