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

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[111.] _Theor_. VI.
Page: 344 (151)
[112.] FINIS.
Page: 344 (151)
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        <div xml:id="echoid-div166" type="section" level="1" n="20">
          <head xml:id="echoid-head23" xml:space="preserve">
            <emph style="sc">Lect.</emph>
          XIV.</head>
          <p style="it">
            <s xml:id="echoid-s6368" xml:space="preserve">_I.</s>
            <s xml:id="echoid-s6369" xml:space="preserve">S_ub pracedentis calcem, Regulam pollicebamur, exemplis ſtipa-
              <lb/>
            tam, ex qua punctorum è variis inflectionibus reſultantes, ima-
              <lb/>
            gines dignoſcantur. </s>
            <s xml:id="echoid-s6370" xml:space="preserve">iſlam nunc exhibemus quàm ſimplicimè conceptam.</s>
            <s xml:id="echoid-s6371" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6372" xml:space="preserve">Sit ABEFO radius principalis, puncti radiantis A ſpeciem per
              <lb/>
              <note position="left" xlink:label="note-0114-01" xlink:href="note-0114-01a" xml:space="preserve">Fig. 149,
                <lb/>
              150.</note>
            oculi centrum O deferens, ex incidente primo AB, & </s>
            <s xml:id="echoid-s6373" xml:space="preserve">inflexis BE,
              <lb/>
            EF, FO (in directum aut ſecùs diſpoſitis) conſtans; </s>
            <s xml:id="echoid-s6374" xml:space="preserve">tum puncti A
              <lb/>
            reſpectu oculi in recta B E poſiti, & </s>
            <s xml:id="echoid-s6375" xml:space="preserve">ex inflectione ad ſuperficiem B
              <lb/>
            reſultans (è præmiſſis utique deſignabilis) imago ſit Z. </s>
            <s xml:id="echoid-s6376" xml:space="preserve">item hujus Z
              <lb/>
            (quod jam veluti radians concipiatur) reſpectu oculi in recta E F
              <lb/>
            conſtituti, & </s>
            <s xml:id="echoid-s6377" xml:space="preserve">ab inflectione ad ſuperficiem E emergens imago ſit Y;
              <lb/>
            </s>
            <s xml:id="echoid-s6378" xml:space="preserve">demùm puncti Y (tanquam in ſuperficiem F radiantis) reſpectu oculi
              <lb/>
            in FO collocati ſit imago X. </s>
            <s xml:id="echoid-s6379" xml:space="preserve">erit hoc punctum Ximago cunctis ab
              <lb/>
            his inflectionibus proveniens. </s>
            <s xml:id="echoid-s6380" xml:space="preserve">neque ſecùs quotcunque fuerint inflecti-
              <lb/>
            ones ſeſe res habebit; </s>
            <s xml:id="echoid-s6381" xml:space="preserve">enimverò ſemper ex illa tali poſtrema inflectione
              <lb/>
            reſultans imago, eadem erit cum illa, quam omnes exhibent.</s>
            <s xml:id="echoid-s6382" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6383" xml:space="preserve">Hujus effati veritas è conſtructione ſatìs apparet; </s>
            <s xml:id="echoid-s6384" xml:space="preserve">è qua facilè colli-
              <lb/>
            gitur proximorum ipſi AB incidentium hinc indè radiorum inflexos
              <lb/>
            tandem circa punctum Xipſum FX interſecare. </s>
            <s xml:id="echoid-s6385" xml:space="preserve">vel ità rem collegeris:
              <lb/>
            </s>
            <s xml:id="echoid-s6386" xml:space="preserve">punctum Z eſt puncti A imago; </s>
            <s xml:id="echoid-s6387" xml:space="preserve">& </s>
            <s xml:id="echoid-s6388" xml:space="preserve">punctum Y ipſius Z; </s>
            <s xml:id="echoid-s6389" xml:space="preserve">denuóque
              <lb/>
            punctum Xipſius Y; </s>
            <s xml:id="echoid-s6390" xml:space="preserve">itaque punctum X ipſius A imago erit, qualem
              <lb/>
            nempe res hîc fert, remota. </s>
            <s xml:id="echoid-s6391" xml:space="preserve">Strictiore longiuſculo diſcurſu poſſet hoc
              <lb/>
            comprobari, ſed quorſum rem ſatìs claram intricare?</s>
            <s xml:id="echoid-s6392" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6393" xml:space="preserve">II. </s>
            <s xml:id="echoid-s6394" xml:space="preserve">Exempla jam, quæ dixi, ſeu è præmiſſis deducta conſectaria
              <lb/>
            ſubnectam. </s>
            <s xml:id="echoid-s6395" xml:space="preserve">Notetur autem imagines, quæ in iis pròponuntur deſig-
              <lb/>
            nandæ, oculum reſpicere Centrum habentem in ipſo radiationis axe
              <lb/>
            (qualis eſt recta BD) conſtitutum. </s>
            <s xml:id="echoid-s6396" xml:space="preserve">item diverſarum ſuperficierum
              <lb/>
            ac radiationum axes ſibimet in directum poni. </s>
            <s xml:id="echoid-s6397" xml:space="preserve">præſumatur etiam in
              <lb/>
            refractionibus ex aere factis ad vitrum fore I. </s>
            <s xml:id="echoid-s6398" xml:space="preserve">R :</s>
            <s xml:id="echoid-s6399" xml:space="preserve">: 5. </s>
            <s xml:id="echoid-s6400" xml:space="preserve">3; </s>
            <s xml:id="echoid-s6401" xml:space="preserve">ad aquam
              <lb/>
            vero fore I. </s>
            <s xml:id="echoid-s6402" xml:space="preserve">R :</s>
            <s xml:id="echoid-s6403" xml:space="preserve">: 4. </s>
            <s xml:id="echoid-s6404" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6405" xml:space="preserve">(hæ nempe rationes veris probè </s>
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