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-s6084" xml:space="preserve">XXI. </s>
            <s xml:id="echoid-s6085" xml:space="preserve">Imò univerſim ſi radii quivis AF, _a_ φ ad circulum refrin-
              <lb/>
              <note position="left" xlink:label="note-0110-01" xlink:href="note-0110-01a" xml:space="preserve">Fig. 144.</note>
            gentem æqualiter inclinentur, híſque conveniant refracti FL, φ λ,
              <lb/>
            erit C λ &</s>
            <s xml:id="echoid-s6086" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6087" xml:space="preserve">CL. </s>
            <s xml:id="echoid-s6088" xml:space="preserve">id quod hoc modo non inelegantèr oſtenditur. </s>
            <s xml:id="echoid-s6089" xml:space="preserve">Du-
              <lb/>
            catur recta BX cum BC angulum efficiens parem angulo refracto
              <lb/>
            ad poſitam inclinationem pertinenti; </s>
            <s xml:id="echoid-s6090" xml:space="preserve">perque puncta F, φ; </s>
            <s xml:id="echoid-s6091" xml:space="preserve">& </s>
            <s xml:id="echoid-s6092" xml:space="preserve">cen-
              <lb/>
            trum C tranſeuntes rectæ ipſi BX occurant punctis P, π. </s>
            <s xml:id="echoid-s6093" xml:space="preserve">tum quo-
              <lb/>
            niam triangula FC L, BCPæquiangula ſunt (angulus enim CB P
              <lb/>
            angulo CFLex conſtructione par eſt, & </s>
            <s xml:id="echoid-s6094" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s6095" xml:space="preserve">BCPverticali ſuo
              <lb/>
            FCLæquatur) nec non latus CB lateri CF æquatur, erit CP =
              <lb/>
            C L. </s>
            <s xml:id="echoid-s6096" xml:space="preserve">Simili planè diſcurſu eſt C π = C λ. </s>
            <s xml:id="echoid-s6097" xml:space="preserve">Porrò quia C φ ad
              <lb/>
            C _a_ (hoc eſt Sinus anguli C _a_ φ ad Sinum anguli C φ _a_) majorem
              <lb/>
            rationem habet, quàm CF ad CA (hoc eſt quàm Sinus anguli CA F
              <lb/>
            ad Sinum anguli AF C, vel æ qualis anguli C φ α) liquet angulum
              <lb/>
            C _a_ φ majorem eſſe angulo CA F, adeóque reliquum _a_ C φ minorem
              <lb/>
            eſſe reliquo AC F; </s>
            <s xml:id="echoid-s6098" xml:space="preserve">vel angulum PCBangulo π CB. </s>
            <s xml:id="echoid-s6099" xml:space="preserve">unde liquet
              <lb/>
            eſſe C π majorem quàm CP; </s>
            <s xml:id="echoid-s6100" xml:space="preserve">hoc eſt C λ majorem eſſe quàm CL:
              <lb/>
            </s>
            <s xml:id="echoid-s6101" xml:space="preserve">Quod E. </s>
            <s xml:id="echoid-s6102" xml:space="preserve">D.</s>
            <s xml:id="echoid-s6103" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6104" xml:space="preserve">_Coroll._ </s>
            <s xml:id="echoid-s6105" xml:space="preserve">Vides arcum BF majorem eſſe arcu B φ.</s>
            <s xml:id="echoid-s6106" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6107" xml:space="preserve">Notes etiam omnes ejuſdem inclinationis refractos ope ductæ rectæ
              <lb/>
            BX promptiſſimè deſignari. </s>
            <s xml:id="echoid-s6108" xml:space="preserve">ſed hæc an πρργδ fuerint neſcio.</s>
            <s xml:id="echoid-s6109" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6110" xml:space="preserve">XXII. </s>
            <s xml:id="echoid-s6111" xml:space="preserve">_Subjiciam & </s>
            <s xml:id="echoid-s6112" xml:space="preserve">hoc Theorema:_ </s>
            <s xml:id="echoid-s6113" xml:space="preserve">Convexo denſiori inciden-
              <lb/>
              <note position="left" xlink:label="note-0110-02" xlink:href="note-0110-02a" xml:space="preserve">Fig. 145.</note>
            tiùm radiorum AM, AN (quorum AN ſit obliquior) refracti
              <lb/>
            MK, NL axem ad eaſdem partes, directè pergentes, ſecent, iſte ad K,
              <lb/>
            hic ad L; </s>
            <s xml:id="echoid-s6114" xml:space="preserve">dico fore CK majorem quàm CL.</s>
            <s xml:id="echoid-s6115" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6116" xml:space="preserve">Nam connexis CN, KN; </s>
            <s xml:id="echoid-s6117" xml:space="preserve">& </s>
            <s xml:id="echoid-s6118" xml:space="preserve">ductâ LH ad KN parallelâ quo-
              <lb/>
            niam, è præmiſſis, eſt CK. </s>
            <s xml:id="echoid-s6119" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s6120" xml:space="preserve">: MK. </s>
            <s xml:id="echoid-s6121" xml:space="preserve">MA. </s>
            <s xml:id="echoid-s6122" xml:space="preserve">& </s>
            <s xml:id="echoid-s6123" xml:space="preserve">CR. </s>
            <s xml:id="echoid-s6124" xml:space="preserve">CL :</s>
            <s xml:id="echoid-s6125" xml:space="preserve">:
              <lb/>
            NA. </s>
            <s xml:id="echoid-s6126" xml:space="preserve">NL. </s>
            <s xml:id="echoid-s6127" xml:space="preserve">erit CK. </s>
            <s xml:id="echoid-s6128" xml:space="preserve">CK + CR. </s>
            <s xml:id="echoid-s6129" xml:space="preserve">CL = MK. </s>
            <s xml:id="echoid-s6130" xml:space="preserve">MA + NA. </s>
            <s xml:id="echoid-s6131" xml:space="preserve">NL.
              <lb/>
            </s>
            <s xml:id="echoid-s6132" xml:space="preserve">eſt autem NK. </s>
            <s xml:id="echoid-s6133" xml:space="preserve">NA&</s>
            <s xml:id="echoid-s6134" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6135" xml:space="preserve">MK. </s>
            <s xml:id="echoid-s6136" xml:space="preserve">MA (quia NK&</s>
            <s xml:id="echoid-s6137" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6138" xml:space="preserve">MK, & </s>
            <s xml:id="echoid-s6139" xml:space="preserve">NA
              <lb/>
            &</s>
            <s xml:id="echoid-s6140" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6141" xml:space="preserve">MA)ergo CK. </s>
            <s xml:id="echoid-s6142" xml:space="preserve">CR + CR. </s>
            <s xml:id="echoid-s6143" xml:space="preserve">CL&</s>
            <s xml:id="echoid-s6144" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6145" xml:space="preserve">NK. </s>
            <s xml:id="echoid-s6146" xml:space="preserve">NA + NA. </s>
            <s xml:id="echoid-s6147" xml:space="preserve">
              <lb/>
            NL. </s>
            <s xml:id="echoid-s6148" xml:space="preserve">hoc eſt CK. </s>
            <s xml:id="echoid-s6149" xml:space="preserve">CL &</s>
            <s xml:id="echoid-s6150" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6151" xml:space="preserve">NK. </s>
            <s xml:id="echoid-s6152" xml:space="preserve">NL. </s>
            <s xml:id="echoid-s6153" xml:space="preserve">hoc eſt NK. </s>
            <s xml:id="echoid-s6154" xml:space="preserve">HL. </s>
            <s xml:id="echoid-s6155" xml:space="preserve">&</s>
            <s xml:id="echoid-s6156" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6157" xml:space="preserve">
              <lb/>
            NK. </s>
            <s xml:id="echoid-s6158" xml:space="preserve">NL. </s>
            <s xml:id="echoid-s6159" xml:space="preserve">quapropter eſt LH&</s>
            <s xml:id="echoid-s6160" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s6161" xml:space="preserve">NL. </s>
            <s xml:id="echoid-s6162" xml:space="preserve">eſt autem angulus LCN
              <lb/>
            obtufus; </s>
            <s xml:id="echoid-s6163" xml:space="preserve">ergò recta LH angulum CLNſecat; </s>
            <s xml:id="echoid-s6164" xml:space="preserve">ac angulus LHC
              <lb/>
            interno LNCmajor eſt; </s>
            <s xml:id="echoid-s6165" xml:space="preserve">hoc eſt angulus KNCangulo LNC
              <lb/>
            major eſt. </s>
            <s xml:id="echoid-s6166" xml:space="preserve">unde liquidò patet fore CK&</s>
            <s xml:id="echoid-s6167" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s6168" xml:space="preserve">CL.</s>
            <s xml:id="echoid-s6169" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6170" xml:space="preserve">_Coroll._ </s>
            <s xml:id="echoid-s6171" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s6172" xml:space="preserve">CL = MK. </s>
            <s xml:id="echoid-s6173" xml:space="preserve">MA + NA. </s>
            <s xml:id="echoid-s6174" xml:space="preserve">NL.</s>
            <s xml:id="echoid-s6175" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6176" xml:space="preserve">XXIII. </s>
            <s xml:id="echoid-s6177" xml:space="preserve">Hinc, ejuſmodi omnes refracti ſeipſos priùs quàm axem
              <lb/>
            interſecant, velut ad X.</s>
            <s xml:id="echoid-s6178" xml:space="preserve">‖ Hoc ſpeciminis loco pro caſu, qui </s>
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