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-s758" xml:space="preserve">
              <pb o="20" file="0038" n="38" rhead=""/>
            pendimus, lucem admittere non debeat; </s>
            <s xml:id="echoid-s759" xml:space="preserve">omnino dicti radii SM, SN,
              <lb/>
            & </s>
            <s xml:id="echoid-s760" xml:space="preserve">conſimiles reflectentur, & </s>
            <s xml:id="echoid-s761" xml:space="preserve">extra atmoſphæram procul abeuntes
              <lb/>
            oculum non pertingent. </s>
            <s xml:id="echoid-s762" xml:space="preserve">Quinimò ſatìs conſtare videtur exhinc, quòd
              <lb/>
            radii quales SN ut viſum afficere queant, aut accedere, verſus per-
              <lb/>
            pendicularem NC refringi debent; </s>
            <s xml:id="echoid-s763" xml:space="preserve">id quod adverſariæ Hypotheſi
              <lb/>
            pariter adverſatur. </s>
            <s xml:id="echoid-s764" xml:space="preserve">Verùm hæc obiter, ac in trancurſu dicta ſunto.</s>
            <s xml:id="echoid-s765" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s766" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s767" xml:space="preserve">Porrò, ſubnotandum eſt, quoad binos caſus ſuprâ tractatos,
              <lb/>
            cùm duo media, diverſimoda comparandò duæ ſe repreſentent propor-
              <lb/>
            tiones, altera, terminorum ſitum tranſponendo, alterius inverſa, re-
              <lb/>
            fractionum ideò menſuras (quoad hæc) iiſdem terminis deſignabiles
              <lb/>
            ordine permutari. </s>
            <s xml:id="echoid-s768" xml:space="preserve">Ut ſi in primo caſu ſinus rectus anguli incidentis ſe
              <lb/>
            habeat ad ſinum rectum anguli refracti, ſicut A ad B, in ſecundo ſinus
              <lb/>
            incidentis ad ſinum refracti ſe inverſè habebit ut B ad A; </s>
            <s xml:id="echoid-s769" xml:space="preserve">nimirum
              <lb/>
            in præcedentibus ſiguris, quanto ZD major eſt quàm ZB, in prima
              <lb/>
            Hypotheſi; </s>
            <s xml:id="echoid-s770" xml:space="preserve">tanto conſtat ZD minorem eſſe quàm ZB, in ſecunda;
              <lb/>
            </s>
            <s xml:id="echoid-s771" xml:space="preserve">mediis ſcilicet iiſdem permanentibus.</s>
            <s xml:id="echoid-s772" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s773" xml:space="preserve">X. </s>
            <s xml:id="echoid-s774" xml:space="preserve">Denique, cùm medii cui radius impingit ſuperficiem hactenus
              <lb/>
            adſumpſerimus planam, advertendum ſupereſt, quamvìs illa curva ſit,
              <lb/>
            eodem tamen abſque ſenſibili diſcrimine ſeſe modo rem habere, ac ſi
              <lb/>
            plano curvam ſuperficiem iſthic, ubi radius occurrit, contingenti im-
              <lb/>
            pingeret. </s>
            <s xml:id="echoid-s775" xml:space="preserve">Incidat nempe radius ABCD in curvam lineam QBR,
              <lb/>
            quam ad incidentiæ punctum B tangat recta EF. </s>
            <s xml:id="echoid-s776" xml:space="preserve">Prorſuseodem mo-
              <lb/>
              <note position="right" xlink:label="note-0038-01" xlink:href="note-0038-01a" xml:space="preserve">Fig. 15.</note>
            do refringetur iſte radius ad curvam QBR, quo ad rectam EF, niſi
              <lb/>
            quòd iſthic arcus D δ in rariori medio decurſus tangentem aliquouſque
              <lb/>
            prætergreditur. </s>
            <s xml:id="echoid-s777" xml:space="preserve">Id quod eximiam radii ſubtilitatem conſiderando,
              <lb/>
            quámque perexiguo diſtet intervallo punctum δ à curvæ vertice B,
              <lb/>
            nullam omnino ſenſibilem (imò nec imaginabilem) inducet differen-
              <lb/>
            tiam. </s>
            <s xml:id="echoid-s778" xml:space="preserve">Quantillus enim iſte circulus eſſe debet, in quo chorda B δ, ra-
              <lb/>
            dii latitudine paullo major, arcum ſubtendet aliqua cum ejus ſenſibili
              <lb/>
            parte comparabilem? </s>
            <s xml:id="echoid-s779" xml:space="preserve">poteſt igitur angulus ZB δ æqualis ſupponi
              <lb/>
            angulo ZBF; </s>
            <s xml:id="echoid-s780" xml:space="preserve">quo conceſſo reliqua fluent eodem tenore, quo præ-
              <lb/>
            cedentia. </s>
            <s xml:id="echoid-s781" xml:space="preserve">Quin unà rationem exhibuimus ſuppoſitionis, quæ paſſim
              <lb/>
            ab Opticis accipitur; </s>
            <s xml:id="echoid-s782" xml:space="preserve">ità tamen precariò, non ut ſubinde nullum
              <lb/>
            in audientibus ſcrupulum relinquat; </s>
            <s xml:id="echoid-s783" xml:space="preserve">nec ut ſemper adſenſu firmo
              <lb/>
            concedatur.</s>
            <s xml:id="echoid-s784" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s785" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s786" xml:space="preserve">Ità primarias iſtas circa radiorum inflectionem Hypotheſes-
              <lb/>
            (vel Axiomata malitis, aut Theoremata) quibus omnis incumbit </s>
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