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-div568" type="section" level="1" n="93">
          <pb o="142" file="0320" n="335" rhead=""/>
        </div>
        <div xml:id="echoid-div569" type="section" level="1" n="94">
          <head xml:id="echoid-head97" style="it" xml:space="preserve">Series undecima.</head>
          <p>
            <s xml:id="echoid-s15801" xml:space="preserve">{_cc_/_a_} - _b_ - _a_ = _n_.</s>
            <s xml:id="echoid-s15802" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15803" xml:space="preserve">_cc_ - _ba_ - _aa_ = _nn_.</s>
            <s xml:id="echoid-s15804" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15805" xml:space="preserve">_cca_ - _baa_ - _a_
              <emph style="sub">3</emph>
            = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15806" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15807" xml:space="preserve">_ccaa_ - _ba_
              <emph style="sub">3</emph>
            - _a_
              <emph style="sub">4</emph>
            = _n_
              <emph style="sub">4</emph>
            , &</s>
            <s xml:id="echoid-s15808" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15809" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15810" xml:space="preserve">In recta BAH ſumatur BA = _b_; </s>
            <s xml:id="echoid-s15811" xml:space="preserve">& </s>
            <s xml:id="echoid-s15812" xml:space="preserve">in AD ad AH perpendi-
              <lb/>
              <note position="left" xlink:label="note-0320-01" xlink:href="note-0320-01a" xml:space="preserve">Fig. 216.</note>
            culari ſit AC = _c_; </s>
            <s xml:id="echoid-s15813" xml:space="preserve">ſintque anguli HAR, HBS ſemirecti; </s>
            <s xml:id="echoid-s15814" xml:space="preserve">tum
              <lb/>
            utcunque ductâ GK ξ ad AH perpendiculari (quæ ipſam BS
              <lb/>
            ſecet in ξ; </s>
            <s xml:id="echoid-s15815" xml:space="preserve">ſit AG. </s>
            <s xml:id="echoid-s15816" xml:space="preserve">AC:</s>
            <s xml:id="echoid-s15817" xml:space="preserve">: AC. </s>
            <s xml:id="echoid-s15818" xml:space="preserve">ξK; </s>
            <s xml:id="echoid-s15819" xml:space="preserve">& </s>
            <s xml:id="echoid-s15820" xml:space="preserve">per K intra _aſymptotos_
              <lb/>
            VD, VS deſcribatur _hyperbola_ KYHK; </s>
            <s xml:id="echoid-s15821" xml:space="preserve">ſint demum curvæ CLHLλ,
              <lb/>
            AMHMμ, ANHNν tales, ut inter AG (vel GZ) & </s>
            <s xml:id="echoid-s15822" xml:space="preserve">GK ſint _me_-
              <lb/>
            _dia_ GL, _bimedia_ GM, _trimedia_ GN; </s>
            <s xml:id="echoid-s15823" xml:space="preserve">hæ propoſito ſervient. </s>
            <s xml:id="echoid-s15824" xml:space="preserve">id
              <lb/>
            quod conſtat, ut in præcedentibus.</s>
            <s xml:id="echoid-s15825" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div571" type="section" level="1" n="95">
          <head xml:id="echoid-head98" style="it" xml:space="preserve">Not.</head>
          <p>
            <s xml:id="echoid-s15826" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15827" xml:space="preserve">Curvæ HLλ, HMμ, HNν ad decimam ſeriem pertinent;
              <lb/>
            </s>
            <s xml:id="echoid-s15828" xml:space="preserve">reliquæ CLH, AMH, ANH ad undecimam.</s>
            <s xml:id="echoid-s15829" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15830" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15831" xml:space="preserve">Curva HL λ eſt _hyperbola æquilatera_, & </s>
            <s xml:id="echoid-s15832" xml:space="preserve">curva CLH _circula_-
              <lb/>
            _ris circumferentiæ_ pars; </s>
            <s xml:id="echoid-s15833" xml:space="preserve">utriuſque commune centrum eſt O, ipſam AB
              <lb/>
            biſecans (unde AH = √{_bb_/4} + _cc_: </s>
            <s xml:id="echoid-s15834" xml:space="preserve">- {_b_/2})</s>
          </p>
          <p>
            <s xml:id="echoid-s15835" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15836" xml:space="preserve">In decima ſerie radix una ſemper habetur, & </s>
            <s xml:id="echoid-s15837" xml:space="preserve">unica; </s>
            <s xml:id="echoid-s15838" xml:space="preserve">in undeci-
              <lb/>
            ma nunc duæ, nunc una, ſubinde nulla.</s>
            <s xml:id="echoid-s15839" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15840" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15841" xml:space="preserve">Aφ = {_cc_/_b_}; </s>
            <s xml:id="echoid-s15842" xml:space="preserve">& </s>
            <s xml:id="echoid-s15843" xml:space="preserve">Aψ = √{_bb_/16} + {_cc_/2}: </s>
            <s xml:id="echoid-s15844" xml:space="preserve">- {_b_/4}; </s>
            <s xml:id="echoid-s15845" xml:space="preserve">& </s>
            <s xml:id="echoid-s15846" xml:space="preserve">ordinentur
              <lb/>
            φ Y, ψ X; </s>
            <s xml:id="echoid-s15847" xml:space="preserve">puncta Y, X ſunt nodi curvarum.</s>
            <s xml:id="echoid-s15848" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15849" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15850" xml:space="preserve">In undecimæ ſecundo gradu ordinata AC eſt maxìma; </s>
            <s xml:id="echoid-s15851" xml:space="preserve">ſin AP
              <lb/>
            = √{_bb_/9} + {_cc_/3}: </s>
            <s xml:id="echoid-s15852" xml:space="preserve">- {_b_/3}; </s>
            <s xml:id="echoid-s15853" xml:space="preserve">& </s>
            <s xml:id="echoid-s15854" xml:space="preserve">à P ad curvam AMH ordinetur Pγ,
              <lb/>
            hæc maxima erit; </s>
            <s xml:id="echoid-s15855" xml:space="preserve">item ſi AQ = √{9_bb_/64} + {_cc_/2}: </s>
            <s xml:id="echoid-s15856" xml:space="preserve">- {3_b_/8}; </s>
            <s xml:id="echoid-s15857" xml:space="preserve">& </s>
            <s xml:id="echoid-s15858" xml:space="preserve"/>
          </p>
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