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-div99" type="section" level="1" n="18">
          <p>
            <s xml:id="echoid-s3844" xml:space="preserve">
              <pb o="64" file="0082" n="82" rhead=""/>
            fecans in N; </s>
            <s xml:id="echoid-s3845" xml:space="preserve">& </s>
            <s xml:id="echoid-s3846" xml:space="preserve">per N ducatur KN G; </s>
            <s xml:id="echoid-s3847" xml:space="preserve">hæc ipſius AN reflexa
              <lb/>
            erit.</s>
            <s xml:id="echoid-s3848" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3849" xml:space="preserve">Nam ob ANq = ACq - Vq. </s>
            <s xml:id="echoid-s3850" xml:space="preserve">erit Vq = ACq - ANq.
              <lb/>
            </s>
            <s xml:id="echoid-s3851" xml:space="preserve">
              <note position="left" xlink:label="note-0082-01" xlink:href="note-0082-01a" xml:space="preserve">Fig. 89.</note>
            adeóque CBq. </s>
            <s xml:id="echoid-s3852" xml:space="preserve">ACq - ANq:</s>
            <s xml:id="echoid-s3853" xml:space="preserve">: (CBq. </s>
            <s xml:id="echoid-s3854" xml:space="preserve">Vq:</s>
            <s xml:id="echoid-s3855" xml:space="preserve">:) CK. </s>
            <s xml:id="echoid-s3856" xml:space="preserve">AC.
              <lb/>
            </s>
            <s xml:id="echoid-s3857" xml:space="preserve">quod, è præmonſtratis, reflectioni proprium eſt. </s>
            <s xml:id="echoid-s3858" xml:space="preserve">ergò liquet pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s3859" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3860" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3861" xml:space="preserve">ltà quidem in hoc caſu; </s>
            <s xml:id="echoid-s3862" xml:space="preserve">at ſi punctum A ponatur aliàs, ut ſit
              <lb/>
            AC &</s>
            <s xml:id="echoid-s3863" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3864" xml:space="preserve">AN; </s>
            <s xml:id="echoid-s3865" xml:space="preserve">reliquis ſtantibus, Sumendum erit intervallum AN
              <lb/>
            = √ : </s>
            <s xml:id="echoid-s3866" xml:space="preserve">ACq + Vq; </s>
            <s xml:id="echoid-s3867" xml:space="preserve">ut ſit ANq - ACq = Vq. </s>
            <s xml:id="echoid-s3868" xml:space="preserve">ut poſthac
              <lb/>
            conſtabit, ubi de concavis agemus. </s>
            <s xml:id="echoid-s3869" xml:space="preserve">Aliter hoc idem. </s>
            <s xml:id="echoid-s3870" xml:space="preserve">Fiat 2 CK.
              <lb/>
            </s>
            <s xml:id="echoid-s3871" xml:space="preserve">C B: </s>
            <s xml:id="echoid-s3872" xml:space="preserve">: </s>
            <s xml:id="echoid-s3873" xml:space="preserve">CB. </s>
            <s xml:id="echoid-s3874" xml:space="preserve">F. </s>
            <s xml:id="echoid-s3875" xml:space="preserve">& </s>
            <s xml:id="echoid-s3876" xml:space="preserve">2 CA. </s>
            <s xml:id="echoid-s3877" xml:space="preserve">CB : </s>
            <s xml:id="echoid-s3878" xml:space="preserve">: </s>
            <s xml:id="echoid-s3879" xml:space="preserve">CB. </s>
            <s xml:id="echoid-s3880" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3881" xml:space="preserve">ſumatúrque CQ = E
              <lb/>
            + F. </s>
            <s xml:id="echoid-s3882" xml:space="preserve">& </s>
            <s xml:id="echoid-s3883" xml:space="preserve">du@ta QN ad AC perpendicularis circulum ſecet in N. </s>
            <s xml:id="echoid-s3884" xml:space="preserve">
              <lb/>
            connexæ AN, KN altera alterius reflexa erit. </s>
            <s xml:id="echoid-s3885" xml:space="preserve">hoc è ſuprà dictis
              <lb/>
            liquidò conſectatur. </s>
            <s xml:id="echoid-s3886" xml:space="preserve">At ſi fuerit AN &</s>
            <s xml:id="echoid-s3887" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3888" xml:space="preserve">AC; </s>
            <s xml:id="echoid-s3889" xml:space="preserve">tum accipi debet
              <lb/>
            CQ = F - E; </s>
            <s xml:id="echoid-s3890" xml:space="preserve">& </s>
            <s xml:id="echoid-s3891" xml:space="preserve">(reliquis nihil immutatis, utì poſtmodùm appa-
              <lb/>
            rebit) factum erit.</s>
            <s xml:id="echoid-s3892" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3893" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s3894" xml:space="preserve">Intra caſus hos _Problema_, ceu videtis, facilè conſtruitur;
              <lb/>
            </s>
            <s xml:id="echoid-s3895" xml:space="preserve">aſt illos; </s>
            <s xml:id="echoid-s3896" xml:space="preserve">alióſque ſpeciales, ſi qui ſunt, excipiendo, generaliter con-
              <lb/>
            ceptum omnino Solidum eſt, & </s>
            <s xml:id="echoid-s3897" xml:space="preserve">certè _δυσ@@νον_; </s>
            <s xml:id="echoid-s3898" xml:space="preserve">vix ut aliud a
              <lb/>
            _Geometris_ hactenus attentatum difficilius reperiatur. </s>
            <s xml:id="echoid-s3899" xml:space="preserve">Et primò qui-
              <lb/>
            dem per lineam extrui, explicaríque poterit ſibi peculiarem, hoc vel
              <lb/>
            adſimili modo deſcribendam.</s>
            <s xml:id="echoid-s3900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3901" xml:space="preserve">Connexâ CA, ſuper diametrum CA deſcribatur circulus AI C;
              <lb/>
            </s>
            <s xml:id="echoid-s3902" xml:space="preserve">item ſemidiametro CA deſcribatur alter circulus AH G. </s>
            <s xml:id="echoid-s3903" xml:space="preserve">tum à C
              <lb/>
            educantur rectæ quotvis CI circulum AICſecantes punctis I; </s>
            <s xml:id="echoid-s3904" xml:space="preserve">& </s>
            <s xml:id="echoid-s3905" xml:space="preserve">per
              <lb/>
            A, I ductæ rectæ circulum AHGſecent punctis H; </s>
            <s xml:id="echoid-s3906" xml:space="preserve">demum per H,
              <lb/>
            & </s>
            <s xml:id="echoid-s3907" xml:space="preserve">X rectæ ducantur ipſas CI decuſſantes punctis N. </s>
            <s xml:id="echoid-s3908" xml:space="preserve">per hujuſmodi
              <lb/>
              <note position="left" xlink:label="note-0082-02" xlink:href="note-0082-02a" xml:space="preserve">Fig. 90.</note>
            puncta quævis deſignabilia tranſibit linea, _Problematis_ expoſiti ſo-
              <lb/>
            lutioni accommodata. </s>
            <s xml:id="echoid-s3909" xml:space="preserve">Sit enim ejus, ac reflectentis circuli quævis
              <lb/>
            interſectio N (qualium certè pro reflectentis circuli magnitudine ſub-
              <lb/>
            inde quatuor, aliquando tres, modò binæ tantùm erunt) & </s>
            <s xml:id="echoid-s3910" xml:space="preserve">connecta-
              <lb/>
            tur AN. </s>
            <s xml:id="echoid-s3911" xml:space="preserve">Et quoniam angulus CIA in Semicirculo rectus eſt, erit
              <lb/>
            recta AH biſecta in I. </s>
            <s xml:id="echoid-s3912" xml:space="preserve">adeóque triangula AN I, HNIſibimet æqua-
              <lb/>
            lia prorſus & </s>
            <s xml:id="echoid-s3913" xml:space="preserve">æquiangala erunt; </s>
            <s xml:id="echoid-s3914" xml:space="preserve">& </s>
            <s xml:id="echoid-s3915" xml:space="preserve">ſpeciatim ang. </s>
            <s xml:id="echoid-s3916" xml:space="preserve">INA = ang.
              <lb/>
            </s>
            <s xml:id="echoid-s3917" xml:space="preserve">IN X. </s>
            <s xml:id="echoid-s3918" xml:space="preserve">unde patet propoſitum.</s>
            <s xml:id="echoid-s3919" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3920" xml:space="preserve">V. </s>
            <s xml:id="echoid-s3921" xml:space="preserve">Verùm quoniam (ut pridem admonitum) hujuſmodi conſtructi-
              <lb/>
            ones, etſi longè faciliores iis quæ per vulgò receptas lineas peraguntur,
              <lb/>
            & </s>
            <s xml:id="echoid-s3922" xml:space="preserve">_Problematum_ naturam magìs in propatulo collocantes à </s>
          </p>
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