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-div571" type="section" level="1" n="95">
          <p>
            <s xml:id="echoid-s15858" xml:space="preserve">
              <pb o="143" file="0321" n="336" rhead=""/>
            Qad curvam AN H ordinetur Q δ, hæc etiam maxima erit; </s>
            <s xml:id="echoid-s15859" xml:space="preserve">unde
              <lb/>
            de radicum limitibus fiet judicium; </s>
            <s xml:id="echoid-s15860" xml:space="preserve">ut in iis, quæ ad ſeriem octavam
              <lb/>
            ſunt adnotata.</s>
            <s xml:id="echoid-s15861" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div572" type="section" level="1" n="96">
          <head xml:id="echoid-head99" style="it" xml:space="preserve">Series duodecima</head>
          <note position="right" xml:space="preserve">Fig. 217</note>
          <p>
            <s xml:id="echoid-s15862" xml:space="preserve">_a_ - _b_ + {_cc_/_a_} = _n_.</s>
            <s xml:id="echoid-s15863" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15864" xml:space="preserve">_aa_ - _ba_ + _cc_ = _nn_.</s>
            <s xml:id="echoid-s15865" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15866" xml:space="preserve">_a
              <emph style="sub">3</emph>
            _ - _baa_ + _cca_ = _n
              <emph style="sub">3</emph>
            _.</s>
            <s xml:id="echoid-s15867" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15868" 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-s15869" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15870" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div573" type="section" level="1" n="97">
          <head xml:id="echoid-head100" style="it" xml:space="preserve">Series decima tertia</head>
          <p>
            <s xml:id="echoid-s15871" xml:space="preserve">_b_ - _a_ - {_cc_/_a_} = _n_.</s>
            <s xml:id="echoid-s15872" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15873" xml:space="preserve">_ba_ - _aa_ - _cc_ = _nn_.</s>
            <s xml:id="echoid-s15874" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15875" xml:space="preserve">_baa_ - _a
              <emph style="sub">3</emph>
            _ - _cca_ = _n
              <emph style="sub">3</emph>
            _.</s>
            <s xml:id="echoid-s15876" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15877" xml:space="preserve">_ba
              <emph style="sub">3</emph>
            _ - _a
              <emph style="sub">4</emph>
            _ - _ccaa_=_n
              <emph style="sub">4</emph>
            _, &</s>
            <s xml:id="echoid-s15878" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15879" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15880" xml:space="preserve">Pro his, Sit AB=_b_; </s>
            <s xml:id="echoid-s15881" xml:space="preserve">& </s>
            <s xml:id="echoid-s15882" xml:space="preserve">AC = _c_; </s>
            <s xml:id="echoid-s15883" xml:space="preserve">& </s>
            <s xml:id="echoid-s15884" xml:space="preserve">angulus. </s>
            <s xml:id="echoid-s15885" xml:space="preserve">AB S ſemire-
              <lb/>
              <note position="right" xlink:label="note-0321-02" xlink:href="note-0321-02a" xml:space="preserve">Fig. 217.</note>
            ctus, & </s>
            <s xml:id="echoid-s15886" xml:space="preserve">G ξ ad AB utcunque perpendicularis, & </s>
            <s xml:id="echoid-s15887" xml:space="preserve">AG . </s>
            <s xml:id="echoid-s15888" xml:space="preserve">AC :</s>
            <s xml:id="echoid-s15889" xml:space="preserve">: AC.
              <lb/>
            </s>
            <s xml:id="echoid-s15890" xml:space="preserve">ξ K; </s>
            <s xml:id="echoid-s15891" xml:space="preserve">& </s>
            <s xml:id="echoid-s15892" xml:space="preserve">KH KI K _byperbola aſymptotis_ SA , SB deſcripta; </s>
            <s xml:id="echoid-s15893" xml:space="preserve">denuò
              <lb/>
            curvæ CLHLILλ, AMHMIMμ, ANHNINν tales ſint, ut inter AG,
              <lb/>
            GK ſit _media_ GL , _bimedia_ GM , _trimedia_ GN .</s>
            <s xml:id="echoid-s15894" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div575" type="section" level="1" n="98">
          <head xml:id="echoid-head101" style="it" xml:space="preserve">Not.</head>
          <p>
            <s xml:id="echoid-s15895" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15896" xml:space="preserve">Curvæ CLH, AMH, ANH, atque curvæ IL λ, IM μ,
              <lb/>
            IN ν ad ſeriem duodecimam ſpectant, verùm intermediæ curvæ HLI,
              <lb/>
            HMI, HNI ad decimam tertiam.</s>
            <s xml:id="echoid-s15897" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15898" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15899" xml:space="preserve">Curvæ CLH, IL λ ſunt _hyperbolæ æquilateræ_, quarum com-
              <lb/>
            mune _centrum_ O (rectam AB biſecans) & </s>
            <s xml:id="echoid-s15900" xml:space="preserve">_ſemiaxis_ OH (vel OI)
              <lb/>
            = √ AO q. </s>
            <s xml:id="echoid-s15901" xml:space="preserve">- AC q reliquæ tales ſunt, quales figura monſtrat.</s>
            <s xml:id="echoid-s15902" xml:space="preserve"/>
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