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-div371" type="section" level="1" n="36">
          <p>
            <s xml:id="echoid-s12267" xml:space="preserve">
              <pb o="82" file="0260" n="275" rhead=""/>
            abjicienda) - 2 _rrma_ = - 4 _q_
              <emph style="sub">3</emph>
            _e_ - 2 _qqma_ - 2 _qmme_. </s>
            <s xml:id="echoid-s12268" xml:space="preserve">vel
              <lb/>
            _rrma_ - qq_ma_ = 2 _q_
              <emph style="sub">3</emph>
            _e_ + _qmme_; </s>
            <s xml:id="echoid-s12269" xml:space="preserve">vel denuò ſubſtituendo _m_
              <lb/>
            pro _a_, & </s>
            <s xml:id="echoid-s12270" xml:space="preserve">_t_ pro _e_, eſt _rrmm_ - _qqmm_ = 2 _q_
              <emph style="sub">3</emph>
            _t_ - _qmmt_; </s>
            <s xml:id="echoid-s12271" xml:space="preserve">vel
              <lb/>
            {_rrmm_ - qq_mm_/2 q
              <emph style="sub">3</emph>
            - q_mm_} = _t_ = PT.</s>
            <s xml:id="echoid-s12272" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div373" type="section" level="1" n="37">
          <head xml:id="echoid-head40" xml:space="preserve">_Exemp_. II.</head>
          <p>
            <s xml:id="echoid-s12273" xml:space="preserve">Sit recta EA (poſitione ac magnitudine data) & </s>
            <s xml:id="echoid-s12274" xml:space="preserve">curva EMO
              <lb/>
            proprietate talis, ut ab ea utcunque ductâ rectâ MP ad EA perpen-
              <lb/>
              <note position="left" xlink:label="note-0260-01" xlink:href="note-0260-01a" xml:space="preserve">Fig. 117.</note>
            diculari _Summa Cuborum_ ex AP, & </s>
            <s xml:id="echoid-s12275" xml:space="preserve">MP æquetur _Cubo_ rectæ AE.</s>
            <s xml:id="echoid-s12276" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12277" xml:space="preserve">Nominentur AE = _r_; </s>
            <s xml:id="echoid-s12278" xml:space="preserve">AP = _f_; </s>
            <s xml:id="echoid-s12279" xml:space="preserve">unde AQ = _f_ + _e_; </s>
            <s xml:id="echoid-s12280" xml:space="preserve">& </s>
            <s xml:id="echoid-s12281" xml:space="preserve">AQ
              <lb/>
            cub. </s>
            <s xml:id="echoid-s12282" xml:space="preserve">= _f_
              <emph style="sub">3</emph>
            + 3 _ffe_ + 3 _fee_ + _e_
              <emph style="sub">3</emph>
            ; </s>
            <s xml:id="echoid-s12283" xml:space="preserve">(ſeu abjectis ſuperfluis, ex præ-
              <lb/>
            ſcripto) = _f_
              <emph style="sub">3</emph>
            + 3 _ffe_. </s>
            <s xml:id="echoid-s12284" xml:space="preserve">Item NQ cub. </s>
            <s xml:id="echoid-s12285" xml:space="preserve">= cub. </s>
            <s xml:id="echoid-s12286" xml:space="preserve">_m_ - _a_ = _m_
              <emph style="sub">3</emph>
            -
              <lb/>
            3 _mma_ + 3 _maa_ - _a_
              <emph style="sub">3</emph>
            (hoc eſt) = _m_
              <emph style="sub">3</emph>
            - 3 _mma_. </s>
            <s xml:id="echoid-s12287" xml:space="preserve">Quapropter
              <lb/>
            eſt _f_
              <emph style="sub">3</emph>
            + 3 _ffe_ + _m_
              <emph style="sub">3</emph>
            - 3 _mma_ = (AQ cub. </s>
            <s xml:id="echoid-s12288" xml:space="preserve">+ NQ cub. </s>
            <s xml:id="echoid-s12289" xml:space="preserve">=
              <lb/>
            AE cub. </s>
            <s xml:id="echoid-s12290" xml:space="preserve">= ) _r_
              <emph style="sub">3</emph>
            . </s>
            <s xml:id="echoid-s12291" xml:space="preserve">abjectíſque datis, eſt 3 _ffe_ = 3 _mma_ = _o_.
              <lb/>
            </s>
            <s xml:id="echoid-s12292" xml:space="preserve">ſeu, _ffe_ = _mma_; </s>
            <s xml:id="echoid-s12293" xml:space="preserve">ſubrogatíſque loco _a_, & </s>
            <s xml:id="echoid-s12294" xml:space="preserve">_e_ ipſis _m_, & </s>
            <s xml:id="echoid-s12295" xml:space="preserve">_t_, erit
              <lb/>
            _fft_ = _m_
              <emph style="sub">3</emph>
            ; </s>
            <s xml:id="echoid-s12296" xml:space="preserve">ſeu _t_ = {_m_
              <emph style="sub">3</emph>
            /_ff_}; </s>
            <s xml:id="echoid-s12297" xml:space="preserve">eſt ergò PT quarta proportionalis in ratio-
              <lb/>
            ne AP ad PM continuata.</s>
            <s xml:id="echoid-s12298" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12299" xml:space="preserve">Similiter, Si fuerit APqq + MPqq = AEqq; </s>
            <s xml:id="echoid-s12300" xml:space="preserve">reperietur
              <lb/>
            fore PT = {_m_
              <emph style="sub">4</emph>
            /_f_
              <emph style="sub">3</emph>
            }; </s>
            <s xml:id="echoid-s12301" xml:space="preserve">vel PM quarta proportionalis in ratione AP ad
              <lb/>
            PM; </s>
            <s xml:id="echoid-s12302" xml:space="preserve">ac ità porrò quod de _Cycloformibus_ iſtis lineis an obſervatu
              <lb/>
            dignum ſit neſcio.</s>
            <s xml:id="echoid-s12303" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div375" type="section" level="1" n="38">
          <head xml:id="echoid-head41" xml:space="preserve">_Exemp_. III</head>
          <p>
            <s xml:id="echoid-s12304" xml:space="preserve">Poſitione data ſit recta AZ, & </s>
            <s xml:id="echoid-s12305" xml:space="preserve">AX magnitudine; </s>
            <s xml:id="echoid-s12306" xml:space="preserve">ſit etiam _curva_
              <lb/>
            AMO talis, ut ductâ utcunque rectâ MP ad AZ normali, ſit AP
              <lb/>
              <note position="left" xlink:label="note-0260-02" xlink:href="note-0260-02a" xml:space="preserve">Fig. 118.
                <lb/>
              _La Galande_</note>
            _cub._ </s>
            <s xml:id="echoid-s12307" xml:space="preserve">+ PM _cub_. </s>
            <s xml:id="echoid-s12308" xml:space="preserve">= AX x AP x PM.</s>
            <s xml:id="echoid-s12309" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12310" xml:space="preserve">Dicantur AX = _b_; </s>
            <s xml:id="echoid-s12311" xml:space="preserve">& </s>
            <s xml:id="echoid-s12312" xml:space="preserve">AP = _f_; </s>
            <s xml:id="echoid-s12313" xml:space="preserve">ergò AQ = _f_ - _e_; </s>
            <s xml:id="echoid-s12314" xml:space="preserve">& </s>
            <s xml:id="echoid-s12315" xml:space="preserve">AQ
              <lb/>
            _cub_. </s>
            <s xml:id="echoid-s12316" xml:space="preserve">= _f_
              <emph style="sub">3</emph>
            - 3 _ffe_; </s>
            <s xml:id="echoid-s12317" xml:space="preserve">& </s>
            <s xml:id="echoid-s12318" xml:space="preserve">QN _cub._ </s>
            <s xml:id="echoid-s12319" xml:space="preserve">= _m_
              <emph style="sub">3</emph>
            - 3 _mma_. </s>
            <s xml:id="echoid-s12320" xml:space="preserve">& </s>
            <s xml:id="echoid-s12321" xml:space="preserve">AQ x
              <lb/>
            QN = _fm_ - _fa_ - _me_ + _ae_ = _fm_ - _fa_ - _me_; </s>
            <s xml:id="echoid-s12322" xml:space="preserve">unde AX x
              <lb/>
            AQ x QN = _bfm_ - _bfa_ - _bme_; </s>
            <s xml:id="echoid-s12323" xml:space="preserve">hinc æquatio _f_ - 3 _ffe_
              <lb/>
            + _m_
              <emph style="sub">3</emph>
            - 3 _mma_ = _bfm_ - _bfa_ - _bme_; </s>
            <s xml:id="echoid-s12324" xml:space="preserve">ſeu amoliendo </s>
          </p>
        </div>
      </text>
    </echo>
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