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-div91" type="section" level="1" n="17">
          <p>
            <s xml:id="echoid-s3321" xml:space="preserve">
              <pb o="59" file="0077" n="77" rhead=""/>
            + HK. </s>
            <s xml:id="echoid-s3322" xml:space="preserve">CN. </s>
            <s xml:id="echoid-s3323" xml:space="preserve">= AC. </s>
            <s xml:id="echoid-s3324" xml:space="preserve">KC + AK. </s>
            <s xml:id="echoid-s3325" xml:space="preserve">AC = AK. </s>
            <s xml:id="echoid-s3326" xml:space="preserve">KC. </s>
            <s xml:id="echoid-s3327" xml:space="preserve">verùm eſt
              <lb/>
            NP. </s>
            <s xml:id="echoid-s3328" xml:space="preserve">CN + AN. </s>
            <s xml:id="echoid-s3329" xml:space="preserve">CN = NP x AN. </s>
            <s xml:id="echoid-s3330" xml:space="preserve">CNq. </s>
            <s xml:id="echoid-s3331" xml:space="preserve">ergò erit AK.
              <lb/>
            </s>
            <s xml:id="echoid-s3332" xml:space="preserve">KC :</s>
            <s xml:id="echoid-s3333" xml:space="preserve">: NP x AN. </s>
            <s xml:id="echoid-s3334" xml:space="preserve">CNq. </s>
            <s xml:id="echoid-s3335" xml:space="preserve">componendóque AC. </s>
            <s xml:id="echoid-s3336" xml:space="preserve">KC :</s>
            <s xml:id="echoid-s3337" xml:space="preserve">: NP
              <lb/>
              <note position="right" xlink:label="note-0077-01" xlink:href="note-0077-01a" xml:space="preserve">Fig. 79, 80.</note>
            x AN + CNq. </s>
            <s xml:id="echoid-s3338" xml:space="preserve">CNq. </s>
            <s xml:id="echoid-s3339" xml:space="preserve">cum ſit igitur NP x AN = AP x AN
              <lb/>
            - ANq. </s>
            <s xml:id="echoid-s3340" xml:space="preserve">& </s>
            <s xml:id="echoid-s3341" xml:space="preserve">AP x AN = ACq - CNq; </s>
            <s xml:id="echoid-s3342" xml:space="preserve">adeóque NP
              <lb/>
            x AN + CNq = ACq - CNq - ANq + CNq; </s>
            <s xml:id="echoid-s3343" xml:space="preserve">= ACq
              <lb/>
            - ANq. </s>
            <s xml:id="echoid-s3344" xml:space="preserve">erit AC. </s>
            <s xml:id="echoid-s3345" xml:space="preserve">KC :</s>
            <s xml:id="echoid-s3346" xml:space="preserve">: ACq - ANq. </s>
            <s xml:id="echoid-s3347" xml:space="preserve">CNq : </s>
            <s xml:id="echoid-s3348" xml:space="preserve">Quod E. </s>
            <s xml:id="echoid-s3349" xml:space="preserve">D.
              <lb/>
            </s>
            <s xml:id="echoid-s3350" xml:space="preserve">_Coroll_. </s>
            <s xml:id="echoid-s3351" xml:space="preserve">AK. </s>
            <s xml:id="echoid-s3352" xml:space="preserve">KC :</s>
            <s xml:id="echoid-s3353" xml:space="preserve">: AN x NP. </s>
            <s xml:id="echoid-s3354" xml:space="preserve">CNq.</s>
            <s xml:id="echoid-s3355" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3356" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s3357" xml:space="preserve">Etiam hoc _Theorema_ ſubdemus: </s>
            <s xml:id="echoid-s3358" xml:space="preserve">Si fiat 2 CA. </s>
            <s xml:id="echoid-s3359" xml:space="preserve">CN :</s>
            <s xml:id="echoid-s3360" xml:space="preserve">:
              <lb/>
            CN. </s>
            <s xml:id="echoid-s3361" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3362" xml:space="preserve">& </s>
            <s xml:id="echoid-s3363" xml:space="preserve">2 CK. </s>
            <s xml:id="echoid-s3364" xml:space="preserve">CN :</s>
            <s xml:id="echoid-s3365" xml:space="preserve">: CN. </s>
            <s xml:id="echoid-s3366" xml:space="preserve">F; </s>
            <s xml:id="echoid-s3367" xml:space="preserve">& </s>
            <s xml:id="echoid-s3368" xml:space="preserve">ſumatur CQ = E + F;
              <lb/>
            </s>
            <s xml:id="echoid-s3369" xml:space="preserve">erit ducta NQ ad CA perpendicularis. </s>
            <s xml:id="echoid-s3370" xml:space="preserve">vel reciprocè; </s>
            <s xml:id="echoid-s3371" xml:space="preserve">poſito quòd
              <lb/>
            ſit NQ ad CA perpendicularis; </s>
            <s xml:id="echoid-s3372" xml:space="preserve">erit CQ = E + F. </s>
            <s xml:id="echoid-s3373" xml:space="preserve">‖ Nam (ut
              <lb/>
            hoc poſterius oſtendamus) quoniam eſt 2 CA. </s>
            <s xml:id="echoid-s3374" xml:space="preserve">CN :</s>
            <s xml:id="echoid-s3375" xml:space="preserve">: CN. </s>
            <s xml:id="echoid-s3376" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3377" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s3378" xml:space="preserve">CN. </s>
            <s xml:id="echoid-s3379" xml:space="preserve">2 CK :</s>
            <s xml:id="echoid-s3380" xml:space="preserve">: F. </s>
            <s xml:id="echoid-s3381" xml:space="preserve">CN. </s>
            <s xml:id="echoid-s3382" xml:space="preserve">erit ex æquo perturbatè 2 CA. </s>
            <s xml:id="echoid-s3383" xml:space="preserve">2 CK
              <lb/>
            :</s>
            <s xml:id="echoid-s3384" xml:space="preserve">: F. </s>
            <s xml:id="echoid-s3385" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3386" xml:space="preserve">vel CA. </s>
            <s xml:id="echoid-s3387" xml:space="preserve">CK :</s>
            <s xml:id="echoid-s3388" xml:space="preserve">: F. </s>
            <s xml:id="echoid-s3389" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3390" xml:space="preserve">componendóque CA + CK. </s>
            <s xml:id="echoid-s3391" xml:space="preserve">CK
              <lb/>
            :</s>
            <s xml:id="echoid-s3392" xml:space="preserve">: F + E. </s>
            <s xml:id="echoid-s3393" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3394" xml:space="preserve">Porrò quoniam eſt ANq = ACq + CNq - 2 AC
              <lb/>
            x CQ; </s>
            <s xml:id="echoid-s3395" xml:space="preserve">erit 2 AC x CQ - CNq = ACq - ANq. </s>
            <s xml:id="echoid-s3396" xml:space="preserve">itaque
              <lb/>
            (juxta præcedentem) erit 2 AC x CQ - CNq. </s>
            <s xml:id="echoid-s3397" xml:space="preserve">CNQ :</s>
            <s xml:id="echoid-s3398" xml:space="preserve">: AC. </s>
            <s xml:id="echoid-s3399" xml:space="preserve">
              <lb/>
            CK. </s>
            <s xml:id="echoid-s3400" xml:space="preserve">hoc eſt ( ob CNq = 2 AC x E) 2 AC x CQ - 2 AC
              <lb/>
            x E. </s>
            <s xml:id="echoid-s3401" xml:space="preserve">2 AC x E :</s>
            <s xml:id="echoid-s3402" xml:space="preserve">: AC. </s>
            <s xml:id="echoid-s3403" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s3404" xml:space="preserve">hoc eſt CQ - E. </s>
            <s xml:id="echoid-s3405" xml:space="preserve">E :</s>
            <s xml:id="echoid-s3406" xml:space="preserve">: AC. </s>
            <s xml:id="echoid-s3407" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s3408" xml:space="preserve">
              <lb/>
            vel componendo CQ. </s>
            <s xml:id="echoid-s3409" xml:space="preserve">E :</s>
            <s xml:id="echoid-s3410" xml:space="preserve">: AC + CK. </s>
            <s xml:id="echoid-s3411" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s3412" xml:space="preserve">erat autem AC
              <lb/>
            + CK. </s>
            <s xml:id="echoid-s3413" xml:space="preserve">CK :</s>
            <s xml:id="echoid-s3414" xml:space="preserve">: F + E. </s>
            <s xml:id="echoid-s3415" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3416" xml:space="preserve">ergò CQ = F + E: </s>
            <s xml:id="echoid-s3417" xml:space="preserve">Quod E. </s>
            <s xml:id="echoid-s3418" xml:space="preserve">D.</s>
            <s xml:id="echoid-s3419" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3420" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s3421" xml:space="preserve">Ex iſtis porrò deducetur, ſi dividatur Semidiameter BC in
              <lb/>
            Z, ut ſit AC. </s>
            <s xml:id="echoid-s3422" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s3423" xml:space="preserve">: CZ. </s>
            <s xml:id="echoid-s3424" xml:space="preserve">BZ; </s>
            <s xml:id="echoid-s3425" xml:space="preserve">punctum Z limes erit citra quem
              <lb/>
            (reſpectu centri C) nullus hujuſmodi reflexus axem decuſſabit. </s>
            <s xml:id="echoid-s3426" xml:space="preserve">Cu-
              <lb/>
            juſvis, inquam, radii AN eſto reflexus GN; </s>
            <s xml:id="echoid-s3427" xml:space="preserve">axi occurrens in K.
              <lb/>
            </s>
            <s xml:id="echoid-s3428" xml:space="preserve">dico fore CK &</s>
            <s xml:id="echoid-s3429" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3430" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s3431" xml:space="preserve">Nam ob hypotheſin (permutandóque) eſt AC. </s>
            <s xml:id="echoid-s3432" xml:space="preserve">
              <lb/>
            CZ :</s>
            <s xml:id="echoid-s3433" xml:space="preserve">: AB. </s>
            <s xml:id="echoid-s3434" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s3435" xml:space="preserve">igitur (antecedentes, & </s>
            <s xml:id="echoid-s3436" xml:space="preserve">conſequentes copulan-
              <lb/>
            do) AC. </s>
            <s xml:id="echoid-s3437" xml:space="preserve">CZ :</s>
            <s xml:id="echoid-s3438" xml:space="preserve">: AC + AB. </s>
            <s xml:id="echoid-s3439" xml:space="preserve">CB. </s>
            <s xml:id="echoid-s3440" xml:space="preserve">quare ( poſterioris hujuſce
              <lb/>
            rationis utrumque terminum in æquales AC - AB, & </s>
            <s xml:id="echoid-s3441" xml:space="preserve">BC ducen-
              <lb/>
            do) erit AC. </s>
            <s xml:id="echoid-s3442" xml:space="preserve">CZ :</s>
            <s xml:id="echoid-s3443" xml:space="preserve">: ACq - ABq. </s>
            <s xml:id="echoid-s3444" xml:space="preserve">CBq. </s>
            <s xml:id="echoid-s3445" xml:space="preserve">eſt autem ACq
              <lb/>
            - ABq &</s>
            <s xml:id="echoid-s3446" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3447" xml:space="preserve">ACq - ANq; </s>
            <s xml:id="echoid-s3448" xml:space="preserve">adeóque ACq - ABq CBq. </s>
            <s xml:id="echoid-s3449" xml:space="preserve">
              <lb/>
            &</s>
            <s xml:id="echoid-s3450" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3451" xml:space="preserve">ACq - ANq. </s>
            <s xml:id="echoid-s3452" xml:space="preserve">CBq :</s>
            <s xml:id="echoid-s3453" xml:space="preserve">: AC. </s>
            <s xml:id="echoid-s3454" xml:space="preserve">CK (è mox oſtenſis hoc) qua-
              <lb/>
            propter erit AC. </s>
            <s xml:id="echoid-s3455" xml:space="preserve">CZ &</s>
            <s xml:id="echoid-s3456" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3457" xml:space="preserve">AC. </s>
            <s xml:id="echoid-s3458" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s3459" xml:space="preserve">indéque CK &</s>
            <s xml:id="echoid-s3460" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3461" xml:space="preserve">CZ: </s>
            <s xml:id="echoid-s3462" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0077-02" xlink:href="note-0077-02a" xml:space="preserve">Fig. 81, 82.</note>
            Q. </s>
            <s xml:id="echoid-s3463" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3464" xml:space="preserve">D.</s>
            <s xml:id="echoid-s3465" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3466" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s3467" xml:space="preserve">Aliter hoc idem; </s>
            <s xml:id="echoid-s3468" xml:space="preserve">ut quibuſdam fortaſſe videbitur, minùs
              <lb/>
            involutè: </s>
            <s xml:id="echoid-s3469" xml:space="preserve">per N ducatur VT circulum contingens. </s>
            <s xml:id="echoid-s3470" xml:space="preserve">& </s>
            <s xml:id="echoid-s3471" xml:space="preserve">quoniam </s>
          </p>
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    </echo>
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