Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Page concordance

< >
Scan Original
291 98
292 99
293 100
294 101
295 102
296 103
297 104
298 105
299 106
300 107
301 108
302 109
303 110
304 111
305 112
306 113
307 114
308 115
309 116
310 117
311 118
312 119
313 120
314 121
315 122
316 123
317 124
318 125
319 126
320 127
< >
page |< < (101) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <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>
      </text>
    </echo>
Impressum