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">
          <p>
            <s xml:id="echoid-s13449" xml:space="preserve">
              <pb o="99" file="0277" n="292" rhead=""/>
            &</s>
            <s xml:id="echoid-s13450" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13451" xml:space="preserve">NO. </s>
            <s xml:id="echoid-s13452" xml:space="preserve">quare liquent ea, quæ Propoſita ſunt.</s>
            <s xml:id="echoid-s13453" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13454" xml:space="preserve">Si _Circulo_ ſubſtituatur _Ellipſis_, eadem concluſio valet idem diſcur-
              <lb/>
            ſus probat; </s>
            <s xml:id="echoid-s13455" xml:space="preserve">pofitâ AH _Ellipſis parametro_.</s>
            <s xml:id="echoid-s13456" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13457" xml:space="preserve">XVIII Habeant _hyperbola_ AEB (cujus axis AZ, parameter AH)
              <lb/>
            & </s>
            <s xml:id="echoid-s13458" xml:space="preserve">_parabola_ AFB axin eundem AD, & </s>
            <s xml:id="echoid-s13459" xml:space="preserve">baſin DB, _parabola_ ſupra
              <lb/>
            DB tota extra _hyperbolam_ cadet, extra verò, ſi infra DB protraha-
              <lb/>
              <note position="right" xlink:label="note-0277-01" xlink:href="note-0277-01a" xml:space="preserve">Fig. 143.</note>
            tur.</s>
            <s xml:id="echoid-s13460" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13461" xml:space="preserve">Nam connexæ ZH occurrat BD in I; </s>
            <s xml:id="echoid-s13462" xml:space="preserve">ergò DI eſt _parabolæ pa-_
              <lb/>
            _rameter_. </s>
            <s xml:id="echoid-s13463" xml:space="preserve">Quòd ſi ſupra BD utcunque ducatur recta FEGK ad BD
              <lb/>
            parallela, ſecans hyperbolam in E, parabolam in F, rectas AD, ZH
              <lb/>
            punctis G, K, erit FGq = AG x DI &</s>
            <s xml:id="echoid-s13464" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13465" xml:space="preserve">AG x GK = EGq. </s>
            <s xml:id="echoid-s13466" xml:space="preserve">qua-
              <lb/>
            re FG &</s>
            <s xml:id="echoid-s13467" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13468" xml:space="preserve">EG. </s>
            <s xml:id="echoid-s13469" xml:space="preserve">Quòd ſiinfra BD, utcunque ducatur recta MNOL
              <lb/>
            ſecans hyperbolam in N, parabolam in M, rectas AD, ZH in O, & </s>
            <s xml:id="echoid-s13470" xml:space="preserve">
              <lb/>
            L, erit NO q = AO x OL &</s>
            <s xml:id="echoid-s13471" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13472" xml:space="preserve">AO x DI = MOq. </s>
            <s xml:id="echoid-s13473" xml:space="preserve">& </s>
            <s xml:id="echoid-s13474" xml:space="preserve">indè NO
              <lb/>
            &</s>
            <s xml:id="echoid-s13475" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13476" xml:space="preserve">MO. </s>
            <s xml:id="echoid-s13477" xml:space="preserve">unde conſtant ea quæ propoſita ſunt.</s>
            <s xml:id="echoid-s13478" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13479" xml:space="preserve">XIX. </s>
            <s xml:id="echoid-s13480" xml:space="preserve">E dictis eliciuntur hæ _ad Circuli dimenſionem pertinentes regu-_
              <lb/>
            _la._ </s>
            <s xml:id="echoid-s13481" xml:space="preserve">Sit BAE circuli portio, cujus axis AD, baſis BE; </s>
            <s xml:id="echoid-s13482" xml:space="preserve">ſitque C
              <lb/>
              <note position="right" xlink:label="note-0277-02" xlink:href="note-0277-02a" xml:space="preserve">Fig. 144.</note>
            centrum circuli, & </s>
            <s xml:id="echoid-s13483" xml:space="preserve">EH ſinus rectus arcus BAE; </s>
            <s xml:id="echoid-s13484" xml:space="preserve">item, ſit AD =
              <lb/>
            {_s_/_t_} CA; </s>
            <s xml:id="echoid-s13485" xml:space="preserve">erit 1. </s>
            <s xml:id="echoid-s13486" xml:space="preserve">{2 _t_ - _s_/3 _t_ - 2 _s_} AD x BE &</s>
            <s xml:id="echoid-s13487" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13488" xml:space="preserve">port. </s>
            <s xml:id="echoid-s13489" xml:space="preserve">BAE.</s>
            <s xml:id="echoid-s13490" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13491" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13492" xml:space="preserve">EH + {4 _t_ - 2 _s_/3 _t_ - 2 _s_} BH &</s>
            <s xml:id="echoid-s13493" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13494" xml:space="preserve">arc. </s>
            <s xml:id="echoid-s13495" xml:space="preserve">BAE.</s>
            <s xml:id="echoid-s13496" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13497" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13498" xml:space="preserve">{2/3} AD x BE &</s>
            <s xml:id="echoid-s13499" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13500" xml:space="preserve">port. </s>
            <s xml:id="echoid-s13501" xml:space="preserve">BAE.</s>
            <s xml:id="echoid-s13502" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13503" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13504" xml:space="preserve">EH + {4/3} BH &</s>
            <s xml:id="echoid-s13505" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13506" xml:space="preserve">arc. </s>
            <s xml:id="echoid-s13507" xml:space="preserve">BAE.</s>
            <s xml:id="echoid-s13508" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13509" xml:space="preserve">XX. </s>
            <s xml:id="echoid-s13510" xml:space="preserve">Itidem hæ deducuntur ad _hyperbolæ dimenſionem ſpectantes re-_
              <lb/>
            _gulæ_. </s>
            <s xml:id="echoid-s13511" xml:space="preserve">Sit _hyperbolæ_ (cujus centrum C) ſegmentum ADB, habens
              <lb/>
              <note position="right" xlink:label="note-0277-03" xlink:href="note-0277-03a" xml:space="preserve">Fig. 145.</note>
            axin AD = {_s_/_t_} CA; </s>
            <s xml:id="echoid-s13512" xml:space="preserve">& </s>
            <s xml:id="echoid-s13513" xml:space="preserve">baſin DB;</s>
            <s xml:id="echoid-s13514" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13515" xml:space="preserve">erit 1. </s>
            <s xml:id="echoid-s13516" xml:space="preserve">{2 _t_ + _s_/3 _t_ + 2 _s_} AD x DB &</s>
            <s xml:id="echoid-s13517" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s13518" xml:space="preserve">ſegm. </s>
            <s xml:id="echoid-s13519" xml:space="preserve">ADB. </s>
            <s xml:id="echoid-s13520" xml:space="preserve">&</s>
            <s xml:id="echoid-s13521" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13522" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13523" xml:space="preserve">{2/3} AD x DB &</s>
            <s xml:id="echoid-s13524" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s13525" xml:space="preserve">ſegm. </s>
            <s xml:id="echoid-s13526" xml:space="preserve">ADB.</s>
            <s xml:id="echoid-s13527" xml:space="preserve"/>
          </p>
        </div>
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    </echo>
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