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-div549" type="section" level="1" n="81">
          <head xml:id="echoid-head84" style="it" xml:space="preserve">Not.</head>
          <p>
            <s xml:id="echoid-s15391" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15392" xml:space="preserve">Si in AD (ad ipſam AB perpendiculari) deſumatur AE = _n_;
              <lb/>
            </s>
            <s xml:id="echoid-s15393" xml:space="preserve">
              <note position="left" xlink:label="note-0312-01" xlink:href="note-0312-01a" xml:space="preserve">Fig. 208.</note>
            & </s>
            <s xml:id="echoid-s15394" xml:space="preserve">ducatur EF ad AB parallela, hujuſce cum lineis expoſitis interſe-
              <lb/>
            ctiones exhibebunt radices _a_ reſpectivè.</s>
            <s xml:id="echoid-s15395" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15396" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15397" xml:space="preserve">Cum ad haſce curvas ordinatæ ſemper terminatæ ſint, & </s>
            <s xml:id="echoid-s15398" xml:space="preserve">inter
              <lb/>
            ipſas maxima quædam detur, hujus _ſeriei æquationes_, pro modulo aſ-
              <lb/>
            ſignatæ AE (vel _n_) ſubinde duas radices veras habent (cùm utique
              <lb/>
            fuerit AE curvæ maximâ ordinatâ minor reſpectivè, hoc eſt cùm EF
              <lb/>
            curvæ bis occurrerit) nonnunquam duntaxat unam (cum AE nempe
              <lb/>
            maximam adæquet, adeóque EF curvam contingat) aliquando nullam
              <lb/>
            (cum ſcilicet AE maximam excedat, adeoque nec EF curvæ unquam
              <lb/>
            occurrat).</s>
            <s xml:id="echoid-s15399" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15400" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15401" xml:space="preserve">In ſecundo gradu ſi AO = OB, & </s>
            <s xml:id="echoid-s15402" xml:space="preserve">ordinetur OT, erit OT
              <lb/>
            maxima; </s>
            <s xml:id="echoid-s15403" xml:space="preserve">(adeóque radicum una major quàm {AB/2}, altera minor) in
              <lb/>
            tertio, ſi AP = 2 PB, & </s>
            <s xml:id="echoid-s15404" xml:space="preserve">ordinetur PV, erit PV maxima (unde
              <lb/>
            radicum una major erit quàm {1/3} AB, altera minor) demùm in quar-
              <lb/>
            to gradu ſi AQ = 3 QB, & </s>
            <s xml:id="echoid-s15405" xml:space="preserve">ordinetur QX, erit QX _maxima_
              <lb/>
            (& </s>
            <s xml:id="echoid-s15406" xml:space="preserve">hinc una radicum ſemper major, quàm {1/4} AB, & </s>
            <s xml:id="echoid-s15407" xml:space="preserve">altera minor).</s>
            <s xml:id="echoid-s15408" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15409" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15410" xml:space="preserve">Hinc conſectatur, ſi fuerit, in ſecundo gradu n &</s>
            <s xml:id="echoid-s15411" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15412" xml:space="preserve">{_b_/2}; </s>
            <s xml:id="echoid-s15413" xml:space="preserve">in tertio
              <lb/>
            _n_
              <emph style="sub">2</emph>
            &</s>
            <s xml:id="echoid-s15414" xml:space="preserve">gt;</s>
            <s xml:id="echoid-s15415" xml:space="preserve">{4_b_
              <emph style="sub">3</emph>
            /9} - {8_b_
              <emph style="sub">3</emph>
            /27
              <unsure/>
            } = {4 _b_
              <emph style="sub">3</emph>
            /27}; </s>
            <s xml:id="echoid-s15416" xml:space="preserve">in quarto _n_
              <emph style="sub">4</emph>
            &</s>
            <s xml:id="echoid-s15417" xml:space="preserve">gt;</s>
            <s xml:id="echoid-s15418" xml:space="preserve">{27/64}_b_
              <emph style="sub">4</emph>
            - {81/256}_b_
              <emph style="sub">4</emph>
            =
              <lb/>
            {27_b_
              <emph style="sub">4</emph>
            /256}; </s>
            <s xml:id="echoid-s15419" xml:space="preserve">nullam dari radicem.</s>
            <s xml:id="echoid-s15420" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15421" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15422" xml:space="preserve">Omnium radicum _maxima_ eſt ipſa AB, vel _b_.</s>
            <s xml:id="echoid-s15423" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15424" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15425" xml:space="preserve">Omnium curvarum communis _interſectio_ (ſeu _nodus_) eſt pun-
              <lb/>
            ctum T; </s>
            <s xml:id="echoid-s15426" xml:space="preserve">& </s>
            <s xml:id="echoid-s15427" xml:space="preserve">ſi fuerit _n_ = {_b_/2}; </s>
            <s xml:id="echoid-s15428" xml:space="preserve">ſemper AO (vel {_b_/2}) eſt una radix.</s>
            <s xml:id="echoid-s15429" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15430" xml:space="preserve">7. </s>
            <s xml:id="echoid-s15431" xml:space="preserve">Curva ALB eſt _Circulus_, reliquæ AMB, ANB eum quo-
              <lb/>
            dammodo referunt.</s>
            <s xml:id="echoid-s15432" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          1. # 2. # 3.
            <lb/>
          _a_ + _b_ = _n_ \\ _a_ + _b_ = {_nn_/_a_} \\ _a_ + _b_ = {_n_
            <emph style="sub">3</emph>
          /_aa_} \\ _a_ + _b_ = {_n_4
            <emph style="sub">4</emph>
          /_a_
            <emph style="sub">3</emph>
          } # _a_ - _b_ = _n_. \\ _a_ - _b_ = {_nn_/_a_} \\ _a_ - _b_ = {_n_
            <emph style="sub">3</emph>
          /_aa_} \\ _a_ - _b_ = {_n_
            <emph style="sub">4</emph>
          /_a_
            <emph style="sub">3</emph>
          3} # {_b_ - _a_ = _n_. \\ _b_ - _a_ = {_nn_/_a_} \\ _b_ - _a_ = {_n_
            <emph style="sub">3</emph>
          /aa} \\ _b_ - _a_ = {_n_
            <emph style="sub">4</emph>
          /_a_
            <emph style="sub">3</emph>
          }
            <lb/>
          </note>
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