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-div222" type="section" level="1" n="31">
          <pb o="39" file="0217" n="232" rhead=""/>
          <p>
            <s xml:id="echoid-s9325" xml:space="preserve">IN deducendis è propoſitâ generatione curvarum affectionibus etiam-
              <lb/>
            num progredimur.</s>
            <s xml:id="echoid-s9326" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9327" xml:space="preserve">_I._ </s>
            <s xml:id="echoid-s9328" xml:space="preserve">Anguli, qui fiunt ab applicatis & </s>
            <s xml:id="echoid-s9329" xml:space="preserve">tangentibus ad diverſa curvæ
              <lb/>
            puncta, ſibimet inæquales ſunt; </s>
            <s xml:id="echoid-s9330" xml:space="preserve">& </s>
            <s xml:id="echoid-s9331" xml:space="preserve">minores ſunt illi qui puncto A (ſe@@
              <lb/>
            vertici) propiores ſnnt.</s>
            <s xml:id="echoid-s9332" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9333" xml:space="preserve">Tangant rectæ TM, XN; </s>
            <s xml:id="echoid-s9334" xml:space="preserve">& </s>
            <s xml:id="echoid-s9335" xml:space="preserve">ad AY parallelæ ſint MP, NQ,
              <lb/>
            dico fore angulum PMT minorem angulo QNX.</s>
            <s xml:id="echoid-s9336" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9337" xml:space="preserve">Nam producta recta TM occurret ipſi QN extra curvam pro-
              <lb/>
              <note position="right" xlink:label="note-0217-01" xlink:href="note-0217-01a" xml:space="preserve">Fig. 26.</note>
            tractæ, puta ad E. </s>
            <s xml:id="echoid-s9338" xml:space="preserve">Item ipſa XN ſecabit applicatam PM extra
              <lb/>
            curvam, puta ad H. </s>
            <s xml:id="echoid-s9339" xml:space="preserve">Manifeſtum eſt autem cùm puncta H, N ſint
              <lb/>
            ad alias, ac alias partes rectæ ME, rectas ME, NH ſeſe inter-
              <lb/>
            ſecare inter parallelas PH, QE; </s>
            <s xml:id="echoid-s9340" xml:space="preserve">quare major eſt angulus externus
              <lb/>
            QNX interno QET, hoc eſt angulo PMT: </s>
            <s xml:id="echoid-s9341" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s9342" xml:space="preserve">E. </s>
            <s xml:id="echoid-s9343" xml:space="preserve">D.</s>
            <s xml:id="echoid-s9344" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9345" xml:space="preserve">_II. </s>
            <s xml:id="echoid-s9346" xml:space="preserve">Hinc_ poriſmatis _loco habetur_ tangentes ſe interſecare inter or-
              <lb/>
            dinatim applicatas per puncta contactuum; </s>
            <s xml:id="echoid-s9347" xml:space="preserve">velut ad F, inter PM,
              <lb/>
            QN protenſas.</s>
            <s xml:id="echoid-s9348" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9349" xml:space="preserve">III. </s>
            <s xml:id="echoid-s9350" xml:space="preserve">Item _angulum PTM angulo QXN majorem eſſe_; </s>
            <s xml:id="echoid-s9351" xml:space="preserve">(ex
              <lb/>
            ternum ſcilicet interno.)</s>
            <s xml:id="echoid-s9352" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9353" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s9354" xml:space="preserve">Item patet vertici propiores applicatas (proindéque rectas
              <lb/>
            quaſvis aliis parallelas) cur
              <unsure/>
            væ obliquiùs incidere quàm remotiores.</s>
            <s xml:id="echoid-s9355" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9356" xml:space="preserve">Cæterùm iſta jam olim de _sectionibus Conicis_ oſtenderat _Apollonius_,
              <lb/>
            ut in edito nuper VI _conicorv
              <unsure/>
            m libro_ eſt videre</s>
          </p>
          <p>
            <s xml:id="echoid-s9357" xml:space="preserve">V. </s>
            <s xml:id="echoid-s9358" xml:space="preserve">In figura præcedente (poſito applicationis angulum TAY
              <lb/>
            rectum eſſe, vel obtuſum) _dico curvæ arcum MN rectâ NH, ma-_
              <lb/>
            _jorem eſſe; </s>
            <s xml:id="echoid-s9359" xml:space="preserve">rectâverò ME minorem_.</s>
            <s xml:id="echoid-s9360" xml:space="preserve"/>
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