Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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        <div xml:id="echoid-div113" type="section" level="1" n="19">
          <p>
            <s xml:id="echoid-s5435" xml:space="preserve">
              <pb o="84" file="0102" n="102" rhead=""/>
            -CEq. </s>
            <s xml:id="echoid-s5436" xml:space="preserve">CEq - CGq :</s>
            <s xml:id="echoid-s5437" xml:space="preserve">: CNq - NEq. </s>
            <s xml:id="echoid-s5438" xml:space="preserve">NEq :</s>
            <s xml:id="echoid-s5439" xml:space="preserve">: CEq. </s>
            <s xml:id="echoid-s5440" xml:space="preserve">NEq.
              <lb/>
            </s>
            <s xml:id="echoid-s5441" xml:space="preserve">quare permutando 4 CGq - CEq. </s>
            <s xml:id="echoid-s5442" xml:space="preserve">CEq :</s>
            <s xml:id="echoid-s5443" xml:space="preserve">: CEq - CGq. </s>
            <s xml:id="echoid-s5444" xml:space="preserve">
              <lb/>
            NE q. </s>
            <s xml:id="echoid-s5445" xml:space="preserve">(hoc eſt) :</s>
            <s xml:id="echoid-s5446" xml:space="preserve">: NGq - NEq. </s>
            <s xml:id="echoid-s5447" xml:space="preserve">NEq. </s>
            <s xml:id="echoid-s5448" xml:space="preserve">ergò componendo
              <lb/>
            4 CGq. </s>
            <s xml:id="echoid-s5449" xml:space="preserve">CEq :</s>
            <s xml:id="echoid-s5450" xml:space="preserve">: NGq. </s>
            <s xml:id="echoid-s5451" xml:space="preserve">NEq. </s>
            <s xml:id="echoid-s5452" xml:space="preserve">& </s>
            <s xml:id="echoid-s5453" xml:space="preserve">ideò 2 CG. </s>
            <s xml:id="echoid-s5454" xml:space="preserve">CE :</s>
            <s xml:id="echoid-s5455" xml:space="preserve">: NG. </s>
            <s xml:id="echoid-s5456" xml:space="preserve">
              <lb/>
            NE. </s>
            <s xml:id="echoid-s5457" xml:space="preserve">quare 2. </s>
            <s xml:id="echoid-s5458" xml:space="preserve">1 + CG. </s>
            <s xml:id="echoid-s5459" xml:space="preserve">CE = NG. </s>
            <s xml:id="echoid-s5460" xml:space="preserve">NE. </s>
            <s xml:id="echoid-s5461" xml:space="preserve">vel 2. </s>
            <s xml:id="echoid-s5462" xml:space="preserve">1 = NG. </s>
            <s xml:id="echoid-s5463" xml:space="preserve">
              <lb/>
            NE + CE. </s>
            <s xml:id="echoid-s5464" xml:space="preserve">CG. </s>
            <s xml:id="echoid-s5465" xml:space="preserve">hoc eſt NZ. </s>
            <s xml:id="echoid-s5466" xml:space="preserve">GZ = NG. </s>
            <s xml:id="echoid-s5467" xml:space="preserve">NE + CE. </s>
            <s xml:id="echoid-s5468" xml:space="preserve">CG. </s>
            <s xml:id="echoid-s5469" xml:space="preserve">
              <lb/>
            unde liquet, è mox antedictis, propoſitum.</s>
            <s xml:id="echoid-s5470" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5471" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s5472" xml:space="preserve">Ex iſta porrò conſtructione facilè colligitur, ſi fuerit 3 Rq
              <lb/>
            = Iq - Rq (hoc eſt ſi 2 R = I) adeóque CQ = CB; </s>
            <s xml:id="echoid-s5473" xml:space="preserve">quòd hu-
              <lb/>
            juſmodi punctum Z non aliud erit ab ipſo D; </s>
            <s xml:id="echoid-s5474" xml:space="preserve">ſeu perpendiculari ipſi
              <lb/>
            AB debitam imaginem ad punctum D conſiſtere; </s>
            <s xml:id="echoid-s5475" xml:space="preserve">eas verò quæ reli-
              <lb/>
            quis refractis conveniunt ejuſmodi imagines intra circulum omnes, vel
              <lb/>
            ſupra peripheriam extare. </s>
            <s xml:id="echoid-s5476" xml:space="preserve">quinetiam ſi fuerit 2 R &</s>
            <s xml:id="echoid-s5477" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5478" xml:space="preserve">I, adeoque
              <lb/>
            CB &</s>
            <s xml:id="echoid-s5479" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5480" xml:space="preserve">CQ, patet nullius refracti imaginem in peripheria exiſtere,
              <lb/>
            ſed omnes ſupra ipſam. </s>
            <s xml:id="echoid-s5481" xml:space="preserve">Enim verò in his caſibus omnes refracti ax-
              <lb/>
            em AD ſupra punctum D interſecant. </s>
            <s xml:id="echoid-s5482" xml:space="preserve">verùm ſi fuerit 2 R &</s>
            <s xml:id="echoid-s5483" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5484" xml:space="preserve">I (uti-
              <lb/>
            que ſicut reverà quoad pleraſque cunctas in hac rerum natura pelluci-
              <lb/>
            das refringentes materias uſu venit) utì reipsâ datur ejuſmodi punctum
              <lb/>
            Z, in perepheria TD alicubi ſitum, ità facilè poterit iſto modo de-
              <lb/>
            terminari.</s>
            <s xml:id="echoid-s5485" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5486" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s5487" xml:space="preserve">Obſervetur porrò ſic definitum punctum Z circuli partem à
              <lb/>
            D verſus T per radios quadranti BT incidentes illuſtratam terminare.
              <lb/>
            </s>
            <s xml:id="echoid-s5488" xml:space="preserve">Omnes enim ipſo MN obliquiùs incidentium refracti ipſam NZ ſupra
              <lb/>
            Z verſus G decuſſabunt; </s>
            <s xml:id="echoid-s5489" xml:space="preserve">adeóque ad partes ZD circulo impingent; </s>
            <s xml:id="echoid-s5490" xml:space="preserve">
              <lb/>
            item omnium ipſo MN rectiorum refracti ipſam NZ infra Z verſus K
              <lb/>
            interſecabunt; </s>
            <s xml:id="echoid-s5491" xml:space="preserve">& </s>
            <s xml:id="echoid-s5492" xml:space="preserve">hinc etiam in arcum ZD cadent.</s>
            <s xml:id="echoid-s5493" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5494" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s5495" xml:space="preserve">Exhinc apparet (id quod _ab eximio D. </s>
            <s xml:id="echoid-s5496" xml:space="preserve">Sluſio_ monitum ami-
              <lb/>
              <note position="left" xlink:label="note-0102-01" xlink:href="note-0102-01a" xml:space="preserve">Fig. 127.</note>
            cus mihi communicavit) potuiſſe _Carteſium_ ſine tabularum confecti-
              <lb/>
            one ſuum _Iridis_ angulum determinare. </s>
            <s xml:id="echoid-s5497" xml:space="preserve">nam aſſumpto arcu DY = DZ;
              <lb/>
            </s>
            <s xml:id="echoid-s5498" xml:space="preserve">angulum iſtum arcus ZY metitur; </s>
            <s xml:id="echoid-s5499" xml:space="preserve">poſito circulum propoſitum per
              <lb/>
            aquei globi centrum tranſire. </s>
            <s xml:id="echoid-s5500" xml:space="preserve">quod ità facilè conſtat. </s>
            <s xml:id="echoid-s5501" xml:space="preserve">Radii cujuſvis
              <lb/>
            diametro BC paralleli MN refractus NZKreflectatur in ZF H; </s>
            <s xml:id="echoid-s5502" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s5503" xml:space="preserve">ZF in FO refringatur; </s>
            <s xml:id="echoid-s5504" xml:space="preserve">ſitque FL ad BD parallela; </s>
            <s xml:id="echoid-s5505" xml:space="preserve">ſumatur eti-
              <lb/>
            am DY = DZ; </s>
            <s xml:id="echoid-s5506" xml:space="preserve">& </s>
            <s xml:id="echoid-s5507" xml:space="preserve">connectantur CZ, CY; </s>
            <s xml:id="echoid-s5508" xml:space="preserve">dico angulum LFO
              <lb/>
            æquari angulo ZC Y. </s>
            <s xml:id="echoid-s5509" xml:space="preserve">Nam imprimìs ob ZN, ZF æqualiter ad pe-
              <lb/>
            ripheriam inclinatos, patet angulum OFHangulo PNZvel CKZ
              <lb/>
            æquari. </s>
            <s xml:id="echoid-s5510" xml:space="preserve">igitur ang. </s>
            <s xml:id="echoid-s5511" xml:space="preserve">HFL- HFO = ang FIC- CKZ = </s>
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