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

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          <p>
            <s xml:id="echoid-s15903" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15904" xml:space="preserve">Curva HLLI eſt _ſemicirculus_; </s>
            <s xml:id="echoid-s15905" xml:space="preserve">reliquas itidem oſtentat
              <lb/>
            Schema.</s>
            <s xml:id="echoid-s15906" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15907" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15908" xml:space="preserve">Si A ζ = {_cc_/_b_}; </s>
            <s xml:id="echoid-s15909" xml:space="preserve">A Ψ = {_b_/4} - √ {_bb_/16} - {_cc_/2}; </s>
            <s xml:id="echoid-s15910" xml:space="preserve">& </s>
            <s xml:id="echoid-s15911" xml:space="preserve">A φ = {_b_/4} +
              <lb/>
            √ {_bb_/16} - {_cc_/2}; </s>
            <s xml:id="echoid-s15912" xml:space="preserve">ordinentúrque rectæ ζ V, ψ X, φ Y; </s>
            <s xml:id="echoid-s15913" xml:space="preserve">erunt puncta V,
              <lb/>
            X, Y _nodi_ curvarum (ſi _b_ &</s>
            <s xml:id="echoid-s15914" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s15915" xml:space="preserve">√ 8 _c c_, deerunt _nodi_ X, Y; </s>
            <s xml:id="echoid-s15916" xml:space="preserve">ſi _b_ = √
              <lb/>
            8 _c c_; </s>
            <s xml:id="echoid-s15917" xml:space="preserve">ii coaleſcent).</s>
            <s xml:id="echoid-s15918" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15919" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15920" xml:space="preserve">Ordinatarum ad curvam CL H _maxima_ eſt ipſa AC ; </s>
            <s xml:id="echoid-s15921" xml:space="preserve">ſin AP
              <lb/>
            = {_b_/3} - √ {_bb_/9} - {_cc_/3}, & </s>
            <s xml:id="echoid-s15922" xml:space="preserve">ordinetur P γ ad curvam AM H; </s>
            <s xml:id="echoid-s15923" xml:space="preserve">erit
              <lb/>
            P γ _maxima_; </s>
            <s xml:id="echoid-s15924" xml:space="preserve">item ſi AQ = {3/8} _b_ - √ {@9/64} _b b_ - {_cc_/2}; </s>
            <s xml:id="echoid-s15925" xml:space="preserve">& </s>
            <s xml:id="echoid-s15926" xml:space="preserve">ordinetur
              <lb/>
            Q δ ad curvam AN H, erit Q δ _maxima_.</s>
            <s xml:id="echoid-s15927" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15928" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15929" xml:space="preserve">Ordinatarum ad curvam HLLI _maxima_ eſt ipſa OT ; </s>
            <s xml:id="echoid-s15930" xml:space="preserve">ſin AP
              <lb/>
            = {_b_/3} + √ {_bb_/9} - {_cc_/3}, & </s>
            <s xml:id="echoid-s15931" xml:space="preserve">ad curvam HM I ordinetur _p g_, erit _p g_
              <lb/>
            _maxima_; </s>
            <s xml:id="echoid-s15932" xml:space="preserve">item ſi A q = {3/8} _b_ + √ {9/64} _b b_ - {_cc_/2}; </s>
            <s xml:id="echoid-s15933" xml:space="preserve">& </s>
            <s xml:id="echoid-s15934" xml:space="preserve">ordinetur _q d_
              <lb/>
            ad curvam HN I, erit _q d maxima_.</s>
            <s xml:id="echoid-s15935" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15936" xml:space="preserve">7. </s>
            <s xml:id="echoid-s15937" xml:space="preserve">Hinc radicum limites dignoſcentur, ut innuitur in iis, quæ ad
              <lb/>
            octavam ſeriem animadverſa ſunt.</s>
            <s xml:id="echoid-s15938" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15939" xml:space="preserve">8. </s>
            <s xml:id="echoid-s15940" xml:space="preserve">Patet in Serie duodecima nunc tres, modo duas, ſemper unam
              <lb/>
            radicem haberi; </s>
            <s xml:id="echoid-s15941" xml:space="preserve">in decima tertia verò ſubinde duas, aliquando tantùm
              <lb/>
            unam, interdum nullam haberi.</s>
            <s xml:id="echoid-s15942" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15943" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15944" xml:space="preserve">Et hæc quidem conſtant poſito fore {_b_/2}&</s>
            <s xml:id="echoid-s15945" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15946" xml:space="preserve">_c_; </s>
            <s xml:id="echoid-s15947" xml:space="preserve">at ſi {_b_/2} = β;
              <lb/>
            </s>
            <s xml:id="echoid-s15948" xml:space="preserve">evaneſcet Series decima tertia; </s>
            <s xml:id="echoid-s15949" xml:space="preserve">coaleſcent puncta H, O, I; </s>
            <s xml:id="echoid-s15950" xml:space="preserve">recta AB
              <lb/>
            _byperbolam_ KK K tanget; </s>
            <s xml:id="echoid-s15951" xml:space="preserve">curvæque CL H, IL λ in rectas lineas
              <lb/>
            degenerabunt.</s>
            <s xml:id="echoid-s15952" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15953" xml:space="preserve">10. </s>
            <s xml:id="echoid-s15954" xml:space="preserve">Sin {_b_/2} &</s>
            <s xml:id="echoid-s15955" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s15956" xml:space="preserve">_c_; </s>
            <s xml:id="echoid-s15957" xml:space="preserve">etiam evaneſcit Series decima tertia; </s>
            <s xml:id="echoid-s15958" xml:space="preserve">_byperbola_ KKK
              <lb/>
            tota infra rectam AB jacente; </s>
            <s xml:id="echoid-s15959" xml:space="preserve">quo caſu curva CL L erit hyperbola
              <lb/>
            æquilatera, habens centrum O, ſemiaxem (ipſi AB perpendicula-
              <lb/>
            rem) OT = √ AC q - AO q; </s>
            <s xml:id="echoid-s15960" xml:space="preserve">tunc & </s>
            <s xml:id="echoid-s15961" xml:space="preserve">curvæ AM M, AN N
              <lb/>
              <note position="left" xlink:label="note-0322-01" xlink:href="note-0322-01a" xml:space="preserve">Fig. 218.</note>
            ad infinitum procurrent, ſic ut æquationes, quæ in Serie duodecima,
              <lb/>
            unam ſemper, & </s>
            <s xml:id="echoid-s15962" xml:space="preserve">unicam radicem obtineant. </s>
            <s xml:id="echoid-s15963" xml:space="preserve">Hæc ſuffecerit inſinu-
              <lb/>
            âſſe; </s>
            <s xml:id="echoid-s15964" xml:space="preserve">quin & </s>
            <s xml:id="echoid-s15965" xml:space="preserve">rem totam hactenus particulatim attigiſſe. </s>
            <s xml:id="echoid-s15966" xml:space="preserve">Subnecte-
              <lb/>
            mus autem notas quaſdam magìs generales.</s>
            <s xml:id="echoid-s15967" xml:space="preserve"/>
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