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-div484" type="section" level="1" n="49">
          <head xml:id="echoid-head52" style="it" xml:space="preserve">Prop. 1.</head>
          <p>
            <s xml:id="echoid-s14744" xml:space="preserve">Si à puncto E in _axe A m coni recti_ ABC _p_ recta infinita EC
              <lb/>
            tranſeat per _coni ſuperficiem_, & </s>
            <s xml:id="echoid-s14745" xml:space="preserve">quieſcente termino E circumferatur
              <lb/>
              <note position="right" xlink:label="note-0297-01" xlink:href="note-0297-01a" xml:space="preserve">Fig. 178.</note>
            recta ECdonec redeat ad locum à quo coepit moveri, ita ut femper
              <lb/>
            aliqua pars ejus ſecet _coni ſuperficiem_ (puta per H) _perbolam_ CFD & </s>
            <s xml:id="echoid-s14746" xml:space="preserve">
              <lb/>
            rectas DAA Cin ſuperficie coni ſitas) _ſolidum comprebenſum à ſuper-_
              <lb/>
            _ficie vel ſuperficiebus genitis à linea_ EC ſic mota & </s>
            <s xml:id="echoid-s14747" xml:space="preserve">à _portione ſuperft-_
              <lb/>
            _ciei_ ejuſdem coni terminatæ à linea vel lineis CFD, DA, ACquas
              <lb/>
            recta ECcircumlata deſcribit in _ſuperficie conica_, erit æquale _Pyra-_
              <lb/>
            _midi_ cujus _Altitudo_ eſt æ qualis _perpendiculari_ E _n_ à puncto E ad latus
              <lb/>
            _Coni_ deductæ _b@ſis_ verò æqualis eidem _ſuperficiei conicœ terminat œ à_
              <lb/>
            linea vel lineis CFD, DA, ACgeneratis à motu lineæ EC.</s>
            <s xml:id="echoid-s14748" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14749" xml:space="preserve">_Solidum_ enim ECF, DAC conſtat ex _infinitis pyramidibus_ EC _o_ A
              <lb/>
            E _o o_ A, &</s>
            <s xml:id="echoid-s14750" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14751" xml:space="preserve">æquialtis perpendiculari E n, quarum baſes omnes
              <lb/>
            ſimul ſumptæ, exhauriunt _ſuperficiem conicam_ CFD, DA, AC.</s>
            <s xml:id="echoid-s14752" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div486" type="section" level="1" n="50">
          <head xml:id="echoid-head53" style="it" xml:space="preserve">Prop. 2.</head>
          <p>
            <s xml:id="echoid-s14753" xml:space="preserve">Datus ſit _Conus rectus_ ABC _p_ ſecetur à plano CFD axi A _m_ pa-
              <lb/>
              <note position="right" xlink:label="note-0297-02" xlink:href="note-0297-02a" xml:space="preserve">Fig. 178.</note>
            rallelo ducantur rectæ AC, ADà vertice _coni_ ad _lineam byperbolicam_
              <lb/>
            CFD, & </s>
            <s xml:id="echoid-s14754" xml:space="preserve">ſuper _triangulo_ ACD erigatur _pyramis_ EACD habens
              <lb/>
            _verticem_ E in _axe coni_; </s>
            <s xml:id="echoid-s14755" xml:space="preserve">ſitque E δ plano ACD perpendicularis, & </s>
            <s xml:id="echoid-s14756" xml:space="preserve">
              <lb/>
            E _n_ lateri coni.</s>
            <s xml:id="echoid-s14757" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14758" xml:space="preserve">Dico, _ſuperficies conica_ terminata à _linea byperbolica_ CFD & </s>
            <s xml:id="echoid-s14759" xml:space="preserve">re-
              <lb/>
            ctis DA, ACita ſe habet ad ACD _baſem pyramidis_ EACD ut
              <lb/>
            _altitudo_ E δ _pyramidis_ EACD ad perpendiculum E _n._ </s>
            <s xml:id="echoid-s14760" xml:space="preserve">Quoniam
              <lb/>
            enim Conici ACF D, ECFD habent vertices A & </s>
            <s xml:id="echoid-s14761" xml:space="preserve">E in plano baſi
              <lb/>
            CFD (quæ eſt utrique Conico communis) parallelo ergo ſunt æ-
              <lb/>
            quales. </s>
            <s xml:id="echoid-s14762" xml:space="preserve">Si ergò à ſolido quod componitur à conico ACFDaddito
              <lb/>
            pyramide ECADauferatur conicus ECFDreliquum erit ſolidum
              <lb/>
            ECFDACquale in propoſitione prima deſcribitur motu rectæ EC
              <lb/>
            æquale pyramidi EAC D. </s>
            <s xml:id="echoid-s14763" xml:space="preserve">Quoniam verò _œqualium pyramidum_ re-
              <lb/>
            ciprocæ ſunt _baſes al@itudinibus_, ut _altitudo_ E δ _pyramidis_ EACD
              <lb/>
            ad perpendiculum E _n_ ita erit _ſuperſicies conica_ terminata à _linea by-_
              <lb/>
            _perbolica_ CFD & </s>
            <s xml:id="echoid-s14764" xml:space="preserve">rectis DA, ACad Triangulum ACD. </s>
            <s xml:id="echoid-s14765" xml:space="preserve">q. </s>
            <s xml:id="echoid-s14766" xml:space="preserve">E. </s>
            <s xml:id="echoid-s14767" xml:space="preserve">D.</s>
            <s xml:id="echoid-s14768" xml:space="preserve"/>
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