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-div399" type="section" level="1" n="42">
          <pb o="101" file="0279" n="294" rhead=""/>
          <p>
            <s xml:id="echoid-s13581" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s13582" xml:space="preserve">Nè ſpeculatio præſens, _ob bujuſmodi complures metbodos Cy-_
              <lb/>
            _clometricas indies promulgatas_, aſpernanda videatur, adjungemus con-
              <lb/>
            ſectarium unum vel alterum, quibus fortè ſolis hæc paucula meruerant
              <lb/>
              <note position="right" xlink:label="note-0279-01" xlink:href="note-0279-01a" xml:space="preserve">Fig. 148.</note>
            impendi; </s>
            <s xml:id="echoid-s13583" xml:space="preserve">à quibus nempe _Maxima, Minimaque_ ſui generis innume-
              <lb/>
            ra determinantur.</s>
            <s xml:id="echoid-s13584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13585" xml:space="preserve">Sit _Semicirculus_ ABZ, cujus centrum C; </s>
            <s xml:id="echoid-s13586" xml:space="preserve">ſitque _ſegmentum
              <unsure/>
            _
              <lb/>
            ADB; </s>
            <s xml:id="echoid-s13587" xml:space="preserve">& </s>
            <s xml:id="echoid-s13588" xml:space="preserve">huic adſcripta _paraboliformis_ AFB, cujus exponens {_u_/_m_};
              <lb/>
            </s>
            <s xml:id="echoid-s13589" xml:space="preserve">ſit item AD = {_m_ - 2 _n_/_m_ - _n_} CA; </s>
            <s xml:id="echoid-s13590" xml:space="preserve">_paraboliform@s_ autem _parameter_ (hoc
              <lb/>
            eſt recta, cujus aliqua poteſtas in poteſtatem ſegmenti axis, ſeu AD,
              <lb/>
            ducta conficit _poteſtatem_ ordinatæ, ceu D B) nominetur _p_; </s>
            <s xml:id="echoid-s13591" xml:space="preserve">erit _p_ in ſuo
              <lb/>
            genere _maximum_.</s>
            <s xml:id="echoid-s13592" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13593" xml:space="preserve">Nam utcunque ducatur GE ad DB parallela, & </s>
            <s xml:id="echoid-s13594" xml:space="preserve">ad GE poſita
              <lb/>
            concipiatur _paraboliformis_, ipſi AFB coordinata, cujus _parameter_ di-
              <lb/>
            catur _q_. </s>
            <s xml:id="echoid-s13595" xml:space="preserve">quum ergò _paraboliformis_ AFB _circulum_ extrorſum contin-
              <lb/>
            gat, erit GF &</s>
            <s xml:id="echoid-s13596" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13597" xml:space="preserve">GE; </s>
            <s xml:id="echoid-s13598" xml:space="preserve">adeóque GF {_m_/ } &</s>
            <s xml:id="echoid-s13599" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13600" xml:space="preserve">GE {_m_/ }; </s>
            <s xml:id="echoid-s13601" xml:space="preserve">hoc eſt _p_ {_m_ - _n_/ } x
              <lb/>
            AG {_n_/ } &</s>
            <s xml:id="echoid-s13602" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13603" xml:space="preserve">q {_m_ - _n_/ } x AG {_n_/ }; </s>
            <s xml:id="echoid-s13604" xml:space="preserve">quare _p_ &</s>
            <s xml:id="echoid-s13605" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13606" xml:space="preserve">_q_.</s>
            <s xml:id="echoid-s13607" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13608" xml:space="preserve">Notandum eſt eſſe _p_ {2 _m_ - 2 _n_/ } = ZD
              <emph style="sub">_m_</emph>
            x AD {_m_ - 2 _n_/ }. </s>
            <s xml:id="echoid-s13609" xml:space="preserve">& </s>
            <s xml:id="echoid-s13610" xml:space="preserve">q {2 _m_ - 2 _n_/ }
              <lb/>
            = ZG {_m_/ } x AG {_m_ - 2 _n_/ }. </s>
            <s xml:id="echoid-s13611" xml:space="preserve">unde ZD {_m_/ } x AD {_m_ - 2 _n_/ } &</s>
            <s xml:id="echoid-s13612" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13613" xml:space="preserve">ZG {_m_/ } x AG {_m_ - 2 _n_/ }.
              <lb/>
            </s>
            <s xml:id="echoid-s13614" xml:space="preserve">quare ZD {_m_/ } x AD {_m_ - 2 _n_/ } eſt maximum.</s>
            <s xml:id="echoid-s13615" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13616" xml:space="preserve">Exemp. </s>
            <s xml:id="echoid-s13617" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13618" xml:space="preserve">Sit _n_ = 1, & </s>
            <s xml:id="echoid-s13619" xml:space="preserve">_m_ = 3. </s>
            <s xml:id="echoid-s13620" xml:space="preserve">erit ideò _p_ {4/ } = ZD {3/ } x AD =
              <lb/>
            ZD_q_ x BD_q_; </s>
            <s xml:id="echoid-s13621" xml:space="preserve">vel _p_
              <emph style="sub">2</emph>
            = ZD x BD. </s>
            <s xml:id="echoid-s13622" xml:space="preserve">Item AD =
              <lb/>
            {1/2} CA.</s>
            <s xml:id="echoid-s13623" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13624" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13625" xml:space="preserve">Sit _n_ = 3, & </s>
            <s xml:id="echoid-s13626" xml:space="preserve">_m_ = 10. </s>
            <s xml:id="echoid-s13627" xml:space="preserve">erit p {14/ } = ZD
              <emph style="sub">10</emph>
            x AD
              <emph style="sub">4</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s13628" xml:space="preserve">vel p {7/ } = ZD {5/ } x AD
              <emph style="sub">2</emph>
            = ZD
              <emph style="sub">3</emph>
            x BD
              <emph style="sub">4</emph>
            . </s>
            <s xml:id="echoid-s13629" xml:space="preserve">& </s>
            <s xml:id="echoid-s13630" xml:space="preserve">AD
              <lb/>
            = {4/7} CA.</s>
            <s xml:id="echoid-s13631" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13632" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s13633" xml:space="preserve">Sit item _hyperbola_ (æquilatera) cujus centrum C, axis
              <lb/>
            ZA; </s>
            <s xml:id="echoid-s13634" xml:space="preserve">& </s>
            <s xml:id="echoid-s13635" xml:space="preserve">huic inſcripta _paraboliformis_ AFB cujus expo-
              <lb/>
              <note position="right" xlink:label="note-0279-02" xlink:href="note-0279-02a" xml:space="preserve">Fig. 149.</note>
            nens {_n_/_m_} _parameter p_; </s>
            <s xml:id="echoid-s13636" xml:space="preserve">ſitque AD = {2_n_ - _m_/_m_ - _n_} CA; </s>
            <s xml:id="echoid-s13637" xml:space="preserve">erit _p_ ſui gene-
              <lb/>
            neris maximum.</s>
            <s xml:id="echoid-s13638" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13639" xml:space="preserve">Nam utcunque ducatur EG ad BD parallela; </s>
            <s xml:id="echoid-s13640" xml:space="preserve">& </s>
            <s xml:id="echoid-s13641" xml:space="preserve">ad EG conſtituta
              <lb/>
            intelligatur _paraboliformis_, ipſi AFB coordinata, cujus _parameter q._
              <lb/>
            </s>
            <s xml:id="echoid-s13642" xml:space="preserve">quum ergo _paraboliformis_ AFB _hyperbolam_ introrſum contingat,
              <lb/>
            erit GF {_m_/ } &</s>
            <s xml:id="echoid-s13643" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13644" xml:space="preserve">GE {_n_/ }; </s>
            <s xml:id="echoid-s13645" xml:space="preserve">hoc eſt _p_ {_m_ - _n_/ } x AG
              <emph style="sub">n</emph>
            &</s>
            <s xml:id="echoid-s13646" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13647" xml:space="preserve">_q_ {_m_ - _n_/ } x AG
              <emph style="sub">n</emph>
            ; </s>
            <s xml:id="echoid-s13648" xml:space="preserve">
              <lb/>
            quare _p_ &</s>
            <s xml:id="echoid-s13649" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13650" xml:space="preserve">_q_.</s>
            <s xml:id="echoid-s13651" xml:space="preserve"/>
          </p>
        </div>
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