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

Table of handwritten notes

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          <p>
            <s xml:id="echoid-s3471" xml:space="preserve">
              <pb o="60" file="0078" n="78" rhead=""/>
            biſecat angulum ANK; </s>
            <s xml:id="echoid-s3472" xml:space="preserve">erit AN. </s>
            <s xml:id="echoid-s3473" xml:space="preserve">NK :</s>
            <s xml:id="echoid-s3474" xml:space="preserve">: AT. </s>
            <s xml:id="echoid-s3475" xml:space="preserve">TK. </s>
            <s xml:id="echoid-s3476" xml:space="preserve">&</s>
            <s xml:id="echoid-s3477" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3478" xml:space="preserve">AB.
              <lb/>
            </s>
            <s xml:id="echoid-s3479" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s3480" xml:space="preserve">quare BZ. </s>
            <s xml:id="echoid-s3481" xml:space="preserve">AB + AN. </s>
            <s xml:id="echoid-s3482" xml:space="preserve">NK &</s>
            <s xml:id="echoid-s3483" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3484" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s3485" xml:space="preserve">AB + AB. </s>
            <s xml:id="echoid-s3486" xml:space="preserve">BK
              <lb/>
            (communem adſciſcendo rationem BZ ad AB). </s>
            <s xml:id="echoid-s3487" xml:space="preserve">eſt autem BZ. </s>
            <s xml:id="echoid-s3488" xml:space="preserve">
              <lb/>
            AB + AN. </s>
            <s xml:id="echoid-s3489" xml:space="preserve">NK = CZ. </s>
            <s xml:id="echoid-s3490" xml:space="preserve">AC + AC. </s>
            <s xml:id="echoid-s3491" xml:space="preserve">CK = CZ. </s>
            <s xml:id="echoid-s3492" xml:space="preserve">CK & </s>
            <s xml:id="echoid-s3493" xml:space="preserve">
              <lb/>
            BZ. </s>
            <s xml:id="echoid-s3494" xml:space="preserve">AB + AB. </s>
            <s xml:id="echoid-s3495" xml:space="preserve">BK = BZ. </s>
            <s xml:id="echoid-s3496" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s3497" xml:space="preserve">ergo CZ. </s>
            <s xml:id="echoid-s3498" xml:space="preserve">CK &</s>
            <s xml:id="echoid-s3499" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3500" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s3501" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s3502" xml:space="preserve">
              <lb/>
            permutandóque CZ. </s>
            <s xml:id="echoid-s3503" xml:space="preserve">BZ &</s>
            <s xml:id="echoid-s3504" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3505" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s3506" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s3507" xml:space="preserve">quin & </s>
            <s xml:id="echoid-s3508" xml:space="preserve">componendo CB. </s>
            <s xml:id="echoid-s3509" xml:space="preserve">
              <lb/>
            BZ &</s>
            <s xml:id="echoid-s3510" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3511" xml:space="preserve">CB. </s>
            <s xml:id="echoid-s3512" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s3513" xml:space="preserve">ideóque BZ &</s>
            <s xml:id="echoid-s3514" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3515" xml:space="preserve">BK; </s>
            <s xml:id="echoid-s3516" xml:space="preserve">quare punctum Z centro
              <lb/>
            propinquius eſt, quàm ipſum K: </s>
            <s xml:id="echoid-s3517" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s3518" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3519" xml:space="preserve">D.</s>
            <s xml:id="echoid-s3520" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3521" xml:space="preserve">_Coroll_. </s>
            <s xml:id="echoid-s3522" xml:space="preserve">Hinc ſi puncta Z, ζ fuerint limites punctorum radiantium
              <lb/>
            A, _a_ (quorum A fit à fpeculo remotiùs, quàm _a_) erit CZ &</s>
            <s xml:id="echoid-s3523" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3524" xml:space="preserve">C ζ.
              <lb/>
            </s>
            <s xml:id="echoid-s3525" xml:space="preserve">Nam eſt BC. </s>
            <s xml:id="echoid-s3526" xml:space="preserve">AB &</s>
            <s xml:id="echoid-s3527" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3528" xml:space="preserve">BC, _a_ B. </s>
            <s xml:id="echoid-s3529" xml:space="preserve">adeóque compoſitè AC. </s>
            <s xml:id="echoid-s3530" xml:space="preserve">AB &</s>
            <s xml:id="echoid-s3531" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3532" xml:space="preserve">
              <lb/>
            _a_ C. </s>
            <s xml:id="echoid-s3533" xml:space="preserve">_a_ B. </s>
            <s xml:id="echoid-s3534" xml:space="preserve">hoc eſt CZ. </s>
            <s xml:id="echoid-s3535" xml:space="preserve">BZ &</s>
            <s xml:id="echoid-s3536" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3537" xml:space="preserve">C ζ. </s>
            <s xml:id="echoid-s3538" xml:space="preserve">B ζ. </s>
            <s xml:id="echoid-s3539" xml:space="preserve">quare componendo
              <lb/>
            BC. </s>
            <s xml:id="echoid-s3540" xml:space="preserve">BZ &</s>
            <s xml:id="echoid-s3541" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3542" xml:space="preserve">BC. </s>
            <s xml:id="echoid-s3543" xml:space="preserve">B ζ. </s>
            <s xml:id="echoid-s3544" xml:space="preserve">& </s>
            <s xml:id="echoid-s3545" xml:space="preserve">indè BZ &</s>
            <s xml:id="echoid-s3546" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3547" xml:space="preserve">B ζ.</s>
            <s xml:id="echoid-s3548" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3549" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s3550" xml:space="preserve">Porrò, conſectatur è præmiſſis, quòd ſi duorum quorumvis
              <lb/>
            incidentium AN, AR reflexi GN, HR axem interſecent punctis
              <lb/>
            K, L; </s>
            <s xml:id="echoid-s3551" xml:space="preserve">erit CL, CK :</s>
            <s xml:id="echoid-s3552" xml:space="preserve">: ACq - ANq. </s>
            <s xml:id="echoid-s3553" xml:space="preserve">ACq - ARq. </s>
            <s xml:id="echoid-s3554" xml:space="preserve">‖ Nam
              <lb/>
            quoniam eſt AC. </s>
            <s xml:id="echoid-s3555" xml:space="preserve">CK :</s>
            <s xml:id="echoid-s3556" xml:space="preserve">: ACq - ANq. </s>
            <s xml:id="echoid-s3557" xml:space="preserve">CBq. </s>
            <s xml:id="echoid-s3558" xml:space="preserve">itémque CL.
              <lb/>
            </s>
            <s xml:id="echoid-s3559" xml:space="preserve">AC :</s>
            <s xml:id="echoid-s3560" xml:space="preserve">: CBq. </s>
            <s xml:id="echoid-s3561" xml:space="preserve">ACq - ARq. </s>
            <s xml:id="echoid-s3562" xml:space="preserve">erit ex æquo perturbatè CL. </s>
            <s xml:id="echoid-s3563" xml:space="preserve">
              <lb/>
            CK :</s>
            <s xml:id="echoid-s3564" xml:space="preserve">: ACq - ANq. </s>
            <s xml:id="echoid-s3565" xml:space="preserve">ACq - ARq.</s>
            <s xml:id="echoid-s3566" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3567" xml:space="preserve">X. </s>
            <s xml:id="echoid-s3568" xml:space="preserve">Simili planè diſcurſu, ſi fuerit AC. </s>
            <s xml:id="echoid-s3569" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s3570" xml:space="preserve">: CZ. </s>
            <s xml:id="echoid-s3571" xml:space="preserve">ZB.
              <lb/>
            </s>
            <s xml:id="echoid-s3572" xml:space="preserve">erit CZ. </s>
            <s xml:id="echoid-s3573" xml:space="preserve">CK :</s>
            <s xml:id="echoid-s3574" xml:space="preserve">: ACq - ANq. </s>
            <s xml:id="echoid-s3575" xml:space="preserve">ACq - ABq. </s>
            <s xml:id="echoid-s3576" xml:space="preserve">& </s>
            <s xml:id="echoid-s3577" xml:space="preserve">CL. </s>
            <s xml:id="echoid-s3578" xml:space="preserve">CZ :</s>
            <s xml:id="echoid-s3579" xml:space="preserve">:
              <lb/>
            ACq - ARq. </s>
            <s xml:id="echoid-s3580" xml:space="preserve">ACq - ABq.</s>
            <s xml:id="echoid-s3581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3582" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s3583" xml:space="preserve">Hinc perſpicuum eſt obliquioris reflexi concurſum à centro
              <lb/>
            magìs elongari quam rectioris; </s>
            <s xml:id="echoid-s3584" xml:space="preserve">quod nempe ſit CL &</s>
            <s xml:id="echoid-s3585" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3586" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s3587" xml:space="preserve">Cùm
              <lb/>
            enim ſit ACq - ANq &</s>
            <s xml:id="echoid-s3588" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3589" xml:space="preserve">ACq - ARq; </s>
            <s xml:id="echoid-s3590" xml:space="preserve">erit CL &</s>
            <s xml:id="echoid-s3591" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3592" xml:space="preserve">CK.</s>
            <s xml:id="echoid-s3593" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3594" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s3595" xml:space="preserve">Hinc neceſſariò duo quilibet ad eaſdem axis partes incidentium
              <lb/>
            reflexi (quales NK, RL) ſeſe priùs quàm axem interſecabunt, puta
              <lb/>
            ad X. </s>
            <s xml:id="echoid-s3596" xml:space="preserve">quo poſito.</s>
            <s xml:id="echoid-s3597" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3598" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s3599" xml:space="preserve">Adnotari poteſt angulum GXH vel KXL (à reflexis oc-
              <lb/>
            currentibus incluſum) æquari angulo NCR unà cum differentia angu-
              <lb/>
            lorum incidentiæ; </s>
            <s xml:id="echoid-s3600" xml:space="preserve">vel, duplo angulo NCR unà cum ang. </s>
            <s xml:id="echoid-s3601" xml:space="preserve">NAR. </s>
            <s xml:id="echoid-s3602" xml:space="preserve">‖ Etenim
              <lb/>
            ang. </s>
            <s xml:id="echoid-s3603" xml:space="preserve">KXL = ang. </s>
            <s xml:id="echoid-s3604" xml:space="preserve">ALR - AKN = ang. </s>
            <s xml:id="echoid-s3605" xml:space="preserve">ACR + CRL -: </s>
            <s xml:id="echoid-s3606" xml:space="preserve">ang.
              <lb/>
            </s>
            <s xml:id="echoid-s3607" xml:space="preserve">
              <note position="left" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve">Fig. 83.</note>
            ACN + CNK = ang. </s>
            <s xml:id="echoid-s3608" xml:space="preserve">ACR - ACN + : </s>
            <s xml:id="echoid-s3609" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s3610" xml:space="preserve">CRL -
              <lb/>
            CNK = ang NCR +: </s>
            <s xml:id="echoid-s3611" xml:space="preserve">ang CRS - CNP. </s>
            <s xml:id="echoid-s3612" xml:space="preserve">‖ Quinetiam ang.
              <lb/>
            </s>
            <s xml:id="echoid-s3613" xml:space="preserve">CRS - CNP = ang. </s>
            <s xml:id="echoid-s3614" xml:space="preserve">RCA + CAR -: </s>
            <s xml:id="echoid-s3615" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s3616" xml:space="preserve">NCA </s>
          </p>
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