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-div560" type="section" level="1" n="87">
          <pb o="139" file="0317" n="332" rhead=""/>
          <p>
            <s xml:id="echoid-s15631" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15632" xml:space="preserve">Conſequentèr in harum ſecundo gradu ſin &</s>
            <s xml:id="echoid-s15633" xml:space="preserve">gt;_</s>
            <s xml:id="echoid-s15634" xml:space="preserve">c_; </s>
            <s xml:id="echoid-s15635" xml:space="preserve">in tertio, ſi _n_
              <emph style="sub">3</emph>
              <lb/>
            &</s>
            <s xml:id="echoid-s15636" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15637" xml:space="preserve">_cc_√{_cc_/3} - {_cc_/3} √ {_cc_/3} = {2/3}_cc_ √ {_cc_/3}; </s>
            <s xml:id="echoid-s15638" xml:space="preserve">vel _n_
              <emph style="sub">6</emph>
            &</s>
            <s xml:id="echoid-s15639" xml:space="preserve">gt;</s>
            <s xml:id="echoid-s15640" xml:space="preserve">{@@/27}_c_
              <unsure/>
              <emph style="sub">6</emph>
            ; </s>
            <s xml:id="echoid-s15641" xml:space="preserve">in quar-
              <lb/>
            to ſi _n_
              <emph style="sub">4</emph>
            &</s>
            <s xml:id="echoid-s15642" xml:space="preserve">gt;</s>
            <s xml:id="echoid-s15643" xml:space="preserve">{_c_
              <emph style="sub">4</emph>
            /4} - {_c_
              <emph style="sub">4</emph>
            /16} = {3/16}_c_
              <emph style="sub">4</emph>
            ; </s>
            <s xml:id="echoid-s15644" xml:space="preserve">nulla radix habetur; </s>
            <s xml:id="echoid-s15645" xml:space="preserve">unam in iſtis
              <lb/>
            caſibus recta EF curvas ſupergreditur; </s>
            <s xml:id="echoid-s15646" xml:space="preserve">nec iis occurrit.</s>
            <s xml:id="echoid-s15647" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15648" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15649" xml:space="preserve">Itidem in his omnibus maxima poſſibilis radix eſt AH = AC.</s>
            <s xml:id="echoid-s15650" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15651" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15652" xml:space="preserve">Curva CYH eſt _Circuli quadrans_, reliquæ AMH, ANH
              <lb/>
            quodammodo κυχλο{ει}δ{ετ}ς.</s>
            <s xml:id="echoid-s15653" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15654" xml:space="preserve">7. </s>
            <s xml:id="echoid-s15655" xml:space="preserve">Ad ſextam ſeriem pertinentium curva HLL eſt _byperbola æqui_-
              <lb/>
            _latera_, cujus axis AH; </s>
            <s xml:id="echoid-s15656" xml:space="preserve">reliquæ ſunt _Hyperboliformes_. </s>
            <s xml:id="echoid-s15657" xml:space="preserve">Unde quoad
              <lb/>
            hanc ſeriem liquent cætera.</s>
            <s xml:id="echoid-s15658" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div561" type="section" level="1" n="88">
          <head xml:id="echoid-head91" style="it" xml:space="preserve">Series ſeptima.</head>
          <p>
            <s xml:id="echoid-s15659" xml:space="preserve">_a_ + _b_ + {_cc_/_a_} = _n_.</s>
            <s xml:id="echoid-s15660" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15661" xml:space="preserve">_aa_ + _ba_ + _cc_ = _nn._</s>
            <s xml:id="echoid-s15662" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15663" xml:space="preserve">_a_
              <emph style="sub">3</emph>
            + _baa_ + _cca_ = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15664" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15665" 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-s15666" xml:space="preserve">c
              <unsure/>
            .</s>
            <s xml:id="echoid-s15667" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15668" xml:space="preserve">In recta BAH indefinitè protensâ capiatur AB = _b_; </s>
            <s xml:id="echoid-s15669" xml:space="preserve">& </s>
            <s xml:id="echoid-s15670" xml:space="preserve">in AD
              <lb/>
              <note position="right" xlink:label="note-0317-01" xlink:href="note-0317-01a" xml:space="preserve">Fig. 214.</note>
            ad BH perpendiculari ſit AC = _c_; </s>
            <s xml:id="echoid-s15671" xml:space="preserve">ſint etiam anguli HAR, HBS Semi-
              <lb/>
            recti; </s>
            <s xml:id="echoid-s15672" xml:space="preserve">tum arbitrariè ductâ GY ad AH perpendiculari quæ ipſam
              <lb/>
            BS ſecet in Y; </s>
            <s xml:id="echoid-s15673" xml:space="preserve">fiat AG. </s>
            <s xml:id="echoid-s15674" xml:space="preserve">AC:</s>
            <s xml:id="echoid-s15675" xml:space="preserve">: AC. </s>
            <s xml:id="echoid-s15676" xml:space="preserve">YK; </s>
            <s xml:id="echoid-s15677" xml:space="preserve">& </s>
            <s xml:id="echoid-s15678" xml:space="preserve">per K intra angulum
              <lb/>
            DVS deſcribatur _hyperbola_ KKK; </s>
            <s xml:id="echoid-s15679" xml:space="preserve">ſint demum curvæ CLL, AMM,
              <lb/>
            ANN tales, ut inter AG (vel GZ) & </s>
            <s xml:id="echoid-s15680" xml:space="preserve">GK ſit _media_ GL, _bime_-
              <lb/>
            _dia_ GM, _trimedia_ GN; </s>
            <s xml:id="echoid-s15681" xml:space="preserve">hæ ſatisfacient negotio. </s>
            <s xml:id="echoid-s15682" xml:space="preserve">Nam eſt GK = _a_
              <lb/>
            + _b_ + {_cc_/_a_}; </s>
            <s xml:id="echoid-s15683" xml:space="preserve">& </s>
            <s xml:id="echoid-s15684" xml:space="preserve">GLq = _aa_ + _ba_ + _cc_; </s>
            <s xml:id="echoid-s15685" xml:space="preserve">& </s>
            <s xml:id="echoid-s15686" xml:space="preserve">GMcub = _a_
              <emph style="sub">3</emph>
            + _baa_
              <lb/>
            + _cca_; </s>
            <s xml:id="echoid-s15687" xml:space="preserve">& </s>
            <s xml:id="echoid-s15688" xml:space="preserve">GNqq = _a_
              <emph style="sub">4</emph>
            + _ba_
              <emph style="sub">3</emph>
            + _ccaa_.</s>
            <s xml:id="echoid-s15689" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div563" type="section" level="1" n="89">
          <head xml:id="echoid-head92" style="it" xml:space="preserve">Not.</head>
          <p>
            <s xml:id="echoid-s15690" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15691" xml:space="preserve">Secundi gradûs curva CLL eſt pars _hyperbolæ æquilateræ_, cujus
              <lb/>
            _centrum_ O, ipſam AB biſecans; </s>
            <s xml:id="echoid-s15692" xml:space="preserve">& </s>
            <s xml:id="echoid-s15693" xml:space="preserve">ſiquidem AC&</s>
            <s xml:id="echoid-s15694" xml:space="preserve">gt;</s>
            <s xml:id="echoid-s15695" xml:space="preserve">AO, eſt OH
              <lb/>
            (ad AB perpendicularis, &)</s>
            <s xml:id="echoid-s15696" xml:space="preserve"> = √ ACq - AO qejus _ſemiaxis_;
              <lb/>
            </s>
            <s xml:id="echoid-s15697" xml:space="preserve">ſin AC&</s>
            <s xml:id="echoid-s15698" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s15699" xml:space="preserve">AO, ejus axis eſt OI = √ AOq - ACq. </s>
            <s xml:id="echoid-s15700" xml:space="preserve">reliquæ
              <lb/>
            verò curvæ AMM, ANN ſunt _hyperboliformes_.</s>
            <s xml:id="echoid-s15701" xml:space="preserve"/>
          </p>
        </div>
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