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

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      <text xml:lang="la" type="free">
        <div xml:id="echoid-div375" type="section" level="1" n="38">
          <p>
            <s xml:id="echoid-s12324" xml:space="preserve">
              <pb o="83" file="0261" n="276" rhead=""/>
            ctanea, _bfa_ - 3 _mma_ = 3 _ffe_ - _bme_; </s>
            <s xml:id="echoid-s12325" xml:space="preserve">ſubſtituendóque _bfm_ -
              <lb/>
            3 _m_
              <emph style="sub">3</emph>
            = 3 _fft_ - _bmt_; </s>
            <s xml:id="echoid-s12326" xml:space="preserve">ſeu, {_bfm_ - 3 _m_
              <emph style="sub">3</emph>
            /3 _ff_ - _bm_} = _t_.</s>
            <s xml:id="echoid-s12327" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div377" type="section" level="1" n="39">
          <head xml:id="echoid-head42" xml:space="preserve">Exemp. IV.</head>
          <p>
            <s xml:id="echoid-s12328" xml:space="preserve">Sit _Quadratrix_ CMV (ad circulum CEB pertinens cui centrum
              <lb/>
            A,) cujus axis VA; </s>
            <s xml:id="echoid-s12329" xml:space="preserve">ordinatæ CA. </s>
            <s xml:id="echoid-s12330" xml:space="preserve">MP ad VA perpendicula-
              <lb/>
            res.</s>
            <s xml:id="echoid-s12331" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12332" xml:space="preserve">Protractis rectis AME, ANF, ductíſque rectis EK, FL ad AB
              <lb/>
              <note position="right" xlink:label="note-0261-01" xlink:href="note-0261-01a" xml:space="preserve">Fig. 119.</note>
            perpendicularibus, dicantur arcus CB = _p_; </s>
            <s xml:id="echoid-s12333" xml:space="preserve">radius AC = _r_; </s>
            <s xml:id="echoid-s12334" xml:space="preserve">recta
              <lb/>
            AP = _f_; </s>
            <s xml:id="echoid-s12335" xml:space="preserve">AM = _k_. </s>
            <s xml:id="echoid-s12336" xml:space="preserve">Eſtque jam CA arc. </s>
            <s xml:id="echoid-s12337" xml:space="preserve">CB:</s>
            <s xml:id="echoid-s12338" xml:space="preserve">: NR. </s>
            <s xml:id="echoid-s12339" xml:space="preserve">arc. </s>
            <s xml:id="echoid-s12340" xml:space="preserve">FE.
              <lb/>
            </s>
            <s xml:id="echoid-s12341" xml:space="preserve">hoc eſt, _r. </s>
            <s xml:id="echoid-s12342" xml:space="preserve">p_:</s>
            <s xml:id="echoid-s12343" xml:space="preserve">: _a_. </s>
            <s xml:id="echoid-s12344" xml:space="preserve">{_pa_/_r_} = arc. </s>
            <s xml:id="echoid-s12345" xml:space="preserve">FE. </s>
            <s xml:id="echoid-s12346" xml:space="preserve">& </s>
            <s xml:id="echoid-s12347" xml:space="preserve">AM. </s>
            <s xml:id="echoid-s12348" xml:space="preserve">MP:</s>
            <s xml:id="echoid-s12349" xml:space="preserve">: AE. </s>
            <s xml:id="echoid-s12350" xml:space="preserve">EK; </s>
            <s xml:id="echoid-s12351" xml:space="preserve">hoc
              <lb/>
            eſt, _k. </s>
            <s xml:id="echoid-s12352" xml:space="preserve">m_:</s>
            <s xml:id="echoid-s12353" xml:space="preserve">: _r_. </s>
            <s xml:id="echoid-s12354" xml:space="preserve">{_rm_/_k_} = EK; </s>
            <s xml:id="echoid-s12355" xml:space="preserve">item AE. </s>
            <s xml:id="echoid-s12356" xml:space="preserve">EK:</s>
            <s xml:id="echoid-s12357" xml:space="preserve">: arc. </s>
            <s xml:id="echoid-s12358" xml:space="preserve">FE. </s>
            <s xml:id="echoid-s12359" xml:space="preserve">LK. </s>
            <s xml:id="echoid-s12360" xml:space="preserve">hoc
              <lb/>
            eſt, _r_. </s>
            <s xml:id="echoid-s12361" xml:space="preserve">{_rm_:</s>
            <s xml:id="echoid-s12362" xml:space="preserve">: _pa_/_kr_.</s>
            <s xml:id="echoid-s12363" xml:space="preserve">} {_pma_/_rk_} = LK. </s>
            <s xml:id="echoid-s12364" xml:space="preserve">Verùm AM. </s>
            <s xml:id="echoid-s12365" xml:space="preserve">AE:</s>
            <s xml:id="echoid-s12366" xml:space="preserve">: AP. </s>
            <s xml:id="echoid-s12367" xml:space="preserve">AK; </s>
            <s xml:id="echoid-s12368" xml:space="preserve">
              <lb/>
            hoc eſt _k_._</s>
            <s xml:id="echoid-s12369" xml:space="preserve">r_:</s>
            <s xml:id="echoid-s12370" xml:space="preserve">: _f_. </s>
            <s xml:id="echoid-s12371" xml:space="preserve">{_rf_/_k_} = AK. </s>
            <s xml:id="echoid-s12372" xml:space="preserve">ergò {_rf_/_k_} - {_pma_/_rk_} = AL. </s>
            <s xml:id="echoid-s12373" xml:space="preserve">Et{_rrff_/_kk_} -
              <lb/>
            {2 _fmpa_/_kk_} (abjectis ſuperfluis) = AL_q_; </s>
            <s xml:id="echoid-s12374" xml:space="preserve">adeóque LF_q_ =
              <lb/>
            {_rrkk_ - _rrff_ + 2 _fmpa_/_kk_} = {_rrmm_ + 2 _fmpa_.</s>
            <s xml:id="echoid-s12375" xml:space="preserve">/_kk_}</s>
          </p>
          <p>
            <s xml:id="echoid-s12376" xml:space="preserve">Eſt autem AQ_q_. </s>
            <s xml:id="echoid-s12377" xml:space="preserve">QN_q_:</s>
            <s xml:id="echoid-s12378" xml:space="preserve">: AL_q_. </s>
            <s xml:id="echoid-s12379" xml:space="preserve">LF_q_; </s>
            <s xml:id="echoid-s12380" xml:space="preserve">hoc eſt Q: </s>
            <s xml:id="echoid-s12381" xml:space="preserve">_f_ - _e_.
              <lb/>
            </s>
            <s xml:id="echoid-s12382" xml:space="preserve">Q: </s>
            <s xml:id="echoid-s12383" xml:space="preserve">_m_ + _a_:</s>
            <s xml:id="echoid-s12384" xml:space="preserve">: ALq. </s>
            <s xml:id="echoid-s12385" xml:space="preserve">LFq. </s>
            <s xml:id="echoid-s12386" xml:space="preserve">hoc eſt _ff_ - 2 _fe_. </s>
            <s xml:id="echoid-s12387" xml:space="preserve">_mm_ + 2 _ma_:</s>
            <s xml:id="echoid-s12388" xml:space="preserve">:
              <lb/>
            _rrff_ - 2 _fmpa_. </s>
            <s xml:id="echoid-s12389" xml:space="preserve">_rrmm_ + 2 _fmpa_. </s>
            <s xml:id="echoid-s12390" xml:space="preserve">Unde (ſublatis ex nor-
              <lb/>
            ma rejectaneis) emerget _æquatio_, _ffpa_ + _mmpa_ - _rrfa_ = _rrme_; </s>
            <s xml:id="echoid-s12391" xml:space="preserve">ſeu
              <lb/>
            _kkpa_ - _rrfa_ = _rrme_; </s>
            <s xml:id="echoid-s12392" xml:space="preserve">vel ſubſtituendo juxta _præſcriptum_; </s>
            <s xml:id="echoid-s12393" xml:space="preserve">_kkpm_ - _rrfm_
              <lb/>
            = _rrmt_; </s>
            <s xml:id="echoid-s12394" xml:space="preserve">vel {_kkp_/_rr_} - _f_ = _t_. </s>
            <s xml:id="echoid-s12395" xml:space="preserve">Hinc colligitur eſſe rectam AT =
              <lb/>
            {_kk_/_rr_} _p_; </s>
            <s xml:id="echoid-s12396" xml:space="preserve">hoc eſt (quoniam, ut notum eſt, AV = {_rr_/_p_}) erit AT =
              <lb/>
            {AMq/AV}; </s>
            <s xml:id="echoid-s12397" xml:space="preserve">ſeu, AV. </s>
            <s xml:id="echoid-s12398" xml:space="preserve">AM:</s>
            <s xml:id="echoid-s12399" xml:space="preserve">: AM. </s>
            <s xml:id="echoid-s12400" xml:space="preserve">AT.</s>
            <s xml:id="echoid-s12401" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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