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-div379" type="section" level="1" n="40">
          <head xml:id="echoid-head43" xml:space="preserve">Eæemp. V.</head>
          <p>
            <s xml:id="echoid-s12402" xml:space="preserve">Sit DEB _Quadrans Circuli_, quem tangat recta BX; </s>
            <s xml:id="echoid-s12403" xml:space="preserve">tum linea
              <lb/>
              <note position="left" xlink:label="note-0262-01" xlink:href="note-0262-01a" xml:space="preserve">Fig. 120,
                <lb/>
              121.</note>
            AMO talis, ut in recta AV utcunque ſumptâ AP, quæ arcum BE
              <lb/>
            adæquet, erectáque PM ad AV normali, ſit PM æqualis arcûs BE
              <lb/>
            tangenti BG.</s>
            <s xml:id="echoid-s12404" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12405" xml:space="preserve">Sumpto arcu BF = AQ: </s>
            <s xml:id="echoid-s12406" xml:space="preserve">& </s>
            <s xml:id="echoid-s12407" xml:space="preserve">ductâ CFH; </s>
            <s xml:id="echoid-s12408" xml:space="preserve">demiſſis EK, FL
              <lb/>
            ad CB normalibus; </s>
            <s xml:id="echoid-s12409" xml:space="preserve">nominentur CB = _r_. </s>
            <s xml:id="echoid-s12410" xml:space="preserve">CK = _f_: </s>
            <s xml:id="echoid-s12411" xml:space="preserve">KE = _g_.
              <lb/>
            </s>
            <s xml:id="echoid-s12412" xml:space="preserve">Et quoniam eſt CE. </s>
            <s xml:id="echoid-s12413" xml:space="preserve">EK:</s>
            <s xml:id="echoid-s12414" xml:space="preserve">: arc. </s>
            <s xml:id="echoid-s12415" xml:space="preserve">EF. </s>
            <s xml:id="echoid-s12416" xml:space="preserve">LK; </s>
            <s xml:id="echoid-s12417" xml:space="preserve">vel CE. </s>
            <s xml:id="echoid-s12418" xml:space="preserve">EK:</s>
            <s xml:id="echoid-s12419" xml:space="preserve">: QF. </s>
            <s xml:id="echoid-s12420" xml:space="preserve">
              <lb/>
            LK; </s>
            <s xml:id="echoid-s12421" xml:space="preserve">hoc eſt _r_. </s>
            <s xml:id="echoid-s12422" xml:space="preserve">_g_:</s>
            <s xml:id="echoid-s12423" xml:space="preserve">: _e_. </s>
            <s xml:id="echoid-s12424" xml:space="preserve">{_ge_/_r_} = LK; </s>
            <s xml:id="echoid-s12425" xml:space="preserve">erit CL = _f_ + {_ge_.</s>
            <s xml:id="echoid-s12426" xml:space="preserve">/_r_} Et LF
              <lb/>
            = √ _rr_ - _ff_ - {2 _fge_/_r_} = √ _gg_ - {2 _fge_.</s>
            <s xml:id="echoid-s12427" xml:space="preserve">/_r_}</s>
          </p>
          <p>
            <s xml:id="echoid-s12428" xml:space="preserve">Eſt autem CL. </s>
            <s xml:id="echoid-s12429" xml:space="preserve">LF:</s>
            <s xml:id="echoid-s12430" xml:space="preserve">: (CB. </s>
            <s xml:id="echoid-s12431" xml:space="preserve">BH:</s>
            <s xml:id="echoid-s12432" xml:space="preserve">:) CB. </s>
            <s xml:id="echoid-s12433" xml:space="preserve">QN. </s>
            <s xml:id="echoid-s12434" xml:space="preserve">hoc eſt,
              <lb/>
            _f_ + {_ge_.</s>
            <s xml:id="echoid-s12435" xml:space="preserve">/_r_} √ _gg_ - {2 _fge_/_r_}:</s>
            <s xml:id="echoid-s12436" xml:space="preserve">: _r_. </s>
            <s xml:id="echoid-s12437" xml:space="preserve">_m_ - _a_. </s>
            <s xml:id="echoid-s12438" xml:space="preserve">vel (quadrando) _ff_ +
              <lb/>
            {2 _fge._</s>
            <s xml:id="echoid-s12439" xml:space="preserve">/_r_} _gg_ - {2 _fge_/_r_}:</s>
            <s xml:id="echoid-s12440" xml:space="preserve">: _rr._ </s>
            <s xml:id="echoid-s12441" xml:space="preserve">_mm_ - 2 _ma_. </s>
            <s xml:id="echoid-s12442" xml:space="preserve">Unde (dimiſſis quæ
              <lb/>
            oportet) obtinetur æquatio, _rfma_ = _grre_ + _gmme_. </s>
            <s xml:id="echoid-s12443" xml:space="preserve">unde
              <lb/>
            ſubſtituendo, eſt _rfmm_ = _grrt_ + _gmmt_. </s>
            <s xml:id="echoid-s12444" xml:space="preserve">vel {_rfmm_/_grr_ + _gmm_} = _t_.
              <lb/>
            </s>
            <s xml:id="echoid-s12445" xml:space="preserve">ſeu (quoniam eſt _m_ = {_rg_/_f_}) erit _t_ = {_rr_/_rr_ + _mm_} _m_ = {CB_q_/CG_q_} BG =
              <lb/>
            {CK_q_/CE_q_} BG.</s>
            <s xml:id="echoid-s12446" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12447" xml:space="preserve">Hæc ſufficere videntur huic methodo elucidandæ.</s>
            <s xml:id="echoid-s12448" xml:space="preserve"/>
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