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-s2455" xml:space="preserve">
              <pb o="44" file="0062" n="62" rhead=""/>
            ſimplicibus triplicatas ſubſtituendo rationes, eſt γ Q. </s>
            <s xml:id="echoid-s2456" xml:space="preserve">QB &</s>
            <s xml:id="echoid-s2457" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2458" xml:space="preserve">YP .
              <lb/>
            </s>
            <s xml:id="echoid-s2459" xml:space="preserve">PB. </s>
            <s xml:id="echoid-s2460" xml:space="preserve">& </s>
            <s xml:id="echoid-s2461" xml:space="preserve">his æquales rationes adjungendo eſt QN. </s>
            <s xml:id="echoid-s2462" xml:space="preserve">γ Q + γ Q. </s>
            <s xml:id="echoid-s2463" xml:space="preserve">QB&</s>
            <s xml:id="echoid-s2464" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2465" xml:space="preserve">
              <lb/>
            PN . </s>
            <s xml:id="echoid-s2466" xml:space="preserve">YP + YP. </s>
            <s xml:id="echoid-s2467" xml:space="preserve">PB; </s>
            <s xml:id="echoid-s2468" xml:space="preserve">hoc eſt QN. </s>
            <s xml:id="echoid-s2469" xml:space="preserve">QB &</s>
            <s xml:id="echoid-s2470" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2471" xml:space="preserve">PN. </s>
            <s xml:id="echoid-s2472" xml:space="preserve">PB. </s>
            <s xml:id="echoid-s2473" xml:space="preserve">compo-
              <lb/>
            nendóque BN. </s>
            <s xml:id="echoid-s2474" xml:space="preserve">QB &</s>
            <s xml:id="echoid-s2475" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s2476" xml:space="preserve">BN. </s>
            <s xml:id="echoid-s2477" xml:space="preserve">P B. </s>
            <s xml:id="echoid-s2478" xml:space="preserve">ergo QB &</s>
            <s xml:id="echoid-s2479" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s2480" xml:space="preserve">PB. </s>
            <s xml:id="echoid-s2481" xml:space="preserve">unde rurſus
              <lb/>
            liquet rectam X Qipſis AB; </s>
            <s xml:id="echoid-s2482" xml:space="preserve">ZP interjacere: </s>
            <s xml:id="echoid-s2483" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s2484" xml:space="preserve">E. </s>
            <s xml:id="echoid-s2485" xml:space="preserve">D.</s>
            <s xml:id="echoid-s2486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2487" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s2488" xml:space="preserve">Conſimili prorſus argumentatione conſtabit obliquio-
              <lb/>
            rum incidentium refractos ultra punctum Z ipſam KN interſe-
              <lb/>
            care.</s>
            <s xml:id="echoid-s2489" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2490" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s2491" xml:space="preserve">Quinimò rurſus exertiùs apparet non niſi binos refractos
              <lb/>
            in eodem puncto convenire.</s>
            <s xml:id="echoid-s2492" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2493" xml:space="preserve">XI X. </s>
            <s xml:id="echoid-s2494" xml:space="preserve">Addo cum ipſo KN concurrentes refractos circa punctum
              <lb/>
            Z conglomerari, præſertim illos, qui ad partes F (obliquius) inci-
              <lb/>
            dentes pertinent.</s>
            <s xml:id="echoid-s2495" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2496" xml:space="preserve">Nam accipiantur, exempli causâ, ſibi pares N S, ST ; </s>
            <s xml:id="echoid-s2497" xml:space="preserve">& </s>
            <s xml:id="echoid-s2498" xml:space="preserve">ſit BP
              <lb/>
              <note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve">Fig. 61.</note>
            quarta proportionalis in ratione YB ad BN; </s>
            <s xml:id="echoid-s2499" xml:space="preserve">& </s>
            <s xml:id="echoid-s2500" xml:space="preserve">BQ quarta proportionalis
              <lb/>
            in ratione YB ad BS; </s>
            <s xml:id="echoid-s2501" xml:space="preserve">& </s>
            <s xml:id="echoid-s2502" xml:space="preserve">BR itidem quarta talis in ratione YB ad
              <lb/>
            BT; </s>
            <s xml:id="echoid-s2503" xml:space="preserve">& </s>
            <s xml:id="echoid-s2504" xml:space="preserve">à punctis P, Q, R erectæ perpendiculares ipſam NKZ
              <lb/>
            ſecent in Z, X, & </s>
            <s xml:id="echoid-s2505" xml:space="preserve">V. </s>
            <s xml:id="echoid-s2506" xml:space="preserve">patet (è mox oſtenſis) omnium ſpatio NS
              <lb/>
            incidentium refractos cum NK concurrere intra ZX; </s>
            <s xml:id="echoid-s2507" xml:space="preserve">nec non omnes
              <lb/>
            ipſi ST incidentium refractos intra XV cum eodem convenire. </s>
            <s xml:id="echoid-s2508" xml:space="preserve">por-
              <lb/>
            rò rectæ BP , BQ, BR ſe habent invicem ut _Cubi_ rectarum BN,
              <lb/>
            BS, BT, ( vel ſunt in ipſarum BN, BS, BT _ratione triplicata_ : </s>
            <s xml:id="echoid-s2509" xml:space="preserve">nam
              <lb/>
            BP. </s>
            <s xml:id="echoid-s2510" xml:space="preserve">YB :</s>
            <s xml:id="echoid-s2511" xml:space="preserve">: BN cub. </s>
            <s xml:id="echoid-s2512" xml:space="preserve">BY cub. </s>
            <s xml:id="echoid-s2513" xml:space="preserve">& </s>
            <s xml:id="echoid-s2514" xml:space="preserve">YB . </s>
            <s xml:id="echoid-s2515" xml:space="preserve">BQ :</s>
            <s xml:id="echoid-s2516" xml:space="preserve">: YB cub. </s>
            <s xml:id="echoid-s2517" xml:space="preserve">BS cub.
              <lb/>
            </s>
            <s xml:id="echoid-s2518" xml:space="preserve">adeóque ex æquo BP. </s>
            <s xml:id="echoid-s2519" xml:space="preserve">BQ :</s>
            <s xml:id="echoid-s2520" xml:space="preserve">: BN cub . </s>
            <s xml:id="echoid-s2521" xml:space="preserve">BS cub. </s>
            <s xml:id="echoid-s2522" xml:space="preserve">& </s>
            <s xml:id="echoid-s2523" xml:space="preserve">conſimili ratione
              <lb/>
            BP. </s>
            <s xml:id="echoid-s2524" xml:space="preserve">BR :</s>
            <s xml:id="echoid-s2525" xml:space="preserve">: BN cub. </s>
            <s xml:id="echoid-s2526" xml:space="preserve">BT cub.) </s>
            <s xml:id="echoid-s2527" xml:space="preserve">undè faciiè monſtrabitur eſſe PQ
              <lb/>
            multo minorem quàm QR; </s>
            <s xml:id="echoid-s2528" xml:space="preserve">xel ZX quàm XV (verbis parco multis
              <lb/>
            in re ſatis manifeſta) . </s>
            <s xml:id="echoid-s2529" xml:space="preserve">quare dicti refracti circa punctum Z ſpiſſiùs
              <lb/>
            ipſum NK decuſſabunt.</s>
            <s xml:id="echoid-s2530" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2531" xml:space="preserve">XX. </s>
            <s xml:id="echoid-s2532" xml:space="preserve">Ex his demùm conficitur omnibus bene trutinatis, oculo
              <lb/>
            (O) centrum habenti in refracto NK uſpiam conſtituto, puncti A
              <lb/>
            imaginem ad ipſum conditione præditum toties inſinuatâ punctum Z
              <lb/>
            conſiſtere. </s>
            <s xml:id="echoid-s2533" xml:space="preserve">Sit enim CD pupillæ (in plano ABC jacens) _Diameter;_
              <lb/>
            </s>
            <s xml:id="echoid-s2534" xml:space="preserve">_axi Optico_ KN perpendicularis; </s>
            <s xml:id="echoid-s2535" xml:space="preserve">& </s>
            <s xml:id="echoid-s2536" xml:space="preserve">per ejus extrema C, D tranſeant
              <lb/>
            refracti IM LR ipſi KN occurrentes punctis X, V. </s>
            <s xml:id="echoid-s2537" xml:space="preserve">ex oſtenſis patet
              <lb/>
            omnium intra ſpatium MN incidentium radiorum refractos intra ten-
              <lb/>
            minos ZX principalem refractum interſecare; </s>
            <s xml:id="echoid-s2538" xml:space="preserve">neque non omnes </s>
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