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-div537" type="section" level="1" n="74">
          <pb o="131" file="0309" n="324"/>
        </div>
        <div xml:id="echoid-div539" type="section" level="1" n="75">
          <head xml:id="echoid-head78" xml:space="preserve">
            <emph style="sc">Lect</emph>
          . XIII.</head>
          <p>
            <s xml:id="echoid-s15242" xml:space="preserve">Æ _Quationum_ naturam è terminorum _analogia_ expoſuit _Vieta_;
              <lb/>
            </s>
            <s xml:id="echoid-s15243" xml:space="preserve">illam ex eorum in ſe ductu dilucidiùs explicuit _Carteſius_. </s>
            <s xml:id="echoid-s15244" xml:space="preserve">Eam
              <lb/>
            ego jam è linearum ſingulis appropriatarum deſcriptione conabor ali-
              <lb/>
            quatenus enucleatam dare; </s>
            <s xml:id="echoid-s15245" xml:space="preserve">qui ſanè modus rem præſertim elucidare
              <lb/>
            videtur, ac ob oculos ponere, agedum.</s>
            <s xml:id="echoid-s15246" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15247" xml:space="preserve">_Notetur_, In ſequentibus perpetim ad eaſdem ſeries redigi æquatio-
              <lb/>
            nes, quæ _coefficientes_ habent eaſdem.</s>
            <s xml:id="echoid-s15248" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div540" type="section" level="1" n="76">
          <head xml:id="echoid-head79" style="it" xml:space="preserve">Æquationum
            <unsure/>
          Series prima.</head>
          <p>
            <s xml:id="echoid-s15249" xml:space="preserve">_a_ + _b_ = _n_.</s>
            <s xml:id="echoid-s15250" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15251" xml:space="preserve">_aa_ + _ba_ = _nn_.</s>
            <s xml:id="echoid-s15252" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15253" xml:space="preserve">_a_
              <emph style="sub">3</emph>
            + _baa_ = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15254" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15255" xml:space="preserve">_a_
              <emph style="sub">4</emph>
            + _ba_
              <emph style="sub">3</emph>
            = _n_
              <emph style="sub">4</emph>
            , &</s>
            <s xml:id="echoid-s15256" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15257" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15258" xml:space="preserve">Sumatur recta BA æqualis coefficienti _b_, & </s>
            <s xml:id="echoid-s15259" xml:space="preserve">hæc verſus H indefini-
              <lb/>
              <note position="right" xlink:label="note-0309-01" xlink:href="note-0309-01a" xml:space="preserve">Fig. 206.</note>
            tè protendatur; </s>
            <s xml:id="echoid-s15260" xml:space="preserve">ſint anguli RAH, SBH ſemirecti, ſintque lineæ
              <lb/>
            ALL, AMM, ANN tales, ut rectâ GK ductâ ad AH utcunque
              <lb/>
            perpendiculari (quæ dictas lineas ordine ſecet punctis L, M, N; </s>
            <s xml:id="echoid-s15261" xml:space="preserve">re-
              <lb/>
            ctaſque BS, AR punctis K, Z) ſit inter GZ, GK _media_ GL ,
              <note symbol="*" position="right" xlink:label="note-0309-02" xlink:href="note-0309-02a" xml:space="preserve">Vid. pag. 90.</note>
            _media_ GM, _trimedia_ GM; </s>
            <s xml:id="echoid-s15262" xml:space="preserve">hæ lineæ propoſitarum æquationum
              <lb/>
            naturæ explicandæ inſervient. </s>
            <s xml:id="echoid-s15263" xml:space="preserve">Nam ſi AG (vel GZ) dicatur _a_; </s>
            <s xml:id="echoid-s15264" xml:space="preserve">erit
              <lb/>
            BG (vel GK) = _b_ + _a_; </s>
            <s xml:id="echoid-s15265" xml:space="preserve">atque GLq = _aa_ + _ba_; </s>
            <s xml:id="echoid-s15266" xml:space="preserve">& </s>
            <s xml:id="echoid-s15267" xml:space="preserve">GM cub.
              <lb/>
            </s>
            <s xml:id="echoid-s15268" xml:space="preserve"> = _a_
              <emph style="sub">3</emph>
            + _baa_; </s>
            <s xml:id="echoid-s15269" xml:space="preserve">& </s>
            <s xml:id="echoid-s15270" xml:space="preserve">GN_qq_ = _a_
              <emph style="sub">4</emph>
            + _ba_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15271" xml:space="preserve"/>
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