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-s2889" xml:space="preserve">
              <pb o="52" file="0070" n="70" rhead=""/>
            diſtinctius exhibet obtuenti. </s>
            <s xml:id="echoid-s2890" xml:space="preserve">quod erat propoſitum oſtendere. </s>
            <s xml:id="echoid-s2891" xml:space="preserve">Et
              <lb/>
            hæc quidem ad locum imaginis determinandum attinentia pleraque
              <lb/>
            propter oculum in axe ſitum ſuffecerit attigiſſe. </s>
            <s xml:id="echoid-s2892" xml:space="preserve">Supereſt ut idem
              <lb/>
            oculi gratiâ ſecùs conſtituti pertentemus. </s>
            <s xml:id="echoid-s2893" xml:space="preserve">id operis ſequenti depu-
              <lb/>
            tamus.</s>
            <s xml:id="echoid-s2894" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div81" type="section" level="1" n="16">
          <head xml:id="echoid-head19" xml:space="preserve">
            <emph style="sc">Lect.</emph>
          VI I.</head>
          <p>
            <s xml:id="echoid-s2895" xml:space="preserve">I. </s>
            <s xml:id="echoid-s2896" xml:space="preserve">ID nunc agimus, ut ab infinito quoad ſenſum intervallo radiantis
              <lb/>
            puncti, è reflectione circularem ad peripheriam peracta oriun-
              <lb/>
            dæ imaginis, oculi reſpectu præter axem ſiti, locum exquiramus.
              <lb/>
            </s>
            <s xml:id="echoid-s2897" xml:space="preserve">quocirca primùm ipſa recta linea determinanda venit, in qua locus
              <lb/>
            iſte verſatur; </s>
            <s xml:id="echoid-s2898" xml:space="preserve">tum ipſiſſimum præciſè punctum eſt deſignandum. </s>
            <s xml:id="echoid-s2899" xml:space="preserve">In
              <lb/>
            primi verò propoſiti gratiam hoc _Problema_ confici debet.</s>
            <s xml:id="echoid-s2900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2901" xml:space="preserve">II. </s>
            <s xml:id="echoid-s2902" xml:space="preserve">Dato circulo reflectente BNP (cujus centrum C) rectâque
              <lb/>
            CB poſitione data; </s>
            <s xml:id="echoid-s2903" xml:space="preserve">deſignandus eſt huic parallelus radius, cujus re-
              <lb/>
            flexus per datum tranſeat punctum.</s>
            <s xml:id="echoid-s2904" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2905" xml:space="preserve">III. </s>
            <s xml:id="echoid-s2906" xml:space="preserve">Si datum punctum ( puta K) in ipſa CB exiſtat, facilimè pe-
              <lb/>
              <note position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve">Fig. 70.</note>
            ragitur negotium. </s>
            <s xml:id="echoid-s2907" xml:space="preserve">nam ſi centro K, intervallo KC deſcribatur circulus,
              <lb/>
            ipſi reflectenti occurrens in N; </s>
            <s xml:id="echoid-s2908" xml:space="preserve">erit KN reſlexus ducti ad CB paralle-
              <lb/>
            li; </s>
            <s xml:id="echoid-s2909" xml:space="preserve">prout ex antedictis abunde perſpicuum eſt.</s>
            <s xml:id="echoid-s2910" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2911" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s2912" xml:space="preserve">Si datum punctum (puta jam X) in ipſa reflectentis circumfe-
              <lb/>
            rentia verſetur; </s>
            <s xml:id="echoid-s2913" xml:space="preserve">arcûs triſectione ſtatim exhauritur _Problema_. </s>
            <s xml:id="echoid-s2914" xml:space="preserve">Nam
              <lb/>
            ducatur XH ad BC parallela (quæ quidem ipſa uno modo proble-
              <lb/>
            mati ſatisfacit) & </s>
            <s xml:id="echoid-s2915" xml:space="preserve">interceptus arcus XH ſecetur punctis N, P, ut
              <lb/>
              <note position="left" xlink:label="note-0070-02" xlink:href="note-0070-02a" xml:space="preserve">Fig. 71.</note>
            ſint arcus XN, NP, PH æquales inter ſe; </s>
            <s xml:id="echoid-s2916" xml:space="preserve">connectantúrque rectæ
              <lb/>
            XN, NP. </s>
            <s xml:id="echoid-s2917" xml:space="preserve">dico factum. </s>
            <s xml:id="echoid-s2918" xml:space="preserve">etenim ducantur CN, XP; </s>
            <s xml:id="echoid-s2919" xml:space="preserve">& </s>
            <s xml:id="echoid-s2920" xml:space="preserve">patet an-
              <lb/>
            gulum CN X ipſi CNP æquari; </s>
            <s xml:id="echoid-s2921" xml:space="preserve">adeóque fore XN reflexum ipſius
              <lb/>
            PN; </s>
            <s xml:id="echoid-s2922" xml:space="preserve">quinetiam ang. </s>
            <s xml:id="echoid-s2923" xml:space="preserve">NP X æquatur angulo HXP; </s>
            <s xml:id="echoid-s2924" xml:space="preserve">proindéque
              <lb/>
            NP ipſi XH, hoc eſt ipſi BC, parallela eſt. </s>
            <s xml:id="echoid-s2925" xml:space="preserve">itaque factum.</s>
            <s xml:id="echoid-s2926" xml:space="preserve"/>
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