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-div189" type="section" level="1" n="23">
          <p>
            <s xml:id="echoid-s7706" xml:space="preserve">
              <pb o="117" file="0135" n="135" rhead=""/>
            ſuggerens haud aſpernanda. </s>
            <s xml:id="echoid-s7707" xml:space="preserve">relinquantur igitur ei cætera, mihi
              <lb/>
            ſuffecerit, quòd veriorem _phænomena{εμ}
              <unsure/>
            _ detegendi declarandíque me-
              <lb/>
            thodum adniſus ſim aliquatenus enucleare. </s>
            <s xml:id="echoid-s7708" xml:space="preserve">pergamus ad alios caſus,
              <lb/>
            haud ità pertractatos.</s>
            <s xml:id="echoid-s7709" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7710" xml:space="preserve">XIX Objiciatur ſpeculo MBND recta FAG, rectæ CA (per
              <lb/>
            ſpeculi centrum C tranſeunti) perpendicularis; </s>
            <s xml:id="echoid-s7711" xml:space="preserve">adverto, ſi fuerit ipſa
              <lb/>
              <note position="right" xlink:label="note-0135-01" xlink:href="note-0135-01a" xml:space="preserve">Fig. 189.</note>
            CA major quàm CZ, quadrans diametri BD, quòd rectæ FAG
              <lb/>
            ad infinitum utrinque protractæ ad totum circulum (ejus ad partes
              <lb/>
            intelligo concavas ſimul acconvexas) imago abſoluta (quinetiam ima-
              <lb/>
            go ad oculum in ipſo centro C conſtitutum relata) erit _Ellipſis_. </s>
            <s xml:id="echoid-s7712" xml:space="preserve">item
              <lb/>
            ſi CA minor ſit, quàm CZ, quòd ipſius FA G imago abſoluta
              <lb/>
            (vel dicto modo relata) conſtabit ex hyperbolis oppoſitis; </s>
            <s xml:id="echoid-s7713" xml:space="preserve">ſi denuò
              <lb/>
            CA ipſam CZ adæquet (vel FG per ipſum Z tranſeat) quòd ad
              <lb/>
            parabolam ejuſmodi conſiſtet imago. </s>
            <s xml:id="echoid-s7714" xml:space="preserve">Sed modum tranſgrederer hæc
              <lb/>
            jam aggrediens demonſtrare. </s>
            <s xml:id="echoid-s7715" xml:space="preserve">Expectent igitur.</s>
            <s xml:id="echoid-s7716" xml:space="preserve">‖</s>
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        <div xml:id="echoid-div199" type="section" level="1" n="24">
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            <emph style="sc">Lect.</emph>
          XVII.</head>
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            <s xml:id="echoid-s7717" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7718" xml:space="preserve">ADea, quæ ſub finitam præcedentem propoſuimus demon-
              <lb/>
            ſtranda _neceſſariam, alioquin notabilem, Conicarum Sectionum_
              <lb/>
            _proprietatem_ imprimìs oſtendemus.</s>
            <s xml:id="echoid-s7719" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7720" xml:space="preserve">Sit triangulum ACE, rectum habens angulum ad C; </s>
            <s xml:id="echoid-s7721" xml:space="preserve">& </s>
            <s xml:id="echoid-s7722" xml:space="preserve">inde-
              <lb/>
              <note position="right" xlink:label="note-0135-02" xlink:href="note-0135-02a" xml:space="preserve">Fig. 190.</note>
            finitè protractis lateribus AC, AE, in AC ſumatur quod piam pun-
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            ctum X, ducatúrque XG ad CE parallela; </s>
            <s xml:id="echoid-s7723" xml:space="preserve">inſeratur autem angulo
              <lb/>
            CXG recta CZ æqualis ipſi XG; </s>
            <s xml:id="echoid-s7724" xml:space="preserve">dico punctum indeterminatum Z ad
              <lb/>
            ſectionum conicarum aliquam conſiſtere.</s>
            <s xml:id="echoid-s7725" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7726" xml:space="preserve">II. </s>
            <s xml:id="echoid-s7727" xml:space="preserve">Nempe primò, ſit angulus A ſemirecto minor (vel AC &</s>
            <s xml:id="echoid-s7728" xml:space="preserve">gt;
              <lb/>
            </s>
            <s xml:id="echoid-s7729" xml:space="preserve">CE) erit punctum Z ad ellipſin, quæ determinatur hoc pacto: </s>
            <s xml:id="echoid-s7730" xml:space="preserve">An-
              <lb/>
            guli LCP ſemirecti fiant (ad utramque rectæ CE partem) liquet
              <lb/>
            igitur rectas CP ipſi AE occurrere, puta ad puncta R, & </s>
            <s xml:id="echoid-s7731" xml:space="preserve">S. </s>
            <s xml:id="echoid-s7732" xml:space="preserve">ab </s>
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