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-div555" type="section" level="1" n="84">
          <p>
            <s xml:id="echoid-s15544" xml:space="preserve">
              <pb o="137" file="0315" n="330" rhead=""/>
            in quarto _a_ + {_cc_/4_a_}&</s>
            <s xml:id="echoid-s15545" xml:space="preserve">gt;_</s>
            <s xml:id="echoid-s15546" xml:space="preserve">n_; </s>
            <s xml:id="echoid-s15547" xml:space="preserve">quæ tamen inæqualitas eo minor eſt, quò
              <lb/>
            AE (vel _n_) major exiſtit.</s>
            <s xml:id="echoid-s15548" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15549" xml:space="preserve">_a_ + {_cc_/_a_} = _n_.</s>
            <s xml:id="echoid-s15550" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15551" xml:space="preserve">_a_ + {_cc_/_a_} = {_nn_/_a_}.</s>
            <s xml:id="echoid-s15552" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15553" xml:space="preserve">_a_ + {_cc_/_a_} = {_n_
              <emph style="sub">3</emph>
            /_aa_}.</s>
            <s xml:id="echoid-s15554" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15555" xml:space="preserve">_a_ + {_cc_/_a_} = {_n_
              <emph style="sub">4</emph>
            /_a_
              <emph style="sub">3</emph>
            }.</s>
            <s xml:id="echoid-s15556" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15557" xml:space="preserve">Poſſit hæc ſeries explicari juxta præcedentium modum ſecundum,
              <lb/>
              <note position="right" xlink:label="note-0315-01" xlink:href="note-0315-01a" xml:space="preserve">Fig. 212.</note>
            & </s>
            <s xml:id="echoid-s15558" xml:space="preserve">eaſdem adhibendo curvas LXL, MXM, NXN; </s>
            <s xml:id="echoid-s15559" xml:space="preserve">quarum nimi-
              <lb/>
            rum proprietas eſt, ut rectâ GK ductâ ad AH utcunque perpendicu-
              <lb/>
            lari, ſit GL = {_nn_/AG}; </s>
            <s xml:id="echoid-s15560" xml:space="preserve">& </s>
            <s xml:id="echoid-s15561" xml:space="preserve">GM = {_n_
              <emph style="sub">3</emph>
            /AGq}; </s>
            <s xml:id="echoid-s15562" xml:space="preserve">& </s>
            <s xml:id="echoid-s15563" xml:space="preserve">GN = {_n_
              <emph style="sub">4</emph>
            /AGcub}.</s>
            <s xml:id="echoid-s15564" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15565" xml:space="preserve">Nam ſi fiat angulus HAR ſemirectus, & </s>
            <s xml:id="echoid-s15566" xml:space="preserve">utcunque ducatur GEO
              <lb/>
            ad AH perpendicularis; </s>
            <s xml:id="echoid-s15567" xml:space="preserve">& </s>
            <s xml:id="echoid-s15568" xml:space="preserve">ſit GE. </s>
            <s xml:id="echoid-s15569" xml:space="preserve">_c_:</s>
            <s xml:id="echoid-s15570" xml:space="preserve">:_c_. </s>
            <s xml:id="echoid-s15571" xml:space="preserve">EO; </s>
            <s xml:id="echoid-s15572" xml:space="preserve">& </s>
            <s xml:id="echoid-s15573" xml:space="preserve">per O intra a-
              <lb/>
            ſymptotos AD, AR deſcribatur _hyperbola_ OO; </s>
            <s xml:id="echoid-s15574" xml:space="preserve">hujuſce cum expo-
              <lb/>
            ſitis lineis LXL, MXM, NXN interſectiones, radices _a_ reſpectivas
              <lb/>
            determinabunt; </s>
            <s xml:id="echoid-s15575" xml:space="preserve">ductis utique LG, MG, NG ad AH perpendicu-
              <lb/>
            laribus; </s>
            <s xml:id="echoid-s15576" xml:space="preserve">erunt interceptæ AG ipſis _a_ æquales reſpectivè.</s>
            <s xml:id="echoid-s15577" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15578" xml:space="preserve">Poſſint conſimili modo ſubſequentes omnes æquationes explicari;
              <lb/>
            </s>
            <s xml:id="echoid-s15579" xml:space="preserve">ſed eas modo duntaxat priore dabimus expoſitas.</s>
            <s xml:id="echoid-s15580" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div557" type="section" level="1" n="85">
          <head xml:id="echoid-head88" style="it" xml:space="preserve">Series quinta.</head>
          <note position="right" xml:space="preserve">Fig. 213.</note>
          <p>
            <s xml:id="echoid-s15581" xml:space="preserve">{_cc_/_a_} - _a_ = _n_.</s>
            <s xml:id="echoid-s15582" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15583" xml:space="preserve">_cc_ - _aa_ = _nn_.</s>
            <s xml:id="echoid-s15584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15585" xml:space="preserve">_cca_ - _a_
              <emph style="sub">3</emph>
            = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15586" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15587" xml:space="preserve">_ccaa_ - _a_
              <emph style="sub">4</emph>
            = _n_
              <emph style="sub">4</emph>
            .</s>
            <s xml:id="echoid-s15588" xml:space="preserve"/>
          </p>
        </div>
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