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-s9620" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s9621" xml:space="preserve">Si à puncto quopiam Hin perpendiculari HM aſſumpto
              <lb/>
            ducantur ad curvam rectæ HN, HO; </s>
            <s xml:id="echoid-s9622" xml:space="preserve">harum propior HN, remoti-
              <lb/>
            ore HO rectiùs incidet.</s>
            <s xml:id="echoid-s9623" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9624" xml:space="preserve">Nam ducantur EN, FO curvæ perpendiculares, & </s>
            <s xml:id="echoid-s9625" xml:space="preserve">IN, KO ad
              <lb/>
              <note position="right" xlink:label="note-0221-01" xlink:href="note-0221-01a" xml:space="preserve">Fig. 34.</note>
            ipſam HM parallelæ. </s>
            <s xml:id="echoid-s9626" xml:space="preserve">Eſt igitur ang. </s>
            <s xml:id="echoid-s9627" xml:space="preserve">FOK &</s>
            <s xml:id="echoid-s9628" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9629" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s9630" xml:space="preserve">ENI. </s>
            <s xml:id="echoid-s9631" xml:space="preserve">Item
              <lb/>
            ang. </s>
            <s xml:id="echoid-s9632" xml:space="preserve">OHM &</s>
            <s xml:id="echoid-s9633" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9634" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s9635" xml:space="preserve">NHM. </s>
            <s xml:id="echoid-s9636" xml:space="preserve">hoc eſt ang. </s>
            <s xml:id="echoid-s9637" xml:space="preserve">KOH &</s>
            <s xml:id="echoid-s9638" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9639" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s9640" xml:space="preserve">INH.
              <lb/>
            </s>
            <s xml:id="echoid-s9641" xml:space="preserve">quare ang. </s>
            <s xml:id="echoid-s9642" xml:space="preserve">FOK + KOH &</s>
            <s xml:id="echoid-s9643" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9644" xml:space="preserve">ang ENI + INH. </s>
            <s xml:id="echoid-s9645" xml:space="preserve">hoc eſt ang. </s>
            <s xml:id="echoid-s9646" xml:space="preserve">
              <lb/>
            FOH &</s>
            <s xml:id="echoid-s9647" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9648" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s9649" xml:space="preserve">ENH. </s>
            <s xml:id="echoid-s9650" xml:space="preserve">Unde conſtat Propoſitum.</s>
            <s xml:id="echoid-s9651" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9652" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s9653" xml:space="preserve">Hinc patet à perpendiculari progrediendo, (ab uno
              <lb/>
            nempe puncto H) iucidentium _obliquitatem_ creſcere, donec ad illam
              <lb/>
            devenitur, quæ _curvam_ tangit, omnium obliquiſſima.</s>
            <s xml:id="echoid-s9654" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9655" xml:space="preserve">XIX. </s>
            <s xml:id="echoid-s9656" xml:space="preserve">Porrò ſi introrſum jam ſumatur punctum H, & </s>
            <s xml:id="echoid-s9657" xml:space="preserve">ab eo in-
              <lb/>
              <note position="right" xlink:label="note-0221-02" xlink:href="note-0221-02a" xml:space="preserve">Fig. 35.</note>
            cidens HM ſit omnium curvæ incidentium minima; </s>
            <s xml:id="echoid-s9658" xml:space="preserve">erit HM _curvæ_
              <lb/>
            perpendicularis, ſeu tangenti MT.</s>
            <s xml:id="echoid-s9659" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9660" xml:space="preserve">Nam dicaliam MR tangenti perpendicularem eſſe. </s>
            <s xml:id="echoid-s9661" xml:space="preserve">ergò HR &</s>
            <s xml:id="echoid-s9662" xml:space="preserve">lt;
              <lb/>
            </s>
            <s xml:id="echoid-s9663" xml:space="preserve">
              <note position="right" xlink:label="note-0221-03" xlink:href="note-0221-03a" xml:space="preserve">_Apoll. V._ 32.</note>
            HM. </s>
            <s xml:id="echoid-s9664" xml:space="preserve">& </s>
            <s xml:id="echoid-s9665" xml:space="preserve">magìs HO &</s>
            <s xml:id="echoid-s9666" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s9667" xml:space="preserve">HM. </s>
            <s xml:id="echoid-s9668" xml:space="preserve">quare HM non eſt minima contra
              <lb/>
            _Hypotheſin_.</s>
            <s xml:id="echoid-s9669" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9670" xml:space="preserve">XX. </s>
            <s xml:id="echoid-s9671" xml:space="preserve">Item ſi recta HM ſit omnium ab H curvæ incidentium _maxima_,
              <lb/>
              <note position="right" xlink:label="note-0221-04" xlink:href="note-0221-04a" xml:space="preserve">_Apoll. V._ 29.</note>
            erit HM curvæ perpendicularis.</s>
            <s xml:id="echoid-s9672" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9673" xml:space="preserve">Nam Circulus Centro H per M deſcriptus extra curvam totus ca-
              <lb/>
              <note position="right" xlink:label="note-0221-05" xlink:href="note-0221-05a" xml:space="preserve">Fig. 36.</note>
            det. </s>
            <s xml:id="echoid-s9674" xml:space="preserve">ergò ſi recta MT Circulum tangat, hæc magìs extra curvam
              <lb/>
            cadet, eámq; </s>
            <s xml:id="echoid-s9675" xml:space="preserve">proinde continget. </s>
            <s xml:id="echoid-s9676" xml:space="preserve">Eſt autem ang. </s>
            <s xml:id="echoid-s9677" xml:space="preserve">HMT rectus. </s>
            <s xml:id="echoid-s9678" xml:space="preserve">er-
              <lb/>
            gò liquet.</s>
            <s xml:id="echoid-s9679" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9680" xml:space="preserve">XXI. </s>
            <s xml:id="echoid-s9681" xml:space="preserve">Hinc ſi MT ſit minimæ vel maximæ HM perpendicularis;
              <lb/>
            </s>
            <s xml:id="echoid-s9682" xml:space="preserve">
              <note position="right" xlink:label="note-0221-06" xlink:href="note-0221-06a" xml:space="preserve">_Apoll. V._ 30, 39,</note>
            hæc _curvam_ tanget.</s>
            <s xml:id="echoid-s9683" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9684" xml:space="preserve">Nam ſi dicatur alia MX tangere; </s>
            <s xml:id="echoid-s9685" xml:space="preserve">erit ideò ang. </s>
            <s xml:id="echoid-s9686" xml:space="preserve">XMH rectus, & </s>
            <s xml:id="echoid-s9687" xml:space="preserve">
              <lb/>
            par angulo TMH: </s>
            <s xml:id="echoid-s9688" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s9689" xml:space="preserve">E. </s>
            <s xml:id="echoid-s9690" xml:space="preserve">A.</s>
            <s xml:id="echoid-s9691" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9692" xml:space="preserve">XXII. </s>
            <s xml:id="echoid-s9693" xml:space="preserve">Exhinc ſi recta YM non ſit curvæ perpendicularis; </s>
            <s xml:id="echoid-s9694" xml:space="preserve">in ea
              <lb/>
            nulla ſumi poteſt _maxima_, vel _minima._</s>
            <s xml:id="echoid-s9695" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9696" xml:space="preserve">Nam ſi ſumi poſſet, eſſet ex eo ipſo YM curvæ perpendicularis
              <lb/>
              <note position="right" xlink:label="note-0221-07" xlink:href="note-0221-07a" xml:space="preserve">_Apoll. V._ 31, 47.</note>
            contra _Hypotbeſin_.</s>
            <s xml:id="echoid-s9697" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9698" xml:space="preserve">XXIII. </s>
            <s xml:id="echoid-s9699" xml:space="preserve">Si HM ſit incidentium minima, & </s>
            <s xml:id="echoid-s9700" xml:space="preserve">intra ipſam ſumatur
              <lb/>
              <note position="right" xlink:label="note-0221-08" xlink:href="note-0221-08a" xml:space="preserve">_Apoll. V._ 30.</note>
            punctum quodpiam I; </s>
            <s xml:id="echoid-s9701" xml:space="preserve">erit etiam IM minima.</s>
            <s xml:id="echoid-s9702" xml:space="preserve"/>
          </p>
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