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-div557" type="section" level="1" n="85">
          <pb o="138" file="0316" n="331" rhead=""/>
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        <div xml:id="echoid-div558" type="section" level="1" n="86">
          <head xml:id="echoid-head89" style="it" xml:space="preserve">Series ſexta.</head>
          <p>
            <s xml:id="echoid-s15589" xml:space="preserve">_a_ - {_cc_/_a_} = _x_.</s>
            <s xml:id="echoid-s15590" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15591" xml:space="preserve">_aa_ - _cc_ = _nn_.</s>
            <s xml:id="echoid-s15592" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15593" xml:space="preserve">_a_
              <emph style="sub">3</emph>
            - _cca_ = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15594" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15595" xml:space="preserve">_a_
              <emph style="sub">4</emph>
            - _ccaa_ = _n_
              <emph style="sub">4</emph>
            .</s>
            <s xml:id="echoid-s15596" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15597" xml:space="preserve">Fiat angulus RAI ſemirectus, & </s>
            <s xml:id="echoid-s15598" xml:space="preserve">AD ad AI perpendicularis;
              <lb/>
            </s>
            <s xml:id="echoid-s15599" xml:space="preserve">
              <note position="left" xlink:label="note-0316-01" xlink:href="note-0316-01a" xml:space="preserve">Fig. 213</note>
            in qua AC = _c_; </s>
            <s xml:id="echoid-s15600" xml:space="preserve">tum utcunque ductâ GZ ad AD parallelâ, ſit
              <lb/>
            AG (vel GZ). </s>
            <s xml:id="echoid-s15601" xml:space="preserve">AC:</s>
            <s xml:id="echoid-s15602" xml:space="preserve">: AC. </s>
            <s xml:id="echoid-s15603" xml:space="preserve">ZK, & </s>
            <s xml:id="echoid-s15604" xml:space="preserve">per K, intra angulum DAR
              <lb/>
            deſcribatur _hyperbola_ KYK; </s>
            <s xml:id="echoid-s15605" xml:space="preserve">tum ſint curvæ CLYHLλ, AMYHMμ,
              <lb/>
            ANYHN ν
              <unsure/>
            tales, ut inter AG (vel GZ) & </s>
            <s xml:id="echoid-s15606" xml:space="preserve">GK ſit _media_ GL,
              <lb/>
            _bimedia_ GM, _trimedia_ GN; </s>
            <s xml:id="echoid-s15607" xml:space="preserve">hæ propofito deſervient.</s>
            <s xml:id="echoid-s15608" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15609" xml:space="preserve">Conſtat hoc, ut in præcedente; </s>
            <s xml:id="echoid-s15610" xml:space="preserve">& </s>
            <s xml:id="echoid-s15611" xml:space="preserve">quo pacto radices reſpectivè
              <lb/>
            determinantur. </s>
            <s xml:id="echoid-s15612" xml:space="preserve">Verùm adnotetur prætereà.</s>
            <s xml:id="echoid-s15613" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div560" type="section" level="1" n="87">
          <head xml:id="echoid-head90" style="it" xml:space="preserve">Not.</head>
          <p>
            <s xml:id="echoid-s15614" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15615" xml:space="preserve">Curvæ CLH, AMH, ANH ad quintam ſeriem pertinent; </s>
            <s xml:id="echoid-s15616" xml:space="preserve">re-
              <lb/>
            liquæ HL λ, HM μ, HN ν ad ſextam.</s>
            <s xml:id="echoid-s15617" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15618" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15619" xml:space="preserve">Quoad curvas ad quintam ſeriem pertinentes; </s>
            <s xml:id="echoid-s15620" xml:space="preserve">ſi A φ = √{ACq/2};
              <lb/>
            </s>
            <s xml:id="echoid-s15621" xml:space="preserve">& </s>
            <s xml:id="echoid-s15622" xml:space="preserve">ordinetur φ Y; </s>
            <s xml:id="echoid-s15623" xml:space="preserve">erit Y communis linearum interſectio, ſeu _no_-
              <lb/>
            _dus._</s>
            <s xml:id="echoid-s15624" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15625" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15626" xml:space="preserve">In harum primo gradu ordinata AK eſt inſinita in ſecundo AC
              <lb/>
            eſt maxima; </s>
            <s xml:id="echoid-s15627" xml:space="preserve">in tertio ſi fuerit AP = √{ACq/3}, & </s>
            <s xml:id="echoid-s15628" xml:space="preserve">ordinetur PV,
              <lb/>
            erit PV maxima(unde radicum una ſemper major eſt quam √{ACq/3}
              <lb/>
            altera minor) in quarto ſi AQ = √{ACq/4} = {AC/2}, & </s>
            <s xml:id="echoid-s15629" xml:space="preserve">ordinetur QX,
              <lb/>
            erit QX maxima (unde radicum una major erit, altera minor ipsâ
              <lb/>
            {AC/2}).</s>
            <s xml:id="echoid-s15630" xml:space="preserve"/>
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