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-div480" type="section" level="1" n="47">
          <p>
            <s xml:id="echoid-s14675" xml:space="preserve">
              <pb o="118" file="0296" n="311" rhead=""/>
            dinatam BDin I, & </s>
            <s xml:id="echoid-s14676" xml:space="preserve">lineam RSin X) ſit MP. </s>
            <s xml:id="echoid-s14677" xml:space="preserve">ME:</s>
            <s xml:id="echoid-s14678" xml:space="preserve">: VG. </s>
            <s xml:id="echoid-s14679" xml:space="preserve">IX;
              <lb/>
            </s>
            <s xml:id="echoid-s14680" xml:space="preserve">vel, ſit linea AL talis, ut ductâ MPY ad BDparallelâ (quæ ſecet
              <lb/>
            axem ADin P, & </s>
            <s xml:id="echoid-s14681" xml:space="preserve">lineam ALin Y) ſit PE. </s>
            <s xml:id="echoid-s14682" xml:space="preserve">ME:</s>
            <s xml:id="echoid-s14683" xml:space="preserve">: VG. </s>
            <s xml:id="echoid-s14684" xml:space="preserve">PY; </s>
            <s xml:id="echoid-s14685" xml:space="preserve">erit
              <lb/>
              <note position="left" xlink:label="note-0296-01" xlink:href="note-0296-01a" xml:space="preserve">Fig. 177.</note>
            tunc utrumque _ſpatium_ (ſingillatim) BRS D, vel ADL duplum _ſu-_
              <lb/>
            _perfici@i conicœ_, quod ex recta per V & </s>
            <s xml:id="echoid-s14686" xml:space="preserve">curvam AMB mota progene-
              <lb/>
            ratur.</s>
            <s xml:id="echoid-s14687" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14688" xml:space="preserve">Nam ſumatur MNindefinita curvæ particula; </s>
            <s xml:id="echoid-s14689" xml:space="preserve">& </s>
            <s xml:id="echoid-s14690" xml:space="preserve">per N ducantur
              <lb/>
            rectæ NOKTad ipſam AD, & </s>
            <s xml:id="echoid-s14691" xml:space="preserve">NQZ ad BDparallelæ (quæ li-
              <lb/>
            neas expoſitas, ut _Schema_ monſtrat, ſecent) connectantúrque rectæ
              <lb/>
            VM, VN. </s>
            <s xml:id="echoid-s14692" xml:space="preserve">eſtque MO. </s>
            <s xml:id="echoid-s14693" xml:space="preserve">MN:</s>
            <s xml:id="echoid-s14694" xml:space="preserve">: MP. </s>
            <s xml:id="echoid-s14695" xml:space="preserve">MF:</s>
            <s xml:id="echoid-s14696" xml:space="preserve">: VG. </s>
            <s xml:id="echoid-s14697" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s14698" xml:space="preserve">quare
              <lb/>
            MN x VG = MO x IX = IK x IX. </s>
            <s xml:id="echoid-s14699" xml:space="preserve">Item eſt NO. </s>
            <s xml:id="echoid-s14700" xml:space="preserve">MN:</s>
            <s xml:id="echoid-s14701" xml:space="preserve">: PE.
              <lb/>
            </s>
            <s xml:id="echoid-s14702" xml:space="preserve">ME:</s>
            <s xml:id="echoid-s14703" xml:space="preserve">: VG. </s>
            <s xml:id="echoid-s14704" xml:space="preserve">PY. </s>
            <s xml:id="echoid-s14705" xml:space="preserve">unde MN x VG = NO x PY = QP x PY. </s>
            <s xml:id="echoid-s14706" xml:space="preserve">
              <lb/>
            Eſt autem MN x VG duplum trianguli MVN. </s>
            <s xml:id="echoid-s14707" xml:space="preserve">quapropter tam IK
              <lb/>
            x IX, quàm QP x PY duplum eſt _trianguli_ MVN. </s>
            <s xml:id="echoid-s14708" xml:space="preserve">pariter autem
              <lb/>
            ubique fit. </s>
            <s xml:id="echoid-s14709" xml:space="preserve">ergò conſtat Propoſitum.</s>
            <s xml:id="echoid-s14710" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div482" type="section" level="1" n="48">
          <head xml:id="echoid-head51" style="it" xml:space="preserve">Exemplum.</head>
          <p>
            <s xml:id="echoid-s14711" xml:space="preserve">Sit curva AMB _byperbola æquilatera_, cujus _Centrum_ C, ſitque
              <lb/>
              <note position="left" xlink:label="note-0296-02" xlink:href="note-0296-02a" xml:space="preserve">Fig. 177.</note>
            CV = CA = _r._ </s>
            <s xml:id="echoid-s14712" xml:space="preserve">& </s>
            <s xml:id="echoid-s14713" xml:space="preserve">CP = _x_ (nam hujuſmodi _calculo_ plerunque
              <lb/>
            rem expedit peragere) tum connexâ MC; </s>
            <s xml:id="echoid-s14714" xml:space="preserve">patet eſſe EC = {_rr_/_x_};
              <lb/>
            </s>
            <s xml:id="echoid-s14715" xml:space="preserve">& </s>
            <s xml:id="echoid-s14716" xml:space="preserve">MCq = 2 _xx_ - _rr_ (nam PMq = _xx_ - _rr_) item eſt MCq. </s>
            <s xml:id="echoid-s14717" xml:space="preserve">
              <lb/>
            CPq:</s>
            <s xml:id="echoid-s14718" xml:space="preserve">: MEq. </s>
            <s xml:id="echoid-s14719" xml:space="preserve">MPq; </s>
            <s xml:id="echoid-s14720" xml:space="preserve">hoc eſt MCq.</s>
            <s xml:id="echoid-s14721" xml:space="preserve">CPq:</s>
            <s xml:id="echoid-s14722" xml:space="preserve">: ECq. </s>
            <s xml:id="echoid-s14723" xml:space="preserve">CGq. </s>
            <s xml:id="echoid-s14724" xml:space="preserve">hoc
              <lb/>
            eſt 2 _xx_ - _rr_. </s>
            <s xml:id="echoid-s14725" xml:space="preserve">_xx_:</s>
            <s xml:id="echoid-s14726" xml:space="preserve">: {_r_
              <emph style="sub">4</emph>
            /_xx_}. </s>
            <s xml:id="echoid-s14727" xml:space="preserve">CGq = {_r_
              <emph style="sub">4</emph>
            /2 _xx_ - _rr_}. </s>
            <s xml:id="echoid-s14728" xml:space="preserve">quare VGq = {_r_
              <emph style="sub">4</emph>
            /2 _xx_ - _rr_} +
              <lb/>
            _rr_ = {2 _rrxx_/2 _xx_ - _rr_} = {VAq x CPq/MCq}.</s>
            <s xml:id="echoid-s14729" xml:space="preserve">vel VG = {VA x CP/MC}. </s>
            <s xml:id="echoid-s14730" xml:space="preserve">quare
              <lb/>
            VG. </s>
            <s xml:id="echoid-s14731" xml:space="preserve">VA:</s>
            <s xml:id="echoid-s14732" xml:space="preserve">: (CP. </s>
            <s xml:id="echoid-s14733" xml:space="preserve">MC):</s>
            <s xml:id="echoid-s14734" xml:space="preserve">: MP. </s>
            <s xml:id="echoid-s14735" xml:space="preserve">ME. </s>
            <s xml:id="echoid-s14736" xml:space="preserve">hinc conſectatur in hoc
              <lb/>
            caſu, quum ubique ſit IX = VA, _lineam_ RS fore _rectam_; </s>
            <s xml:id="echoid-s14737" xml:space="preserve">& </s>
            <s xml:id="echoid-s14738" xml:space="preserve">_rectan-_
              <lb/>
            _gulum_ BRSD _ſuperficiei conicœ_ AMBV _duplum eſſe._</s>
            <s xml:id="echoid-s14739" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14740" xml:space="preserve">Cæterùm hoc _elegans exemplum_ ſuppeditavit Generoſus, ingenio ac
              <lb/>
            eruditione præſtans, Vir (_Collegii noſtri, quod olim Sociorum Com-_
              <lb/>
            _menſalis incoluit_, ornamentum) D. </s>
            <s xml:id="echoid-s14741" xml:space="preserve">_Franciſcus Feſſopius_, Armiger;
              <lb/>
            </s>
            <s xml:id="echoid-s14742" xml:space="preserve">cujus in hanc rem perquam ingenioſo mihi comiter impertito ſcripto
              <lb/>
            (ipſius injuſſu quidem, at ſpero non ingratiis) ſeu _Gemmâ_ quâdam au-
              <lb/>
            debo mea condecorare.</s>
            <s xml:id="echoid-s14743" xml:space="preserve"/>
          </p>
        </div>
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    </echo>
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