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

Table of contents

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[91.] Series nona.
Page: 333 (140)
[92.] Not.
Page: 333 (140)
[93.] Series decima.
Page: 334 (141)
[94.] Series undecima.
Page: 335 (142)
[95.] Not.
Page: 335 (142)
[96.] Series duodecima
Page: 336 (143)
[97.] Series decima tertia
Page: 336 (143)
[98.] Not.
Page: 336 (143)
[99.] Laus DEOO ptimo Maximo. FINIS.
Page: 340 (147)
[100.] ERRATA
Page: 341
[101.] Addenda Lectionibus Geometricis.
Page: 342 (149)
[102.] _Probl_. I.
Page: 342 (149)
[103.] _Probl_. II.
Page: 342 (149)
[104.] _Probl_. III.
Page: 342 (149)
[105.] Addenda Lectionibus Geometricis.
Page: 343 (150)
[106.] _Theor_. I.
Page: 343 (150)
[107.] _Theor_. II.
Page: 343 (150)
[108.] _Theor_. III.
Page: 343 (150)
[109.] _Theor_. IV.
Page: 344 (151)
[110.] _Theor_. V.
Page: 344 (151)
[111.] _Theor_. VI.
Page: 344 (151)
[112.] FINIS.
Page: 344 (151)
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          <p>
            <s xml:id="echoid-s15702" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15703" xml:space="preserve">Hinc conſtat in ſecundo gradu ſi fuerit _n_&</s>
            <s xml:id="echoid-s15704" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s15705" xml:space="preserve">C, nullam veram
              <lb/>
            radicem dari; </s>
            <s xml:id="echoid-s15706" xml:space="preserve">alioquin in omnibus una ſemper habetur, & </s>
            <s xml:id="echoid-s15707" xml:space="preserve">unica;
              <lb/>
            </s>
            <s xml:id="echoid-s15708" xml:space="preserve">quoniam recta EF curvas ſemel interſecabit, nec pluries,</s>
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        <div xml:id="echoid-div564" type="section" level="1" n="90">
          <head xml:id="echoid-head93" style="it" xml:space="preserve">Series octava.</head>
          <p>
            <s xml:id="echoid-s15709" xml:space="preserve">{_cc_/_a_} + _b_ - _a_ = _n_.</s>
            <s xml:id="echoid-s15710" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Fig. 215.</note>
          <p>
            <s xml:id="echoid-s15711" xml:space="preserve">_cc_ + _ba_ - _aa_ = _nn._</s>
            <s xml:id="echoid-s15712" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15713" xml:space="preserve">_cca_ + _baa_ - _a_
              <emph style="sub">3</emph>
            = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15714" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15715" xml:space="preserve">_ccaa_ + _ba_
              <emph style="sub">3</emph>
            - _a_
              <emph style="sub">4</emph>
            = _n_
              <emph style="sub">4</emph>
            , &</s>
            <s xml:id="echoid-s15716" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15717" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div565" type="section" level="1" n="91">
          <head xml:id="echoid-head94" style="it" xml:space="preserve">Series nona.</head>
          <p>
            <s xml:id="echoid-s15718" xml:space="preserve">_a_ - _b_ - {_cc_/_a_} = _n._</s>
            <s xml:id="echoid-s15719" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15720" xml:space="preserve">_aa_ - _ba_ - _cc_ = _nn._</s>
            <s xml:id="echoid-s15721" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15722" xml:space="preserve">_a_
              <emph style="sub">3</emph>
            - _baa_ - _cca_ = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15723" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15724" xml:space="preserve">_a_
              <emph style="sub">4</emph>
            - _ba_
              <emph style="sub">3</emph>
            - _ccaa_ = _n_
              <emph style="sub">4</emph>
            . </s>
            <s xml:id="echoid-s15725" xml:space="preserve">&</s>
            <s xml:id="echoid-s15726" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15727" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15728" xml:space="preserve">In recta AI ſumatur AB = _b_; </s>
            <s xml:id="echoid-s15729" xml:space="preserve">& </s>
            <s xml:id="echoid-s15730" xml:space="preserve">in AD ad ipſam AI perpen-
              <lb/>
              <note position="left" xlink:label="note-0318-02" xlink:href="note-0318-02a" xml:space="preserve">Fig. 215.</note>
            diculari ſit AC = _c_; </s>
            <s xml:id="echoid-s15731" xml:space="preserve">fiant autem anguli IAR, ABS ſemirecti;
              <lb/>
            </s>
            <s xml:id="echoid-s15732" xml:space="preserve">ducatúrque recta ZGK ad AI utcunque perpendicularis, ipſam BS
              <lb/>
            ſecans ad ξ; </s>
            <s xml:id="echoid-s15733" xml:space="preserve">& </s>
            <s xml:id="echoid-s15734" xml:space="preserve">ſit AG. </s>
            <s xml:id="echoid-s15735" xml:space="preserve">AC:</s>
            <s xml:id="echoid-s15736" xml:space="preserve">: AC. </s>
            <s xml:id="echoid-s15737" xml:space="preserve">ξ K; </s>
            <s xml:id="echoid-s15738" xml:space="preserve">tum per K intra angu-
              <lb/>
            lum DSB deſcribatur _byperbola_ KYHK; </s>
            <s xml:id="echoid-s15739" xml:space="preserve">ſint denuò curvæ CLHLλ,
              <lb/>
            AMHMμ, ANHNν tales, ut inter AG, GK ſint _media_ GL, _bime-_-
              <lb/>
            _dia_ GM, _trimedia_ GN; </s>
            <s xml:id="echoid-s15740" xml:space="preserve">hæ curvæ propoſito ſatisfacient; </s>
            <s xml:id="echoid-s15741" xml:space="preserve">conſtat
              <lb/>
            autem hoc ut in præcedente.</s>
            <s xml:id="echoid-s15742" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div567" type="section" level="1" n="92">
          <head xml:id="echoid-head95" style="it" xml:space="preserve">Not.</head>
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            <s xml:id="echoid-s15743" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15744" xml:space="preserve">Curvæ CLH, AMH, ANH ad octavam ſeriem pertinent, re-
              <lb/>
            liquæ verò HLλ, HMμ, HN@, ad nonam.</s>
            <s xml:id="echoid-s15745" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15746" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15747" xml:space="preserve">Quoad octavam ſeriem, ſi biſecetur AB in O, & </s>
            <s xml:id="echoid-s15748" xml:space="preserve">ordinetur OT
              <lb/>
            ad curvam CLH eſt OT maxima; </s>
            <s xml:id="echoid-s15749" xml:space="preserve">ſin ſiat AP = {_b_/3} + √{_bb_/9} </s>
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