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-div173" type="section" level="1" n="21">
          <pb o="108" file="0126" n="126" rhead=""/>
          <p>
            <s xml:id="echoid-s7214" xml:space="preserve">Nam ob OZq - ZT x ZS. </s>
            <s xml:id="echoid-s7215" xml:space="preserve">OZq :</s>
            <s xml:id="echoid-s7216" xml:space="preserve">: OZ. </s>
            <s xml:id="echoid-s7217" xml:space="preserve">OC; </s>
            <s xml:id="echoid-s7218" xml:space="preserve">erit OZ cub
              <lb/>
            = OC x OZq - OC x ZT x ZS. </s>
            <s xml:id="echoid-s7219" xml:space="preserve">tranſponendóque OC x ZT x ZS = OC
              <lb/>
            x OZq - OZ cub. </s>
            <s xml:id="echoid-s7220" xml:space="preserve">atqui propter OZ. </s>
            <s xml:id="echoid-s7221" xml:space="preserve">ZS :</s>
            <s xml:id="echoid-s7222" xml:space="preserve">: OC. </s>
            <s xml:id="echoid-s7223" xml:space="preserve">CN. </s>
            <s xml:id="echoid-s7224" xml:space="preserve">eſt
              <lb/>
            OZ x CN = ZS x OC. </s>
            <s xml:id="echoid-s7225" xml:space="preserve">quare OZ x CN x ZT = OC x OZq
              <lb/>
            - OZ cub; </s>
            <s xml:id="echoid-s7226" xml:space="preserve">adeóque (elidendo OZ) erit CN x ZT = OC
              <lb/>
            x OZ - OZq. </s>
            <s xml:id="echoid-s7227" xml:space="preserve">vel CN. </s>
            <s xml:id="echoid-s7228" xml:space="preserve">OC - OZ:</s>
            <s xml:id="echoid-s7229" xml:space="preserve">: OZ. </s>
            <s xml:id="echoid-s7230" xml:space="preserve">ZT; </s>
            <s xml:id="echoid-s7231" xml:space="preserve">hoc eſt CB. </s>
            <s xml:id="echoid-s7232" xml:space="preserve">CZ:</s>
            <s xml:id="echoid-s7233" xml:space="preserve">:
              <lb/>
            OT. </s>
            <s xml:id="echoid-s7234" xml:space="preserve">ZT.</s>
            <s xml:id="echoid-s7235" xml:space="preserve">. & </s>
            <s xml:id="echoid-s7236" xml:space="preserve">componendo BZ. </s>
            <s xml:id="echoid-s7237" xml:space="preserve">CZ :</s>
            <s xml:id="echoid-s7238" xml:space="preserve">: OT. </s>
            <s xml:id="echoid-s7239" xml:space="preserve">ZT :</s>
            <s xml:id="echoid-s7240" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s7241" xml:space="preserve">R. </s>
            <s xml:id="echoid-s7242" xml:space="preserve">itaque
              <lb/>
            primò liquet punctum Z imaginem eſſe puncti A, ex refractione
              <lb/>
            factam ad circulum BN. </s>
            <s xml:id="echoid-s7243" xml:space="preserve">quinetiam ob CY. </s>
            <s xml:id="echoid-s7244" xml:space="preserve">YN :</s>
            <s xml:id="echoid-s7245" xml:space="preserve">: ρ O. </s>
            <s xml:id="echoid-s7246" xml:space="preserve">O σ :</s>
            <s xml:id="echoid-s7247" xml:space="preserve">:
              <lb/>
            R. </s>
            <s xml:id="echoid-s7248" xml:space="preserve">I; </s>
            <s xml:id="echoid-s7249" xml:space="preserve">palàm eſt NO refractum eſſe radii ad CY, hoc eſt ad FO
              <lb/>
            paralleli. </s>
            <s xml:id="echoid-s7250" xml:space="preserve">liquidò proinde conſtat propoſitum.</s>
            <s xml:id="echoid-s7251" xml:space="preserve">‖</s>
          </p>
          <p>
            <s xml:id="echoid-s7252" xml:space="preserve">In hoc caſu debet eſſe OZq &</s>
            <s xml:id="echoid-s7253" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7254" xml:space="preserve">ZT x ZS. </s>
            <s xml:id="echoid-s7255" xml:space="preserve">Haud abſimili ratione quoad
              <lb/>
            alios caſus (ut ſi circuli refringentis cavum objecto exponatur, & </s>
            <s xml:id="echoid-s7256" xml:space="preserve">c.)
              <lb/>
            </s>
            <s xml:id="echoid-s7257" xml:space="preserve">peragetur negotium. </s>
            <s xml:id="echoid-s7258" xml:space="preserve">ego ſpecimen tantùm _inſtitui Problematis,_ juxta
              <lb/>
            quod viſibilis objecti ſpecies per refractionem circularem ſecundum
              <lb/>
            præſtitutas quantitatem atque diſtantiam utcunque poſſit immutari.</s>
            <s xml:id="echoid-s7259" xml:space="preserve">‖</s>
          </p>
        </div>
        <div xml:id="echoid-div181" type="section" level="1" n="22">
          <head xml:id="echoid-head25" style="it" xml:space="preserve">APPENDICVLA.</head>
          <p>
            <s xml:id="echoid-s7260" xml:space="preserve">UT hæc paullò ſtrigoſior Lectio nonnihil incraſſetur, faciam hîc
              <lb/>
            (quanquam alienore loco) quod alibi (ſi mihi tunc in mentem
              <lb/>
            veniſſet) factum oportebat; </s>
            <s xml:id="echoid-s7261" xml:space="preserve">raciociniis noſtris adverſantem, à viro
              <lb/>
            doctiſſimo (alioquin opinor rarò dormitante) commiſſum paralo-
              <lb/>
            giſmum, nè cui fraudi ſit, detegam ac amoliar; </s>
            <s xml:id="echoid-s7262" xml:space="preserve">unáque doctrinam
              <lb/>
            noſtram confirmabo. </s>
            <s xml:id="echoid-s7263" xml:space="preserve">horſum è præmiſſis conſequens, ſed & </s>
            <s xml:id="echoid-s7264" xml:space="preserve">expe-
              <lb/>
            rientiæ (ut videbimus) conſonum hoc præſterno: </s>
            <s xml:id="echoid-s7265" xml:space="preserve">E refractione quavis
              <lb/>
            (nec non è reflectione ad circulum) duobus oculis apprehenſum ob-
              <lb/>
            jectum (puta lwcidum punctum A) reverà duplum apparet, ſeu duas (ad
              <lb/>
            minus) obtinet imagines.</s>
            <s xml:id="echoid-s7266" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7267" xml:space="preserve">Nam à puncto A exeuntes inſlectenti M N incidant duo quicunque
              <lb/>
              <note position="left" xlink:label="note-0126-01" xlink:href="note-0126-01a" xml:space="preserve">Fig. 176.</note>
            radii AM, AN; </s>
            <s xml:id="echoid-s7268" xml:space="preserve">quorum inflexi ſint ME, NF; </s>
            <s xml:id="echoid-s7269" xml:space="preserve">concurrentes in X;
              <lb/>
            </s>
            <s xml:id="echoid-s7270" xml:space="preserve">in his autem uſpiam conſtituantur oculorum centra O, P. </s>
            <s xml:id="echoid-s7271" xml:space="preserve">quòd puncti
              <lb/>
            A imago nulla ad occurſum X exiſtat, è ſupra poſitis, ac probatis con-
              <lb/>
            ſectatur (omnes enim imagines ad illa conſiſtere docuimus inflexorum
              <lb/>
            puncta, ad quæ nulli illos alii inflexi interſecant) itaque duæ ſunt
              <lb/>
            imagines puncti A, una in inflexo EM (qualis α) ad oculum O per-
              <lb/>
            tinens; </s>
            <s xml:id="echoid-s7272" xml:space="preserve">altera in inflexo FN (qualis α) oculo P deputanda.</s>
            <s xml:id="echoid-s7273" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7274" xml:space="preserve">Hinc liquet etiam magnitudinis cujuſvis hoc modo ſpectatæ duplicem
              <lb/>
            imaginem haberi.</s>
            <s xml:id="echoid-s7275" xml:space="preserve"/>
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