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-div544" type="section" level="1" n="78">
          <p>
            <s xml:id="echoid-s15325" xml:space="preserve">
              <pb o="133" file="0311" n="326" rhead=""/>
            GZ, GK media GL, bimedia GM, trimedia GN; </s>
            <s xml:id="echoid-s15326" xml:space="preserve">propoſitas æ-
              <lb/>
            quationes explicabunt hæ lineæ. </s>
            <s xml:id="echoid-s15327" xml:space="preserve">Nam ſi AG (vel GZ) vocetur _a_;
              <lb/>
            </s>
            <s xml:id="echoid-s15328" xml:space="preserve">erit BG (vel GK) = _a_ - _b_; </s>
            <s xml:id="echoid-s15329" xml:space="preserve">& </s>
            <s xml:id="echoid-s15330" xml:space="preserve">GLq = _aa_ - _ba_; </s>
            <s xml:id="echoid-s15331" xml:space="preserve">& </s>
            <s xml:id="echoid-s15332" xml:space="preserve">GM cub. </s>
            <s xml:id="echoid-s15333" xml:space="preserve">
              <lb/>
            = _a_
              <emph style="sub">3</emph>
            - _baa_; </s>
            <s xml:id="echoid-s15334" xml:space="preserve">& </s>
            <s xml:id="echoid-s15335" xml:space="preserve">GN _qq_ = _a_
              <emph style="sub">4</emph>
            - _ba_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15336" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div546" type="section" level="1" n="79">
          <head xml:id="echoid-head82" style="it" xml:space="preserve">Not.</head>
          <p>
            <s xml:id="echoid-s15337" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15338" xml:space="preserve">Ductâ AD ad AI perpendiculari, & </s>
            <s xml:id="echoid-s15339" xml:space="preserve">EF ad AI parallelâ, ſi
              <lb/>
            AE ponatur æqualis ipſi _n_; </s>
            <s xml:id="echoid-s15340" xml:space="preserve">erunt EK, EL, EM, EN radices æqua-
              <lb/>
            tionum reſpectivæ, ſeu æquales quæſitis _a_.</s>
            <s xml:id="echoid-s15341" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15342" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15343" xml:space="preserve">Quoniam ordinatæ GK, GL, GM, GN à termino B verſus I
              <lb/>
            infinitè excreſcunt, ſemper habetur una vera radix, & </s>
            <s xml:id="echoid-s15344" xml:space="preserve">unica.</s>
            <s xml:id="echoid-s15345" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15346" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15347" xml:space="preserve">Curva BLL eſt _hyperbola æquilatera_, cujus _axis_ AB, reliquæ
              <lb/>
            curvæ ſunt _hyperboliformes._</s>
            <s xml:id="echoid-s15348" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15349" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15350" xml:space="preserve">Si AB biſecetur in O, triſecetur in P, quadriſecetur in Q, du-
              <lb/>
            cantúrque ad AR parallelæ OT, PV, QX, erunt hæ curvarum BLL,
              <lb/>
            BMM, BNN _aſymptoti._</s>
            <s xml:id="echoid-s15351" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15352" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15353" xml:space="preserve">Hinc ſeqiutur in ſecundo gradu fore _a_ &</s>
            <s xml:id="echoid-s15354" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15355" xml:space="preserve">_n_ + {_b_/2}; </s>
            <s xml:id="echoid-s15356" xml:space="preserve">in tertio
              <lb/>
            _a_ &</s>
            <s xml:id="echoid-s15357" xml:space="preserve">gt;_</s>
            <s xml:id="echoid-s15358" xml:space="preserve">n_ + {_b_/3}; </s>
            <s xml:id="echoid-s15359" xml:space="preserve">in quarto _a_ &</s>
            <s xml:id="echoid-s15360" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15361" xml:space="preserve">_n_ + {_b_/4}; </s>
            <s xml:id="echoid-s15362" xml:space="preserve">quòd ſi _n_ ſatis magna ſit,
              <lb/>
            iſtæ inæqualitates ad æqualitatem proximè accedunt.</s>
            <s xml:id="echoid-s15363" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15364" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15365" xml:space="preserve">Verarum in his radicum habetur _minima;_ </s>
            <s xml:id="echoid-s15366" xml:space="preserve">ſcilicet ipſa AB, vel _b_.</s>
            <s xml:id="echoid-s15367" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div547" type="section" level="1" n="80">
          <head xml:id="echoid-head83" style="it" xml:space="preserve">Series tertia.</head>
          <p>
            <s xml:id="echoid-s15368" xml:space="preserve">_b_ - _a_ = _n_.</s>
            <s xml:id="echoid-s15369" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15370" xml:space="preserve">_ba_ - _aa_ = _nn_.</s>
            <s xml:id="echoid-s15371" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15372" xml:space="preserve">_baa_ - _a_
              <emph style="sub">3</emph>
            = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15373" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15374" xml:space="preserve">_ba_
              <emph style="sub">3</emph>
            -_a_
              <emph style="sub">4</emph>
            = _n_
              <emph style="sub">4</emph>
            . </s>
            <s xml:id="echoid-s15375" xml:space="preserve">&</s>
            <s xml:id="echoid-s15376" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15377" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15378" xml:space="preserve">Sit AB = _b_, & </s>
            <s xml:id="echoid-s15379" xml:space="preserve">anguli RAB, SBA ſemirecti; </s>
            <s xml:id="echoid-s15380" xml:space="preserve">tum curvæ
              <lb/>
              <note position="right" xlink:label="note-0311-01" xlink:href="note-0311-01a" xml:space="preserve">Fig. 280.</note>
            ALB, AMB, ANB tales, ut ductâ rectâ GK ad AB utcunque
              <lb/>
            perpendiculari (quæ lineas expoſitas ſecet, ut vides) ſit inter AG
              <lb/>
            (ſeu GZ) & </s>
            <s xml:id="echoid-s15381" xml:space="preserve">GK _media_ GL, _bimedia_ GM, _trimedia_ GN; </s>
            <s xml:id="echoid-s15382" xml:space="preserve">pro-
              <lb/>
            poſitas æquationes explicatas dabunt hæ lineæ. </s>
            <s xml:id="echoid-s15383" xml:space="preserve">Nam poſito fore AG
              <lb/>
            = _a_, erit GK = _b_ - _a_; </s>
            <s xml:id="echoid-s15384" xml:space="preserve">& </s>
            <s xml:id="echoid-s15385" xml:space="preserve">GLq = _ba_ - _aa_; </s>
            <s xml:id="echoid-s15386" xml:space="preserve">& </s>
            <s xml:id="echoid-s15387" xml:space="preserve">GMq =
              <lb/>
            _baa_ - _a_
              <emph style="sub">3</emph>
            . </s>
            <s xml:id="echoid-s15388" xml:space="preserve">& </s>
            <s xml:id="echoid-s15389" xml:space="preserve">GNq = _ba_
              <emph style="sub">3</emph>
            - _a_
              <emph style="sub">4</emph>
            .</s>
            <s xml:id="echoid-s15390" xml:space="preserve"/>
          </p>
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