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-div301" type="section" level="1" n="33">
          <head xml:id="echoid-head36" xml:space="preserve">
            <emph style="sc">Lect</emph>
          . VIII.</head>
          <p>
            <s xml:id="echoid-s11074" xml:space="preserve">MIhi ſanè videor ( videbor & </s>
            <s xml:id="echoid-s11075" xml:space="preserve">vobis, opinor ) quod irridebat
              <lb/>
            _ſapiensille Scurra, perquam exiguæ Civitati portas ingentes_
              <lb/>
            _extrnxiſſe_ Nec enim adhuc aliud quàm ad rem aliquanto propiùs eni-
              <lb/>
            timur. </s>
            <s xml:id="echoid-s11076" xml:space="preserve">ad illam.</s>
            <s xml:id="echoid-s11077" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11078" xml:space="preserve">I. </s>
            <s xml:id="echoid-s11079" xml:space="preserve">Hæcadſumimus. </s>
            <s xml:id="echoid-s11080" xml:space="preserve">Si duæ lineæ ( OMO, TMT ) ſeſe con-
              <lb/>
              <note position="right" xlink:label="note-0241-01" xlink:href="note-0241-01a" xml:space="preserve">Fig. 76,
                <lb/>
              77.</note>
            tingant, angulosipſæ comprehendunt ( OMT ) rectilineo quovis an-
              <lb/>
            gulo minores. </s>
            <s xml:id="echoid-s11081" xml:space="preserve">Et vice versâ: </s>
            <s xml:id="echoid-s11082" xml:space="preserve">Si duæ lineæ ( OMO. </s>
            <s xml:id="echoid-s11083" xml:space="preserve">TMT ) an-
              <lb/>
            gulos contineant quovis rectilineo minores, illæ ſeſe contingent _(_con-
              <lb/>
            tingentibus ſaltem æquipollebunt_)_.</s>
            <s xml:id="echoid-s11084" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11085" xml:space="preserve">Hujus _effati_ rationem jampridem _(_ni fallor_)_ attigimus.</s>
            <s xml:id="echoid-s11086" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11087" xml:space="preserve">II. </s>
            <s xml:id="echoid-s11088" xml:space="preserve">Hinc; </s>
            <s xml:id="echoid-s11089" xml:space="preserve">Si duas lineas OMO, TMT tertia quæpiam linea
              <lb/>
            PM P contingat, ipſæ etiam lineæ OMO, TMT ſeſe contin-
              <lb/>
            gent.</s>
            <s xml:id="echoid-s11090" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11091" xml:space="preserve">Nam quoniam lineæ OMO, PM P ſeſe contingunt, erit angulus
              <lb/>
            OM P quovis _rectilineo_ minor. </s>
            <s xml:id="echoid-s11092" xml:space="preserve">Item, ob linearum TMT, PMP
              <lb/>
            _contractum_, erit _angulus_ TM P quovis etiam _rectilineo_ minor. </s>
            <s xml:id="echoid-s11093" xml:space="preserve">Erit
              <lb/>
            igitur angulus TMO _rectilineo_ quovis minor. </s>
            <s xml:id="echoid-s11094" xml:space="preserve">Unde lineæ OMO,
              <lb/>
            TMT ſe mutuo contingent.</s>
            <s xml:id="echoid-s11095" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11096" xml:space="preserve">III. </s>
            <s xml:id="echoid-s11097" xml:space="preserve">Tangat recta FA curvam FX in F; </s>
            <s xml:id="echoid-s11098" xml:space="preserve">ſitque poſitione data recta
              <lb/>
            FE; </s>
            <s xml:id="echoid-s11099" xml:space="preserve">ſint item duæ curvæ EY, EZ tales, ut ductâ utcunque rectâ
              <lb/>
              <note position="right" xlink:label="note-0241-02" xlink:href="note-0241-02a" xml:space="preserve">Fig 78.</note>
            IL ad EF parallelâ ( quæ lineas expoſitas ſecet, ut vides ) ſit ſemper
              <lb/>
            intercepta KL æqualis interceptæ I G; </s>
            <s xml:id="echoid-s11100" xml:space="preserve">etiam curvæ EY, EZ ſeſe
              <lb/>
            contingent.</s>
            <s xml:id="echoid-s11101" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11102" xml:space="preserve">Si non tangant, poteſt inter ipſas conſtitui angulus rectilineus, puta
              <lb/>
            BEC; </s>
            <s xml:id="echoid-s11103" xml:space="preserve">hunc utcunque ſecet ad FE parallela I L; </s>
            <s xml:id="echoid-s11104" xml:space="preserve">ſumatúrque G H
              <lb/>
            = BC, & </s>
            <s xml:id="echoid-s11105" xml:space="preserve">connectatur F H; </s>
            <s xml:id="echoid-s11106" xml:space="preserve">ſunt igitur è parallelis ad FE à </s>
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