Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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          <p>
            <s xml:id="echoid-s15749" xml:space="preserve">
              <pb o="141" file="0319" n="334" rhead=""/>
            {_cc_/3}, ac ordinetur PV ad curvam AMH, erit PV maxima; </s>
            <s xml:id="echoid-s15750" xml:space="preserve">item ſi
              <lb/>
            AQ = {3/8}_b_ + √{9/64}_bb_ + {_cc_/2}, & </s>
            <s xml:id="echoid-s15751" xml:space="preserve">ordinetur QX ad curvam ANH
              <lb/>
            erit QX maxima.</s>
            <s xml:id="echoid-s15752" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15753" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15754" xml:space="preserve">Hinc, ſi in ſecundo harum gradu ſit _n_&</s>
            <s xml:id="echoid-s15755" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15756" xml:space="preserve">√ _cc_ + {_bb_/4}; </s>
            <s xml:id="echoid-s15757" xml:space="preserve">in ter-
              <lb/>
            tio ſi (poſito fore f = {_b_/3} + √{_bb_/9} + {_cc_/3}) ſit _n_
              <emph style="sub">3</emph>
            &</s>
            <s xml:id="echoid-s15758" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15759" xml:space="preserve">_ccf_ + _bff_
              <lb/>
            - _f_
              <emph style="sub">3</emph>
            ; </s>
            <s xml:id="echoid-s15760" xml:space="preserve">in quarto, ſi (poſito fore _g_ = {3/8}_b_ + √{9/64}_bb_ + {_cc_/2}) ſit _n_
              <emph style="sub">4</emph>
              <lb/>
            &</s>
            <s xml:id="echoid-s15761" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15762" xml:space="preserve">_ccgg_ + _bg_
              <emph style="sub">3</emph>
            - _g_
              <emph style="sub">4</emph>
            ; </s>
            <s xml:id="echoid-s15763" xml:space="preserve">nulla datur radix; </s>
            <s xml:id="echoid-s15764" xml:space="preserve">nam his ſupp ſitis,
              <lb/>
            recta EF curvis non occurret, reſpectivè.</s>
            <s xml:id="echoid-s15765" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15766" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15767" xml:space="preserve">Si fuerit Aφ = {_b_/4} + √{_bb_/16} + {_cc_/2}, & </s>
            <s xml:id="echoid-s15768" xml:space="preserve">ordinetur φ Y; </s>
            <s xml:id="echoid-s15769" xml:space="preserve">erit Y
              <lb/>
            _Nodus_ curvarum; </s>
            <s xml:id="echoid-s15770" xml:space="preserve">unde ſi _n_ = Aφ; </s>
            <s xml:id="echoid-s15771" xml:space="preserve">erit Aφ una radicum in omni-
              <lb/>
            bus.</s>
            <s xml:id="echoid-s15772" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15773" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15774" xml:space="preserve">Curva CLH, eſt _circumferentia Circuli_, cujus _Centrum_ O;
              <lb/>
            </s>
            <s xml:id="echoid-s15775" xml:space="preserve">reliquæ AMH, ANH ſunt _Cycliformes_.</s>
            <s xml:id="echoid-s15776" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15777" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15778" xml:space="preserve">Peculiare eſt in ſecundo gradu, quòd ſi n&</s>
            <s xml:id="echoid-s15779" xml:space="preserve">lt;</s>
            <s xml:id="echoid-s15780" xml:space="preserve">c, detur una tan-
              <lb/>
            tùm radix.</s>
            <s xml:id="echoid-s15781" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15782" xml:space="preserve">7. </s>
            <s xml:id="echoid-s15783" xml:space="preserve">In hac radicum maxima (quæ & </s>
            <s xml:id="echoid-s15784" xml:space="preserve">minima eſt in nona ſerie) eſt
              <lb/>
            AH = {_b_/2} + √{_bb_/4} + _cc_.</s>
            <s xml:id="echoid-s15785" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15786" xml:space="preserve">8. </s>
            <s xml:id="echoid-s15787" xml:space="preserve">Curva HL λ eſt _hyperbola æquilatera_, cujus _ſemiaxis_ OH; </s>
            <s xml:id="echoid-s15788" xml:space="preserve">re-
              <lb/>
            liquæ HMμ, HNν ſunt _hyperboliformes_; </s>
            <s xml:id="echoid-s15789" xml:space="preserve">unde patet in ſerie nona
              <lb/>
            ſemper unam, & </s>
            <s xml:id="echoid-s15790" xml:space="preserve">hanc unicam radicem haberi.</s>
            <s xml:id="echoid-s15791" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div568" type="section" level="1" n="93">
          <head xml:id="echoid-head96" style="it" xml:space="preserve">Series decima.</head>
          <note position="right" xml:space="preserve">Fig. 216.</note>
          <p>
            <s xml:id="echoid-s15792" xml:space="preserve">_a_ + _b_ - {_cc_/_a_} = _n_.</s>
            <s xml:id="echoid-s15793" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15794" xml:space="preserve">_aa_ + _ba_ - _cc_ = _nn_.</s>
            <s xml:id="echoid-s15795" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15796" xml:space="preserve">_a_
              <emph style="sub">3</emph>
            + _baa_ - _cca_ = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15797" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15798" xml:space="preserve">_a_
              <emph style="sub">4</emph>
            + _ba_
              <emph style="sub">3</emph>
            -_ccaa_ = _n_
              <emph style="sub">4</emph>
            , &</s>
            <s xml:id="echoid-s15799" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15800" xml:space="preserve"/>
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